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Supporting Info (1)»Supporting Information Supporting Information

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Abstract

Accurate predictions of DNA stability in physiological and enzyme buffers are important for the design of many biological and biochemical assays. We therefore investigated the effects of magnesium, potassium, sodium, Tris ions, and deoxynucleoside triphosphates on melting profiles of duplex DNA oligomers and collected large melting data sets. An empirical correction function was developed that predicts melting temperatures, transition enthalpies, entropies, and free energies in buffers containing magnesium and monovalent cations. The new correction function significantly improves the accuracy of predictions and accounts for ion concentration, G-C base pair content, and length of the oligonucleotides. The competitive effects of potassium and magnesium ions were characterized. If the concentration ratio of [Mg²⁺]^0.5/[Mon⁺] is less than 0.22 M^−1/2, monovalent ions (K⁺, Na⁺) are dominant. Effects of magnesium ions dominate and determine duplex stability at higher ratios. Typical reaction conditions for PCR and DNA sequencing (1.5−5 mM magnesium and 20−100 mM monovalent cations) fall within this range. Conditions were identified where monovalent and divalent cations compete and their stability effects are more complex. When duplexes denature, some of the Mg²⁺ ions associated with the DNA are released. The number of released magnesium ions per phosphate charge is sequence dependent and decreases surprisingly with increasing oligonucleotide length.

Interactions of magnesium, sodium and potassium ions with DNA1 and RNA molecules are important for essential functions of living cells and for molecular biology applications. Both divalent and monovalent cations bind to nucleic acid molecules and affect their physical properties (1). Magnesium cations stabilize nucleic acid duplexes and facilitate their folding into secondary and tertiary structures (2), which are biologically active. Mg²⁺ ions are also necessary cofactors of many enzymatic reactions involving nucleic acids (3). The total magnesium concentrations in various cells range from 5 to 30 mM; however, free Mg²⁺ concentrations are tightly controlled between 0.4 and 1.2 mM (4). Binding of monovalent cations also increases duplex stability. The major intracellular monovalent cation is K⁺, while the major monovalent cation in extracellular fluid is Na⁺.

Abbreviations: CE, capillary electrophoresis; DNA, deoxyribonucleic acid; dNTP, deoxynucleoside triphosphates; DSC, differential scanning calorimetry; EDTA, ethylenediaminetetraacetic acid; MOPS, 3-(N-morpholino)-propanesulfonic acid; NIST, National Institute of Standards and Technology; PCR, polymerase chain reaction; RNA, ribonucleic acid; SVD, singular value decomposition; TBI, tightly bound ion model; Tris, tris(hydroxymethyl)aminomethane; UV, ultraviolet.

Several theoretical models have been proposed to describe the complex phenomena of associations between cations and nucleic acids. The most widely used approaches are the mean-field approximation of the Poisson−Boltzmann equation (5-8), the counterion condensation model (9, 10), and Monte Carlo simulations (11, 12). There have been few experimental studies addressing effects of Mg²⁺ ion on the stability of short DNA duplexes (13-16), and comprehensive experimental melting data are not available. The majority of melting studies in magnesium buffers investigated genomic DNAs (e.g., calf thymus) (5, 17-19), long polymeric repeats (20-22), or biologically active RNA molecules (2, 23). Pioneering experiments done over 40 years ago (17, 24) showed that magnesium ions stabilize DNA duplexes significantly more than the same concentrations of monovalent ions. For example, 10 mM Mg²⁺ stabilizes a six base pair duplex nearly as much as a 1 M Na⁺ solution (13), which is substantially more than what would be expected from the magnesium ion contribution to the ionic strength of the solution.

Numerous methods in molecular biology today (such as the polymerase chain reaction (PCR) and automated DNA sequencing) rely upon enzymatic reactions performed in the presence of Mg²⁺. Most commonly, these buffers contain a mixture of monovalent cations (20−100 mM) and magnesium ions (1.5−5 mM). Specifically, PCR is usually done in buffers containing a mixture of magnesium chloride, tris(hydroxymethyl)aminomethane (Tris), deoxynucleoside triphosphates (dNTP), and KCl (3). Magnesium concentration is the critical parameter that influences both the efficiency and specificity of PCR (25-29), especially when total genomic DNA is used, long products are synthesized, or multiplex reactions are run. Low magnesium concentrations decrease the efficiency and yield of PCR. High Mg²⁺ concentrations increase the stability of primer−template duplexes and the efficiency of amplification; however, specificity is reduced because primers may anneal to incorrect template sites and unwanted sequences are more likely to be amplified (27). The optimal annealing temperature is 2−5 °C below the melting temperatures of primer−template duplexes (26). It is therefore desirable to predict melting temperatures accurately when PCR assays are designed.

Melting temperatures are usually predicted using the nearest-neighbor model with parameters determined for 1 M Na⁺ buffer (30, 31). Since biological assays are implemented in various salt conditions, melting temperatures must be “corrected” for the presence and concentrations of all ions. Several empirical equations that correct T_m values in the presence of both Mg²⁺ and Na⁺ ions have been suggested (7, 15, 16, 32), which are reviewed in the Results section. Our analysis demonstrated that use of these equations can lead to large errors in the predicted value of T_m (>10 °C). Better methods are needed to facilitate design of molecular biology experiments. We conducted a large set of UV melting experiments in solutions containing magnesium and monovalent (K⁺, Tris⁺, Na⁺) ions to develop improved T_m magnesium correction methods. These experiments explored a wide range of magnesium and potassium ion concentrations under well-controlled conditions. Important physiologically relevant concentrations (1−10 mM Mg²⁺, 50−200 mM KCl) were included. Novel, more accurate empirical formulas are presented that enable reliable T_m predictions in buffers containing dNTPs, magnesium, and monovalent ions.

Materials and Methods

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DNA Oligonucleotides

This work employed the same sets of DNA oligomers which were used in a previous study that explored the effects of sodium cations on T_m(33). All oligonucleotides were purified by denaturing polyacrylamide gel electrophoresis. Each single strand had an OH group on the 5′-end as well as on the 3′-end. All oligonucleotide samples passed two quality control tests. Capillary electrophoresis analysis (33) showed that oligonucleotides were at least 92% pure. Mass spectrometry using an Oligo HTCS system (Novatia, Princeton, NJ) confirmed DNA identity and purity. Experimentally measured molecular masses of all oligodeoxyribonucleotides deviated less than 3 g/mol from expected molecular masses.

UV Melting Studies

Typical PCR buffers contain 1.5 mM MgCl₂, 50 mM KCl, and 10 mM Tris-HCl (pH 8.3 at 25 °C). Studies of the pH effects on T_m were conducted in buffers where Tris was replaced with 10 mM potassium cacodylate for pH range from 6.5 to 7.7. The pH 8.3 buffer contained 10 mM 3-(N-morpholino)-propanesulfonic acid, MOPS. A combination glass electrode (Cat. No. 476306, Corning Inc., Corning, NY) with a Corning pH meter 240 was used to measure pH values. The electrode signal was compensated for temperature changes, which were measured by an ATC probe connected to the pH meter.

The effects of magnesium ions on T_m were examined in various buffers containing 10 mM Tris-HCl, 0−600 mM MgCl₂, and 0−1 M KCl. The pH was adjusted to 8.3 ± 0.03 with 0.1 M HCl at 25 °C. Buffers without KCl contained the lowest concentrations of Tris that were found to have sufficient buffering capacity, so that the pH of solutions at 25 °C before and after melting experiments did not differ by more than 0.1 unit. Specifically, 2 mM Tris was used for 0.5−20 mM magnesium buffers and 10 mM Tris was necessary for solutions of higher magnesium concentrations. Magnesium chloride was added from a 200 mM stock solution, because solid MgCl₂ is very hygroscopic and cannot be accurately estimated by weight. A complexometric assay (34) was employed to verify Mg²⁺ concentrations in each lot of the buffer. EDTA titrations showed that magnesium concentrations deviated less than 2% from expected values.

DNA concentrations were determined from absorbance (33). Complementary single-strands were mixed in a 1:1 molar ratio. Duplexes were desalted by dialysis against water in a 28-well microdialysis system (Invitrogen, Carlsbad, California), aliquoted based on solution weight, lyophilized in a Speed-Vac concentrator, rehydrated in magnesium melting buffers, and stored in −20 °C. Total single strand concentrations, C_t, were 2 ± 0.2 µM and were verified from recorded melting curves using absorbances of upper baselines. Several DNA duplexes were also dialyzed directly against magnesium buffers to check whether the desalting method led to complete exchange of the buffers. Since melting profiles of the same DNA sequences were superimposable, we can conclude that the desalting method exchanges melting buffers as effectively as direct dialysis against a melting buffer.

Melting experiments were conducted on a single beam Beckman DU 650 spectrophotometer with a Micro Tm Analysis accessory, a Beckman High Performance Peltier Controller, and 1 cm path length quartz cuvettes (Beckman Coulter, Fullerton, CA). Spectrophotometer software was modified to improve resolution and to more finely control rate of temperature changes (33). Both denaturation and renaturation transition curves were collected, and temperature was increased linearly at a rate of 24.9 ± 0.3 °C/h. Absorbance values at 268 nm were recorded every 0.1 °C. We employed Beckman cuvettes (Cat. No. 523880) wherein the top was sealed with a Teflon stopper to prevent evaporation. These cuvettes are small (∼330 µL) and have thin walls, so heat is quickly distributed and the cuvettes are easily equilibrated to desired temperatures. Accuracy of temperature measurements inside of the cuvettes was validated using an external probe with a thermistor thermometer 874C (Tegam, Inc.). The thermistor (type K) was calibrated using a NIST traceable mercury thermometer of 0.1 °C resolution when both thermometers measured temperatures of both boiling water and ice−water mixture. Temperature values reported by the spectrophotometer were found to agree with the temperature values reported by the thermistor within 0.5 °C throughout the range from 15 to 97 °C.

Melting experiments were analyzed using previously published procedures (30, 33). Melting curves of buffers alone were subtracted from raw DNA melting curves. Regions of linear increase of absorbance before and after the melting transition were least-squares fitted to lower and upper linear baselines, and the fraction of broken base pairs, θ, was calculated as described previously (33). All melting curves showed a single, S-shaped transition for all buffers studied, allowing T_m to be unambiguously determined (see Figure S1 of the Supporting Information). Both upper and lower linear baselines were well established even when the melting temperatures were above 80 °C. In such cases, absorbance values were collected up to 99 °C. Melting profiles were smoothed and T_m values were determined (35) as temperatures where θ = 0.5. Three to eight melting profiles were acquired for each DNA sample in two different cuvettes, and their T_m values were averaged. The average standard deviation of UV experimental melting temperatures, σ_Tm, was estimated to be 0.3 °C.

Differential Scanning Calorimetry (DSC)

Experiments were conducted using a Nano II differential scanning calorimeter (Calorimetry Sciences Corporation, American Fork, UT) and a 60 base pair long DNA duplex, 5′-TTC GCG GAT TAG CCC TAC GCA TCG GTT ACA AAC GAG GAC CTT ATG CAC TTT GAC AGC ATG-3′. Samples were degassed for 17 min at 25 mmHg vacuum. Buffer scans were subtracted from DNA scans (33). The total single strand concentration was 2 µM. Melting temperatures at the maxima of the excess heat capacity curve, T_m(DSC), were reproducible within 0.3 °C.

Statistical Analysis of T_m Predictions

To critically evaluate the accuracy of T_m magnesium corrections, average errors of T_m predictions, ⟨|ΔT_m|⟩_AV, and reduced χ_r² values were calculated for each T_m magnesium correction function. Experimentally observed melting temperatures, T_m(experiment,i), were compared with predicted melting temperatures, T_m(prediction,i), for a set of n measurements,

(1)

(2) where |T_m(prediction,i) − T_m(experiment,i)| is the absolute value of the difference between predicted and experimentally measured melting temperatures and ν is the number of degrees of freedom. F-tests (36, 37) were conducted to determine the goodness-of-fit and accuracy of T_m predictions. The χ_r² values were compared between different T_m magnesium correction functions. A smaller χ_r² value reflects a better ability of the model to describe experimental results. Probabilities, P, of the null hypothesis that observed differences in χ_r² values were insignificant and could happen by random chance alone were evaluated. The smaller the P value is, the more significant the difference is between two magnesium corrections. If the P value was less than 0.05, the null hypothesis was rejected and the differences in goodness-of-fit were considered to be statistically significant. This analysis assumed that errors of melting data were normally distributed and was implemented using the Excel FDIST function.

Results

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Effects of Buffer pH on Melting Temperature

Phosphate, cacodylate or citrate buffers are commonly used in DNA melting experiments. In this study, we wished to characterize melting behavior in buffers that are used in biological applications. We therefore employed Tris buffer, since this is the most widely used buffer in molecular biology applications, including PCR. The pH values of Tris buffers decrease with increasing temperature. This change is rather large in comparison with other biological buffers (38, 39). Since DNA contains several groups capable of deprotonation and protonation, questions arise about pH changes during PCR and their effects on duplex stability. We therefore measured the pH of a typical PCR buffer (1.5 mM MgCl₂, 50 mM KCl and 10 mM Tris-HCl, pH = 8.3 at 25 °C) when the temperature was increased from 10 to 90 °C. The pH was found to be a linear function of temperature with a d(pH)/dT coefficient of −0.020 K⁻¹ (data not shown). To examine effects of changes in pH on melting temperatures, the same DNA duplexes were melted in the PCR buffer and in buffers where Tris was replaced with either 10 mM potassium cacodylate or 10 mM MOPS (see Materials and Methods). These two compounds manifest a much lower dependence of pK_a on temperature than Tris; the published values of d(pH)/dT are 0.0019 K⁻¹ and −0.011 K⁻¹ for cacodylic acid and MOPS, respectively (39, 40).

Figure 1 shows DNA melting temperatures in cacodylate and MOPS buffers of various pH. Twelve DNA oligomers ranging in length from 15 to 30 base pairs and in fraction of G·C base pairs, f_GC, from 0.3 to 0.7 were studied. Melting temperatures in environments of pH from 6.5 to 8.3 varied less than 0.5 °C. T_m values were found to be independent of pH and in agreement with T_m values observed in the PCR buffer that was prepared from Tris. Although the pH of the PCR Tris buffer decreased from 8.3 to 6.9 when temperature increased from 25 to 95 °C, the resulting pH changes had insignificant effects on melting temperatures of native duplex DNAs. This result is consistent with previous studies where melting temperatures of a DNA hairpin (41), T₂ phage DNA (42), and calf thymus DNA (43) did not change significantly in the range of pH values from 6.5 to 8.0.

Figure 1. Melting temperatures of DNA duplex oligomers are independent of pH in the range from 6.5 to 8.3. Solid symbols are 15-mers, open symbols are 30-mers, fraction of G·C base pairs vary from 0.3 to 0.7. Sequences are TTCTACCTATGTGAT (solid triangle), GCAGTGGATGTGAGA (solid circle), CAGCCTCGTCGCAGC (solid square), CTTAAGATATGAGAACTTCAACTAATGTGT (open triangle), AGTCTGGTCTGGATCTGAGAACTTCAGGCT (open circle), GACCTGACGTGGACCGCTCCTGGGCGTGGT (open square). Buffers contained 1.5 mM MgCl₂, 50 mM KCl and 10 mM cacodylic acid or MOPS.

Comparison of DNA Duplex Stability in Na⁺ and K⁺ buffers

Since PCR buffers typically contain potassium and Tris ions, it is of interest to compare the stabilizing effects of these monovalent ions with sodium ions. Nakano et al. (14) found in the study of a single DNA duplex, d(GCCAGTTAA), that the effects of Na⁺ and K⁺ on T_m were equivalent. However, we recently discovered that the influence of sodium ions on duplex stability is far more complex than previously thought (33). The stabilizing effect is sequence dependent and cannot be described by a simple linear relationship with respect to ln [Na⁺]. We therefore examined a larger set of duplexes to compare the effects of sodium and potassium cations.

Twelve DNA duplexes were melted in buffers containing 10 mM Tris and KCl of various concentrations ranging from 50 mM to 1 M as well as in sodium buffers (33). The stabilizing effect of K⁺ ions is also sequence dependent, and the dependence of 1/T_m on ln [K⁺] is nonlinear. Comparison of melting temperatures is shown in Figure 2. Differences between T_m values measured in sodium and potassium solutions of the same concentrations are within experimental errors. The best T_m agreement is achieved when Tris ions are taken into account. About half of the Tris molecules are protonated in the PCR buffer, i.e., 10 mM Tris buffer adds approximately 5 mM to the total monovalent ion concentration, [Mon⁺]. In summary, K⁺, Na⁺, Tris⁺ ions stabilize DNA duplexes with similar potency, and their effects on duplex stability are additive,

(3) The published T_m correction formula for sodium ions (33) is therefore also applicable to buffers containing Tris or KCl,

(4) where T_m(Mon⁺) is the melting temperature in the buffer containing a mixture of monovalent ions and T_m(1 M Na⁺) is the melting temperature in reference 1 M Na⁺ buffer. Equations 3 and 4 may be less accurate in high concentrations (above 100 mM) of monovalent ions capable to form hydrogen bonds (ammonium, Tris) and for bulkier monovalent ions (tetramethylammonium). Affinity of these ions to DNA has been reported to differ slightly from the affinity of Na⁺ and K⁺(67, 68). We have not investigated the bulkier monovalent ions under such conditions.

Figure 2. Comparison of effects of Na⁺ and K⁺ on melting temperatures in buffers of 55 mM (open triangle) and 205 mM (closed circle) monovalent ion concentrations. Duplex sequences (C_t = 2 µM) are in Table 4. Oligonucleotide lengths range from 15 to 30 base pairs. Melting temperatures determined in 10 mM Tris-HCl and 50 or 200 mM KCl buffers are plotted versus melting temperatures measured in 10 mM sodium phosphate and NaCl buffers (33). Diagonal solid line connects points where melting temperatures in both buffers would be the same.

Previously Published T_m Magnesium Corrections

The nearest-neighbor model and thermodynamic parameters (30, 31, 66) provide accurate predictions of duplex stability in 1 M Na⁺ buffer from DNA sequence and oligonucleotide concentration. To predict melting temperatures in magnesium buffers, T_m(Mg²⁺), a correction function that scales melting temperatures from the reference 1 M Na⁺ buffer to the magnesium buffer is applied. Although magnesium ions stabilize duplexes significantly more than the same concentration of sodium ions (13, 17), previously published T_m correction formulas generally assume that the stabilizing effects of magnesium ions are qualitatively similar to the better characterized stabilizing effects of sodium ions. These formulas use the T_m salt correction for sodium ions to predict duplex stability in Mg²⁺ solutions using a simple adjustment wherein Mg²⁺ ion concentration is converted to an “equivalent” Na⁺ concentration, [Na⁺_eq], which is then directly used in the T_m sodium salt correction. The “equivalent” Na⁺ concentration is defined as the concentration of sodium ions in a buffer that stabilizes duplexes to the same extent as the magnesium buffer. The following formula was suggested,

(5) where concentrations are in mol/L (15, 16, 32). Effects of magnesium and monovalent ions are assumed to be additive in eq 5. The total concentration of monovalent ions, [Mon⁺], is the sum of concentrations of alkali metal and amine cations (Na⁺, K⁺, Tris⁺). Values from 3.3 to 4.0 have been used for the parameter β (15, 16, 32). The equivalent [Na⁺_eq] values are entered into the T_m corrections for sodium salts (31, 45) to correct melting temperatures for magnesium solutions. Peyret used this concept and proposed the following empirical correction in his doctoral dissertation (16) where the salt dependence was presumed to be entirely entropic:

(6)N_bp is the number of base pairs in the duplex, and ΔH° is the standard enthalpy of duplex annealing (cal/mol) that can be measured experimentally or estimated from nearest-neighbor parameters (31, 66). T_m values have units of kelvins. The term N_bp − 1 is relevant for synthetic oligonucleotides and reflects the number of phosphate groups in the duplex divided by 2 (31). The melting data used to develop eq 6 have not been published, and the accuracy of T_m predictions using this method has not been established.

Ahsen et al. (15) compiled a set of melting temperatures for 162 probes determined using a real-time PCR LightCycler system. Either the probes were dye-labeled or buffers contained SYBR Green I. A revised version of eq 6 was proposed with a larger β value of the magnesium term,

(7) In their analysis, Ahsen et al. did not consider thermodynamic effects of fluorescent dyes and quenchers on DNA duplex stability, although these effects can be significant (34). The authors reported that their heating rates (0.1−0.2 °C/s) were probably too fast to achieve equilibrium conditions and T_ms may have been slightly overestimated. Even with these limitations, the standard error of T_m predictions was 1.8 °C for perfectly matched duplexes (15).

Mitsuhashi (32) suggested an even larger value of β and combined eq 5 with an earlier T_m sodium correction function derived by Schildkraut and Lifson (45):

(8) The accuracy of eq 8 was not reported. Equations 6−8 are routinely used for solutions containing magnesium ions in the presence, or absence, of other monovalent ions.

Recently, Tan and chen proposed the tightly bound ion model, TBI, which employs separate treatments for tightly bound ions and for diffuse ions surrounding DNA molecules (7, 46). The model accounts for discrete modes of counterion binding. Fluctuations and correlations between the ions tightly bound to DNA are considered, while these effects were neglected in previous models based solely on the mean-field approach of the Poisson−Boltzmann equation. The TBI model provides new practical formulas for thermodynamic parameters as a function of magnesium and sodium concentrations. For T_m, the following relationship is obtained:

(9) where x₁ and x₂ are the fractional contributions of Na⁺ and Mg²⁺ to the duplex stability and Δg_l and Δg₂ are the mean electrostatic folding free energies per base stack in pure Na⁺ or Mg²⁺ solutions (kcal/mol), respectively (46). The crossing term Δg_l2 accounts for interference and competition of Na⁺ ions with Mg²⁺ counterions (e.g., Δg_l2 = 0 for pure magnesium solutions). Expression 9 was proposed to be appropriate for duplexes with six or more base pairs (7, 46).

To examine the validity of these previous models, we initially studied melting temperatures for several duplexes ranging from 10 to 30 base pairs in length. Magnesium concentrations varied from 0.5 mM to 125 mM in the presence of 10 mM Tris buffer with no Na⁺ or K⁺. Figure 3 illustrates results of predictions using eqs 6−9 starting from the experimentally measured T_m in 1 M Na⁺ buffer for one such duplex. Predicted T_m values were found to deviate substantially from measured values over the entire range of magnesium concentrations. Qualitatively similar results were seen for the remaining sequences. Errors of greater than 10 °C in the predicted melting temperature were observed in some cases. Since the published T_m correction functions did not accurately predict melting temperatures, we proceeded to study systematically a larger data set and develop new equations to model T_m in the presence of Mg²⁺.

Figure 3. Comparison of some commonly used T_m magnesium correction functions. Experimentally measured (solid circle) and predicted melting temperatures for 30-mer duplex, ODN11, 5′-AGTCTGGTCTGGATCTGAGAACTTCAGGCT-3′ in buffers containing 10 mM Tris-HCl and various amounts of Mg²⁺ ions are shown.

Magnesium Ions and DNA Melting Temperatures

We first characterized the effects of magnesium ions on DNA duplex stability in a simple system where monovalent ions had negligible thermodynamic effects and magnesium ions were dominant. In this set of experiments, melting temperatures were measured in 0.5−600 mM Mg²⁺. To maintain stable pH, 2 mM Tris was present for 0.5−20 mM Mg²⁺ solutions, and 10 mM Tris was used in the 50−600 mM Mg²⁺ buffers. No KCl was added. As shown later, effects of Tris ions on T_m are negligible under these conditions.

Table 1 illustrates sequences studied and trends in their melting temperatures. The remaining data are presented in Table S1 of the Supporting Information. The set consisted of 92 DNA duplex oligomers (33) ranging in f_GC from 0.2 to 0.8 and in the number of base pairs from 10 to 30. Oligonucleotides annealed into blunt-ended, non-self-complementary duplexes and were designed to avoid self-dimer, hairpin, or other competing structures. Circular dichroism spectra demonstrated that the secondary structure of DNA with Mg²⁺ as the counterion is similar to that with Na⁺, throughout the range of magnesium concentrations used in biological assays (Figure S2 of the Supporting Information). However, subtle changes of secondary structure occur at high magnesium concentrations (>130 mM). Long regions of consecutive G·C or A·T base pairs were removed from sequences to decrease non-two-state melting behavior. All 10 internal nearest-neighbor doublets and 2 end (initiation) interactions were well represented, so that sequence dependent properties could be examined (30, 44, 66). Over 3000 UV melting profiles were collected. All melting curves showed a single, S-shaped transition (see Figure S1). Samples were deemed to be in thermodynamic equilibrium because their denaturation and renaturation melting profiles overlapped. No decreases of absorbance at 268 nm or increases of absorbance at 350 nm, which are characteristic of DNA aggregation or precipitation (18, 19, 22), were observed during melting transitions. Representative examples of the dependence of melting temperatures on ln [Mg²⁺] are shown in Figure 4. The relationships are nonlinear functions of oligonucleotide length, G·C base pair content, and magnesium concentration. When Mg²⁺ is added to a solution of duplex DNAs, the melting temperature increases until a maximum is reached. Higher Mg²⁺ concentrations destabilize duplexes slightly. Figure 4 demonstrates that the peaks of maximum stability are wide. The magnesium concentration at which the maximal T_m value occurs is sequence dependent, varying from 25 mM to 350 mM Mg²⁺ for different duplexes in the data set. The maximum T_m shifts to a lower magnesium concentration the higher the fraction of G·C base pairs (see Figure S3 of the Supporting Information). As magnesium concentration is increased, stabilizing T_m effects are saturated first for G·C rich duplexes and later for A·T rich duplexes.

Table 1. Experimental Melting Temperatures for 18 DNA Duplex Oligomers in Buffers of a Wide Range of Magnesium Concentrations

	T_m (°C) at [Mg²⁺] indicateda
DNA sequence (5′ to 3′)	0.5 mMb	1.5 mMb	3.0 mMb	10 mMb	20 mMb	50 mMc	125 mMc	300 mMc	600 mMc
TTGTAGTCAT	27.2	30.9	32.3	34.9	36.0	37.3	37.5	37.1	35.4
ATCGTCTGGA	35.1	38.9	40.6	43.4	43.4	43.7	44.4	43.0	41.6
GATGCGCTCG	44.0	47.7	48.8	50.7	51.2	51.6	51.9	49.9	47.7
GGGACCGCCT	48.3	51.9	53.7	55.5	55.9	55.4	56.1	54.9	52.2
CGTACACATGC	40.2	44.2	45.7	48.1	48.0	48.1	48.6	47.0	44.9
CCATTGCTACC	38.9	42.7	44.2	46.3	46.9	47.2	47.5	47.0	44.8
TTCTACCTATGTGAT	43.3	46.1	47.8	50.2	50.4	51.0	51.5	50.7	49.4
GCAGTGGATGTGAGA	52.3	55.1	56.5	58.1	58.7	59.2	59.0	58.2	56.1
CAGCCTCGTCGCAGC	61.9	64.1	65.3	66.8	67.3	67.5	67.3	65.5	63.7
TGATTCTACCTATGTGATTT	51.8	54.6	55.8	57.7	58.2	59.3	59.5	58.8	57.7
AGCTGCAGTGGATGTGAGAA	61.1	63.7	64.8	66.3	66.8	67.7	67.3	66.3	64.7
CAGCCTCGTTCGCACAGCCC	68.9	71.3	72.3	73.4	73.9	74.2	73.9	72.3	70.3
GTTCTATACTCTTGAAGTTGATTAC	57.2	59.7	60.8	62.4	63.0	63.8	64.0	63.5	62.6
CTGGTCTGGATCTGAGAACTTCAGG	65.6	67.7	68.7	69.8	70.3	70.7	70.6	69.8	68.6
CAGTGGGCTCCTGGGCGTGCTGGTC	73.5	75.3	76.2	77.3	77.6	78.2	77.4	75.9	74.0
CTTAAGATATGAGAACTTCAACTAATGTGT	61.0	63.1	64.1	65.5	66.0	67.1	67.1	66.2	65.2
AGTCTGGTCTGGATCTGAGAACTTCAGGCT	69.8	71.6	72.5	73.6	73.9	74.2	74.4	73.5	72.2
GACCTGACGTGGACCGCTCCTGGGCGTGGT	76.1	77.8	78.6	79.4	79.7	80.0	79.8	78.1	76.4

C_t = 2 ± 0.2 µM. Buffers do not contain any KCl.

2 mM Tris-HCl buffers.

10 mM Tris-HCl buffers.

Figure 4. Dependence of melting temperatures on magnesium concentrations is plotted for representative duplexes, which are 15 (solid symbols) and 25 (open symbols) base pairs long. Percentages of G·C base pairs were either 32−33% (circle) or 72−73% (triangle). Tris⁺ ions are present at low concentrations where they have negligible effects on duplex stability. Experimental data were fitted with quadratic curves to illustrate trends.

Since thermodynamic parameters and the nearest-neighbor model predict DNA stability in 1 M Na⁺, we employed this ionic environment as the reference salt concentration, as has been done in previous studies (15, 16, 31, 33). Differences between reciprocal T_m values in each magnesium buffer and 1 M Na⁺(33) were calculated. Figure 5 shows the dependence of these differences on f_GC, and N_bp present in the DNA duplexes. At fixed oligonucleotide length and constant magnesium concentration, the 1/T_m differences vary approximately linearly with f_GC:

(10) Deviations from linear relationships seen in Figure 5 are caused by experimental errors and by additional sequence-dependent effects (e.g., nearest-neighbor interactions). However, incorporation of nearest-neighbor parameters instead of a single term for f_GC did not significantly improve the accuracy of the T_m correction (Supporting Information, Table S5). Similarly, attempts to develop nearest-neighbor parameters for the effect of monovalent ions did not improve the accuracy of the T_m salt correction for sodium ions (33). The slopes S_GC are negative in buffers of low magnesium concentration (Figure 5A,B) and increase with increasing magnesium concentration. The fitted lines become flat at about 14 mM Mg²⁺ where the difference 1/T_m(Mg²⁺) − 1/T_m(1 M Na⁺) is independent of the fraction of G·C base pairs. In buffers having higher Mg²⁺ concentrations, the slopes are positive (Figure 5D).

Figure 5. Differences between 1/T_m values in buffers of various Mg²⁺ concentrations and 1 M Na⁺ buffer are shown as a function of f_GC. Inset shows colored symbols used for oligonucleotides of various lengths. (A) 0.5 mM Mg²⁺, (B) 3 mM Mg²⁺, (C) 10 mM Mg²⁺, (D) 125 mM Mg²⁺.

In comparison with experimental errors, differences in the slopes were minor. In order to simplify fitting of the data, we averaged S_GC slopes at each magnesium concentration. Averages were weighted based on the number of oligonucleotides of given length. These weight-averaged S_GC values are plotted versus the natural logarithm of magnesium concentration in Figure 6A. A linear relationship is observed (r² = 0.993):

(11) where the fitted parameters c and d are equal to 6.47 × 10⁻⁵ and 1.46 × 10⁻⁵ K⁻¹, respectively ([Mg²⁺] is in mol/L). Substitution of eq 11 into eq 10 allows us to calculate intercepts Y_GC:

(12)

Figure 6. Slopes (A) and intercepts (B) of fitted straight lines from Figure 5 are examined. Panels (C) and (D) display dependence of slopes and intercepts of fitted straight lines from Figure 6B on Mg²⁺ concentrations.

Figure 5 shows that Y_GC values change with N_bp and hence the number of negatively charged phosphate groups, Z, and seem to approach a limiting value with increasing duplex length. Since our chemically synthesized DNA duplexes do not contain phosphate groups on the 3′ or 5′ termini, Z is equal to 2(N_bp − 1). In Figure 6B, values of Y_GC calculated from eq 12 and averaged for each oligomer length are plotted versus 1/[2(N_bp − 1)]. Linear relationships are observed, so Y_GC can be described by the following equation:

(13) where the slope S_Nbp and intercept I_Nbp vary with magnesium concentration. Figure 6C and Figure 6D show that these relationships can be approximated as

(14)

(15) where a, b, e, f, and g are empirical parameters.

Combination of eqs 10, 11, and 13−15 yields the T_m magnesium correction,

(16) This equation can be used to scale melting temperatures of DNA duplex oligomers to different magnesium buffers when DNA concentration is fixed.

Stepwise fits allowed us to develop eq 16; however, the parameters obtained from these consecutive fits are not optimal because experimental data are not weighted equally. We therefore applied multivariate linear regression and fitted the seven parameters of eq 16 (a, b, c, d, e, f, g) in one step. The experimental data set consisted of 680 T_m values for 92 unique duplex DNAs measured in various Mg²⁺ concentrations (Tables 1 and S1). The set of empirically derived parameters and their errors are presented in Table 2. Extra significant figures of the parameters are included to prevent rounding errors. The multivariate fits were calculated using the Excel LINEST function as well as the numerically stable REGRL function (Matrix and Linear Algebra for Excel v.1.8.1, Foxes team, Roma, Italy, http://digilander.libero.it/foxes). Both functions gave identical results. Errors were estimated from residuals of the fit and from bootstrap simulations (47). The bootstrap estimates of the standard errors were up to 35% higher than errors from the residuals of multivariate regression and serve as a liberal estimate of the parameter errors reported in the third column of Table 2. Ten thousand bootstrap sample data sets were generated using Microsoft Excel. Each bootstrap data set was of the same size (680 T_mʼs) and was constructed by random drawing of T_m values, with replacement, from the original experimental data set. In other words, the entire experimental data set was used in each drawing. The parameters (a, b, c, d, e, f, g) were obtained from each bootstrap data set using the multivariate fit. Averages of bootstrap parameters agreed with values calculated from the original experimental data set. Standard deviation of each parameter was estimated from ten thousand bootstrap parameters (47).

Table 2. Parameters Obtained Using the Multivariate Fit to Eq 16 in Reciprocal Kelvins

parameter	value (K⁻¹)	standard error (K⁻¹)
a	3.92 × 10⁻⁵	0.2 × 10⁻⁵
b	−9.11 × 10⁻⁶	0.5 × 10⁻⁶
c	6.26 × 10⁻⁵	0.4 × 10⁻⁵
d	1.42 × 10⁻⁵	0.08 × 10⁻⁵
e	−4.82 × 10⁻⁴	0.7 × 10⁻⁴
f	5.25 × 10⁻⁴	0.2 × 10⁻⁴
g	8.31 × 10⁻⁵	0.2 × 10⁻⁵

Singular value decomposition (SVD) was employed to examine fits and correlations between parameters (37). The rank of the SVD design matrix was seven for the experimental and bootstrap data sets. Therefore, the seven fitted parameters were unique, i.e., none of the parameters could be obtained from linear combinations of the remaining parameters. An F-test was carried out to evaluate the significance of each of the parameters. The probability was estimated whether improvements in χ_r² could happen by random chance alone when the parameter and its term are added to the remaining 6 parameters (36). The null hypothesis assumed that the parameter does not improve fit and does not decrease χ_r² significantly. Since the probabilities were less than 10⁻¹⁸ for all parameters, the null hypotheses were rejected and each of the seven parameters in eq 16 was found to be statistically significant. If any single parameter is neglected, the accuracy of the T_m predictions declines.

It is important to assess the accuracy of T_m predictions obtained from eq 16. Figure S4 of the Supporting Information shows errors of the T_m predictions as a function of G·C base-pair content, number of base pairs, and magnesium concentrations. Similar accuracy is seen for various duplexes and magnesium concentrations. No systematic trends are observed. From 680 melting temperatures in the experimental data set, 96% are predicted within 1.3 °C and 99% are predicted within 2.0 °C. The average error of the T_m predictions is 0.5 °C.

Several additional terms and modifications of eq 16 were considered. Because they did not improve the fit, they are not included in the final equation. For example, if the term 1/[2(N_bp − 1)]² was used in eq 16 instead of the 1/[2(N_bp − 1)] term, the goodness-of-fit decreased. Furthermore, addition of a (ln [Mg²⁺])² term to the I_Nbp relationship (eq 14) provided only marginal improvement of the fit, which was not statistically significant. This is consistent with Figure 6D, which shows that the dependence of I_Nbp on ln [Mg²⁺] is approximately linear.

Since the Y_GC intercepts seem to approach a limiting value with increasing N_bp (Figure 5), we examined a model where oligonucleotide-length-dependent terms of eq 16 (e, f, g parameters) were neglected for longer duplexes (N_bp ≥ 20). The remaining parameters were optimized and fitted to the experimental T_m data set. Predictions of melting temperatures for DNA oligomers from 20 to 60 base pairs were compared with the experimental data. This simplified correction function was found to be as accurate as eq 16 at low magnesium concentrations (∼1.5 mM), but predictions in higher magnesium concentrations were less accurate. We conclude that the magnesium correction function depends significantly on oligonucleotide lengths even for these longer duplexes.

Accuracy and Limitations of the New T_m Magnesium Correction

Accuracy of the new eq 16 was compared with previous T_m magnesium correction equations using the experimental data sets from Tables 1 and S1. The average errors of these T_m predictions are summarized in Table 3. Predictions obtained using all of the earlier equations were less accurate, showing an average T_m error of 2.9 °C or larger, compared with an error of only 0.5 °C when the new eq 16 was used. These accuracy differences are statistically significant. Probabilities, P, that differences in χ_r² between eq 16 and the other corrections can occur by random chance are less than 10⁻³⁰⁰. For certain sequences, the error in prediction of T_m using the previously published formulas (eqs 6−9) is quite large (10−18 °C). The largest error observed with eq 16 was 2.9 °C for the entire experimental data set of 680 measurements.

Table 3. Accuracy of Various T_m Magnesium Corrections Evaluated for Data Set of 92 DNA Duplex Oligomers in Magnesium Buffers When Effects of Monovalent Ions Are Negligible and Effects of Magnesium Ions Dominate

eq no.	T_m magnesium correction	χ_r²	⟨\|ΔT_m\|⟩_AV (°C)
16	this work	4.6	0.5
6	Peyret−SantaLucia	163.1	2.9
7	Ahsen−Wittwer−Schütz	185.3	3.0
9	Tan−Chen	176.4	3.3
8	Mitsuhashi	350.7	4.7

It is important to consider limitations of the new T_m magnesium correction function. Equation 16 was derived from melting data in the range of 0.5 mM to 600 mM Mg²⁺ at neutral pH (7−8) and is accurate in these ranges. The parameters were obtained under conditions in which the effects of monovalent ions were negligible. At higher concentrations, monovalent ions can significantly compete with magnesium ions. In this setting, the relationship between ion concentrations and T_m becomes more complex and some of the parameters require adjustment (see below).

It is the free magnesium concentration which affects duplex stability and enters into salt correction formula 16. In our experiments, magnesium ions were present in vast excess compared to DNA. Under these conditions, the free magnesium concentration is equal to the total magnesium concentration. When concentrations of Mg²⁺ and DNA phosphate groups are of the same magnitude, binding of magnesium ions to DNA must be taken into account. Such low magnesium concentrations occur rarely in biological applications.

The experimental data set employed to develop eq 16 contained DNA duplexes from 10 to 30 base pairs in length. An analysis of 40 and 60 base pair duplexes shows that eq 16 remains accurate in scaling T_m for these longer DNAs (see Table S2 of Supporting Information). Although these longer duplexes showed a single transition and had a well established T_m, they may melt in a non-two-state fashion. That is, in the narrow temperature range over which melting occurs (2−3 °C), partially melted duplexes may exist. However, the derivation of eq 16 was not dependent on the two-state assumption. It is valid for short oligomers (10−20 base pairs) which do melt in a two-state fashion as well as longer sequences that exhibit a single transition.

Although UV melting experiments reported in Tables 1 and S1 were conducted at a total single strand concentration of 2 µM, the utility of eq 16 is not limited to this DNA concentration. Melting studies were performed for a subset of 21 sequences in 1.5 mM Mg²⁺ buffer using differential scanning calorimetry where DNA concentrations were 90-fold higher (C_t = 180 µM). See Table S4 of the Supporting Information. The T_m values under these conditions were predicted using eq 16 while the melting temperatures obtained from earlier calorimetric experiments in 1 M Na⁺ (33) were used as the reference point. Melting temperatures of the DSC data set were predicted with an accuracy (⟨|ΔT_m|⟩_AV = 0.4 °C) similar to the accuracy of the UV melting data set (⟨|ΔT_m|⟩_AV = 0.5 °C).

Deoxynucleoside Triphosphates Decrease Effects of Magnesium Ions

PCR reactions require deoxynucleoside triphosphates (dNTPs) in mixture with short oligomer primers, probes and longer nucleic acid targets. Magnesium ions bind to all of these components, and this binding decreases the concentration of free magnesium ions. As DNA synthesis proceeds during PCR, dNTPs are incorporated into the products and pyrophosphate is released. Pyrophosphate also binds magnesium ions. Complex linked equilibria of Mg²⁺ binding occur. It was empirically observed in PCR reactions that magnesium ion concentration must exceed the total concentration of dNTPs to achieve efficient amplification (3, 26). It has been suggested that the free magnesium ion concentration, [Mg²⁺], is a critical parameter to be optimized in PCR and that it can be estimated from the difference between the total magnesium ion and the total dNTP concentrations (15). To verify this notion, melting experiments of DNA duplexes were done in the presence and absence of dNTPs. Because DNA and dNTP molecules absorb light at similar wavelengths, ultraviolet spectroscopy is not a suitable technique to study denaturation of DNA duplexes when dNTPs are present in excess. We therefore employed differential scanning calorimetry (DSC). Until recently, DSC experiments required the use of high DNA concentrations (∼100 µM), which are more than 2 orders of magnitude larger than the concentrations of primers typically used in PCR experiments (<1 µM). However, new ultrasensitive calorimeters are available that allow measurement of T_m values using less than 5 µM concentration of a duplex (48). We studied a sixty base pair long DNA duplex (see Materials and Methods) that exhibited a single, sharp reproducible melting transition. Melting temperatures were determined at the same DNA concentration (C_t = 2 µM, i.e., 0.06 mM/base pair) while buffer composition was varied. Results are presented in Figure 7. Experiments 1−3 were done in 50 mM KCl and 10 mM Tris-HCl. We found that addition of dATP or an equimolar mixture of all four dNTPs did not affect the T_m when magnesium was absent. Experiments 4−12 contained various amounts of Mg²⁺ ions. Comparison of experiments 4, 5, and 11 shows that raising the magnesium concentrations from 0.5 to 3 mM increased the T_m. Addition of 1 mM dATP to the 1.5 mM Mg²⁺ buffer decreased the T_m of the duplex from 81.6 ± 0.3 (experiment 5) to 79.7 ± 0.3 °C (experiment 6), which is identical within experimental error to the melting temperature of that duplex in 0.5 mM Mg²⁺ buffer alone (experiment 4, 79.5 ± 0.4 °C). Analogous observations were made for stability of the duplex in 3.0 mM Mg²⁺ plus 1.5 mM dATP (experiment 12). The duplex had a T_m of 81.7 ± 0.1 °C, which is equal to its T_m in 1.5 mM Mg²⁺ buffer when no dATP was present (81.6 ± 0.3 °C, experiment 5). Experiments 6−10 in Figure 7 demonstrate that addition of dATP, dGTP, dTTP, and dCTP impact T_m by similar amounts. Affinity for magnesium ions is grossly similar between different dNTPs and is primarily determined by properties of the triphosphate and ribose groups (49, 50).

Figure 7. Experimental melting temperatures of the 60-mer duplex (see Materials and Methods) were obtained using DSC at low DNA concentration (C_t = 2 µM). Buffers contained 50 mM KCl, 10 mM Tris-HCl (pH = 8.3) and various amounts of magnesium ions and deoxynucleotide triphosphates. Concentrations (mM) used in each experiment are indicated below the graph. The first row is the free [Mg²⁺], which is calculated as the difference between total Mg²⁺ and dNTP concentrations. dNTP “mix” contained equimolar concentrations of dATP, dGTP, dCTP and dTTP. The sum of their concentrations is shown in the table below the graph.

These results confirm that dNTPs bind magnesium ions stochiometrically (1:1) with high affinity and that the remaining free magnesium ions determine the melting temperature of a DNA duplex. Therefore, in connection with the use of T_m correction eq 16, the magnesium ion concentration should be adjusted for the total concentration of dNTPs. That is, the free concentration of magnesium ions, [Mg²⁺], can be assumed to equal the difference between the total magnesium concentration, c_Mg, and the total concentration of dNTPs, c_dNTP. This relationship will not hold if the total dNTP concentration is larger or similar (within 20%) to the total magnesium ion concentration. In that case, the free magnesium ion concentration will be very low and may be approximated from the relationship for the Mg-dNTP association constant,

(17) By using published experimental data for ribonucleotides (49-51), we estimate that K_a is approximately 3 × 10⁴ for the Mg−dNTP complex in a PCR buffer of 50 mM KCl and 10 mM Tris. In situations when the free magnesium ion concentration is very low, effects of monovalent ions on duplex stability will often be dominant.

Competition between Magnesium and Monovalent Ions in Duplex Stabilization

Equation 16 and its parameters were determined in solutions with very low concentrations of Tris cations (1−5 mM) where magnesium ions are dominant in their effects on melting temperatures. We next examined duplex stability in mixed buffers containing significant amounts of both magnesium and monovalent ions. Figure 8A illustrates that the observed T_m effects are a complex function of monovalent ion and magnesium ion concentrations. The highest T_m was achieved in 1 M KCl solution; the maximal T_m reached in magnesium solutions was lower. This might not be true for very short oligomers (N_bp ≤ 10) where Mg²⁺ ions may provide larger stabilizing effects than a 1 M solution of monovalent ions (13, 52).

Figure 8. Competitive effects of K⁺ and Mg²⁺ examined for the 25 bp long duplex, ODN8, CTGGTCTGGATCTGAGAACTTCAGG. (A) Dependence of T_m on concentrations of magnesium and monovalent ions. (B) Solid circles are T_ms plotted against ln R, where R = [Mg²⁺]^0.5/[Mon⁺]. Buffers are composed of constant 1.5 mM Mg²⁺ while KCl concentration varies. The solid line shows melting temperatures predicted by sodium salt correction (eq 4) when no Mg²⁺ is present. The dashed line indicates T_m in magnesium buffer when no KCl is present. The dominant ion crossover that occurs on average at R of 0.22 is indicated with the dotted vertical line.

Cations bound to DNA are subject to an ion-exchange reaction in which the associated cations are released into bulk solvent. NMR line-shape analysis (53), UV melting (5, 14), electrophoresis (54, 67) and buffer equilibration−atomic emission spectroscopy (68) experiments have demonstrated that the extent of Mg²⁺ binding to DNA decreases with increasing monovalent ion concentration indicating that magnesium and monovalent ions compete for DNA binding. Table 4 presents results of melting experiments for 12 DNA duplexes 15 to 30 base pairs long. Their GC content ranged from 30 to 73%. For each buffer and oligonucleotide, the T_m value in the mixed buffer was compared to T_m values in reference buffers, which were missing either potassium ions (first rows of T_m data in Table 4) or magnesium ions (first column of T_m data). Depending on buffer composition, either monovalent or magnesium ions were found to be dominant and largely determine the melting temperature, the remaining ions having only minor effects on duplex stability (ΔT_m < 3 °C). At each Mg²⁺ concentration, a concentration of monovalent ions is eventually reached at which the T_m is accurately predicted by the effect of monovalent ions alone (eq 4). This analysis determined the crossover point at which the dominant ion changes from magnesium to monovalent ions. This did not occur at a unique value of the ratio [Mg²⁺]/[Mon⁺]. With increasing monovalent ion concentration, this ratio was found to increase. However, the ratio R = ([Mg²⁺])^1/2/[Mon⁺] at this point is independent of ion concentrations and nearly identical for all 12 sequences. The value of R at the crossover point is 0.22 M^−1/2. This provides a convenient measure to determine whether divalent or monovalent ions are dominant in their effects on T_m (Figure 8B). If R is equal to or greater than 0.22, magnesium effects dominate and T_m correction eq 16 should be employed (the influence of monovalent ions can be neglected). If R is less than 0.22, the T_m correction for monovalent ions (eq 4) should be used (33). Under these conditions, monovalent ions are dominant and determine T_m, and the presence of Mg²⁺ can be ignored.

Table 4. Experimental Melting Temperatures (°C) for 12 Duplex Oligodeoxynucleotides (C_t = 2 µM) in Buffers of Various Magnesium and Monovalent Ion (K⁺, Tris⁺) Concentrations

	[Mg²⁺]
[Mon⁺]	0 mM	0.5 mM	1.5 mM	3.0 mM	10 mM	20 mM	50 mM	125 mM
TTCTACCTATGTGAT (ODN1)a
1 mM		43.3	46.1	47.8	50.2	50.4
5 mM		42.1	45.6	47.6	49.5	50.4	51.0	51.5
55 mM	39.3	42.5	44.7	46.2	49.1	49.6	51.0	51.5
105 mM	43.8	44.8	45.8	47.1	49.1	50.1	51.1	51.6
205 mM	47.7		48.1		49.9		51.1	51.4
605 mM	52.1		51.9		51.9		51.8	51.7
1.005 M	53.2		53.0		53.0		52.0	51.4
GCAGTGGATGTGAGA (ODN2)a
1 mM		52.3	55.1	56.5	58.1	58.7
5 mM		51.9	54.7	56.2	58.2	58.8	59.2	59.0
55 mM	49.5	52.5	54.6	56.0	58.0	58.8	59.3	59.1
105 mM	53.8	54.6	55.8	56.6	58.2	58.9	59.4	59.4
205 mM	57.3		57.9		59.1		59.4	59.5
605 mM	61.6		61.3		61.1		60.2	59.5
1.005 M	62.4		62.3		61.7		60.3	59.6
CAGCCTCGTCGCAGC (ODN3)a
1 mM		61.9	64.1	65.3	66.8	67.3
5 mM		61.1	64.2	65.1	67.2	67.5	67.5	67.3
55 mM	58.9	62.0	64.0	65.2	66.6	67.4	68.1	67.4
105 mM	63.1	63.8	65.0	65.7	67.5	67.5	67.8	67.2
205 mM	66.5		67.0		68.1		67.6	67.3
605 mM	69.9		69.8		69.4		67.9	67.3
1.005 M	70.6		70.3		70.1		68.1	66.9
TGATTCTACCTATGTGATTT (ODN4)a
1 mM		51.8	54.6	55.8	57.7	58.2
5 mM		51.0	54.5	55.8	58.1	58.5	59.3	59.5
55 mM	47.6	51.1	53.8	55.4	57.9	58.9	59.4	59.5
105 mM	51.9	53.0	54.7	55.4	57.9	58.4	59.5	59.7
205 mM	56.1		57.0		58.7		59.4	59.9
605 mM	61.6		61.7		61.6		60.7	60.3
1.005 M	63.2		63.2		63.0		61.4	60.7
AGCTGCAGTGGATGTGAGAA (ODN5)a
1 mM		61.1	63.7	64.8	66.3	66.8
5 mM		60.7	63.9	65.1	66.9	67.3	67.7	67.3
55 mM	57.8	61.1	63.2	64.6	65.8	67.1	67.8	67.5
105 mM	62.4	63.3	64.8	65.2	67.0	67.4	67.7	67.7
205 mM	66.4		67.1		68.1		67.5	67.8
605 mM	71.2		71.1		70.7		68.7	68.2
1.005 M	72.3		72.2		71.7		69.7	68.5
CAGCCTCGTTCGCACAGCCC (ODN6)a
1 mM		68.9	71.3	72.3	73.4	73.9
5 mM		68.7	71.3	72.3	73.8	74.0	74.2	73.9
55 mM	65.0	68.7	70.8	71.9	73.2	74.0	74.2	73.8
105 mM	69.4	70.8	72.0	72.6	74.0	74.2	74.4	73.8
205 mM	73.5		74.0		74.8		74.4	73.9
605 mM	77.6		77.6		77.0		75.2	74.2
1.005 M	78.4		78.2		77.5		75.5	74.3
GTTCTATACTCTTGAAGTTGATTAC (ODN7)a
1 mM		57.2	59.7	60.8	62.4	63.0
5 mM		56.3	59.4	60.7	62.6	63.1	63.8	64.0
55 mM	50.7	54.6	57.5	59.1	61.5	63.0	63.8	64.2
105 mM	55.9	57.3	58.9	60.0	62.2	63.2	63.9	64.3
205 mM	60.3		61.3		63.1		63.9	64.4
605 mM	66.1		66.2		66.0		65.2	64.9
1.005 M	68.0		67.9		67.5		66.1	65.5
CTGGTCTGGATCTGAGAACTTCAGG (ODN8)a
1 mM		65.6	67.7	68.7	69.8	70.3
5 mM		65.1	67.6	68.5	70.1	70.3	70.7	70.6
55 mM	60.3	64.5	66.9	68.1	69.7	70.4	70.7	70.8
105 mM	64.9	66.2	68.0	68.8	70.3	70.7	71.0	70.9
205 mM	69.1		70.0		71.2		71.1	71.0
605 mM	74.2		74.1		74.0		72.5	71.6
1.005 M	75.8		75.6		75.2		73.2	72.3
CAGTGGGCTCCTGGGCGTGCTGGTC (ODN9)a
1 mM		73.5	75.3	76.2	77.3	77.6
5 mM		73.3	75.9	76.6	78.0	78.0	78.2	77.4
55 mM	70.6	73.9	75.6	76.5	77.3	78.1	78.3	78.0
105 mM	74.3	75.6	77.2	77.4	78.7	78.4	78.3	77.8
205 mM	78.2		79.3		79.5		78.2	77.8
605 mM	82.6		82.6		81.9		79.4	78.3
1.005 M	83.4		83.3		82.6		79.8	78.4
CTTAAGATATGAGAACTTCAACTAATGTGT (ODN10)a
1 mM		61.0	63.1	64.1	65.5	66.0
5 mM		60.5	63.2	64.4	65.9	66.4	67.1	67.1
55 mM	55.2	59.2	61.8	63.4	65.2	66.1	67.3	67.2
105 mM	60.2	61.5	63.0	64.0	66.0	66.6	67.2	67.2
205 mM	64.6		65.3		66.8		67.0	67.3
605 mM	70.4		70.4		70.1		68.5	68.1
1.005 M	72.4		72.0		71.4		69.6	68.5
AGTCTGGTCTGGATCTGAGAACTTCAGGCT (ODN11)a
1 mM		69.8	71.6	72.5	73.6	73.9
5 mM		68.8	71.6	72.3	73.8	73.9	74.2	74.4
55 mM	64.6	68.5	71.0	72.1	73.8	74.1	74.4	74.7
105 mM	68.9	70.3	72.1	73.0	74.2	74.3	74.9	74.7
205 mM	73.2		74.3		75.1		74.7	74.9
605 mM	78.4		78.2		78.1		76.4	75.6
1.005 M	80.1		79.9		79.4		77.2	76.2
GACCTGACGTGGACCGCTCCTGGGCGTGGT (ODN12)a
1 mM		76.1	77.8	78.6	79.4	79.7
5 mM		75.9	78.1	79.0	79.8	79.9	80.0	79.8
55 mM	73.2	76.5	78.0	79.0	79.5	80.0	80.3	79.6
105 mM	77.4	78.6	79.7	79.9	80.7	80.6	80.4	79.7
205 mM	81.2		81.8		81.8		80.5	79.9
605 mM	85.6		85.5		84.4		81.9	80.6
1.005 M	86.7		86.3		85.2		82.5	81.0

DNA sequence (5′ to 3′) (duplex ID).

Figure 8B also illustrates that the addition of K⁺ at concentrations of 50−100 mM to magnesium buffers can paradoxically decrease the value of T_m by 1−2 °C. This effect, although small, was observed for all 12 sequences. It occurs for values of R in the range of 0.22 to 6.0 and is most pronounced for oligonucleotides of low GC content. A similar effect was observed for genomic DNAs (5, 17). Importantly, PCR buffers fall in this range of R values. Therefore, it seemed worthwhile to determine if the T_m prediction could be improved by taking this effect of ion competition into account. This is best achieved by allowing the parameters a, b, c, d, e, f, g of eq 16 to vary with monovalent ion concentrations. When we allowed only two parameters to vary with [Mon⁺] and kept the remaining parameters constant, no significant improvements in the accuracy of T_m predictions were seen. When sets of three parameters were allowed to change, the best improvements of T_m predictions were observed for the set where parameters a, d, and g varied. Potential empirical equations for parameters were tabulated using the TableCurve 2D software package (SYSTAT Software Inc., Richmond, CA). The following simplest equations were selected:

(18)

(19)

(20) Concentrations are in units of mol/L. Use of eq 16 modified with parameters a, d, g adjusted according to eqs 18−20 predicts the drop in T_m observed when R lies in the range from 0.22 to 6.0. The overall fit of the data in Table 4 is also improved slightly when parameters a, d, g of eq 16 are allowed to vary (Table 5).

A general scheme for selecting the most accurate T_m correction function to employ based upon the relative amounts of monovalent and magnesium cations is shown in Figure 9. Starting from experimentally measured reference T_ms in 1.0 M Na⁺ buffer (33), melting temperatures from Table 4 were predicted according to this algorithm as well as previously published equations. Statistical comparisons between these methods are reported in Table 5. The most accurate predictions, with an average error of 0.8 °C, are obtained when parameters a, d, g are allowed to vary with monovalent ion concentration. If the parameters of eq 16 are set to constant values from Table 2, the accuracy is decreased (P < 2 × 10⁻⁵). Previously published eqs 6−9 are significantly less accurate (P < 10⁻¹¹⁸).

Figure 9. Flowchart for algorithm used to select the most accurate T_m salt correction equation depending on the relative amounts of monovalent and magnesium cations present.

Table 5. Accuracy of Various T_m Magnesium Correction Equations Evaluated in Buffers Where Magnesium and Potassium Ions Compete in Their Effects on DNA Duplex Stability

		data from Table 4 a (n = 456)		validation data setb (n = 69)
eq no.	T_m correction function	⟨\|ΔT_m\|⟩_AV (°C)	χ_r²	⟨\|ΔT_m\|⟩_AV (°C)	χ_r²
4, 16, 18−20	this work allowing parameters a, d, g to vary with [Mon⁺]	0.8	10.0	0.9	22.8
4, 16	this work with constant parameters	0.9	15.3	1.0	23.2
6	Peyret−SantaLucia	2.6	137.5	1.6	66.1
7	Ahsen−Wittwer−Schütz	2.9	163.1	1.9	81.0
9	Tan−Chen	2.6	116.5	1.9	105.1
8	Mitsuhashi	3.8	250.0	2.4	102.8

Buffers where both Mg²⁺ and K⁺ were present.

Data from Table S2 of the Supporting Information.

Equations 6, 7, 8, 9 and the algorithm from Figure 9 were used to predict melting temperatures for a validation data set of duplex DNA oligomers in Table S2 of the Supporting Information. This independent validation data set includes both published T_m values from other groups and new data presented here, comprising 69 unique pairs of T_m measurements for 39 sequences ranging in length from 9 to 60 base pairs. These sequences were not used to develop our new T_m magnesium salt correction formulas, so this is a more meaningful test of performance than can be achieved using the original derivation data sets (Tables 1, S1 and 4). Experimentally measured melting temperatures in the absence of magnesium ions (buffer 1) were used as the reference T_m, and various correction formulas were applied to predict T_m values in the presence of magnesium ions (buffer 2). Statistical comparisons of the results are shown in the last two columns of Table 5. The new magnesium correction algorithm predicted melting temperatures with the lowest error (0.9 °C) and χ_r² value. The predictions obtained from eqs 6−9 were significantly worse (P < 9 × 10⁻⁵). The algorithm shown in Figure 9 is therefore currently the most accurate method to scale melting temperatures between solutions of different monovalent and magnesium cation concentrations.

Example of Calculations Using the New T_m Magnesium Correction

Below we illustrate use of algorithm in Figure 9 to estimate the melting temperature for a 20 base-pair duplex, 5′-AAGGCGAGTCAGGCTCAGTG-3′ with 12 G·C base pairs (f_GC = 12/20 = 0.600), in 1.5 mM Mg²⁺, 10 mM Tris-HCl buffer. A reference T_m(1 M Na⁺) of 76.3 °C was measured (33) in 1 M Na⁺ and C_t = 2 µM. Since total monovalent ion concentration is 5 mM, R = (0.0015)^1/2/0.005 = 7.75. As the ratio R is larger than 0.22, magnesium ions will exhibit dominant effects on T_m. Because R is larger than 6.0, parameters a, d, g in the magnesium T_m correction eq 16 do not need to vary with [Mon⁺] but can be taken directly from Table 2,

The predicted T_m(Mg²⁺) under these conditions is 341.0 K (67.9 °C). This compares to a value of 68.5 °C measured experimentally

Discussion

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Melting temperatures of DNA duplex oligomers were studied systematically in buffers containing Mg²⁺, K⁺ and Tris⁺ ions. Novel T_m magnesium correction functions were developed that can be used to accurately scale melting temperatures between various salt environments. Statistical analysis showed that use of these new formulas significantly improves T_m predictions. Previous T_m magnesium correction eqs 6−8 assume “equivalent” effects of sodium and magnesium ions on duplex stability. Our analysis indicates that the effects of divalent cations on T_m differ both quantitatively and qualitatively from the effects of monovalent cations. The dependence of T_m on GC content is different for Mg²⁺ and monovalent ions. The relationship to oligonucleotide length is also different. Duplex melting demonstrates end-effects in magnesium solutions, which led to inclusion of terms dependent on oligonucleotide length into eq 16. In contrast, length dependent terms are unnecessary for the T_m correction function for sodium ions (eq 4) (33). T_m changes mediated by monovalent ions are independent of the number of base pairs and depend primarily on the f_GC. The concept of “equivalency” of Na⁺ and Mg²⁺ effects is therefore not justified. As a result, algorithms based on insertion of an “equivalent” sodium ion concentration into equations developed to predict the effect of monovalent ions on T_m fail to give accurate estimates of T_m in magnesium solutions.

The TBI theory developed by Tan and Chen (7, 46) represents an improvement from earlier theoretical models in that it does predict the saturation effect of magnesium ions on T_m (see Figure 3). However, the overall accuracy of the prediction of T_m with this model is not improved (Table 3). It may be possible to modify certain assumptions made in the TBI theory to more accurately predict experimental melting data. However, even with such improvements it would not appear possible to account for the observed sequence dependent effects using electrostatic principles alone.

The saturation effect on T_m seen with magnesium occurs at lower concentrations the higher the GC content of the duplex (Figure S3). A similar effect was observed previously for the binding of Na⁺ ions (33). This sequence specific behavior is consistent with a study of repeating polymers using ²⁵Mg NMR spectroscopy (55), in which G·C base pairs were found to bind Mg²⁺ up to 100-fold more strongly than A·T base pairs. Sequence dependent Mg²⁺ binding was also detected when hydration of DNA duplexes was investigated using ultrasonic velocity measurements (56). DNA A·T base pairs were proposed to interact with magnesium ions by outer-sphere complex formation, while G·C base pairs exhibited substantial dehydration changes typical for inner-sphere complexes.

Two modes of ion binding have been suggested for the interaction of metal ions with DNA (23, 56). “Site binding” refers to specific binding of the ion to negatively charged groups or pockets on nucleic acids. This more intimate interaction is often observed in tertiary folds of RNA molecules where phosphates are clustered (23). Unique, specific sites take up an integral number of ions. Site-bound ions may lose some of their coordinated water molecules. The second binding mode, “diffuse binding”, refers to all nonspecific interactions of ions with DNA where ions are highly delocalized in areas surrounding the DNA molecule. Specifically, this refers to the process whereby magnesium or monovalent cations form an ionic sleeve around single-stranded or double-stranded DNA and neutralize its negatively charged phosphate backbone. Localization of diffusely bound ions is difficult to determine experimentally as the ions are relatively free to move within areas of similar electrostatic potential.

Diffuse magnesium ions are thought to be bound through “outer-sphere” complexes where magnesium ions coordinate six water molecules, [Mg(H₂O)₆]²⁺, and the water molecules establish a network of hydrogen bonds. This was observed using ²⁵Mg NMR (57) and crystallographic studies (58, 59). Electrostatic effects, therefore, cannot be completely decoupled from changes of hydration caused by counterion binding (56). Changes in the solvation shells of participating ions and hydrogen binding between water molecules in the hydration shells of Mg²⁺ and Na⁺ may make important contributions to the energetics of cation binding to DNA.

In our experiments, we found a small but significant decrease in T_m at very high magnesium concentrations (Figure 4). This agrees with a previous study of the duplex dGCATGC (13) and melting experiments of genomic DNAs (18, 19, 60). These destabilizing effects may be caused by binding of magnesium to additional sites on denatured DNA (e.g., bases), by conformational changes of DNA and/or by ion−ion repulsions in the ionic atmosphere surrounding the DNA duplex (7). Magnesium ions have a strong preference for association with phosphate groups (1, 49). If binding of magnesium ions to the bases does occur, the association constants must be several orders of magnitude smaller than the binding constants of magnesium ions with the phosphate backbone.

Binding of Magnesium Cations to Single Stranded versus Double Stranded DNA

Magnesium ions bind to nucleic acids in both the duplex and single strand states but to a greater degree in the duplex form. Denaturation of a duplex is therefore accompanied by a net release of Δn magnesium ions. Assuming a two-state melting transition, the value of Δn can be estimated from the dependence of the melting temperature on magnesium ion concentration (5):

(21) Figure 10 shows analysis of Δn values normalized to the number of phosphate groups as a function of oligonucleotide length and f_GC. The values of d(1/T_m)/d(ln [Mg²⁺]) were calculated for each DNA duplex from quadratic fits to plots of 1/T_m versus ln [Mg²⁺]. The enthalpy of duplex denaturation, ΔH°, was calculated from the unified nearest-neighbor thermodynamic parameters (31, 66) and was assumed to be independent of magnesium ion and monovalent ion concentrations (31, 33). The ΔH° values were also measured directly using DSC for a set of 21 sequences in 1.5 mM Mg²⁺ buffer (Table S3, Supporting Information). The enthalpies were found to be similar in magnesium and sodium buffers. Experimental errors are in the range of 5−10%. Therefore, the assumption that the enthalpies of duplex denaturation are salt independent is valid under the conditions studied. Equation 21 was used to calculate Δn values for oligonucleotides from 10 to 30 base pairs. Shorter oligomers (10−15 base pairs) are likely to melt in a two-state manner. The duplexes longer than 15 base pairs may show deviations from the two-state melting behavior. However, eq 21 still holds for these longer duplexes because their shapes of melting profiles are not dependent on the counterion concentration. Analysis that proves this statement is complex and requires a considerable amount of material. It is therefore shown in the end of the Supporting Information.

Figure 10. Release of magnesium ions associated with duplex denaturation. (A) Experimental values of dT_m/d(ln [Mg²⁺]) are shown in 1.5 mM (open circles), and 10 mM (closed circles) magnesium buffers as well as in the buffer containing both 1.5 mM MgCl₂ and 50 mM KCl (dotted line). The GC content of oligonucleotides ranges from 40 to 60%. For the sake of clarity, experimental data for individual duplexes are not shown for the last buffer; the relationships are approximated with lines fitted to experimental data points. (B) The number of released magnesium ions per phosphate group is plotted as a function of oligonucleotide lengths. Solid lines were predicted from eqs 16 and 21, and from the published average dependence of ΔH° values on oligonucleotide length (35). (C) The number of released magnesium ions per phosphate group decreases with increasing GC content in 1.5 mM Mg²⁺ buffer. These relationships are predicted reasonably well using eqs 16 and 21 (solid lines).

Values of Δn include contributions from the diffusely bound as well as from the site-bound Mg²⁺ ions. Since the value of Δn is derived from purely thermodynamic considerations, it provides no explicit information about the location of ions near the DNA molecule. Nevertheless, Δn is a useful estimate of the overall changes in ion association when the duplex denatures. Figure 10 illustrates that both thedT_m/d(ln [Mg²⁺]) and the value of Δn decrease as the free Mg²⁺ concentration is increased from 1.5 to 10 mM. At higher concentrations, the stabilizing effect of magnesium on the duplex reaches a maximum (see Figure 4). These observations suggest that magnesium ion binding to the single strands increases and eventually saturates as the magnesium ion concentration of the buffer increases.

Both the value of dT_m/d(ln [Mg²⁺]) and the value of Δn per phosphate decrease with increasing oligonucleotide length (see panels (A) and (B) of Figure 10). This is a result of significant end effects in magnesium buffers. Association of cations with ends of both single stranded and double stranded oligonucleotides is lower than with their interior. Thus the number of bound ions per phosphate group is predicted to increase with N_bp as the interior domain becomes larger. However, a larger increase is expected for duplexes because of their higher charge density (11, 46). Since Δn per phosphate group measures the difference of ion association between the duplex and the complementary single strands, it is expected to increase with N_bp. This was observed experimentally for a set of d(TA)_N hairpins (63) with Na⁺ as the counterion. DNA duplexes formed from two complementary strands in Na⁺ buffers do not show a significant dependence of Δn on N_bp(33). This may be due to the fact that the number of negative charges per molecule is halved upon strand separation and thereby masking the Coulombic end effects (11, 61, 62). Surprisingly, we observe the opposite end effects with magnesium ions (Figure 10). The value of Δn per phosphate decreases when oligonucleotide length is increased. Can polyelectrolyte models based on electrostatic interactions explain the different behavior of Na⁺ and Mg²⁺ counterions? Additional theoretical studies will be needed to clarify the interpretation of these results.

Figure 10A also shows that the end effect observed in magnesium buffers is substantially diminished by the addition of monovalent ions (50 mM KCl). Although Mg²⁺ ions remain dominant in 1.5 mM Mg²⁺ and 50 mM K⁺, the values of Δn per phosphate decrease much less with N_bp in this mixed buffer than in 1.5 mM Mg²⁺ buffer where no K⁺was present. This observation is consistent with the study of DNA duplex stability in solutions of sodium ions (33) where the Δn per phosphate was found to be independent of oligonucleotide length.

Figures 10B and 10C demonstrate that our new T_m magnesium correction (eq 16) provides reliable predictions of Δn values. The derivative of d(1/T_m)/d(ln [Mg²⁺]) was entered into eq 21 to obtain an estimate of Δn. The relationships between hybridization enthalpies of duplex annealing and N_bp as well as f_GC were approximated using the unified nearest-neighbor parameters (31, 35, 66) (ΔH° = −8.23(N_bp − 1) + 2.4 kcal/mol for duplexes containing 50% GC; ΔH° = −100.5 − 25.9f_GC kcal/mol for 15-mers and ΔH° = −212.6 − 49.9f_GC kcal/mol for 30-mers). Predicted Δn values shown by the solid lines in Figures 10B and 10C agree well with experimental observations.

Competitive Behavior of Monovalent and Magnesium Cations

Effects of ions on duplex stability are linked to the energetics of ion binding around the folded and the unfolded DNA molecules. These ion distributions are affected by bulk ionic concentrations. Sodium and magnesium ions act in concert to increase T_m at low magnesium/DNA concentration ratios (below 0.5 Mg²⁺ ions per nucleotide) (5). At higher magnesium/nucleotide ratios, magnesium and monovalent ions compete in their binding to DNA (5, 12, 14). We have found that the critical determinant whether magnesium ions or monovalent ions are dominant is the value of the ratio R = ([Mg²⁺])^1/2/[Mon⁺]. Figure 8B illustrates the nature of this competition for a 25 base pair long duplex. When the ratio R is greater than 6, magnesium ions are dominant and the ionic clouds surrounding both single and double stranded DNA contain mostly Mg²⁺ counterions. Under these conditions, the effects of monovalent ions on the T_m are negligible. Data from which eq 16 was derived (Tables 1 and S1) were from experiments where all R values were greater than 20. As the K⁺ concentrations increase, the ratio R decreases. When the value of R falls below ∼6, bound magnesium ions are being displaced by K⁺. As a result, parameters of eq 16 change (eqs 18−20). The melting temperature decreases slightly when potassium ions are added to solutions of magnesium ions under these conditions. This was observed for all 12 duplexes studied (see Table 4). The slight destabilization is predicted by polyectrolyte theory (5, 6, 9) and has also been observed with genomic DNAs (17). Under these conditions, the bulk potassium concentration is much higher than the bulk magnesium concentration. Therefore, the diffuse Debye−Hückel ion atmosphere will be composed mostly of potassium ions. Because of magnesium counterion condensation, a larger effective charge is present on single strands than on double strands and single strands are therefore stabilized more by addition of monovalent ions due to Debye−Hückel screening.

When the value of R falls below 0.22, monovalent ions become dominant. At this point, replacement of the magnesium ions by potassium in the ionic clouds surrounding DNA is essentially complete. The dependence of the melting temperature on the counterion concentration thereafter follows the T_m correction function developed previously for monovalent ions alone (eq 4). Duplex stability then rises with increasing monovalent ion concentration. At 1.5 mM Mg²⁺, the crossover point is at ∼180 mM K⁺. At higher concentrations of magnesium, the crossover point shifts to progressively higher concentrations of monovalent ions. Nakano et al. (14) studied Na⁺−Mg²⁺ competition for the single duplex d(GCCAGTTAA). We calculated from their Figure 6 that the dominant ion changed from magnesium to sodium at value of R equal to 0.24 in good agreement with our findings.

The ionic atmosphere around DNA as a function of Mg²⁺ and Na⁺ concentrations has been modeled using Monte Carlo simulations, Poisson−Boltzmann calculations (12, 64) and the hypernetted chain integral method (65). Using the nonlinear Poisson−Boltzmann equation, Rouzina and Bloomfield (64) predicted that, to maintain the same proportion of sodium and magnesium ions bound to DNA while varying the bulk ionic composition, one should keep the ratio [Mg²⁺]/[Na⁺]² constant. A similar conclusion can be inferred from the theoretical study of Bacquet and Rossky (65). Our experimental results now provide convincing support for these predictions.

Effects of Magnesium Ions on Transition Enthalpies, Entropies and Free Energies

Useful salt-correction equations for free energies, ΔG°, and entropies, ΔS°, of DNA hybridization can be developed from eq 16 if the following assumptions are made: (i) Duplex melting is a two-state process. (ii) Counterion effects are mostly entropic (31, 61, 66). (iii) Enthalpies and entropies of DNA melting reactions are temperature independent, i.e., ΔC_p is zero. Although the last assumption may not be correct over a wide range of temperatures, it is reasonable within the narrow range of temperatures between T_m(Mg²⁺) in a magnesium buffer and the reference T_m(1 M Na⁺) in 1 M Na⁺ buffer (see Table S3, Supporting Information). Using the relationship 1/T_m = ΔS°/ΔH° + (R/ΔH°) ln [C_t/4], eq 16 can be rearranged to obtain the following equations for transition entropies:

(22) and transition free energies at 37 °C,

(23) The units of ΔH° and ΔG °₃₇ are cal/mol. These relationships should be useful for calculating energetics of DNA folding in the presence of magnesium ions.

Implications for PCR and DNA Sequencing

Accurate prediction of T_m in specific reaction conditions is a fundamental step when designing oligodeoxynucleotides for use in PCR, DNA sequencing and other molecular biology applications. T_m prediction is particularly important when working with closely related sequences (allelic variants, single nucleotide polymorphisms, etc.) or when designing multiplex reactions where a large number of primers must function together. We have studied a number of the solution components that can affect DNA duplex stability and therefore impact the design of DNA primers and probes.

Buffers used in molecular biology experiments generally contain a mixture of monovalent cations (Na⁺ or K⁺) and Mg²⁺. As shown in Figure 2, the effects of sodium and potassium ions on duplex stability are equivalent. This is true even under conditions in which Na⁺ and K⁺ compete with Mg²⁺ for binding to DNA. Therefore, nearest-neighbor parameters and salt correction formulas developed for buffers containing Na⁺ can be used interchangeably with K⁺.

We have found that the effect of Mg²⁺ on T_m is dominant over monovalent cations under typical reaction conditions used for PCR and DNA sequencing ([K⁺] = 20−100 mM and [Mg²⁺] = 1.5−5 mM). Values of R range from about 0.3 to 4 M^−1/2. Accurate treatment of the effect of Mg²⁺ on T_m is, therefore, very important in the design of DNA primers and probes for these assays. Using the algorithm of Figure 9 with the correction formulas presented herein, the T_m can be predicted within an average accuracy of 1 °C. Earlier models are less accurate and in some cases lead to large errors (>10 °C). The procedure of converting the Mg²⁺ component to an “equivalent Na⁺ concentration” is not justified. The influence of magnesium and monovalent cations on DNA duplex stability differ with respect to both f_GC and oligonucleotide length and must be treated differently.

Although metal ions present in reaction buffers (Na⁺, K⁺, Mg²⁺) have the greatest impact on T_m, other components contribute and should be taken into account. Most buffers used in molecular biology applications rely on Tris or other ammonium salts, which exhibit a significant dependence of ionization constant on temperature. Tris buffer adjusted to pH of 8.3 at 25 °C decreases to pH 6.9 as temperature is raised to 95 °C. This pH change, however, has little effect on the stability of DNA duplexes (see Figure 1) as pK_Hs of the ionizable groups of the bases lie outside of this range. Nucleic acid−bases have pK_H values lower than 4.5 (dC) and greater than 9.4 (dG) in the single-stranded state which move even further from neutrality in the duplex state (43). Furthermore, the temperature range where primer hybridization and DNA synthesis occur during PCR is usually between 60 °C (the primer annealing step) and 72 °C (the enzymatic extension step). Within this narrow temperature window, pH varies only between 7.6 and 7.4. Thus the large pH shifts seen in Tris buffers with changes in temperature should have no effect on hybridization efficiency during PCR or other thermal cycling reactions. However, the protonated form of Tris is a monovalent cation and should be added to the total monovalent cation concentration when performing T_m calculations. Due to the relative extent of ionization, 10 mM Tris is equivalent to about 5 mM Na⁺.

We have shown that the presence of dNTPs in a reaction mixture decreases the free magnesium ion concentration, which, in turn, lowers the T_m for DNA hybridization reactions done in that buffer. The Mg−dNTP association constant is sufficiently large (50) that the free Mg²⁺ concentration can be approximated simply by the difference between the total magnesium concentration and the total concentration of dNTPs. In a typical PCR reaction, the four dNTPs together are usually present at a concentration of 0.8 mM. Although sample DNA, primers and probes can also bind Mg²⁺, their concentrations are too low to significantly affect the level of free Mg²⁺.

During the course of PCR, dNTPs are consumed as DNA synthesis proceeds. However, this does not necessarily imply that free Mg²⁺ levels increase. Pyrophosphate, a byproduct of DNA synthesis, as well as the newly synthesized double-stranded DNA amplicon can also bind magnesium ions. We have not measured the fluctuations of free magnesium concentration during PCR.

Supporting Information

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Additional sets of T_m values used to develop and validate new magnesium correction, results of DSC and CD experiments, nearest-neighbor model of T_m magnesium correction and Δn calculations for duplexes that melt in non-two-state fashion. This material is available free of charge via the Internet at http://pubs.acs.org. Further, the database of average melting profiles, fraction of melted base pairs versus temperature, is available at http://biophysics.idtdna.com/Paper7/Abstract7.html.

bi702363u-file013.pdf (1.35 MB)

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Acknowledgment

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The authors thank Drs. Isard Dunietz and Zhi-Jie Tan for helpful discussions on the stability of nucleic acid duplexes.

References

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Korolev, Nikolay; Lyubartsev, Alexander P.; Nordenskiold, Lars
Biophysical Journal (1998), 75 (6), 3041-3056CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
Numerical calcns., using Poisson-Boltzmann (PB) and counterion condensation (CC) polyelectrolyte theories, of the electrostatic free energy difference, ΔGel, between single-stranded (coil) and double-helical DNA have been performed for solns. of NaDNA + NaCl with and without added MgCl2. Calcns. have been made for conditions relevant to systems where exptl. values of helix coil transition temp. (Tm) and other thermodn. quantities have been measured. Comparison with exptl. data has been possible by invoking values of Tm for solns. contg. NaCl salt only. Resulting theor. values of enthalpy, entropy, and heat capacity (for NaCl salt-contg. solns.) and of Tm as a function of NaCl concn. in NaCl + MgCl2 solns. have thus been obtained. Qual. and, to a large extent, quant. reprodn. of the exptl. Tm, ΔHm, ΔSm, and ΔCp values have been found from the results of polyelectrolyte theories. However, the quant. resemblance of exptl. data is considerably better for PB theory as compared to the CC model. Furthermore, some rather implausible qual. conclusions are obtained within the CC results for DNA melting in NaCl + MgCl2 solns. Our results argue in favor of the Poisson-Boltzmann theory, as compared to the counterion condensation theory.
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Tan, Z.-J. and Chen, S.-J. (2006) Nucleic acid helix stability: effects of salt concentration, cation valence and size, and chain length Biophys. J. 90, 1175– 1190
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7
Nucleic acid helix stability: effects of salt concentration, cation valence and size, and chain length
Tan, Zhi-Jie; Chen, Shi-Jie
Biophysical Journal (2006), 90 (4), 1175-1190CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
Metal ions play crucial roles in thermal stability and folding kinetics of nucleic acids. For ions (esp. multivalent ions) in the close vicinity of nucleic acid surface, interion correlations and ion-binding mode fluctuations may be important. Poisson-Boltzmann theory ignores these effects whereas the recently developed tightly bound ion (TBI) theory explicitly accounts for these effects. Extensive exptl. data demonstrate that the TBI theory gives improved predictions for multivalent ions (e.g., Mg2+) than the Poisson-Boltzmann theory. In this study, we use the TBI theory to investigate how the metal ions affect the folding stability of B-DNA helixes. We quant. evaluate the effects of ion concn., ion size and valence, and helix length on the helix stability. Moreover, we derive practically useful anal. formulas for the thermodn. parameters as functions of finite helix length, ion type, and ion concn. We find that the helix stability is additive for high ion concn. and long helix and nonadditive for low ion concn. and short helix. All these results are tested against and supported by extensive exptl. data.
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8
Wilson, R. W., Rau, D. C., and Bloomfield, V. A. (1980) Comparison of polyelectrolyte theories of the binding of cations to DNA Biophys. J. 30, 317– 326
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8
Comparison of polyelectrolyte theories of the binding of cations to DNA
Wilson, Robert Wilfred; Rau, Donald C.; Bloomfield, Victor A.
Biophysical Journal (1980), 30 (2), 317-25CODEN: BIOJAU; ISSN:0006-3495.
Predictions of the binding of counterions to DNA made using the counterion condensation theory developed by G. S. Manning (1978) are compared with those made using the Poisson-Boltzmann equation, solved numerically by the Runge-Kutta procedure. Ions are defined as territorially or atmospherically bound if they fall within a given distance, defined by counterion condensation theory, from the DNA surface. Two types of exptl. situations are considered. The 1st is the delocalized binding of a single type of counterion to DNA. In this case the Poisson-Boltzmann treatment predicts somewhat lower extents of binding to DNA, modeled as a 10-Å radius cylinder, than does Manning theory. The 2 theories converge as the radius decreases. The 2nd type of expt. is the competition of ions of different valence for binding to DNA. The theories are compared with literature values of binding consts. of divalent ions in the presence of monovalent ions, and of spermidine3+ in the presence of Na+ or Mg2+. Both predict with fair accuracy the salt dependence of the equil. consts.
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9
Manning, G. S. (1972) On the application of polyelectrolyte “limiting laws” to the helix-coil transition of DNA. II. The effect of Mg⁺² counterions Biopolymers 11, 951– 955
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9
Application of polyelectrolyte "limiting laws" to the helix-coil transition of DNA. II. Effect of Mg2+ counterions
Manning, Gerald S.
Biopolymers (1972), 11 (5), 951-5CODEN: BIPMAA; ISSN:0006-3525.
Previously published techniques are here applied to the case for which the soln. contains, in addn. to excess uni-univalent salt, 1 equiv. of divalent counterions per mol nucleotide. In agreement with the melting temp. measurements of Dove and Davidson for Mg2+, it is predicted that a region of uni-univalent salt concn. then exists in which (dTm/d log mA+), where mA+ = molality of univalent salt, is neg. It is further predicted, in accord with expts., that in the presence of divalent counterions, the helical form of DNA is much more stable than in their absence.
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Manning, G. S. (1978) The molecular theory of polyelectrolyte solutions with applications to the electrostatic properties of polynucleotides Q. Rev. Biophys. 11, 179– 246
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10
The molecular theory of polyelectrolyte solutions with applications to the electrostatic properties of polynucleotides
Manning, Gerald S.
Quarterly Reviews of Biophysics (1978), 11 (2), 179-246CODEN: QURBAW; ISSN:0033-5835.
The theory of polyelectrolyte solns. is extended to cases of interest in polynucleotide chem. The ionic state of an extended polynucleotide structure in an aq. environment of simple counterions is initially discussed. The polynucleotide in such an environment is considered to to be potentiated by its counterions for the spontaneous occurrence of any process that results in the relief of the electrostatic stress on the polynucleotide set up by the repulsive interactions among the phosphate groups. Binding of multivalent cationic substances is a process of this type as are the DNA helix-coil transition and the tendency of DNA to straighten spontaneously from a locally bent configuration. Binding to polynucleotides of cationic substances as diverse as Na+, Mg2+, spermine, polylysine, and lactose repressor is discussed. The anal. of ionic effects on conformational transitions includes those induced by strong elec. fields as well as by temp. increases.
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Olmsted, M. C., Anderson, C. F., and Record, M. T., Jr (1991) Importance of oligoelectrolyte end effects for the thermodynamics of conformational transitions of nucleic acid oligomers: a grand canonical Monte Carlo analysis Biopolymers 31, 1593– 1604
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11
Importance of oligoelectrolyte end effects for the thermodynamics of conformational transitions of nucleic acid oligomers: a grand canonical Monte Carlo analysis
Olmsted, Martha C.; Anderson, Charles F.; Record, M. Thomas, Jr.
Biopolymers (1991), 31 (13), 1593-604CODEN: BIPMAA; ISSN:0006-3525.
Effects of salt concn. on the stabilities of oligonucleotide helixes are analyzed directly in terms of ΔΓN→yN ≡ ΓyNden - INnat, the difference in the salt-nucleotide phosphate preferential interaction coeffs. for the denatured state, having yN phosphate charges, and for the native state, having N phosphate charges (y = 1 for hairpin denaturation and y = 0.5 for dimer denaturation). Previous exptl. studies of the denaturation of hairpin oligonucleotides (having 18 < N < 44) indicate significant differences between ΔΓN→N and ΔΓ∞, the value detd. for the denaturation of the corresponding polynucleotide. These differences are thermodn. manifestations of the oligoelectrolyte end effect. In contrast, the available data on the denaturation of oligonucleotide dimer helixes (N ≤ 22) imply that differences between ΔΓ∞ and ΔΓN→0.5N, and hence oligoelectrolyte end effects, are small or negligible. To det. the origin of these apparently conflicting implications concerning the importance of oligoelectrolyte end effects, the N dependence of ΓN was calcd. from grand canonical Monte Carlo simulations for an idealized model of the structure and charge distribution of each oligomer conformation. The calcns. are in quant. agreement with the exptl. finding for d(TA) hairpin oligomers that -ΔΓN→N decreases linearly as N-1 increases, and with the extant exptl. detns. of ΔΓN→0.5N. These results provide an illustration of how the large electrostatic end effects exhibited by the hairpin denaturation data are masked when ΔΓ∞ is compared with values of ΔΓN→0.5N for short dimer helixes (N ≤ 22). For 0.5N > 24, -ΔΓN→0.5N is predicted to be a linear function of N-1 whose slope has the opposite sign from, and is more salt-concn. dependent than, the corresponding slope of -ΔΓN→N as a function of N-1. Calcns. also yield predictions about the N dependences of the individual values of ΓN that can be tested by detg. Donnan coeffs. from membrane dialysis equil. expts. For long enough hairpin and dimer oligonucleotides (yN ≥ 24), in either native or denatured forms, it is predicted that the (pos.) difference Γ∞ - ΓN increases linearly with increasing N-1. For smaller values of N the difference Γ∞ - ΓN continues to increase with increasing N-1.
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Pack, G. R., Wong, L., and Lamm, G. (1999) Divalent cations and the electrostatic potential around DNA: Monte Carlo and Poisson-Boltzmann calculations Biopolymers 49, 575– 590
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12
Divalent cations and the electrostatic potential around DNA: Monte Carlo and Poisson-Boltzmann calculations
Pack, George R.; Wong, Linda; Lamm, Gene
Biopolymers (1999), 49 (7), 575-590CODEN: BIPMAA; ISSN:0006-3525. (John Wiley & Sons, Inc.)
The predictions of counterion condensation theory for divalent ions were tested by comparison with the results of Monte Carlo calcns. on an all-atom model of DNA. Monovalent-divalent competition at the polyelectrolyte surface was investigated by varying the partial molar volume of divalent ions. To assess the viability of using Poisson-Boltzmann (PB) calcns. for detg. divalent ion concns. at DNA surfaces, Monte Carlo (MC) calcns. were compared with PB calcns. using different models of the dielec. continuum. It was detd. that, while std. PB calcns. of divalent ion surface densities are about 25-30% below those predicted by MC techniques, and somewhat larger than errors previously detd. for monovalent ions, errors due to the use of the mean-field approxn. of PB theory are smaller than those arising from common assumptions regarding the dielec. continuum.
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13
Williams, A. P., Longfellow, C. E., Freier, S. M., Kierzek, R., and Turner, D. H. (1989) Laser temperature-jump, spectroscopic, and thermodynamic study of salt effects on duplex formation by dGCATGC Biochemistry 28, 4283– 4291
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Laser temperature-jump, spectroscopic, and thermodynamic study of salt effects on duplex formation by dGCATGC
Williams, Alison P.; Longfellow, Carl E.; Freier, Susan M.; Kierzek, Ryszard; Turner, Douglas H.
Biochemistry (1989), 28 (10), 4283-91CODEN: BICHAW; ISSN:0006-2960.
Salt effects on duplex formation by dGCATGC were studied with spectroscopic, thermodn., and kinetic methods. CD spectra indicate different salt conditions having little effect on the structures of the duplex and single strand. NMR chem. shifts indicate the structure of the duplex in 1M NaCl is similar to that of the B-form detd. previously in 0.5M KCl (Nilges, M., et al., 1987). Optical melting expts. indicate the effect of Na+ concn. on melting temp. is similar to that expected for a polynucleotide with the same GC content. Laser temp.-jump expts. indicate the effect of Na+ concn. on the rate of duplex formation is much less than that obsd. for polynucleotides. The observations are consistent with expectations based on a counterion condensation model. This is surprising for a duplex with only 10 phosphates.
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Nakano, S., Fujimoto, M., Hara, H., and Sugimoto, N. (1999) Nucleic acid duplex stability: influence of base composition on cation effects Nucleic Acids Res. 27, 2957– 2965
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14
Nucleic acid duplex stability: influence of base composition on cation effects
Nakano, Shu-Ichi; Fujimoto, Mariko; Hara, Hideyuki; Sugimoto, Naoki
Nucleic Acids Research (1999), 27 (14), 2957-2965CODEN: NARHAD; ISSN:0305-1048. (Oxford University Press)
The effects of counter ion on a nucleic acid duplex stability were investigated. Since a linear free energy relationship for the thermostability of oligonucleotide duplexes between those in 1 M and in 100 mM NaCl-phosphate buffer were obsd. regardless of whether they are DNA-DNA, RNA-RNA or RNA-DNA duplexes, simple prediction systems for ΔG037 as well as Tm values in 100 mM NaCl-phosphate buffer were established. These predictions were successful with an av. error of only 2.4°C for Tm and 5.7% for G037 values. The no. of Na+ newly bound to a duplex when the duplex forms (-Δn) was significantly influenced by the base compn., and -Δn for d(GCCAGTTAA)/d(TTAACTGGC) was different for MgCl2, CaCl2, BaCl2 and MnCl2 (from 0.70 to 0.76 with the same order of the duplex stability). Almost no additive effects on the duplex stability was obsd. for NaCl and MgCl2, suggesting a competitive binding for these cations. The sequence-dependent manner of Δn suggests the presence of preferential base pairs or nearest-neighbor base pairs for the cation binding, which would affect nearest-neighbor parameters.
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von Ahsen, N., Wittwer, C. T., and Schütz, E. (2001) Oligonucleotide melting temperatures under PCR conditions: nearest-neighbor corrections for Mg²⁺, deoxynucleotide triphosphate, and dimethyl sulfoxide concentrations with comparison to alternative empirical formulas Clin. Chem. 47, 1956– 1961
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15
Oligonucleotide melting temperatures under PCR conditions: nearest-neighbor corrections for Mg2+, deoxynucleotide triphosphate, and dimethyl sulfoxide concentrations with comparison to alternative empirical formulas
Von Ahsen, Nicolas; Wittwer, Carl T.; Schutz, Ekkehard
Clinical Chemistry (Washington, DC, United States) (2001), 47 (11), 1956-1961CODEN: CLCHAU; ISSN:0009-9147. (American Association for Clinical Chemistry)
Background: Many techniques in mol. biol. depend on the oligonucleotide melting temp. (Tm), and several formulas have been developed to est. Tm. Nearest-neighbor (N-N) models provide the highest accuracy for Tm prediction, but it is not clear how to adjust these models for the effects of reagents commonly used in PCR, such as Mg2+, deoxynucleotide triphosphates (dNTPs), and DMSO. Methods: The exptl. TmS of 475 matched or mismatched target/probe duplexes were obtained in our labs. or were compiled from the literature based on studies using the same real-time PCR platform. This data set was used to evaluate the contributions of [Mg2+], [dNTPs], and [DMSO] in N-N calcns. In addn., best-fit coeffs. for common empirical formulas based on GC content, length, and the equiv. sodium ion concn. of cations [Na+eq] were obtained by multiple regression. Results: When we used [Na+eq] = [Monovalent cations] + 120([Mg2+] - [dNTPs]) (the concns. in this formula are mmol/L) to correct ΔS0 and a DMSO term of 0.75 (%DMSO), the SE of the N-N Tm est. was 1.76 for perfectly matched duplexes (n = 217). Alternatively, the empirical formula Tm (°C) = 77.1+11.7 × log[Na+eq] + 0.41(%GC) - 528/bp - 0.75(%DMSO) gave a slightly higher SE of 1.87. When all duplexes (matched and mismatched; n = 475) were included in N-N calcns., the SE was 2.06. Conclusions: This robust model, accounting for the effects of Mg2+, DMSO, and dNTPs on oligonucleotide Tm in PCR, gives reliable Tm predictions using thermodn. N-N calcns. or empirical formulas.
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Peyret, N. (2000)
Prediction of Nucleic Acid Hybridization: Parameters and Algorithms
, Ph.D. Thesis, Section 5.4.2, pp 128, Wayne State University, Detroit, MI.
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17
Dove, W. F. and Davidson, N. (1962) Cation effects on the denaturation of DNA J. Mol. Biol. 5, 467– 478
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17
Cation effects on the denaturation of deoxyribonucleic acid (DNA)
Dove, William F.; Davidson, Norman
Journal of Molecular Biology (1962), 5 (), 467-78CODEN: JMOBAK; ISSN:0022-2836.
The midpoint (Tm) of the thermal denaturation curve of various DNA's increases linearly with the logarithm of the ionic strength (μ) for 0.0003 to 0.5M. This ionic strength dependence is unrelated to the base ratio of the DNA. The transition breadth increases with decreasing ionic strength. The broadening effect is interpreted as indicating that the transition is less cooperative at low μ. At μ = 3 × 10-4M, the bivalent ions Mg2+ and Co2+ are bound almost stoichiometrically by DNA, and Tm increases by 35-45°. The transition breadth is greater for 1/2 equiv. of bivalent ion/mole DNA phosphate than for zero or 1 equiv.; this is attributed to stronger ion binding by native than by denatured DNA. Ag+ at a ratio of 0.2 Ag+/base increases Tm by about 40° and broadens the transition. The pH values for denaturation by acid and base are reported for several DNA's. The resp. values at 25° are calf thymus pH 2.95, 11.78; Diplococcus pneumoniae 2.92, 11.78; Escherichia coli 2.89, 11.92; Micrococcus lysodeikticus 2.74, 11.99.
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Lyons, J. W. and Kotin, L. (1965) The effect of magnesium ion on the secondary structure of deoxyribonucleic acid J. Am. Chem. Soc. 87, 1781– 1785
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18
The effect of magnesium ion on the secondary structure of deoxyribonucleic acid
Lyons, John W.; Kotin, Leonard
Journal of the American Chemical Society (1965), 87 (8), 1781-5CODEN: JACSAT; ISSN:0002-7863.
The effect of Mg2+ on the thermal and phase stability of DNA was studied by means of spectrophotometric and N.M.R. techniques to yield certain conclusions. (1) Mg2+ interacts with DNA at the phosphate sites only. (2) Whereas aq. solutions of the pure Mg salt of DNA are relatively resistant to thermal denaturation, their thermal stability is reduced in the presence of added MgCl2. (3) The proposed mechanism for the pptn. of DNA with an excess of Mg2+ is that site-bound Mg2+ forms ionic links between sepd. DNA strands through -P-O-Mg-O-P complexes leading to the exposure of the bases to solvent. This is followed by hydrophobic base-base interaction, leading to large aggregates and, finally, phase sepn.
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Ott, G. S., Ziegler, R., and Bauer, W. R. (1975) The DNA melting transition in aqueous magnesium salt solutions Biochemistry 14, 3431– 3438
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DNA melting transition in aqueous magnesium salt solutions
Ott, Gary S.; Ziegler, Robert; Bauer, William R.
Biochemistry (1975), 14 (15), 3431-8CODEN: BICHAW; ISSN:0006-2960.
The melting transition of the Mg salt of DNA was systematically examd. in the presence of various types of anions. The addn. of ClO4- to a concn. of 3.0N resulted in a biphasic optical transition, with the 1st phase exhibiting rapid reversibility and independence of DNA concn. This subtransition, which is interpreted as an intramol. condensation to a collapsed form of DNA, was followed by a DNA concn.-dependent aggregation reaction. The aggregation was reversed by increasing the ClO4- concn. to 6.0N while elevating the temp. to posttransition levels. Alternatively, both the collapse and the aggregation were prevented by melting in the presence of trichloroacetate, a strong chaotropic solvent for DNA. The forces responsible for mediating both the collapse and the aggregation are superficially similar to those involved in maintaining duplex stability. The collapsed form, in particular, possibly possesses features in common with the condensed structures which are produced in aq. soln. of certain polymers, e.g., polyethylene glycol.
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Krakauer, H. (1971) The binding of Mg⁺² ions to polyadenylate, polyuridylate, and their complexes Biopolymers 10, 2459– 2490
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20
Binding of Mg2+ ions to polyadenylate, polyuridylate, and their complexes
Krakauer, Henry
Biopolymers (1971), 10 (12), 2459-90CODEN: BIPMAA; ISSN:0006-3525.
The binding of Mg2+ to polyadenylate (poly A), polyuridylate (poly U), and their complexes, poly (A+U) and poly (A+2U), was studied by means of a technique in which the dye eriochrome black T is used to measure the concn. of free Mg2+. The apparent binding const. Kx=[MgN]/[Mg2+][N], N=site for Mg2+ binding (the phosphate group of the nucleotide), was found to decrease rapidly as the extent of binding increased and, at low extents of binding, as the concn. of Na+ increased in poly A, poly (A+U), and poly (A+2U), and somewhat less so in poly U. Kx is generally in the range 104>Kx>102. The cause of these dependences is apparently, primarily, the displacement of Na+ by Mg2+ in poly U and poly (A+U) on the basis of the similarity of extents of displacement measured in this work and those measured potentiometrically.
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Krakauer, H. (1974) A thermodynamic analysis of the influence of simple mono- and divalent cations on conformational transitions of polynucleotide complexes Biochemistry 13, 2579– 2589
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Thermodynamic analysis of the influence of simple mono- and divalent cations on the conformational transitions of polynucleotide complexes
Krakauer, Henry
Biochemistry (1974), 13 (12), 2579-89CODEN: BICHAW; ISSN:0006-2960.
The complex dependence of the conformational transitions among the structures formed by poly(A) [24937-83-5] and poly(U) [27416-86-0] on the concns. of Na+ [7440-23-5] and Mg2+ [7439-95-4] is described and is satisfactorily interpreted in terms of the measured interactions of these ions with the polynucleotides. The anal. is phenomenol. and not predicated on any model of the interactions, but is consistent with the notion that those with Na+ are qual. different from those with Mg2+, the latter but not the former resulting in a definite complex.
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Kankia, B. I. (2003) Binding of Mg²⁺ to single-stranded polynucleotides: hydration and optical studies Biophys. Chem. 104, 643– 654
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22
Binding of Mg2+ to single-stranded polynucleotides: hydration and optical studies
Kankia, Besik I.
Biophysical Chemistry (2003), 104 (3), 643-654CODEN: BICIAZ; ISSN:0301-4622. (Elsevier Science B.V.)
The binding of Mg2+ to single-stranded ribo- and deoxy-polynucleotides, poly(rA), poly(rU), poly(dA) and poly(dT), has been investigated in dil. aq. solns. at pH 7.5 and 20°. A combination of ultrasound velocimetry, d., UV and CD spectroscopy have been employed to study hydration and spectral effects of Mg2+ binding to the polynucleotides. Vol. and compressibility effects of Mg2+ binding to random-coiled poly(rU) and poly(dT) correspond to two coordination bonds probably between the adjacent phosphate groups. The same parameters for poly(rA)+Mg2+ correspond to an inner-sphere complex with three-four direct contacts. However, almost no hydration effects are arising in binding to its deoxy analog, poly(dA), indicating mostly a delocalized binding mode. In agreement with hydration studies, optical investigations revealed almost no influence of Mg2+ on poly(dA) properties, while it stabilizes and aggregates poly(rA) single-helix. The evidence presented here indicates that Mg2+ are able to bind specifically to single-stranded polynucleotides, and recognize their compn. and backbone conformation.
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Draper, D. E. (2004) A guide to ions and RNA structure RNA 10, 335– 343
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A guide to ions and RNA structure
Draper, David E.
RNA (2004), 10 (3), 335-343CODEN: RNARFU; ISSN:1355-8382. (Cold Spring Harbor Laboratory Press)
A review. RNA folding into stable tertiary structures is remarkably sensitive to the concns. and types of cations present; an understanding of the phys. basis of ion-RNA interactions is therefore a prerequisite for a quant. accounting of RNA stability. This article summarizes the energetic factors that must be considered when ions interact with two different RNA environments. "Diffuse ions" accumulate near the RNA because of the RNA electrostatic field and remain largely hydrated. A "chelated" ion directly contacts a specific location on the RNA surface and is held in place by electrostatic forces. Energetic costs of ion chelation include displacement of some of the waters of hydration by the RNA surface and repulsion of diffuse ions. Methods are discussed for computing both the free energy of the set of diffuse ions assocd. with an RNA and the binding free energies of individual chelated ions. Such calcns. quant. account for the effects of Mg2+ on RNA stability where exptl. data are available. An important conclusion is that diffuse ions are a major factor in the stabilization of RNA tertiary structures.
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24
Zubay, G. and Doty, P. (1958) Nucleic acid interactions with metal ions and amino acids Biochim. Biophys. Acta 29, 47– 58
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24
Nucleic acid interactions with metal ions and amino acids
Zubay, Geoffrey; Doty, Paul
Biochimica et Biophysica Acta (1958), 29 (), 47-58CODEN: BBACAQ; ISSN:0006-3002.
Conductometric titrations and equil. dialysis measurements were used to measure the binding of Na+, Mg++, and Cu++ by deoxyribonucleic acid (DNA) and the binding of amino acids by DNA and ribonucleic acid, all in the presence of 0.2M NaCl. About 1/2 the Na+ counterions appeared to be held near the DNA by the electrostatic field. Mg++ ions were bound to specific sites, but very weakly. However, on thermal denaturation of the DNA the binding became much stronger. The no. of sites was about 70% of the no. of nucleotides/mol. Cu++ ions were tightly bound to undenatured DNA and caused marked aggregation. Arginine (0.01M) was bound to DNA to the extent of about 6 mols./100 nucleotides. Nonbasic amino acids (serine and glutamic acid) were not bound significantly by either denatured or undenatured DNA. Binding of glutamic acid, threonine, and proline by ribonucleic acid amounted to less than 1 mol./100 nucleotides, over the range of concns. studied.
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25
Rychlik, W., Spencer, W. J., and Rhoads, R. E. (1990) Optimization of the annealing temperature for DNA amplification in vitro Nucleic Acids Res. 18, 6409– 6412
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25
Optimization of the annealing temperature for DNA amplification in vitro
Rychlik, W.; Spencer, W. J.; Rhoads, R. E.
Nucleic Acids Research (1990), 18 (21), 6409-12CODEN: NARHAD; ISSN:0305-1048.
In the polymerase chain reaction (PCR) technique, DNA is amplified in vitro by a series of polymn. cycles consisting of 3 temp.-dependent steps: DNA denaturation, primer-template annealing, and DNA synthesis by a thermostable DNA polymerase. The purity and yield of the reaction products depend on several parameters, one of which is the annealing temp. (Ta). At both sub- and super-optimal Ta values, non-specific products may be formed, and the yield of products is reduced. Optimizing the Ta is esp. crit. when long products are synthesized or when total genomic DNA is the substrate for PCR. In this article the authors exptl. det. the optimal annealing temp. (TaOPT) values for several primer-template pairs and develop a method for its calcn. The TaOPT is found to be a function of the melting temps. of the less stable primer-template pair and of the product. The fact that exptl. and calcd. TaOPT values agree to within 0.7° eliminates the need for detg. TaOPT exptl. Synthesis of DNA fragments shorter than 1 kb is more efficient if a variable Ta is used, such that the Ta is higher in each consecutive cycle.
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26
Harris, S. and Jones, D. B. (1997) Optimisation of the polymerase chain reaction Br. J. Biomed. Sci. 54, 166– 173
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26
Optimization of the polymerase chain reaction
Harris, S.; Jones, D. B.
British Journal of Biomedical Science (1997), 54 (3), 166-173CODEN: BJMSEO; ISSN:0967-4845. (Royal Society of Medicine Press)
The polymerase chain reaction (PCR) is a method by which specific sequences of DNA can be copied many times, allowing detailed mol. studies to be performed on as little as a single cell. Numerous and diverse applications of PCR are being developed across all disciplines of diagnostic pathol. and research, and no single protocol is appropriate for all situations. Optimizing PCR requires a delicate balance between the amplification of specific products and avoiding the prodn. of non-specific products. Each step, from DNA template extn. to cycling times and temps., needs to be considered carefully. The aim of this study is to assess which parameters influence DNA amplification efficiency and specificity. The parameters evaluated are the denaturation, annealing and extension temps., the no. of cycles performed, and the primer, magnesium chloride, dNTP, Taq DNA polymerase and DNA template concns. The important parameters for efficient, specific amplification were denaturation time and temp., stringent annealing temps. and magnesium chloride concn. The importance of DNA concn. was found to depend upon the source from which the DNA was extd.
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27
Henegariu, O., Heerema, N. A., Dlouhy, S. R., Vance, G. H., and Vogt, P. H. (1997) Multiplex PCR: critical parameters and step-by-step protocol BioTechniques 23, 504– 511
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27
Multiplex PCR: critical parameters and step-by-step protocol
Henegariu, O.; Heerema, N. A.; Dlouhy, S. R.; Vance, G. H.; Vogt, P. H.
BioTechniques (1997), 23 (3), 504-511CODEN: BTNQDO; ISSN:0736-6205. (Eaton)
By simultaneously amplifying more than one locus in the same reaction, multiplex PCR is becoming a rapid and convenient screening assay in both the clin. and the research lab. While numerous papers and manuals discuss in detail conditions influencing the quality of PCR in general, relatively little has been published about the important exptl. factors and the common difficulties frequently encountered with multiplex PCR. We have examd. various conditions of the multiplex PCR, using a large no. of primer pairs. Esp. important for a successful multiplex PCR assay are the relative concns. of the primers at the various loci, the concn. of the PCR buffer, the cycling temps. and the balance between the magnesium chloride and deoxynucleotide concns. Based on our experience, we propose a protocol for developing a multiplex PCR assay and suggest ways to overcome commonly encountered problems.
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28
Markoulatos, P., Siafakas, N., and Moncany, M. (2002) Multiplex polymerase chain reaction: a practical approach J. Clin. Lab. Anal. 16, 47– 51
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28
Multiplex polymerase chain reaction: A practical approach
Markoulatos, P.; Siafakas, N.; Moncany, M.
Journal of Clinical Laboratory Analysis (2002), 16 (1), 47-51CODEN: JCANEM; ISSN:0887-8013. (Wiley-Liss, Inc.)
A review. Considerable time and effort can be saved by simultaneously amplifying multiple sequences in a single reaction, a process referred to as multiplex polymerase chain reaction (PCR). Multiplex PCR requires that primers lead to amplification of unique regions of DNA, both in individual pairs and in combinations of many primers, under a single set of reaction conditions. In addn., methods must be available for the anal. of each individual amplification product from the mixt. of all the products. Multiplex PCR is becoming a rapid and convenient screening assay in both the clin. and the research lab. The development of an efficient multiplex PCR usually requires strategic planning and multiple attempts to optimize reaction conditions. For a successful multiplex PCR assay, the relative concn. of the primers, concn. of the PCR buffer, balance between the magnesium chloride and deoxynucleotide concns., cycling temps., and amt. of template DNA and Taq DNA polymerase are important. An optimal combination of annealing temp. and buffer concn. is essential in multiplex PCR to obtain highly specific amplification products. Magnesium chloride concn. needs only to be proportional to the amt. of dNTP, while adjusting primer concn. for each target sequence is also essential. The list of various factors that can influence the reaction is by no means complete. Optimization of the parameters discussed in the present review should provide a practical approach toward resolving the common problems encountered in multiplex PCR (such as spurious amplification products, uneven or no amplification of some target sequences, and difficulties in reproducing some results). Thorough evaluation and validation of new multiplex PCR procedures is essential. The sensitivity and specificity must be thoroughly evaluated using standardized purified nucleic acids. Where available, full use should be made of external and internal quality controls, which must be rigorously applied. As the no. of microbial agents detectable by PCR increases, it will become highly desirable for practical purposes to achieve simultaneous detection of multiple agents that cause similar or identical clin. syndromes and/or share similar epidemiol. features.
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29
Ignatov, K. B., Miroshnikov, A. I., and Kramarov, V. M. (2003) A new approach to enhanced PCR specificity Rus. J. Bioorg. Chem. 29, 368– 371
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29
A new approach to enhanced PCR specificity
Ignatov, K. B.; Miroshnikov, A. I.; Kramarov, V. M.
Russian Journal of Bioorganic Chemistry (Translation of Bioorganicheskaya Khimiya) (2003), 29 (4), 368-371CODEN: RJBCET; ISSN:1068-1620. (MAIK Nauka/Interperiodica Publishing)
A new approach to enhanced specificity and product yield of polymerase chain reaction is proposed. It is based on control of DNA polymerase activity during PCR by changing the magnesium ion concn., which depends on the temp. of the reaction mixt. A slightly sol. magnesium salt, magnesium oxalate, whose soly. depends on temp., was used as a source of magnesium ions. During PCR, magnesium oxalate was maintained at satg. concn. by the presence of an insol. excess of this salt, and the concn. of magnesium ions depended on the salt soly.: binding of magnesium ions at lower temps. and their release at higher temps. was shown to affect the DNA polymerase activity and to favor the specific PCR amplification of the target DNA fragment.
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30
Owczarzy, R., Vallone, P. M., Gallo, F. J., Paner, T. M., Lane, M. J., and Benight, A. S. (1997) Predicting sequence-dependent melting stability of short duplex DNA oligomers Biopolymers 44, 217– 239
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30
Predicting sequence-dependent melting stability of short duplex DNA oligomers
Owczarzy, Richard; Vallone, Peter M.; Gallo, Frank J.; Paner, Teodoro M.; Lane, Michael J.; Benight, Albert S.
Biopolymers (1998), 44 (3), 217-239CODEN: BIPMAA; ISSN:0006-3525. (John Wiley & Sons, Inc.)
A review with 63 refs. Many important applications of DNA sequence-dependent hybridization reactions have recently emerged. This has sparked a renewed interest in anal. calcns. of sequence-dependent melting stability of duplex DNA. In particular, for many applications it is often desirable to accurately predict the transition temp., or tm, of short duplex DNA oligomers (∼ 20 base pairs or less) from their sequence and concn. The thermodn. anal. method underlying these predictive calcns. is based on the nearest-neighbor model. At least 11 sets of nearest-neighbor sequence-dependent thermodn. parameters for DNA have been published. These sets are compared. Use of the nearest-neighbor sets in predicting tm from the DNA sequence is demonstrated, and the ability of the nearest-neighbor parameters to provide accurate predictions of exptl. tm's of short duplex DNA oligomers is assessed.
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31
SantaLucia, J., Jr. and Hicks, D. (2004) The thermodynamics of DNA structural motifs Annu. Rev. Biophys. Biomol. Struct. 33, 415– 440
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31
The thermodynamics of DNA structural motifs
SantaLucia, John, Jr.; Hicks, Donald
Annual Review of Biophysics and Biomolecular Structure (2004), 33 (), 415-440, 2 platesCODEN: ABBSE4; ISSN:1056-8700. (Annual Reviews Inc.)
A review. DNA secondary structure plays an important role in biol., genotyping diagnostics, a variety of mol. biol. techniques, in vitro-selected DNA catalysts, nanotechnol., and DNA-based computing. Accurate prediction of DNA secondary structure and hybridization using dynamic programming algorithms requires a database of thermodn. parameters for several motifs including Watson-Crick base pairs, internal mismatches, terminal mismatches, terminal dangling ends, hairpins, bulges, internal loops, and multibranched loops. To make the database useful for predictions under a variety of salt conditions, empirical equations for monovalent and Mg2+ dependence of thermodn. have been developed. Bimol. hybridization is often inhibited by competing unimol. folding of a target or probe DNA. Powerful numerical methods have been developed to solve multistate-coupled equil. in bimol. and higher-order complexes. This review presents the current parameter set available for making accurate DNA structure predictions and also points to future directions for improvement.
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32
Mitsuhashi, M. (1996) Technical Report: Part 1. Basic requirements for designing optimal oligonucleotide probe sequences J. Clin. Lab. Anal. 10, 277– 284
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32
Technical report: Part 1. Basic requirements for designing optimal oligonucleotide probe sequences
Mitsuhashi, Masato
Journal of Clinical Laboratory Analysis (1996), 10 (5), 277-284CODEN: JCANEM; ISSN:0887-8013. (Wiley-Liss)
Although oligonucleotides can be easily synthesized and used in a variety of scientific fields, a major problem exists for each application: the difficulty of obtaining optimal oligonucleotide sequences. Oligonucleotide sequences have been described in each publication; however, little is disclosed on how to design such sequences and how specific each sequence is. This report introduces a new concept of computer hybridization simulation based on "thermodn. hybridizability," which can overcome the problems of conventional homol. analyses. Then, all the necessary components and factors for designing optimal probe sequences, such as hybridization strength, specificity, secondary structure, length of probes, probe-to-probe interaction, are discussed in detail. Also included are procedures for manipulating various types of data for selection of optimal oligonucleotides. This report provides a general guideline for optimal probe design and encourages basic and clin. scientists to enhance their research activities by using optimal oligonucleotides.
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33
Owczarzy, R., You, Y., Moreira, B. G., Manthey, J. A., Huang, L., Behlke, M. A., and Walder, J. A. (2004) Effects of sodium ions on DNA duplex oligomers: improved predictions of melting temperatures Biochemistry 43, 3537– 3554
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33
Effects of Sodium Ions on DNA Duplex Oligomers: Improved Predictions of Melting Temperatures
Owczarzy, Richard; You, Yong; Moreira, Bernardo G.; Manthey, Jeffrey A.; Huang, Lingyan; Behlke, Mark A.; Walder, Joseph A.
Biochemistry (2004), 43 (12), 3537-3554CODEN: BICHAW; ISSN:0006-2960. (American Chemical Society)
Melting temps., Tm, were systematically studied for a set of 92 DNA duplex oligomers in a variety of sodium ion concns. ranging from 69 mM to 1.02 M. The relationship between Tm and ln [Na+] was nonlinear over this range of sodium ion concns., and the obsd. melting temps. were poorly predicted by existing algorithms. A new empirical relationship was derived from UV melting data that employs a quadratic function, which better models the melting temps. of DNA duplex oligomers as sodium ion concn. is varied. Statistical anal. shows that this improved salt correction is significantly more accurate than previously suggested algorithms and predicts salt-cor. melting temps. with an av. error of only 1.6° when tested against an independent validation set of Tm measurements obtained from the literature. Differential scanning calorimetry studies demonstrate that this Tm salt correction is insensitive to DNA concn. The Tm salt correction function was found to be sequence-dependent and varied with the fraction of G·C base pairs, in agreement with previous studies of genomic and polymeric DNAs. The salt correction function is independent of oligomer length, suggesting that end-fraying and other end effects have little influence on the amt. of sodium counterions released during duplex melting. The results are discussed in the context of counterion condensation theory.
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34
Moreira, B. G., You, Y., Behlke, M. A., and Owczarzy, R. (2005) Effects of fluorescent dyes, quenchers, and dangling ends on DNA duplex stability Biochem. Biophys. Res. Commun. 327, 473– 484
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34
Effects of fluorescent dyes, quenchers, and dangling ends on DNA duplex stability
Moreira, Bernardo G.; You, Yong; Behlke, Mark A.; Owczarzy, Richard
Biochemical and Biophysical Research Communications (2005), 327 (2), 473-484CODEN: BBRCA9; ISSN:0006-291X. (Elsevier)
Single and dual-labeled fluorescent oligodeoxynucleotides are used in many mol. biol. applications. We investigated the effects of commonly used fluorescent dyes and quenchers on the thermodn. stability of a model probe-target DNA duplex. We demonstrate that those effects can be significant. Fluorescent dyes and quenchers were attached to the probe ends. In certain combinations, these groups stabilized the duplex up to 1.8 kcal/mol and increased Tm up to 4.3°. None of the groups tested significantly destabilized the duplex. Rank order of potency was, starting with the most stabilizing group: Iowa Black RQ ∼ Black Hole 2 > Cy5 ∼ Cy3 > Black Hole 1 > QSY7 ∼ Iowa Black FQ > Texas Red ∼ TAMRA > FAM ∼ HEX ∼ Dabcyl > TET. Longer linkers decreased stabilizing effects. Hybridizations to targets with various dangling ends were also studied and were found to have only minor effects on thermodn. stability. Depending on the dye/quencher combination employed, it can be important to include thermodn. contributions from fluorophore and quencher when designing oligonucleotide probe assays.
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35
Owczarzy, R. (2005) Melting temperatures of nucleic acids: discrepancies in analysis Biophys. Chem. 117, 207– 215
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35
Melting temperatures of nucleic acids: Discrepancies in analysis
Owczarzy, Richard
Biophysical Chemistry (2005), 117 (3), 207-215CODEN: BICIAZ; ISSN:0301-4622. (Elsevier B.V.)
Melting temp., Tm, is an important property of nucleic acid duplexes. It is typically detd. from spectroscopic or calorimetric melting expts. More than one anal. method has been used to ext. T m values from exptl. melting data. Unfortunately, different methods do not give the same results; the same melting data can be assigned different T m values depending upon which method is used to process that data. Inconsistencies or systematic errors between T ms reported in published data sets can be significant and add confusion to the field. Errors introduced from anal. can be greater than exptl. errors, ranging from a fraction of degree to several degrees. Of the various methods, the most consistent and meaningful approach defines melting temp. as the temp. at the transition midpoint where half of the base pairs are melted and std. free energy is zero. Assuming a two-state melting behavior, we present here a set of general equations that can be used to reconcile these anal. T m differences and convert results to the correct melting temps. at the transition midpoint. Melting temps. collected from published sources, which were analyzed using different methods, can now be cor. for these discrepancies and compared on equal footing. The similar corrections apply to Tm differences between calorimetric and spectroscopic melting curves. New algorithm for selection of linear sloping baselines, 2nd deriv. method, is suggested, which can be used to automate melting curve anal.
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36
Bevington, P. R. and Robinson, D. K. (1992) Data Reduction and Error Analysis for the Physical Sciences, WCB/McGraw-Hill, Boston, MA.
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37
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1996) Numerical Recipes in Fortran 77: The Art of Scientific Computing, Cambridge University Press, Cambridge.
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38
Good, N. E., Winget, G. D., Winter, W., Connolly, T. N., Izawa, S., and Singh, R. M. M. (1966) Hydrogen ion buffers for biological research Biochemistry 5, 467– 477
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38
Hydrogen ion buffers for biological research
Good, Norman E.; Winget, G. Douglas; Winter, Wilhelmina; Connolly, Thomas N.; Izawa, Seikichi; Singh, Raizada M. M.
Biochemistry (1966), 5 (2), 467-77CODEN: BICHAW; ISSN:0006-2960.
Twelve new or little used H+ buffers covering the range pKa = 6.15-8.35 were prepd. and tested. Ten are zwitterionic amino acids, either N-substituted taurines or N-substituted glycines, and 2 are cationic primary aliphatic amines. All of the zwitterionic buffers are better than conventional buffers in the Hill reaction and in the phosphorylation-coupled oxidn. of succinate by bean mitochondria. Two of the zwitterions, N-tris-(hydroxymethyl)-methylaminoethanesulfonic acid and N-2-hydroxyethylpiperazine-N'-2-ethanesulfonic acid, give particularly active and stable mitochondrial prepns. These 2 also give higher rates of protein synthesis in cell-free bacterial prepns. than do Tris or phosphate buffers.
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39
Dawson, R. M. C., Elliot, D. C., Elliot, W. H., and Jones, K. M. (1986) Data for Biochemical Research, Oxford University Press, Oxford, U.K., pp 424.
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40
Fukada, H. and Takahashi, K. (1998) Enthalpy and heat capacity changes for the proton dissociation of various buffer components in 0.1M potassium chloride Proteins 33, 159– 166
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40
Enthalpy and heat capacity changes for the proton dissociation of various buffer components in 0.1 M potassium chloride
Fukada, Harumi; Takahashi, Katsutada
Proteins: Structure, Function, and Genetics (1998), 33 (2), 159-166CODEN: PSFGEY; ISSN:0887-3585. (Wiley-Liss, Inc.)
Enthalpy and heat capacity changes for the deprotonation of 18 buffers were calorimetrically detd. in 0.1 M potassium chloride at temps. ranging from 5 to 45°. The values of the dissocn. const. were also detd. by means of potentiometric titrn. The enthalpy changes for the deprotonation of buffers, except for the phosphate and glycerol 2-phosphate buffers, were found to be characterized by a linear function of temp. The enthalpy changes for the second dissocn. of phosphate and glycerol 2-phosphate where divalent anion is formed on dissocn. were fitted with the second order function of temp. rather than the first order. Temp. dependence of buffer pH calcd. by using the enthalpy and heat capacity changes obtained was in good agreement with the temp. variation of the pH values actually measured in the temp. range between 0 and 50° for all the buffers studied. On the basis of the results obtained, a numeric table showing the temp. dependence of pK values for the 18 buffers is presented.
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41
Plum, G. E. and Breslauer, K. J. (1995) Thermodynamics of an intramolecular DNA triple helix: a calorimetric and spectroscopic study of pH and salt dependence of thermally induced structural transitions J. Mol. Biol. 248, 679– 695
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41
Thermodynamics of an intramolecular DNA triple helix: a calorimetric and spectroscopic study of the pH and salt dependence of thermally induced structural transitions
Plum, G. Eric; Breslauer, Kenneth J.
Journal of Molecular Biology (1995), 248 (3), 679-95CODEN: JMOBAK; ISSN:0022-2836. (Academic)
We have characterized thermodynamically the melting transitions of a DNA 31-mer oligonucleotide (5'GAAGAGGTTTTTCCTCTTCTTTTTCTTCTCC-3') which is designed to fold into an intramol. triple helix. The first 19 residues fold back on themselves to form an antiparallel Watson-Crick hairpin duplex with a T5 loop. The 3'-terminal seven residues, which are connected to the Watson-Crick hairpin duplex by a second T5 loop, form Hoogsteen interactions in the major groove of the Watson-Crick hairpin. From UV melting studies we find that the 31-mer exhibits either one or two transitions, depending on soln. conditions. We use pH- and temp.-dependent CD to assign the initial and final states assocd. with each transition. We find that the disruption of the Hoogsteen hairpin is accompanied by a release of protons and an uptake of sodium ions while the disruption of the Watson-Crick hairpin is accompanied by a release of sodium ions with no change in protonation state. from these data, we construct a phase diagram for this intramol. DNA triple helix as a function of pH, sodium ion concn., and temp. We characterize the energies of each transition using a van't Hoff anal. and differential scanning calorimetry (DSC). Significantly, the DSC data provide a model-independent thermodn. characterization of the thermally induced transitions of this triplex. By combining the spectroscopic and calorimetric data, we develop a semi-empirical model which describes the state of the 31-mer as a function of pH, sodium ion concn., and temp. With this model we successfully predict characteristics of the 31-mer, which are beyond the data which are used in establishing the model (for example, the salt dependence of the apparent pKa of the Hoogsteen strand). This semi-empirical model may serve as a prototype for developing a method to predict the phase diagrams of intramol. triple helix systems.
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42
Privalov, P. L. and Ptitsyn, O. B. (1969) Determination of stability of the DNA double helix in an aqueous medium Biopolymers 8, 559– 571
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Determination of stability of the DNA double helix in an aqueous medium
Privalov, P. L.; Ptitsyn, O. B.; Birshtein, T. M.
Biopolymers (1969), 8 (5), 559-71CODEN: BIPMAA; ISSN:0006-3525.
The possibility of detg. the free energy of stabilization (ΔG0) of native DNA structure with the help of calorimetric data on the heats of transition from the native to denatured state is considered. Results of microcalorimetric measurements of heats of denaturation of T2 phage DNA at different values of pH and ionic strength of soln. are given. Values for the free energy of stabilization of the DNA native structure under various conditions were obtained. Under conditions close to physiol., ΔG0 approaches 1200 cal/mole per base pair.
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43
Record, M. T., Jr (1967) Electrostatic effects on polynucleotide transitions. II. Behavior of titrated systems Biopolymers 5, 993– 1008
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43
Electrostatic effects on polynucleotide transitions. II. Behavior of titrated systems
Record, M. Thomas, Jr.
Biopolymers (1967), 5 (10), 993-1008CODEN: BIPMAA; ISSN:0006-3525.
The effects of monovalent counterion concn. upon polynucleotide structural stability under conditions of titrn. of the bases are discussed, based on the previously developed theory (Record (1967)). For any class of transition, the melting temp. Tm at const. pH is a linear function of the log of the monovalent counterion concn., M. At high salt concns., the log of the depression of the melting temp. by pH titrn. is proportional to the pH change, and the stability of the ordered form as measured by its melting temp. at neutral pH is a monotonic function of pHm/pK, where pHm and pK are the pH of melting and the monomer base pK, resp., both measured under similar conditions of temp. and ionic strength. For the transition from double helix to coil, dTm/dlog M, a measure of the neg. of the electrostatic free energy change in the transition, decreases with increasing pH. In acid soln., where the coil is more extensively protonated than the helix, the change in electrostatic free energy in the transition is larger than at neutral pH, whereas in alkali the electrostatic free energy change is smaller than at neutral pH. At sufficiently high pH, dTm/dlog M becomes neg., indicating that the electrostatic free energy change is pos. in the transition of this region. Literature data on the ionic strength dependence of the melting temp. for the acid helices of poly A, poly C, and poly dC are considered theoretically.
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44
Gray, D. M. (1997) Derivation of nearest-neighbor properties from data on nucleic acid oligomers. I. Simple sets of independent sequences and the influence of absent nearest neighbors Biopolymers 42, 783– 793
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Derivation of nearest-neighbor properties from data on nucleic acid oligomers. I. Simple sets of independent sequences and the influence of absent nearest neighbors
Gray, Donald M.
Biopolymers (1997), 42 (7), 783-793CODEN: BIPMAA; ISSN:0006-3525. (John Wiley & Sons, Inc.)
The constraints on combinations of nearest neighbors in nucleic acid sequences and the nos. of independent sequences needed to describe nearest-neighbor properties of oligomers and polymers are derived and summarized. It has been pointed out in previous work [D. M. Gray and I. Tinoco, Jr. (1970) Biopolymers, Vol. 9, pp. 223-244; R. F. Goldstein and A. S. Benight (1992) Biopolymers, Vol. 32, pp. 1679-1693] that these constraints restrict the information available from measurements of properties of sequence combinations. The emphasis in this paper is on the properties of oligomer sequences that vary in length, where each nucleotide or base pair at the end of the sequence makes a significant contribution to the measured property by interacting with its boundary of fixed sequence or solvent. In such cases it is not possible to det. values of properties of individual nearest neighbors, except for the like neighbors [e.g., d(A-A), d(G-G), d(T-T), and d(C-C) nucleotide neighbors in single-stranded DNA or d(A-A)/d(T-T) and d(G-G)/d(C-C) base pair neighbors in double-stranded DNA], solely from measurements of properties of different sequences. Even values for properties of the like neighbors cannot be detd. from such oligomeric sequences if the sequences are all of the same length. Nearest-neighbor properties of oligomer sequences that vary in length can be summarized in terms of the values for independent sets of sequences that are nearest neighbors and monomers all with boundaries of the fixed sequence or solvent. Straightforward combinations of the values for the independent sequences will give the values of the property for any dependent sequence, without explicit knowledge of the individual nearest-neighbor values. These considerations have important consequences for the derivation of widely used thermodn. parameters, as discussed in the following paper.
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45
Schildkraut, C. and Lifson, S. (1965) Dependence of the melting temperature of DNA on salt concentration Biopolymers 3, 195– 208
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45
Dependence of the melting temperature of DNA on salt concentration
Schildkraut, Carl; Lifson, Shneior
Biopolymers (1965), 3 (2), 195-208CODEN: BIPMAA; ISSN:0006-3525.
Data on the decrease of the DNA melting temp. Tm with the salt concn., M, are reported and discussed. The electrostatic free energy change in the helix-coil transition, ΔFe, was related to the potential, ψ, which represented the electrostatic repulsion between the phosphate charges; ψ was calcd. as a function of M and of the distances between the charges of the 2 strands. The Debye-Hueckel approximation was shown to overest. ψ. It was suggested that the high local concn. of the counterions in the immediate vicinity of the fixed charges screened these charges from interacting with other fixed charges, to the extent that the system behaved as if the fixed ions carried a reduced charge. The notion of a reduced charge represented in a single parameter the deviation of the Debye-Hueckel approximation from the true potential. A plot of Tm versus ΔFe gave a straight line as predicted. ΔHo was calcd. from the slope and found to be consistent with exptl. detd. values. The calcns. supported the hypothesis that the change of Tm with salt concn. was due to changes in the screened interactions between the fixed phosphate charges. In analyzing the results of these calens., it was possible on the one hand to indicate some of the limitations of the theoretical model and, on the other hand, draw some conclusions about the order of magnitude of the nonelectrostatic energy of formation of the double helix.
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Tan, Z.-J. and Chen, S.-J. (2007) RNA helix stability in mixed Na⁺/Mg²⁺ solution Biophys. J. 92, 3615– 3632
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46
RNA helix stability in mixed Na+/Mg2+ solution
Tan, Zhi-Jie; Chen, Shi-Jie
Biophysical Journal (2007), 92 (10), 3615-3632CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
A recently developed tightly bound ion model can account for the correlation and fluctuation (i.e., different binding modes) of bound ions. However, the model cannot treat mixed ion solns., which are physiol. relevant and biol. significant, and the model was based on B-DNA helixes and thus cannot directly treat RNA helixes. In the present study, we investigate the effects of ion correlation and fluctuation on the thermodn. stability of finite length RNA helixes immersed in a mixed soln. of monovalent and divalent ions. Exptl. comparisons demonstrate that the model gives improved predictions over the Poisson-Boltzmann theory, which has been found to underestimate the roles of multivalent ions such as Mg2+ in stabilizing DNA and RNA helixes. The tightly bound ion model makes quant. predictions on how the Na+-Mg2+ competition dets. helix stability and its helix length-dependence. In addn., the model gives empirical formulas for the thermodn. parameters as functions of Na+/Mg2+ concns. and helix length. Such formulas can be quite useful for practical applications.
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47
Efron, B. and Tibshirani, R. J. (1993) . An Introduction to the Bootstrap, Chapman & Hall/CRC, Boca Raton, FL.
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48
Völker, J., Klump, H. H., Manning, G. S., and Breslauer, K. J. (2001) Counterion association with native and denatured nucleic acids: an experimental approach J. Mol. Biol. 310, 1011– 1025
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48
Counterion association with native and denatured nucleic acids: an experimental approach
Volker, Jens; Klump, Horst H.; Manning, Gerald S.; Breslauer, Kenneth J.
Journal of Molecular Biology (2001), 310 (5), 1011-1025CODEN: JMOBAK; ISSN:0022-2836. (Academic Press)
The melting temp. of the poly(dA)·poly(dT) double helix is exquisitely sensitive to salt concn., and the helix-to-coil transition is sharp. Modern calorimetric instrumentation allows this transition to be detected and characterized with high precision at extremely low duplex concns. The authors have taken advantage of these properties to show that this duplex can be used as a sensitive probe to detect and to characterize the influence of other solutes on soln. properties. The authors demonstrate how the temp. assocd. with poly(dA)·poly(dT) melting can be used to define the change in bulk soln. cation concn. imparted by the presence of other duplex and triplex solutes, in both their native and denatured states. The authors use this information to critically evaluate features of counterion condensation theory, as well as to illustrate "crosstalk" between different, noncontacting solute mols. Specifically, the authors probe the melting of a synthetic homopolymer, poly(dA)·poly(dT), in the presence of excess genomic salmon sperm DNA, or in the presence of one of two synthetic RNA polymers (the poly(rA)·poly(rU) duplex or the poly(rU)·poly(rA)·poly(rU) triplex). The authors find that these addns. cause a shift in the melting temp. of poly(dA)·poly(dT), which is proportional to the concn. of the added polymer and dependent on its conformational state (B vs. A, native vs. denatured, and triplex vs. duplex). To a first approxn., the magnitude of the obsd. tm shift does not depend significantly on whether the added polymer is RNA or DNA, but it does depend on the no. of strands making up the helix of the added polymer. The authors ascribe the obsd. changes in melting temp. of poly(dA)·poly(dT) to the increase in ionic strength of the bulk soln. brought about by the presence of the added nucleic acid and its assocd. counterions. The authors refer to this communication between noncontacting biopolymers in soln. as solvent-mediated crosstalk. By comparison with a known std. curve of tm vs. log[Na+] for poly(dA)·poly(dT), the authors est. the magnitude of the apparent change in ionic strength resulting from the presence of the bulk nucleic acid, and the authors compare these results with predictions from theory. The authors find that current theor. considerations correctly predict the direction of the tm shift (the melting temp. increases), while overestimating its magnitude. Specifically, the authors observe an apparent increase in ionic strength equal to 5% of the concn. of the added duplex DNA or RNA (in mol phosphate), and an addnl. apparent increase of about 9.5% of the nucleic acid concn. (mol phosphate) upon denaturation of the added DNA or RNA, yielding a total apparent increase of 14.5%. For the poly(rU)·poly(rA)·poly(rU) triplex, the total apparent increase in ionic strength corresponds to about 13.6% of the amt. of added triplex (moles phosphate). The effect the authors observe is due to coupled equil. between the solute mols. mediated by modulations in cation concn. induced by the presence and/or the transition of one of the solute mols. The authors note that the results are general, so one can use a different solute probe sensitive to proton binding to characterize subtle changes in soln. pH induced by the presence of another solute in soln. The authors discuss some of the broader implications of these measurements/results in terms of nucleic acid melting in multicomponent systems, in terms of probing counterion environments, and in terms of potential regulatory mechanisms. (c) 2001 Academic Press.
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Philips, R. (1966) Adenosine and the adenine nucleotides. Ionization, metal complex formation, and conformation in solution Chem. Rev. 66, 501– 527
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50
Sigel, H. (1993) Interactions of metal ions with nucleotides and nucleic acids and their constituents Chem. Soc. Rev. 22, 255– 267
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50
Interactions of metal ions with nucleotides and nucleic acids and their constituents
Sigel, Helmut
Chemical Society Reviews (1993), 22 (4), 255-67CODEN: CSRVBR; ISSN:0306-0012.
A review, with 86 refs. Nucleotides, due to their ambivalent properties towards metal ions, are a true challenge to coordination chemists. A metal ion may interact with the phosphate group(s), the sugar moiety, and the base residue of a nucleotide. Moreover, such a base residue itself is already ambivalent; e.g., an adenine residue offers to a metal ion the N-1, N-3, and N-7 sites for binding. It is the aim of this overview briefly to elucidate the binding properties of the various mentioned constituents and to consider 'recognition reactions' of nucleotides and nucleic acids. Which properties govern selectivity in nature.
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Pecoraro, V. L., Hermes, J. D., and Cleland, W. W. (1984) Stability constants of Mg²⁺ and Cd²⁺ complexes of adenine nucleotides and thionucleotides and rate constants for formation and dissociation of MgATP and MgADP Biochemistry 23, 5262– 5271
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51
Stability constants of magnesium and cadmium complexes of adenine nucleotides and thionucleotides and rate constants for formation and dissociation of magnesium-ATP and magnesium-ADP
Pecoraro, Vincent L.; Hermes, Jeffrey D.; Cleland, W. W.
Biochemistry (1984), 23 (22), 5262-71CODEN: BICHAW; ISSN:0006-2960.
Stability consts. for the Mg2+ and Cd2+ complexes of ATP, ADP, ATPαS, ATPβS, and ADPαS (where ATPαS, ATPβS, and ADPαS are nucleotides substituted with S on the indicated phosphate group) were detd. at 30° and μ = 0.1M by 31P NMR. In addn. to being of the utmost importance for detg. species distributions for enzymic studies, these consts. allow an estn. of the dependence of Cd2+ for S vs. O coordination in phosphorothioate complexes. Stability consts. for Mg2+ complexes decrease when S replaces O (log K: ADP, 4.11; ADPαS, 3.66; ATP, 4.70; ATPαS, 4.47; ATPβS, 4.04) because of (1) a statistical factor resulting from the loss of one potential phosphate O ligand and (2) either an alteration in the charge distribution between O and S or destabilization of the chelate ring structure by loss of an internal H-bond between an O of coordinated phosphate and metal-bound H2O. Cd2+ complexes with S-substituted nucleotides are more stable than those without S (log K: ADP, 3.58; ADPαS, 4.95; ATP, 4.36; ATPαS, 4.42; ATPβS, 5.44) because of the preferential binding of Cd3+ to S rather than O, which is estd. to be ∼60 in CdADPαS and CdATPβS. The proportion of tridentate coordination is estd. to be 50-60% in MgATP and MgATPβS, ∼27% in MgATPαS, ∼16% in CdATP or CdATPβS, but ∼75% in CdATPαS. By anal. of the data of E. J. Jaffe and M. Cohn (1979), it is concluded that the preference for O over S coordination to ATPβS is 31,000 for Mg2+, 3100-3900 for Ca2+, and 158-193 for Mn2+. 1H NMR demonstrates that bidentate Cd2+ complexes form intramol. chelates with the N-7 atom of adenine, whereas Mg2+ nucleotides and the tridentate CdATPαS do not. An anal. of the 31P NMR line-widths shows that the rate consts. for dissocn. of MgADP and MgATP are both 7000 s-1, whereas the assocn. rate consts. are 7 × 107 and 4 × 108 M-1 s-1, resp. The obsd. dependence of the line width on nucleotide concn. is best explained by a base-stacking model at nucleotide concns. of >5 mM.
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Hudson, R. H. E., Uddin, A. H., and Damha, M. J. (1995) Association of branched nucleic acids: structural and physicochemical analysis of antiparallel T•AT triple-helical DNA J. Am. Chem. Soc. 117, 12470– 12477
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52
Association of branched nucleic acids: structural and physicochemical analysis of antiparallel T·AT triple-helical DNA
Hudson, Robert H. E.; Uddin, Andre H.; Damha, Masad J.
Journal of the American Chemical Society (1995), 117 (50), 12470-7CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
The authors report the first example of a stable triple-stranded helix consisting of exclusively T·AT (reverse-Hoogsteen·Watson-Crick) base triplets. The orientation of the third (T) strand in this triplex is anti-parallel with respect to the purine strand of the underlying duplex. Previous studies have examd. the formation of these "antiparallel" T·AT triplets within a G·GC-rich environment; however, the present study demonstrates that G·GC triplets are not a requirement. The approach to induce and stabilize the antiparallel triplex involves the use of a branched oligonucleotide with two parallel dT10 strands joined to riboadenosine via 2'-5' and 3'-5' phosphodiester linkages, i.e., rA[2'-5'-dT10]3'-5'-dT10. This triplex was further stabilized by MgCl2 or NaCl at neutral pH. Triple helix formation by branched oligonucleotide 1 and dA10 was investigated by thermal denaturation anal. and CD spectroscopy. The melting curves at 260 and 284 nm show a single transition from bound to unbound species, indicative of cooperative melting. A linear oligonucleotide with a loop made of four dC residues between two dT10 strands, and with a 5'-5'-phosphodiester linkage at one of the C/T10 junctions, i.e., 3'-dT10C4-5'-5'-dT10-3', did not form a similar triple helical structure. This result shows that the conformational rigidity imparted to the pyrimidine strands, by the branch point in 1, serves to preorganize and stabilize the complex. Potassium ions inhibited triplex helix formation. In accord with what has been demonstrated previously for "parallel" Py·PuPy (Hoogsteen-Watson-Crick) triplexes, the authors show that short oligoadenylates (i.e., dA4 and dA5) can bind cooperatively to the branched oligomer 1. The triplex-inducing capacity of branched oligonucleotides has potentially important implications in the study of intramol. triplexes that occur in vivo.
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Rose, D. M., Bleam, M. L., Record, M. T., Jr., and Bryant, R. G. (1980) ²⁵Mg NMR in DNA solutions: dominance of site binding effects Proc. Natl. Acad. Sci. U.S.A. 77, 6289– 6292
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53
Magnesium-25 NMR in DNA solutions: Dominance of site binding effects
Rose, D. Murk; Bleam, M. L.; Record, M. T., Jr.; Bryant, R. G.
Proceedings of the National Academy of Sciences of the United States of America (1980), 77 (11), 6289-92CODEN: PNASA6; ISSN:0027-8424.
25Mg NMR spectroscopy is applied to a study of Mg2+ interactions with DNA, which is considered as a model for a linear polyelectrolyte. The Mg2+ spectrum is complicated by a non-Lorentzian lineshape and is dominated by the effects of chem. exchange with macromol.-binding sites. A distinction is made between specific-site interactions in which Mg2+ loses a H2O mol. from the 1st coordination sphere on binding and those interactions, referred to as territorial binding, in which the ion maintains its 1st coordination sphere complement of solvent. The 1st type of site-binding interactions dominates the 25Mg NMR spectrum, based on a consideration of the magnitudes of the obsd. 25Mg relaxation rates compared with 23Na relaxation rates, the clear contributions of chem. exchange-limited relaxation, and an ion-displacement expt. employing Na+.
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Ma, C. and Bloomfield, V. A. (1995) Gel electrophoresis measurement of counterion condensation on DNA Biopolymers 35, 211– 216
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54
Gel electrophoresis measurement of counterion condensation on DNA
Ma, Chenglie; Bloomfield, Victor A.
Biopolymers (1995), 35 (2), 211-16CODEN: BIPMAA; ISSN:0006-3525. (Wiley)
We used agarose gel electrophoresis to measure the effective charge neutralization of DNA of counterions of different structure and valence, including Na+, Mg2+, Co(NH3)63+ and spermidine3+, which competed for binding with an excess of Tris acetate buffer. Linear DNA molecules ranged in size from 1 to 5 kilobases, and supercoiled plasmid pUC18 was also measured. In all cases, the results were in good agreement with theor. predictions from counterion condensation theory for two-counterion mixts.
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Cowan, J. A., Huang, H.-W., and Hsu, L. Y. (1993) Sequence selective coordination of Mg²⁺(aq) to DNA J. Inorg. Biochem. 52, 121– 129
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55
Sequence selective coordination of magnesium (aq) to DNA
Cowan, J. A.; Huang, H. W.; Hsu, L. Y.
Journal of Inorganic Biochemistry (1993), 52 (2), 121-9CODEN: JIBIDJ; ISSN:0162-0134.
Thermodn. parameters for magnesium binding to a series of DNA mols. of defined sequence have been evaluated by 25Mg NMR spectroscopy. These results demonstrate that G/C-DNA binds Mg2+ (aq) up to 40 to 100-fold more strongly than A/T-DNA, i.e., coordination of Mg2+(aq) to G/C-DNA is ca. 2.1-2.7 kcal (mole Mg2+)-1 more stable relative to A/T-DNA. Activation free energies [ΔG* ∼(12.7-13.3) × 103 kcal] and exchange rates [kex ∼(0.5-3.0) × 103s-1] were estd. by variable temp. expts. The low value of the quadrupole coupling consts. (χB = 0.2-0.6 MHz) is indicative of outer-sphere coordination by Mg(H2O)62+.
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Buckin, V. A., Kankiya, B. I., Rentzeperis, D., and Marky, L. A. (1994) Mg²⁺ recognizes the sequence of DNA through its hydration shell J. Am. Chem. Soc. 116, 9423– 9429
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Mg2+ recognizes the sequence of DNA through its hydration shell
Buckin, Vitaly A.; Kankiya, B. I.; Rentzeperis, Dionisios; Marky, Luis A.
Journal of the American Chemical Society (1994), 116 (21), 9423-9CODEN: JACSAT; ISSN:0002-7863.
The authors have studied the interaction of Mg2+ with six deoxyoctanucleotide duplexes of known sequence. Specifically, the authors have measured the resulting hydration changes by following the change in the concn. increment of ultrasonic velocity, δA, of each of these six duplexes, in their Cs+ salt at 1.2°, during a course of a titrn. with Mg2+. The addn. of Mg2+ results in the initial lowering of δA that levels off at [Mg2+]/[Pi] molar ratios ranging from 12 to 30, depending on the duplex, and corresponds to a dehydration event from the exchange of Cs+ counterions by Mg2+ in the ionic atm. of the duplexes. This is followed by a further lowering of δA at higher [Mg2+]/[Pi] ratios that may result from DNA aggregation and/or conformational change. The authors obtained a change in the molar concn. increment of ultrasonic velocity per mol of bound Mg2+, ΔAMg2+, and binding affinities, Kapp, ranging from -4.4 cm3 mol-1 and 150 M-1 for d(A)8·d(T)8 and -18 cm3 mol-1 and 40 M-1 for [d(CG)4]2, resp., by fitting the first portion of each titrn. curve and assuming an overall binding of 0.5 Mg2+ per phosphate. Thus, the overall magnitude of the dehydration effect, which is detd. by the structure of the Mg2+-DNA complex, and the Kapp are functions of the DNA sequence. Furthermore, the dehydration effect of Mg2+ binding correlates with the hydration state of the DNA: the higher its hydration state, the lower the dehydration effect of Mg2+ binding is. Mg2+ recognizes the sequence of DNA through its overall hydration state, probably by forming mostly outer-sphere complexes with oligomers contg. exclusively dA·dT base pairs and inner-sphere complexes with dG·dC oligomers.
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Black, C. B. and Cowan, J. A. (1994) Quantitative evaluation of electrostatic and hydrogen-bonding contributions to metal cofactor binding to nucleic acids J. Am. Chem. Soc. 116, 1174– 1178
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57
Quantitative Evaluation of Electrostatic and Hydrogen-Bonding Contributions to Metal Cofactor Binding to Nucleic Acids
Black, C. B.; Cowan, J. A.
Journal of the American Chemical Society (1994), 116 (4), 1174-8CODEN: JACSAT; ISSN:0002-7863.
The binding free energy (ΔGb) of a hydrated alkali or alk. earth ion to double-strand nucleic acids is dominated by electrostatic (ΔGes) and hydrogen-bonding (ΔGhb) contributions. The authors have estd. the relative magnitudes of these two terms by use of metal complexes of defined charge and hydrogen-bonding capability. A strategy is described where ΔGb for Mn+(aq) is compared with values obtained from substitutionally-inert cobaltic-ammine complexes of similar charge ([Co(NH3)6-zXz]n+, X = NH3, NO2-). Values for the latter are dominated by the electrostatic term, and so ΔGhb can be detd. by direct comparison with the hydrated Mg2+(aq) or Na+(aq) ion of equiv. charge. Apparent binding affinities (Ka, M-1) for a series of aquated metal ions (Mg2+(aq), Na+(aq)) and cobalt coordination complexes (Co(NH3)63+, [Co(NH3)5NO2]2+, [Co(NH3)4(NO2)2]+) to B- and A-configuration nucleic acids have been detd. in 20 mM Tris (pH 7.0) by NMR line-shape anal. and the neighbor exclusion model of McGhee-von Hippel. B-conformer nucleic acids: [Co(NH3)6]3+, 14 800 M-1; [Co(NH3)5NO2]2+, 1500 M-1; [Co(NH3)4(NO2)2]+, 20 M-1; Mg2+(aq), 12 800 M-1; Na+(aq), 150 M-1. A-conformer nucleic acids: [Co(NH3)6]3+, 4200 M-1; [Co(NH3)5NO2]2+, 250 M-1; [Co(NH3)4(NO2)2]+, undetd.; Mg2+(aq), 2500 M-1; Na+(aq), 8 M-1. Individual contributions from electrostatic attraction and hydrogen bonding have been evaluated and found to be additive for each specific configuration. The results are consistent with the expectations of polyelectrolyte theory. Stronger binding to B-conformers results from electrostatic terms, while the contribution from hydrogen bonding is apparently conformation independent. Variable temp. expts. demonstrate that the main factor dictating the exchange region for bound and free metal species derives from extensive hydrogen bonding to the polynucleotide.
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Gessner, R. V., Quigley, G. J., Wang, A. H.-J., van der Marel, G. A., van Boom, J. H., and Rich, A. (1985) Structural basis for stabilization of Z-DNA by cobalt hexaammine and magnesium cations Biochemistry 24, 237– 240
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Structural basis for stabilization of Z-DNA by cobalt hexaammine and magnesium cations
Gessner, Reinhard V.; Quigley, Gary J.; Wang, Andrew H. J.; Van der Marel, Gijs A.; Van Boom, Jacques H.; Rich, Alexander
Biochemistry (1985), 24 (2), 237-40CODEN: BICHAW; ISSN:0006-2960.
In the equil. between B-DNA and Z-DNA in poly(dC-dG), [Co(NH3)6]3+ stabilizes the Z form 4 orders of magnitude more effectively than does Mg2+. The structural basis of this difference is revealed in Z-DNA crystal structures of d(CpGpCpGpCpG) stabilized by either Na+/Mg2+ or Na+/Mg2+ plus [Co(NH3)6]3+. The crystals diffract x-rays to high resoln., and the structures were refined at 1.25 Å. [Co(NH3)6]3+ forms 5 H bonds on the surface of Z-DNA, bonding to a guanine O6 and N7 as well as to a phosphate group in the ZII conformation. The Mg2+ ion binds through its hydration shell with ≤3 H bonds to guanine N7 and O6. Higher charge, specific fitting of more H bonds, and a more stable complex all contribute to the great effectiveness of [Co(NH3)6]3+ in stabilizing Z-DNA.
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Sines, C. C., McFail-Isom, L., Howerton, S. B., VanDerveer, D., and Willimas, L. D. (2000) Cation mediate B-DNA conformational heterogeneity J. Am. Chem. Soc. 122, 11048– 11056
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Cations Mediate B-DNA Conformational Heterogeneity
Sines, Chad C.; McFail-Isom, Lori; Howerton, Shelley B.; VanDerveer, Don; Williams, Loren Dean
Journal of the American Chemical Society (2000), 122 (45), 11048-11056CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
We demonstrate that DNA conformation is sensitive to cationic environment. We describe a high resoln. (1.2 Å) potassium form of CGCGAATTCGCG, detd. from crystals grown in the presence of spermine and magnesium, along with potassium. The structure was refined with anisotropic displacement-factors by SHELX-97 to an R-factor of 13.9%. A comparison of this structure with others, reveals that the conformation of CGCGAATTCGCG varies in direct response to cation type and position. The DNA conformation in the presence of excess magnesium differs from the conformation in the presence of excess spermine. Divalent cations near the minor groove sequester into the lip, which is the region between opposing phosphate groups. Minor groove width is sensitive to, and can be predicted by, cation positions. It appears that minor groove narrowing is facilitated by interactions of cations with opposing phosphate groups.
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Blagoi, Y. U. P., Sorokin, V. A., Valeyev, V. A., Khomenko, S. A., and Gladchenko, G. O. (1978) Magnesium ion effect on the helix-coil transition of DNA Biopolymers 17, 1103– 1118
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Magnesium ion effect on the helix-coil transition of DNA
Blagoi, Yu. P.; Sorokin, V. A.; Valeev, V. A.; Khomenko, S. A.; Gladchenko, G. O.
Biopolymers (1978), 17 (5), 1103-18CODEN: BIPMAA; ISSN:0006-3525.
The effect of Mg2+ on the parameters of the DNA helix-coil transition was studied for the concn. range 10-6-10-1M at an ionic strength of 10-3M Na+. Binding with Mg2+ increased the DNA stability, the effect being obsd. mainly in the concn. range 10-6-10-4M. At a Mg2+ concn. of >10-2M the thermal stability of DNA started to decrease. The melting range extended to concns. ∼10-5M and then decreased to 7-8° at the ion content of 10-3M. Asymmetry of the melting curves was obsd. at low ionic strengths ([Na+] = 10-3M and [Mg2+] ≤10-5M). The results, analyzed in terms of the statistical thermodn. theory of double-stranded homopolymers melting in the presence of ligands, suggest that the effects obsd. might be due to the ion redistribution from denatured to native DNA. An exptl. DNA-Mg2+ phase diagram was obtained which is in good agreement with the theory. Thermal denaturation of the system may be an efficient method for detg. the ion-binding consts. for both native and denatured DNA.
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Anderson, C. F. and Record, M. T., Jr (1995) Salt-nucleic acid interactions Annu. Rev. Phys. Chem. 46, 657– 700
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Salt-nucleic acid interactions
Anderson, Charles F.; Record, M. Thomas, Jr.
Annual Review of Physical Chemistry (1995), 46 (), 657-700CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews)
A review, with 151 refs. Coulombic interactions of salt ions with polymeric and oligomeric nucleic acids in soln. have large and distinctive effects on ion distributions, on thermodn. coeffs., and hence on equil. processes involving nucleic acids, such as their conformational transitions and binding interactions. In exptl. or theor. studies where an oligonucleotide is taken to represent the corresponding polynucleotide, the impact of Coulombic end effects on mol. and thermodn. properties. must be taken into account. Observable consequences of Coulombic interactions in nucleic acid solns. have been calcd. by using models with varying degrees of detail and methods formulated at varying levels of rigor. From comparisons of exptl. results with predictions of the prevalent methods have proved capable of accounting for thermodn. (and some mol.) consequences of Coulombic interactions with a minimal no. of preaveraged parameters that represent the most important structural features of the nucleic acid soln.
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Shkel, I. A. and Record, M. T., Jr (2004) Effect of the number of nucleic acid oligomer charges on the salt dependence of stability (ΔG°₃₇) and melting temperature (T_m): NLPB analysis of experimental data Biochemistry 43, 7090– 7101
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Effect of the Number of Nucleic Acid Oligomer Charges on the Salt Dependence of Stability (ΔG°37) and Melting Temperature (Tm): NLPB Analysis of Experimental Data
Shkel, Irina A.; Record, M. Thomas, Jr.
Biochemistry (2004), 43 (22), 7090-7101CODEN: BICHAW; ISSN:0006-2960. (American Chemical Society)
For nucleic acid oligomers with variable chain lengths, the salt concn. ([salt]) dependences of the denaturation temp. (Tm) and of the free energy of helix formation at 37° (ΔG°37) are predicted using nonlinear Poisson-Boltzmann (NLPB) calcns. Anal. of exptl. data reveals that the ratio of the [salt] deriv. of melting temp. (STm = dTm/d log[salt]) to the value for a polymer with the same base compn. (STm/STm,∞) is independent of base compn. but strongly dependent on the no. of DNA charges (|Z|) below ∼8 bp for two-strand helixes (formed from assocn. of two complementary strands) and below ∼18 bp for hairpin helixes (formed from folding of one self-complementary strand). The authors interpret these STm/STm,∞ ratios in terms of the ratio of thermodn. ion release from the oligomer (Δnu, per charge) to that from the same oligomer embedded in polymeric DNA (Δnu,∞, per charge). Exptl. values of STm/STm,∞ and its dependence on |Z| are in good agreement with NLPB predictions for a preaveraged (essential structural) model of DNA. In particular, the NLPB calcns. describe the stronger |Z| dependence of STm obsd. for melting of oligomeric hairpin helixes than for melting of two-strand helixes. These calcns. predict an exptl. detectable (≥ 10%) difference between STm and STm,∞ which increases strongly with decreasing length for two-strand helix lengths of <15 bp and for hairpin helix lengths of <30 bp. From NLPB values of Δnu/Δnu,∞, the authors predict ΔG°37 as a function of [salt] and |Z|. Predictions of thermodn. and thermal stabilities of oligomeric helixes as functions of length and [salt] are consistent with and represent a significant refinement of the av. oligomer salt effect currently in use in nearest neighbor stability predictions.
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Elson, E. L., Scheffler, I. E., and Baldwin, R. L. (1970) Helix formation by d(TA) oligomers. III. Electrostatic effects J. Mol. Biol. 54, 401– 415
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Helix formation by d(TA) oligomers. III. Electrostatic effects
Elson, Elliot L.; Scheffler, Immo E.; Baldwin, Robert L.
Journal of Molecular Biology (1970), 54 (3), 401-15CODEN: JMOBAK; ISSN:0022-2836.
Expts. with d(TA)n hairpin helices are reported which contradict the simple Ising (or nearest-neighbor interactions) model for the DNA helix-coil transition at low or moderate counterion concns. First the dependence of Tm(n) on lot M (where M is monovalent counterion molarity) falls off sharply with decreasing n in the range 8 ≤ n ≤ 22, so that the set of melting curves is compressed into a narrow temp. range at low M. At M = 0.0028, d(TA)20 has a higher Tm than poly d(AT) and the Tm of d(TA)9 is only slightly lower. Electrostatic interactions have a relatively small effect on the breadths of these melting curves: the curves for all oligomers sharpen slightly as the counterion concn. is reduced. Where zp is the effective charge per phosphate group and D is the effective dielec. const., the melting curves for all oligomers can be represented for all values of M by a single value of zp2/D; it is necessary to count interactions between charges both in the helix and in adjoining nonhelical segments.
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Rouzina, I. and Bloomfield, V. A. (1997) Competitive electrostatic binding of charged ligands to polyelectrolytes: practical approach using the non-linear Poisson-Boltzmann equation Biophys. Chem. 64, 139– 155
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Competitive electrostatic binding of charged ligands to polyelectrolytes: practical approach using the non-linear Poisson-Boltzmann equation
Rouzina, Ioulia; Bloomfield, Victor A.
Biophysical Chemistry (1997), 64 (1-3), 139-155CODEN: BICIAZ; ISSN:0301-4622. (Elsevier)
We have developed a practical anal. treatment of the non-linear Poisson-Boltzmann (P-B) equation to characterize the strong but non-specific binding of charged ligands to DNA and other highly charged macromols. These reactions are notable for their strong salt dependence and anti-cooperativity, features which the theory fully explains. We summarize anal. results for concn. profiles and ion binding in various regimes of surface curvature and ionic strength, and show how counterion size and charge distribution may influence competitive binding. We present several practical applications of the formalism, showing how to est. the ligand concn. needed to effectively compete with a given buffer salt, and how to calc. the amts. of counterion species bound at various distances from the DNA surface under given bulk soln. conditions. We cast our results into the form of a Scatchard binding isotherm, showing how the apparent binding const. Kobs and S = -d log Kobs/d log [M+] can be predicted from the basic theory. Anti-cooperativity arises naturally without steric repulsion, and binding curves can be fitted with Kobs and effective charge as the only free parameters. We extend the anal. P-B anal. to an arbitrary no. of counterion species, and apply the results to fit and predict three-ion competition data.
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Bacquet, R. J. and Rossky, P. J. (1988) Ionic distributions and competitive association in DNA/mixed salt solutions J. Phys. Chem. 92, 3604– 3612
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65
Ionic distributions and competitive association in DNA/mixed salt solutions
Bacquet, Russell J.; Rossky, Peter J.
Journal of Physical Chemistry (1988), 92 (12), 3604-12CODEN: JPCHAX; ISSN:0022-3654.
The hypernetted chain integral equation is used to study ionic distributions near a simple model of DNA in aq. mixts. of NaCl and MgCl2. A wide range of both relative and abs. concns. of the salts is considered, including cases where only one salt is present. In dil. systems (low ionic strength), the soln. compn. near the polyion is more responsive to changes in the bulk soln. compn., and competition by the divalent counterions is more effective. It is found that for reasonable definitions of the polyion vicinity the displacement of Na+ by Mg2+ in this region is approx. 1 for 1, with a corresponding increase in the degree of polyion neutralization at short range, with increasing Mg2+ concn. in the bulk. Calcd. ests. of mean-square elec. field gradients experienced by Na nuclei in these solns. manifest a very good correlation with measured NMR line width, indicating that the obsd. structural phenomena are realistically described.
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66
SantaLucia, J., Jr (1998) A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics Proc. Natl. Acad. Sci. U.S.A. 95, 1460– 1465
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66
A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics
Santalucia, John, Jr.
Proceedings of the National Academy of Sciences of the United States of America (1998), 95 (4), 1460-1465CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
A unified view of polymer, dumbbell, and oligonucleotide nearest-neighbor (NN) thermodn. is presented. DNA NN ΔG37° parameters from seven labs. are presented in the same format so that careful comparisons can be made. The seven studies used data from natural polymers, synthetic polymers, oligonucleotide dumbbells, and oligonucleotide duplexes to derive NN parameters; used different methods of data anal.; used different salt concns.; and presented the NN thermodn. in different formats. As a result of these differences, there has been much confusion regarding the NN thermodn. of DNA polymers and oligomers. Herein I show that six of the studies are actually in remarkable agreement with one another and explanations are provided in cases where discrepancies remain. Further, a single set of parameters, derived from 108 oligonucleotide duplexes, adequately describes polymer and oligomer thermodn. Empirical salt dependencies are also derived for oligonucleotides and polymers.
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Stellwagen, E., Dong, Q., and Stellwagen, N. C. (2007) Quantitative analysis of monovalent counterion binding to random-sequence, double-stranded DNA using the replacement ion method Biochemistry 46, 2050– 2058
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Quantitative Analysis of Monovalent Counterion Binding to Random-Sequence, Double-Stranded DNA Using the Replacement Ion Method
Stellwagen, Earle; Dong, Qian; Stellwagen, Nancy C.
Biochemistry (2007), 46 (7), 2050-2058CODEN: BICHAW; ISSN:0006-2960. (American Chemical Society)
A variation of affinity capillary electrophoresis, called the replacement ion (RI) method, has been developed to measure the binding of monovalent cations to random sequence, double-stranded (ds) DNA. In this method, the ionic strength is kept const. by gradually replacing a nonbinding ion in the soln. with a binding ion and measuring the mobility of binding and nonbinding analytes as a function of binding ion concn. The method was validated by measuring the binding of Li+ ions to adenosine nucleotides; the apparent dissocn. consts. obtained by the RI method are comparable to literature values obtained by other methods. The binding of Tris+, NH4+, Li+, Na+, and K+ to dsDNA was then investigated. The apparent dissocn. consts. obsd. for counterion binding to a random-sequence 26-base pair (bp) oligomer ranged from 71 mM for Tris+ to 173 mM for Na+ and K+. Hence, pos. charged Tris buffer ions will compete with other monovalent cations in Tris-buffered solns. The bound cations identified in this study may correspond to the strongly correlated, tightly bound ions recently postulated to exist as a class of ions near the surface of dsDNA (Tan, Z.-J., and Chen, S.-J., 2006). Monovalent cation binding to random-sequence dsDNA would be expected to occur in addn. to any site-specific binding of cations to A-tracts or other DNA sequence motifs. Single-stranded DNA oligomers do not bind the five tested cations under the conditions investigated here.
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Bai, Y., Greenfeld, M., Travers, K. J., Chu, V. B., Lipfert, J., Doniach, S., and Herschlag, D. (2007) Quantitative and comprehensive decomposition of the ion atmosphere around nucleic acids J. Am. Chem. Soc. 129, 14981– 14988
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68
Quantitative and Comprehensive Decomposition of the Ion Atmosphere around Nucleic Acids
Bai, Yu; Greenfeld, Max; Travers, Kevin J.; Chu, Vincent B.; Lipfert, Jan; Doniach, Sebastian; Herschlag, Daniel
Journal of the American Chemical Society (2007), 129 (48), 14981-14988CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
The ion atm. around nucleic acids critically affects biol. and phys. processes such as chromosome packing, RNA folding, and mol. recognition. However, the dynamic nature of the ion atm. renders it difficult to characterize. The basic thermodn. description of this atm., a full accounting of the type and no. of assocd. ions, has remained elusive. Here we provide the first complete accounting of the ion atm., using buffer equilibration and at. emission spectroscopy (BE-AES) to accurately quantitate the cation assocn. and anion depletion. We have examd. the influence of ion size and charge on ion occupancy around simple, well-defined DNA mols. The relative affinity of monovalent and divalent cations correlates inversely with their size. Divalent cations assoc. preferentially over monovalent cations; e.g., with Na+ in 4-fold excess of Mg2+ (20 vs. 5 mM), the ion atm. nevertheless has 3-fold more Mg2+ than Na+. Further, the dicationic polyamine putrescine2+ does not compete effectively for assocn. relative to divalent metal ions, presumably because of its lower charge d. These and other BE-AES results can be used to evaluate and guide the improvement of electrostatic treatments. As a first step, we compare the BE-AES results to predictions from the widely used nonlinear Poisson Boltzmann (NLPB) theory and assess the applicability and precision of this theory. In the future, BE-AES in conjunction with improved theor. models, can be applied to complex binding and folding equil. of nucleic acids and their complexes, to parse the electrostatic contribution from the overall thermodn. of important biol. processes.
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Abstract
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Figure 1
Figure 1. Melting temperatures of DNA duplex oligomers are independent of pH in the range from 6.5 to 8.3. Solid symbols are 15-mers, open symbols are 30-mers, fraction of G·C base pairs vary from 0.3 to 0.7. Sequences are TTCTACCTATGTGAT (solid triangle), GCAGTGGATGTGAGA (solid circle), CAGCCTCGTCGCAGC (solid square), CTTAAGATATGAGAACTTCAACTAATGTGT (open triangle), AGTCTGGTCTGGATCTGAGAACTTCAGGCT (open circle), GACCTGACGTGGACCGCTCCTGGGCGTGGT (open square). Buffers contained 1.5 mM MgCl₂, 50 mM KCl and 10 mM cacodylic acid or MOPS.
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Figure 2
Figure 2. Comparison of effects of Na⁺ and K⁺ on melting temperatures in buffers of 55 mM (open triangle) and 205 mM (closed circle) monovalent ion concentrations. Duplex sequences (C_t = 2 µM) are in Table 4. Oligonucleotide lengths range from 15 to 30 base pairs. Melting temperatures determined in 10 mM Tris-HCl and 50 or 200 mM KCl buffers are plotted versus melting temperatures measured in 10 mM sodium phosphate and NaCl buffers (33). Diagonal solid line connects points where melting temperatures in both buffers would be the same.
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Figure 3
Figure 3. Comparison of some commonly used T_m magnesium correction functions. Experimentally measured (solid circle) and predicted melting temperatures for 30-mer duplex, ODN11, 5′-AGTCTGGTCTGGATCTGAGAACTTCAGGCT-3′ in buffers containing 10 mM Tris-HCl and various amounts of Mg²⁺ ions are shown.
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Figure 4
Figure 4. Dependence of melting temperatures on magnesium concentrations is plotted for representative duplexes, which are 15 (solid symbols) and 25 (open symbols) base pairs long. Percentages of G·C base pairs were either 32−33% (circle) or 72−73% (triangle). Tris⁺ ions are present at low concentrations where they have negligible effects on duplex stability. Experimental data were fitted with quadratic curves to illustrate trends.
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Figure 5
Figure 5. Differences between 1/T_m values in buffers of various Mg²⁺ concentrations and 1 M Na⁺ buffer are shown as a function of f_GC. Inset shows colored symbols used for oligonucleotides of various lengths. (A) 0.5 mM Mg²⁺, (B) 3 mM Mg²⁺, (C) 10 mM Mg²⁺, (D) 125 mM Mg²⁺.
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Figure 6
Figure 6. Slopes (A) and intercepts (B) of fitted straight lines from Figure 5 are examined. Panels (C) and (D) display dependence of slopes and intercepts of fitted straight lines from Figure 6B on Mg²⁺ concentrations.
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Figure 7
Figure 7. Experimental melting temperatures of the 60-mer duplex (see Materials and Methods) were obtained using DSC at low DNA concentration (C_t = 2 µM). Buffers contained 50 mM KCl, 10 mM Tris-HCl (pH = 8.3) and various amounts of magnesium ions and deoxynucleotide triphosphates. Concentrations (mM) used in each experiment are indicated below the graph. The first row is the free [Mg²⁺], which is calculated as the difference between total Mg²⁺ and dNTP concentrations. dNTP “mix” contained equimolar concentrations of dATP, dGTP, dCTP and dTTP. The sum of their concentrations is shown in the table below the graph.
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Figure 8
Figure 8. Competitive effects of K⁺ and Mg²⁺ examined for the 25 bp long duplex, ODN8, CTGGTCTGGATCTGAGAACTTCAGG. (A) Dependence of T_m on concentrations of magnesium and monovalent ions. (B) Solid circles are T_ms plotted against ln R, where R = [Mg²⁺]^0.5/[Mon⁺]. Buffers are composed of constant 1.5 mM Mg²⁺ while KCl concentration varies. The solid line shows melting temperatures predicted by sodium salt correction (eq 4) when no Mg²⁺ is present. The dashed line indicates T_m in magnesium buffer when no KCl is present. The dominant ion crossover that occurs on average at R of 0.22 is indicated with the dotted vertical line.
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Figure 9
Figure 9. Flowchart for algorithm used to select the most accurate T_m salt correction equation depending on the relative amounts of monovalent and magnesium cations present.
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Figure 10
Figure 10. Release of magnesium ions associated with duplex denaturation. (A) Experimental values of dT_m/d(ln [Mg²⁺]) are shown in 1.5 mM (open circles), and 10 mM (closed circles) magnesium buffers as well as in the buffer containing both 1.5 mM MgCl₂ and 50 mM KCl (dotted line). The GC content of oligonucleotides ranges from 40 to 60%. For the sake of clarity, experimental data for individual duplexes are not shown for the last buffer; the relationships are approximated with lines fitted to experimental data points. (B) The number of released magnesium ions per phosphate group is plotted as a function of oligonucleotide lengths. Solid lines were predicted from eqs 16 and 21, and from the published average dependence of ΔH° values on oligonucleotide length (35). (C) The number of released magnesium ions per phosphate group decreases with increasing GC content in 1.5 mM Mg²⁺ buffer. These relationships are predicted reasonably well using eqs 16 and 21 (solid lines).
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  Korolev, N., Lyubartsev, A. P., and Nordenskiöld, L. (1998) Application of polyelectrolyte theories for analysis of DNA melting in the presence of Na⁺ and Mg²⁺ ions Biophys. J. 75, 3041– 3056
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  6
  Application of polyelectrolyte theories for analysis of DNA melting in the presence of Na+ and Mg2+ ions
  Korolev, Nikolay; Lyubartsev, Alexander P.; Nordenskiold, Lars
  Biophysical Journal (1998), 75 (6), 3041-3056CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
  Numerical calcns., using Poisson-Boltzmann (PB) and counterion condensation (CC) polyelectrolyte theories, of the electrostatic free energy difference, ΔGel, between single-stranded (coil) and double-helical DNA have been performed for solns. of NaDNA + NaCl with and without added MgCl2. Calcns. have been made for conditions relevant to systems where exptl. values of helix coil transition temp. (Tm) and other thermodn. quantities have been measured. Comparison with exptl. data has been possible by invoking values of Tm for solns. contg. NaCl salt only. Resulting theor. values of enthalpy, entropy, and heat capacity (for NaCl salt-contg. solns.) and of Tm as a function of NaCl concn. in NaCl + MgCl2 solns. have thus been obtained. Qual. and, to a large extent, quant. reprodn. of the exptl. Tm, ΔHm, ΔSm, and ΔCp values have been found from the results of polyelectrolyte theories. However, the quant. resemblance of exptl. data is considerably better for PB theory as compared to the CC model. Furthermore, some rather implausible qual. conclusions are obtained within the CC results for DNA melting in NaCl + MgCl2 solns. Our results argue in favor of the Poisson-Boltzmann theory, as compared to the counterion condensation theory.
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7. 7
  Tan, Z.-J. and Chen, S.-J. (2006) Nucleic acid helix stability: effects of salt concentration, cation valence and size, and chain length Biophys. J. 90, 1175– 1190
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  7
  Nucleic acid helix stability: effects of salt concentration, cation valence and size, and chain length
  Tan, Zhi-Jie; Chen, Shi-Jie
  Biophysical Journal (2006), 90 (4), 1175-1190CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
  Metal ions play crucial roles in thermal stability and folding kinetics of nucleic acids. For ions (esp. multivalent ions) in the close vicinity of nucleic acid surface, interion correlations and ion-binding mode fluctuations may be important. Poisson-Boltzmann theory ignores these effects whereas the recently developed tightly bound ion (TBI) theory explicitly accounts for these effects. Extensive exptl. data demonstrate that the TBI theory gives improved predictions for multivalent ions (e.g., Mg2+) than the Poisson-Boltzmann theory. In this study, we use the TBI theory to investigate how the metal ions affect the folding stability of B-DNA helixes. We quant. evaluate the effects of ion concn., ion size and valence, and helix length on the helix stability. Moreover, we derive practically useful anal. formulas for the thermodn. parameters as functions of finite helix length, ion type, and ion concn. We find that the helix stability is additive for high ion concn. and long helix and nonadditive for low ion concn. and short helix. All these results are tested against and supported by extensive exptl. data.
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8. 8
  Wilson, R. W., Rau, D. C., and Bloomfield, V. A. (1980) Comparison of polyelectrolyte theories of the binding of cations to DNA Biophys. J. 30, 317– 326
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  8
  Comparison of polyelectrolyte theories of the binding of cations to DNA
  Wilson, Robert Wilfred; Rau, Donald C.; Bloomfield, Victor A.
  Biophysical Journal (1980), 30 (2), 317-25CODEN: BIOJAU; ISSN:0006-3495.
  Predictions of the binding of counterions to DNA made using the counterion condensation theory developed by G. S. Manning (1978) are compared with those made using the Poisson-Boltzmann equation, solved numerically by the Runge-Kutta procedure. Ions are defined as territorially or atmospherically bound if they fall within a given distance, defined by counterion condensation theory, from the DNA surface. Two types of exptl. situations are considered. The 1st is the delocalized binding of a single type of counterion to DNA. In this case the Poisson-Boltzmann treatment predicts somewhat lower extents of binding to DNA, modeled as a 10-Å radius cylinder, than does Manning theory. The 2 theories converge as the radius decreases. The 2nd type of expt. is the competition of ions of different valence for binding to DNA. The theories are compared with literature values of binding consts. of divalent ions in the presence of monovalent ions, and of spermidine3+ in the presence of Na+ or Mg2+. Both predict with fair accuracy the salt dependence of the equil. consts.
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9. 9
  Manning, G. S. (1972) On the application of polyelectrolyte “limiting laws” to the helix-coil transition of DNA. II. The effect of Mg⁺² counterions Biopolymers 11, 951– 955
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  9
  Application of polyelectrolyte "limiting laws" to the helix-coil transition of DNA. II. Effect of Mg2+ counterions
  Manning, Gerald S.
  Biopolymers (1972), 11 (5), 951-5CODEN: BIPMAA; ISSN:0006-3525.
  Previously published techniques are here applied to the case for which the soln. contains, in addn. to excess uni-univalent salt, 1 equiv. of divalent counterions per mol nucleotide. In agreement with the melting temp. measurements of Dove and Davidson for Mg2+, it is predicted that a region of uni-univalent salt concn. then exists in which (dTm/d log mA+), where mA+ = molality of univalent salt, is neg. It is further predicted, in accord with expts., that in the presence of divalent counterions, the helical form of DNA is much more stable than in their absence.
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10. 10
  Manning, G. S. (1978) The molecular theory of polyelectrolyte solutions with applications to the electrostatic properties of polynucleotides Q. Rev. Biophys. 11, 179– 246
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  10
  The molecular theory of polyelectrolyte solutions with applications to the electrostatic properties of polynucleotides
  Manning, Gerald S.
  Quarterly Reviews of Biophysics (1978), 11 (2), 179-246CODEN: QURBAW; ISSN:0033-5835.
  The theory of polyelectrolyte solns. is extended to cases of interest in polynucleotide chem. The ionic state of an extended polynucleotide structure in an aq. environment of simple counterions is initially discussed. The polynucleotide in such an environment is considered to to be potentiated by its counterions for the spontaneous occurrence of any process that results in the relief of the electrostatic stress on the polynucleotide set up by the repulsive interactions among the phosphate groups. Binding of multivalent cationic substances is a process of this type as are the DNA helix-coil transition and the tendency of DNA to straighten spontaneously from a locally bent configuration. Binding to polynucleotides of cationic substances as diverse as Na+, Mg2+, spermine, polylysine, and lactose repressor is discussed. The anal. of ionic effects on conformational transitions includes those induced by strong elec. fields as well as by temp. increases.
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11. 11
  Olmsted, M. C., Anderson, C. F., and Record, M. T., Jr (1991) Importance of oligoelectrolyte end effects for the thermodynamics of conformational transitions of nucleic acid oligomers: a grand canonical Monte Carlo analysis Biopolymers 31, 1593– 1604
  [Crossref], [PubMed], [CAS], Google Scholar
  11
  Importance of oligoelectrolyte end effects for the thermodynamics of conformational transitions of nucleic acid oligomers: a grand canonical Monte Carlo analysis
  Olmsted, Martha C.; Anderson, Charles F.; Record, M. Thomas, Jr.
  Biopolymers (1991), 31 (13), 1593-604CODEN: BIPMAA; ISSN:0006-3525.
  Effects of salt concn. on the stabilities of oligonucleotide helixes are analyzed directly in terms of ΔΓN→yN ≡ ΓyNden - INnat, the difference in the salt-nucleotide phosphate preferential interaction coeffs. for the denatured state, having yN phosphate charges, and for the native state, having N phosphate charges (y = 1 for hairpin denaturation and y = 0.5 for dimer denaturation). Previous exptl. studies of the denaturation of hairpin oligonucleotides (having 18 < N < 44) indicate significant differences between ΔΓN→N and ΔΓ∞, the value detd. for the denaturation of the corresponding polynucleotide. These differences are thermodn. manifestations of the oligoelectrolyte end effect. In contrast, the available data on the denaturation of oligonucleotide dimer helixes (N ≤ 22) imply that differences between ΔΓ∞ and ΔΓN→0.5N, and hence oligoelectrolyte end effects, are small or negligible. To det. the origin of these apparently conflicting implications concerning the importance of oligoelectrolyte end effects, the N dependence of ΓN was calcd. from grand canonical Monte Carlo simulations for an idealized model of the structure and charge distribution of each oligomer conformation. The calcns. are in quant. agreement with the exptl. finding for d(TA) hairpin oligomers that -ΔΓN→N decreases linearly as N-1 increases, and with the extant exptl. detns. of ΔΓN→0.5N. These results provide an illustration of how the large electrostatic end effects exhibited by the hairpin denaturation data are masked when ΔΓ∞ is compared with values of ΔΓN→0.5N for short dimer helixes (N ≤ 22). For 0.5N > 24, -ΔΓN→0.5N is predicted to be a linear function of N-1 whose slope has the opposite sign from, and is more salt-concn. dependent than, the corresponding slope of -ΔΓN→N as a function of N-1. Calcns. also yield predictions about the N dependences of the individual values of ΓN that can be tested by detg. Donnan coeffs. from membrane dialysis equil. expts. For long enough hairpin and dimer oligonucleotides (yN ≥ 24), in either native or denatured forms, it is predicted that the (pos.) difference Γ∞ - ΓN increases linearly with increasing N-1. For smaller values of N the difference Γ∞ - ΓN continues to increase with increasing N-1.
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12. 12
  Pack, G. R., Wong, L., and Lamm, G. (1999) Divalent cations and the electrostatic potential around DNA: Monte Carlo and Poisson-Boltzmann calculations Biopolymers 49, 575– 590
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  12
  Divalent cations and the electrostatic potential around DNA: Monte Carlo and Poisson-Boltzmann calculations
  Pack, George R.; Wong, Linda; Lamm, Gene
  Biopolymers (1999), 49 (7), 575-590CODEN: BIPMAA; ISSN:0006-3525. (John Wiley & Sons, Inc.)
  The predictions of counterion condensation theory for divalent ions were tested by comparison with the results of Monte Carlo calcns. on an all-atom model of DNA. Monovalent-divalent competition at the polyelectrolyte surface was investigated by varying the partial molar volume of divalent ions. To assess the viability of using Poisson-Boltzmann (PB) calcns. for detg. divalent ion concns. at DNA surfaces, Monte Carlo (MC) calcns. were compared with PB calcns. using different models of the dielec. continuum. It was detd. that, while std. PB calcns. of divalent ion surface densities are about 25-30% below those predicted by MC techniques, and somewhat larger than errors previously detd. for monovalent ions, errors due to the use of the mean-field approxn. of PB theory are smaller than those arising from common assumptions regarding the dielec. continuum.
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13. 13
  Williams, A. P., Longfellow, C. E., Freier, S. M., Kierzek, R., and Turner, D. H. (1989) Laser temperature-jump, spectroscopic, and thermodynamic study of salt effects on duplex formation by dGCATGC Biochemistry 28, 4283– 4291
  [ACS Full Text ], [CAS], Google Scholar
  13
  Laser temperature-jump, spectroscopic, and thermodynamic study of salt effects on duplex formation by dGCATGC
  Williams, Alison P.; Longfellow, Carl E.; Freier, Susan M.; Kierzek, Ryszard; Turner, Douglas H.
  Biochemistry (1989), 28 (10), 4283-91CODEN: BICHAW; ISSN:0006-2960.
  Salt effects on duplex formation by dGCATGC were studied with spectroscopic, thermodn., and kinetic methods. CD spectra indicate different salt conditions having little effect on the structures of the duplex and single strand. NMR chem. shifts indicate the structure of the duplex in 1M NaCl is similar to that of the B-form detd. previously in 0.5M KCl (Nilges, M., et al., 1987). Optical melting expts. indicate the effect of Na+ concn. on melting temp. is similar to that expected for a polynucleotide with the same GC content. Laser temp.-jump expts. indicate the effect of Na+ concn. on the rate of duplex formation is much less than that obsd. for polynucleotides. The observations are consistent with expectations based on a counterion condensation model. This is surprising for a duplex with only 10 phosphates.
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14. 14
  Nakano, S., Fujimoto, M., Hara, H., and Sugimoto, N. (1999) Nucleic acid duplex stability: influence of base composition on cation effects Nucleic Acids Res. 27, 2957– 2965
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  14
  Nucleic acid duplex stability: influence of base composition on cation effects
  Nakano, Shu-Ichi; Fujimoto, Mariko; Hara, Hideyuki; Sugimoto, Naoki
  Nucleic Acids Research (1999), 27 (14), 2957-2965CODEN: NARHAD; ISSN:0305-1048. (Oxford University Press)
  The effects of counter ion on a nucleic acid duplex stability were investigated. Since a linear free energy relationship for the thermostability of oligonucleotide duplexes between those in 1 M and in 100 mM NaCl-phosphate buffer were obsd. regardless of whether they are DNA-DNA, RNA-RNA or RNA-DNA duplexes, simple prediction systems for ΔG037 as well as Tm values in 100 mM NaCl-phosphate buffer were established. These predictions were successful with an av. error of only 2.4°C for Tm and 5.7% for G037 values. The no. of Na+ newly bound to a duplex when the duplex forms (-Δn) was significantly influenced by the base compn., and -Δn for d(GCCAGTTAA)/d(TTAACTGGC) was different for MgCl2, CaCl2, BaCl2 and MnCl2 (from 0.70 to 0.76 with the same order of the duplex stability). Almost no additive effects on the duplex stability was obsd. for NaCl and MgCl2, suggesting a competitive binding for these cations. The sequence-dependent manner of Δn suggests the presence of preferential base pairs or nearest-neighbor base pairs for the cation binding, which would affect nearest-neighbor parameters.
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15. 15
  von Ahsen, N., Wittwer, C. T., and Schütz, E. (2001) Oligonucleotide melting temperatures under PCR conditions: nearest-neighbor corrections for Mg²⁺, deoxynucleotide triphosphate, and dimethyl sulfoxide concentrations with comparison to alternative empirical formulas Clin. Chem. 47, 1956– 1961
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  15
  Oligonucleotide melting temperatures under PCR conditions: nearest-neighbor corrections for Mg2+, deoxynucleotide triphosphate, and dimethyl sulfoxide concentrations with comparison to alternative empirical formulas
  Von Ahsen, Nicolas; Wittwer, Carl T.; Schutz, Ekkehard
  Clinical Chemistry (Washington, DC, United States) (2001), 47 (11), 1956-1961CODEN: CLCHAU; ISSN:0009-9147. (American Association for Clinical Chemistry)
  Background: Many techniques in mol. biol. depend on the oligonucleotide melting temp. (Tm), and several formulas have been developed to est. Tm. Nearest-neighbor (N-N) models provide the highest accuracy for Tm prediction, but it is not clear how to adjust these models for the effects of reagents commonly used in PCR, such as Mg2+, deoxynucleotide triphosphates (dNTPs), and DMSO. Methods: The exptl. TmS of 475 matched or mismatched target/probe duplexes were obtained in our labs. or were compiled from the literature based on studies using the same real-time PCR platform. This data set was used to evaluate the contributions of [Mg2+], [dNTPs], and [DMSO] in N-N calcns. In addn., best-fit coeffs. for common empirical formulas based on GC content, length, and the equiv. sodium ion concn. of cations [Na+eq] were obtained by multiple regression. Results: When we used [Na+eq] = [Monovalent cations] + 120([Mg2+] - [dNTPs]) (the concns. in this formula are mmol/L) to correct ΔS0 and a DMSO term of 0.75 (%DMSO), the SE of the N-N Tm est. was 1.76 for perfectly matched duplexes (n = 217). Alternatively, the empirical formula Tm (°C) = 77.1+11.7 × log[Na+eq] + 0.41(%GC) - 528/bp - 0.75(%DMSO) gave a slightly higher SE of 1.87. When all duplexes (matched and mismatched; n = 475) were included in N-N calcns., the SE was 2.06. Conclusions: This robust model, accounting for the effects of Mg2+, DMSO, and dNTPs on oligonucleotide Tm in PCR, gives reliable Tm predictions using thermodn. N-N calcns. or empirical formulas.
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16. 16
  Peyret, N. (2000)
  Prediction of Nucleic Acid Hybridization: Parameters and Algorithms
  , Ph.D. Thesis, Section 5.4.2, pp 128, Wayne State University, Detroit, MI.
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17. 17
  Dove, W. F. and Davidson, N. (1962) Cation effects on the denaturation of DNA J. Mol. Biol. 5, 467– 478
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  17
  Cation effects on the denaturation of deoxyribonucleic acid (DNA)
  Dove, William F.; Davidson, Norman
  Journal of Molecular Biology (1962), 5 (), 467-78CODEN: JMOBAK; ISSN:0022-2836.
  The midpoint (Tm) of the thermal denaturation curve of various DNA's increases linearly with the logarithm of the ionic strength (μ) for 0.0003 to 0.5M. This ionic strength dependence is unrelated to the base ratio of the DNA. The transition breadth increases with decreasing ionic strength. The broadening effect is interpreted as indicating that the transition is less cooperative at low μ. At μ = 3 × 10-4M, the bivalent ions Mg2+ and Co2+ are bound almost stoichiometrically by DNA, and Tm increases by 35-45°. The transition breadth is greater for 1/2 equiv. of bivalent ion/mole DNA phosphate than for zero or 1 equiv.; this is attributed to stronger ion binding by native than by denatured DNA. Ag+ at a ratio of 0.2 Ag+/base increases Tm by about 40° and broadens the transition. The pH values for denaturation by acid and base are reported for several DNA's. The resp. values at 25° are calf thymus pH 2.95, 11.78; Diplococcus pneumoniae 2.92, 11.78; Escherichia coli 2.89, 11.92; Micrococcus lysodeikticus 2.74, 11.99.
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18. 18
  Lyons, J. W. and Kotin, L. (1965) The effect of magnesium ion on the secondary structure of deoxyribonucleic acid J. Am. Chem. Soc. 87, 1781– 1785
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  18
  The effect of magnesium ion on the secondary structure of deoxyribonucleic acid
  Lyons, John W.; Kotin, Leonard
  Journal of the American Chemical Society (1965), 87 (8), 1781-5CODEN: JACSAT; ISSN:0002-7863.
  The effect of Mg2+ on the thermal and phase stability of DNA was studied by means of spectrophotometric and N.M.R. techniques to yield certain conclusions. (1) Mg2+ interacts with DNA at the phosphate sites only. (2) Whereas aq. solutions of the pure Mg salt of DNA are relatively resistant to thermal denaturation, their thermal stability is reduced in the presence of added MgCl2. (3) The proposed mechanism for the pptn. of DNA with an excess of Mg2+ is that site-bound Mg2+ forms ionic links between sepd. DNA strands through -P-O-Mg-O-P complexes leading to the exposure of the bases to solvent. This is followed by hydrophobic base-base interaction, leading to large aggregates and, finally, phase sepn.
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19. 19
  Ott, G. S., Ziegler, R., and Bauer, W. R. (1975) The DNA melting transition in aqueous magnesium salt solutions Biochemistry 14, 3431– 3438
  [ACS Full Text ], [CAS], Google Scholar
  19
  DNA melting transition in aqueous magnesium salt solutions
  Ott, Gary S.; Ziegler, Robert; Bauer, William R.
  Biochemistry (1975), 14 (15), 3431-8CODEN: BICHAW; ISSN:0006-2960.
  The melting transition of the Mg salt of DNA was systematically examd. in the presence of various types of anions. The addn. of ClO4- to a concn. of 3.0N resulted in a biphasic optical transition, with the 1st phase exhibiting rapid reversibility and independence of DNA concn. This subtransition, which is interpreted as an intramol. condensation to a collapsed form of DNA, was followed by a DNA concn.-dependent aggregation reaction. The aggregation was reversed by increasing the ClO4- concn. to 6.0N while elevating the temp. to posttransition levels. Alternatively, both the collapse and the aggregation were prevented by melting in the presence of trichloroacetate, a strong chaotropic solvent for DNA. The forces responsible for mediating both the collapse and the aggregation are superficially similar to those involved in maintaining duplex stability. The collapsed form, in particular, possibly possesses features in common with the condensed structures which are produced in aq. soln. of certain polymers, e.g., polyethylene glycol.
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20. 20
  Krakauer, H. (1971) The binding of Mg⁺² ions to polyadenylate, polyuridylate, and their complexes Biopolymers 10, 2459– 2490
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  20
  Binding of Mg2+ ions to polyadenylate, polyuridylate, and their complexes
  Krakauer, Henry
  Biopolymers (1971), 10 (12), 2459-90CODEN: BIPMAA; ISSN:0006-3525.
  The binding of Mg2+ to polyadenylate (poly A), polyuridylate (poly U), and their complexes, poly (A+U) and poly (A+2U), was studied by means of a technique in which the dye eriochrome black T is used to measure the concn. of free Mg2+. The apparent binding const. Kx=[MgN]/[Mg2+][N], N=site for Mg2+ binding (the phosphate group of the nucleotide), was found to decrease rapidly as the extent of binding increased and, at low extents of binding, as the concn. of Na+ increased in poly A, poly (A+U), and poly (A+2U), and somewhat less so in poly U. Kx is generally in the range 104>Kx>102. The cause of these dependences is apparently, primarily, the displacement of Na+ by Mg2+ in poly U and poly (A+U) on the basis of the similarity of extents of displacement measured in this work and those measured potentiometrically.
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21. 21
  Krakauer, H. (1974) A thermodynamic analysis of the influence of simple mono- and divalent cations on conformational transitions of polynucleotide complexes Biochemistry 13, 2579– 2589
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  21
  Thermodynamic analysis of the influence of simple mono- and divalent cations on the conformational transitions of polynucleotide complexes
  Krakauer, Henry
  Biochemistry (1974), 13 (12), 2579-89CODEN: BICHAW; ISSN:0006-2960.
  The complex dependence of the conformational transitions among the structures formed by poly(A) [24937-83-5] and poly(U) [27416-86-0] on the concns. of Na+ [7440-23-5] and Mg2+ [7439-95-4] is described and is satisfactorily interpreted in terms of the measured interactions of these ions with the polynucleotides. The anal. is phenomenol. and not predicated on any model of the interactions, but is consistent with the notion that those with Na+ are qual. different from those with Mg2+, the latter but not the former resulting in a definite complex.
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22. 22
  Kankia, B. I. (2003) Binding of Mg²⁺ to single-stranded polynucleotides: hydration and optical studies Biophys. Chem. 104, 643– 654
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  Binding of Mg2+ to single-stranded polynucleotides: hydration and optical studies
  Kankia, Besik I.
  Biophysical Chemistry (2003), 104 (3), 643-654CODEN: BICIAZ; ISSN:0301-4622. (Elsevier Science B.V.)
  The binding of Mg2+ to single-stranded ribo- and deoxy-polynucleotides, poly(rA), poly(rU), poly(dA) and poly(dT), has been investigated in dil. aq. solns. at pH 7.5 and 20°. A combination of ultrasound velocimetry, d., UV and CD spectroscopy have been employed to study hydration and spectral effects of Mg2+ binding to the polynucleotides. Vol. and compressibility effects of Mg2+ binding to random-coiled poly(rU) and poly(dT) correspond to two coordination bonds probably between the adjacent phosphate groups. The same parameters for poly(rA)+Mg2+ correspond to an inner-sphere complex with three-four direct contacts. However, almost no hydration effects are arising in binding to its deoxy analog, poly(dA), indicating mostly a delocalized binding mode. In agreement with hydration studies, optical investigations revealed almost no influence of Mg2+ on poly(dA) properties, while it stabilizes and aggregates poly(rA) single-helix. The evidence presented here indicates that Mg2+ are able to bind specifically to single-stranded polynucleotides, and recognize their compn. and backbone conformation.
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23. 23
  Draper, D. E. (2004) A guide to ions and RNA structure RNA 10, 335– 343
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  23
  A guide to ions and RNA structure
  Draper, David E.
  RNA (2004), 10 (3), 335-343CODEN: RNARFU; ISSN:1355-8382. (Cold Spring Harbor Laboratory Press)
  A review. RNA folding into stable tertiary structures is remarkably sensitive to the concns. and types of cations present; an understanding of the phys. basis of ion-RNA interactions is therefore a prerequisite for a quant. accounting of RNA stability. This article summarizes the energetic factors that must be considered when ions interact with two different RNA environments. "Diffuse ions" accumulate near the RNA because of the RNA electrostatic field and remain largely hydrated. A "chelated" ion directly contacts a specific location on the RNA surface and is held in place by electrostatic forces. Energetic costs of ion chelation include displacement of some of the waters of hydration by the RNA surface and repulsion of diffuse ions. Methods are discussed for computing both the free energy of the set of diffuse ions assocd. with an RNA and the binding free energies of individual chelated ions. Such calcns. quant. account for the effects of Mg2+ on RNA stability where exptl. data are available. An important conclusion is that diffuse ions are a major factor in the stabilization of RNA tertiary structures.
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24. 24
  Zubay, G. and Doty, P. (1958) Nucleic acid interactions with metal ions and amino acids Biochim. Biophys. Acta 29, 47– 58
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  24
  Nucleic acid interactions with metal ions and amino acids
  Zubay, Geoffrey; Doty, Paul
  Biochimica et Biophysica Acta (1958), 29 (), 47-58CODEN: BBACAQ; ISSN:0006-3002.
  Conductometric titrations and equil. dialysis measurements were used to measure the binding of Na+, Mg++, and Cu++ by deoxyribonucleic acid (DNA) and the binding of amino acids by DNA and ribonucleic acid, all in the presence of 0.2M NaCl. About 1/2 the Na+ counterions appeared to be held near the DNA by the electrostatic field. Mg++ ions were bound to specific sites, but very weakly. However, on thermal denaturation of the DNA the binding became much stronger. The no. of sites was about 70% of the no. of nucleotides/mol. Cu++ ions were tightly bound to undenatured DNA and caused marked aggregation. Arginine (0.01M) was bound to DNA to the extent of about 6 mols./100 nucleotides. Nonbasic amino acids (serine and glutamic acid) were not bound significantly by either denatured or undenatured DNA. Binding of glutamic acid, threonine, and proline by ribonucleic acid amounted to less than 1 mol./100 nucleotides, over the range of concns. studied.
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25. 25
  Rychlik, W., Spencer, W. J., and Rhoads, R. E. (1990) Optimization of the annealing temperature for DNA amplification in vitro Nucleic Acids Res. 18, 6409– 6412
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  Optimization of the annealing temperature for DNA amplification in vitro
  Rychlik, W.; Spencer, W. J.; Rhoads, R. E.
  Nucleic Acids Research (1990), 18 (21), 6409-12CODEN: NARHAD; ISSN:0305-1048.
  In the polymerase chain reaction (PCR) technique, DNA is amplified in vitro by a series of polymn. cycles consisting of 3 temp.-dependent steps: DNA denaturation, primer-template annealing, and DNA synthesis by a thermostable DNA polymerase. The purity and yield of the reaction products depend on several parameters, one of which is the annealing temp. (Ta). At both sub- and super-optimal Ta values, non-specific products may be formed, and the yield of products is reduced. Optimizing the Ta is esp. crit. when long products are synthesized or when total genomic DNA is the substrate for PCR. In this article the authors exptl. det. the optimal annealing temp. (TaOPT) values for several primer-template pairs and develop a method for its calcn. The TaOPT is found to be a function of the melting temps. of the less stable primer-template pair and of the product. The fact that exptl. and calcd. TaOPT values agree to within 0.7° eliminates the need for detg. TaOPT exptl. Synthesis of DNA fragments shorter than 1 kb is more efficient if a variable Ta is used, such that the Ta is higher in each consecutive cycle.
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26. 26
  Harris, S. and Jones, D. B. (1997) Optimisation of the polymerase chain reaction Br. J. Biomed. Sci. 54, 166– 173
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  Optimization of the polymerase chain reaction
  Harris, S.; Jones, D. B.
  British Journal of Biomedical Science (1997), 54 (3), 166-173CODEN: BJMSEO; ISSN:0967-4845. (Royal Society of Medicine Press)
  The polymerase chain reaction (PCR) is a method by which specific sequences of DNA can be copied many times, allowing detailed mol. studies to be performed on as little as a single cell. Numerous and diverse applications of PCR are being developed across all disciplines of diagnostic pathol. and research, and no single protocol is appropriate for all situations. Optimizing PCR requires a delicate balance between the amplification of specific products and avoiding the prodn. of non-specific products. Each step, from DNA template extn. to cycling times and temps., needs to be considered carefully. The aim of this study is to assess which parameters influence DNA amplification efficiency and specificity. The parameters evaluated are the denaturation, annealing and extension temps., the no. of cycles performed, and the primer, magnesium chloride, dNTP, Taq DNA polymerase and DNA template concns. The important parameters for efficient, specific amplification were denaturation time and temp., stringent annealing temps. and magnesium chloride concn. The importance of DNA concn. was found to depend upon the source from which the DNA was extd.
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27. 27
  Henegariu, O., Heerema, N. A., Dlouhy, S. R., Vance, G. H., and Vogt, P. H. (1997) Multiplex PCR: critical parameters and step-by-step protocol BioTechniques 23, 504– 511
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  Multiplex PCR: critical parameters and step-by-step protocol
  Henegariu, O.; Heerema, N. A.; Dlouhy, S. R.; Vance, G. H.; Vogt, P. H.
  BioTechniques (1997), 23 (3), 504-511CODEN: BTNQDO; ISSN:0736-6205. (Eaton)
  By simultaneously amplifying more than one locus in the same reaction, multiplex PCR is becoming a rapid and convenient screening assay in both the clin. and the research lab. While numerous papers and manuals discuss in detail conditions influencing the quality of PCR in general, relatively little has been published about the important exptl. factors and the common difficulties frequently encountered with multiplex PCR. We have examd. various conditions of the multiplex PCR, using a large no. of primer pairs. Esp. important for a successful multiplex PCR assay are the relative concns. of the primers at the various loci, the concn. of the PCR buffer, the cycling temps. and the balance between the magnesium chloride and deoxynucleotide concns. Based on our experience, we propose a protocol for developing a multiplex PCR assay and suggest ways to overcome commonly encountered problems.
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28. 28
  Markoulatos, P., Siafakas, N., and Moncany, M. (2002) Multiplex polymerase chain reaction: a practical approach J. Clin. Lab. Anal. 16, 47– 51
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  Multiplex polymerase chain reaction: A practical approach
  Markoulatos, P.; Siafakas, N.; Moncany, M.
  Journal of Clinical Laboratory Analysis (2002), 16 (1), 47-51CODEN: JCANEM; ISSN:0887-8013. (Wiley-Liss, Inc.)
  A review. Considerable time and effort can be saved by simultaneously amplifying multiple sequences in a single reaction, a process referred to as multiplex polymerase chain reaction (PCR). Multiplex PCR requires that primers lead to amplification of unique regions of DNA, both in individual pairs and in combinations of many primers, under a single set of reaction conditions. In addn., methods must be available for the anal. of each individual amplification product from the mixt. of all the products. Multiplex PCR is becoming a rapid and convenient screening assay in both the clin. and the research lab. The development of an efficient multiplex PCR usually requires strategic planning and multiple attempts to optimize reaction conditions. For a successful multiplex PCR assay, the relative concn. of the primers, concn. of the PCR buffer, balance between the magnesium chloride and deoxynucleotide concns., cycling temps., and amt. of template DNA and Taq DNA polymerase are important. An optimal combination of annealing temp. and buffer concn. is essential in multiplex PCR to obtain highly specific amplification products. Magnesium chloride concn. needs only to be proportional to the amt. of dNTP, while adjusting primer concn. for each target sequence is also essential. The list of various factors that can influence the reaction is by no means complete. Optimization of the parameters discussed in the present review should provide a practical approach toward resolving the common problems encountered in multiplex PCR (such as spurious amplification products, uneven or no amplification of some target sequences, and difficulties in reproducing some results). Thorough evaluation and validation of new multiplex PCR procedures is essential. The sensitivity and specificity must be thoroughly evaluated using standardized purified nucleic acids. Where available, full use should be made of external and internal quality controls, which must be rigorously applied. As the no. of microbial agents detectable by PCR increases, it will become highly desirable for practical purposes to achieve simultaneous detection of multiple agents that cause similar or identical clin. syndromes and/or share similar epidemiol. features.
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29. 29
  Ignatov, K. B., Miroshnikov, A. I., and Kramarov, V. M. (2003) A new approach to enhanced PCR specificity Rus. J. Bioorg. Chem. 29, 368– 371
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  A new approach to enhanced PCR specificity
  Ignatov, K. B.; Miroshnikov, A. I.; Kramarov, V. M.
  Russian Journal of Bioorganic Chemistry (Translation of Bioorganicheskaya Khimiya) (2003), 29 (4), 368-371CODEN: RJBCET; ISSN:1068-1620. (MAIK Nauka/Interperiodica Publishing)
  A new approach to enhanced specificity and product yield of polymerase chain reaction is proposed. It is based on control of DNA polymerase activity during PCR by changing the magnesium ion concn., which depends on the temp. of the reaction mixt. A slightly sol. magnesium salt, magnesium oxalate, whose soly. depends on temp., was used as a source of magnesium ions. During PCR, magnesium oxalate was maintained at satg. concn. by the presence of an insol. excess of this salt, and the concn. of magnesium ions depended on the salt soly.: binding of magnesium ions at lower temps. and their release at higher temps. was shown to affect the DNA polymerase activity and to favor the specific PCR amplification of the target DNA fragment.
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30. 30
  Owczarzy, R., Vallone, P. M., Gallo, F. J., Paner, T. M., Lane, M. J., and Benight, A. S. (1997) Predicting sequence-dependent melting stability of short duplex DNA oligomers Biopolymers 44, 217– 239
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  Predicting sequence-dependent melting stability of short duplex DNA oligomers
  Owczarzy, Richard; Vallone, Peter M.; Gallo, Frank J.; Paner, Teodoro M.; Lane, Michael J.; Benight, Albert S.
  Biopolymers (1998), 44 (3), 217-239CODEN: BIPMAA; ISSN:0006-3525. (John Wiley & Sons, Inc.)
  A review with 63 refs. Many important applications of DNA sequence-dependent hybridization reactions have recently emerged. This has sparked a renewed interest in anal. calcns. of sequence-dependent melting stability of duplex DNA. In particular, for many applications it is often desirable to accurately predict the transition temp., or tm, of short duplex DNA oligomers (∼ 20 base pairs or less) from their sequence and concn. The thermodn. anal. method underlying these predictive calcns. is based on the nearest-neighbor model. At least 11 sets of nearest-neighbor sequence-dependent thermodn. parameters for DNA have been published. These sets are compared. Use of the nearest-neighbor sets in predicting tm from the DNA sequence is demonstrated, and the ability of the nearest-neighbor parameters to provide accurate predictions of exptl. tm's of short duplex DNA oligomers is assessed.
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31. 31
  SantaLucia, J., Jr. and Hicks, D. (2004) The thermodynamics of DNA structural motifs Annu. Rev. Biophys. Biomol. Struct. 33, 415– 440
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  The thermodynamics of DNA structural motifs
  SantaLucia, John, Jr.; Hicks, Donald
  Annual Review of Biophysics and Biomolecular Structure (2004), 33 (), 415-440, 2 platesCODEN: ABBSE4; ISSN:1056-8700. (Annual Reviews Inc.)
  A review. DNA secondary structure plays an important role in biol., genotyping diagnostics, a variety of mol. biol. techniques, in vitro-selected DNA catalysts, nanotechnol., and DNA-based computing. Accurate prediction of DNA secondary structure and hybridization using dynamic programming algorithms requires a database of thermodn. parameters for several motifs including Watson-Crick base pairs, internal mismatches, terminal mismatches, terminal dangling ends, hairpins, bulges, internal loops, and multibranched loops. To make the database useful for predictions under a variety of salt conditions, empirical equations for monovalent and Mg2+ dependence of thermodn. have been developed. Bimol. hybridization is often inhibited by competing unimol. folding of a target or probe DNA. Powerful numerical methods have been developed to solve multistate-coupled equil. in bimol. and higher-order complexes. This review presents the current parameter set available for making accurate DNA structure predictions and also points to future directions for improvement.
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32. 32
  Mitsuhashi, M. (1996) Technical Report: Part 1. Basic requirements for designing optimal oligonucleotide probe sequences J. Clin. Lab. Anal. 10, 277– 284
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  Technical report: Part 1. Basic requirements for designing optimal oligonucleotide probe sequences
  Mitsuhashi, Masato
  Journal of Clinical Laboratory Analysis (1996), 10 (5), 277-284CODEN: JCANEM; ISSN:0887-8013. (Wiley-Liss)
  Although oligonucleotides can be easily synthesized and used in a variety of scientific fields, a major problem exists for each application: the difficulty of obtaining optimal oligonucleotide sequences. Oligonucleotide sequences have been described in each publication; however, little is disclosed on how to design such sequences and how specific each sequence is. This report introduces a new concept of computer hybridization simulation based on "thermodn. hybridizability," which can overcome the problems of conventional homol. analyses. Then, all the necessary components and factors for designing optimal probe sequences, such as hybridization strength, specificity, secondary structure, length of probes, probe-to-probe interaction, are discussed in detail. Also included are procedures for manipulating various types of data for selection of optimal oligonucleotides. This report provides a general guideline for optimal probe design and encourages basic and clin. scientists to enhance their research activities by using optimal oligonucleotides.
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33. 33
  Owczarzy, R., You, Y., Moreira, B. G., Manthey, J. A., Huang, L., Behlke, M. A., and Walder, J. A. (2004) Effects of sodium ions on DNA duplex oligomers: improved predictions of melting temperatures Biochemistry 43, 3537– 3554
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  Effects of Sodium Ions on DNA Duplex Oligomers: Improved Predictions of Melting Temperatures
  Owczarzy, Richard; You, Yong; Moreira, Bernardo G.; Manthey, Jeffrey A.; Huang, Lingyan; Behlke, Mark A.; Walder, Joseph A.
  Biochemistry (2004), 43 (12), 3537-3554CODEN: BICHAW; ISSN:0006-2960. (American Chemical Society)
  Melting temps., Tm, were systematically studied for a set of 92 DNA duplex oligomers in a variety of sodium ion concns. ranging from 69 mM to 1.02 M. The relationship between Tm and ln [Na+] was nonlinear over this range of sodium ion concns., and the obsd. melting temps. were poorly predicted by existing algorithms. A new empirical relationship was derived from UV melting data that employs a quadratic function, which better models the melting temps. of DNA duplex oligomers as sodium ion concn. is varied. Statistical anal. shows that this improved salt correction is significantly more accurate than previously suggested algorithms and predicts salt-cor. melting temps. with an av. error of only 1.6° when tested against an independent validation set of Tm measurements obtained from the literature. Differential scanning calorimetry studies demonstrate that this Tm salt correction is insensitive to DNA concn. The Tm salt correction function was found to be sequence-dependent and varied with the fraction of G·C base pairs, in agreement with previous studies of genomic and polymeric DNAs. The salt correction function is independent of oligomer length, suggesting that end-fraying and other end effects have little influence on the amt. of sodium counterions released during duplex melting. The results are discussed in the context of counterion condensation theory.
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34. 34
  Moreira, B. G., You, Y., Behlke, M. A., and Owczarzy, R. (2005) Effects of fluorescent dyes, quenchers, and dangling ends on DNA duplex stability Biochem. Biophys. Res. Commun. 327, 473– 484
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  Effects of fluorescent dyes, quenchers, and dangling ends on DNA duplex stability
  Moreira, Bernardo G.; You, Yong; Behlke, Mark A.; Owczarzy, Richard
  Biochemical and Biophysical Research Communications (2005), 327 (2), 473-484CODEN: BBRCA9; ISSN:0006-291X. (Elsevier)
  Single and dual-labeled fluorescent oligodeoxynucleotides are used in many mol. biol. applications. We investigated the effects of commonly used fluorescent dyes and quenchers on the thermodn. stability of a model probe-target DNA duplex. We demonstrate that those effects can be significant. Fluorescent dyes and quenchers were attached to the probe ends. In certain combinations, these groups stabilized the duplex up to 1.8 kcal/mol and increased Tm up to 4.3°. None of the groups tested significantly destabilized the duplex. Rank order of potency was, starting with the most stabilizing group: Iowa Black RQ ∼ Black Hole 2 > Cy5 ∼ Cy3 > Black Hole 1 > QSY7 ∼ Iowa Black FQ > Texas Red ∼ TAMRA > FAM ∼ HEX ∼ Dabcyl > TET. Longer linkers decreased stabilizing effects. Hybridizations to targets with various dangling ends were also studied and were found to have only minor effects on thermodn. stability. Depending on the dye/quencher combination employed, it can be important to include thermodn. contributions from fluorophore and quencher when designing oligonucleotide probe assays.
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35. 35
  Owczarzy, R. (2005) Melting temperatures of nucleic acids: discrepancies in analysis Biophys. Chem. 117, 207– 215
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  Melting temperatures of nucleic acids: Discrepancies in analysis
  Owczarzy, Richard
  Biophysical Chemistry (2005), 117 (3), 207-215CODEN: BICIAZ; ISSN:0301-4622. (Elsevier B.V.)
  Melting temp., Tm, is an important property of nucleic acid duplexes. It is typically detd. from spectroscopic or calorimetric melting expts. More than one anal. method has been used to ext. T m values from exptl. melting data. Unfortunately, different methods do not give the same results; the same melting data can be assigned different T m values depending upon which method is used to process that data. Inconsistencies or systematic errors between T ms reported in published data sets can be significant and add confusion to the field. Errors introduced from anal. can be greater than exptl. errors, ranging from a fraction of degree to several degrees. Of the various methods, the most consistent and meaningful approach defines melting temp. as the temp. at the transition midpoint where half of the base pairs are melted and std. free energy is zero. Assuming a two-state melting behavior, we present here a set of general equations that can be used to reconcile these anal. T m differences and convert results to the correct melting temps. at the transition midpoint. Melting temps. collected from published sources, which were analyzed using different methods, can now be cor. for these discrepancies and compared on equal footing. The similar corrections apply to Tm differences between calorimetric and spectroscopic melting curves. New algorithm for selection of linear sloping baselines, 2nd deriv. method, is suggested, which can be used to automate melting curve anal.
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36. 36
  Bevington, P. R. and Robinson, D. K. (1992) Data Reduction and Error Analysis for the Physical Sciences, WCB/McGraw-Hill, Boston, MA.
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  Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1996) Numerical Recipes in Fortran 77: The Art of Scientific Computing, Cambridge University Press, Cambridge.
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  Good, N. E., Winget, G. D., Winter, W., Connolly, T. N., Izawa, S., and Singh, R. M. M. (1966) Hydrogen ion buffers for biological research Biochemistry 5, 467– 477
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  Hydrogen ion buffers for biological research
  Good, Norman E.; Winget, G. Douglas; Winter, Wilhelmina; Connolly, Thomas N.; Izawa, Seikichi; Singh, Raizada M. M.
  Biochemistry (1966), 5 (2), 467-77CODEN: BICHAW; ISSN:0006-2960.
  Twelve new or little used H+ buffers covering the range pKa = 6.15-8.35 were prepd. and tested. Ten are zwitterionic amino acids, either N-substituted taurines or N-substituted glycines, and 2 are cationic primary aliphatic amines. All of the zwitterionic buffers are better than conventional buffers in the Hill reaction and in the phosphorylation-coupled oxidn. of succinate by bean mitochondria. Two of the zwitterions, N-tris-(hydroxymethyl)-methylaminoethanesulfonic acid and N-2-hydroxyethylpiperazine-N'-2-ethanesulfonic acid, give particularly active and stable mitochondrial prepns. These 2 also give higher rates of protein synthesis in cell-free bacterial prepns. than do Tris or phosphate buffers.
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39. 39
  Dawson, R. M. C., Elliot, D. C., Elliot, W. H., and Jones, K. M. (1986) Data for Biochemical Research, Oxford University Press, Oxford, U.K., pp 424.
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40. 40
  Fukada, H. and Takahashi, K. (1998) Enthalpy and heat capacity changes for the proton dissociation of various buffer components in 0.1M potassium chloride Proteins 33, 159– 166
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  Enthalpy and heat capacity changes for the proton dissociation of various buffer components in 0.1 M potassium chloride
  Fukada, Harumi; Takahashi, Katsutada
  Proteins: Structure, Function, and Genetics (1998), 33 (2), 159-166CODEN: PSFGEY; ISSN:0887-3585. (Wiley-Liss, Inc.)
  Enthalpy and heat capacity changes for the deprotonation of 18 buffers were calorimetrically detd. in 0.1 M potassium chloride at temps. ranging from 5 to 45°. The values of the dissocn. const. were also detd. by means of potentiometric titrn. The enthalpy changes for the deprotonation of buffers, except for the phosphate and glycerol 2-phosphate buffers, were found to be characterized by a linear function of temp. The enthalpy changes for the second dissocn. of phosphate and glycerol 2-phosphate where divalent anion is formed on dissocn. were fitted with the second order function of temp. rather than the first order. Temp. dependence of buffer pH calcd. by using the enthalpy and heat capacity changes obtained was in good agreement with the temp. variation of the pH values actually measured in the temp. range between 0 and 50° for all the buffers studied. On the basis of the results obtained, a numeric table showing the temp. dependence of pK values for the 18 buffers is presented.
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41. 41
  Plum, G. E. and Breslauer, K. J. (1995) Thermodynamics of an intramolecular DNA triple helix: a calorimetric and spectroscopic study of pH and salt dependence of thermally induced structural transitions J. Mol. Biol. 248, 679– 695
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  Thermodynamics of an intramolecular DNA triple helix: a calorimetric and spectroscopic study of the pH and salt dependence of thermally induced structural transitions
  Plum, G. Eric; Breslauer, Kenneth J.
  Journal of Molecular Biology (1995), 248 (3), 679-95CODEN: JMOBAK; ISSN:0022-2836. (Academic)
  We have characterized thermodynamically the melting transitions of a DNA 31-mer oligonucleotide (5'GAAGAGGTTTTTCCTCTTCTTTTTCTTCTCC-3') which is designed to fold into an intramol. triple helix. The first 19 residues fold back on themselves to form an antiparallel Watson-Crick hairpin duplex with a T5 loop. The 3'-terminal seven residues, which are connected to the Watson-Crick hairpin duplex by a second T5 loop, form Hoogsteen interactions in the major groove of the Watson-Crick hairpin. From UV melting studies we find that the 31-mer exhibits either one or two transitions, depending on soln. conditions. We use pH- and temp.-dependent CD to assign the initial and final states assocd. with each transition. We find that the disruption of the Hoogsteen hairpin is accompanied by a release of protons and an uptake of sodium ions while the disruption of the Watson-Crick hairpin is accompanied by a release of sodium ions with no change in protonation state. from these data, we construct a phase diagram for this intramol. DNA triple helix as a function of pH, sodium ion concn., and temp. We characterize the energies of each transition using a van't Hoff anal. and differential scanning calorimetry (DSC). Significantly, the DSC data provide a model-independent thermodn. characterization of the thermally induced transitions of this triplex. By combining the spectroscopic and calorimetric data, we develop a semi-empirical model which describes the state of the 31-mer as a function of pH, sodium ion concn., and temp. With this model we successfully predict characteristics of the 31-mer, which are beyond the data which are used in establishing the model (for example, the salt dependence of the apparent pKa of the Hoogsteen strand). This semi-empirical model may serve as a prototype for developing a method to predict the phase diagrams of intramol. triple helix systems.
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  Privalov, P. L. and Ptitsyn, O. B. (1969) Determination of stability of the DNA double helix in an aqueous medium Biopolymers 8, 559– 571
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  Determination of stability of the DNA double helix in an aqueous medium
  Privalov, P. L.; Ptitsyn, O. B.; Birshtein, T. M.
  Biopolymers (1969), 8 (5), 559-71CODEN: BIPMAA; ISSN:0006-3525.
  The possibility of detg. the free energy of stabilization (ΔG0) of native DNA structure with the help of calorimetric data on the heats of transition from the native to denatured state is considered. Results of microcalorimetric measurements of heats of denaturation of T2 phage DNA at different values of pH and ionic strength of soln. are given. Values for the free energy of stabilization of the DNA native structure under various conditions were obtained. Under conditions close to physiol., ΔG0 approaches 1200 cal/mole per base pair.
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43. 43
  Record, M. T., Jr (1967) Electrostatic effects on polynucleotide transitions. II. Behavior of titrated systems Biopolymers 5, 993– 1008
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  Electrostatic effects on polynucleotide transitions. II. Behavior of titrated systems
  Record, M. Thomas, Jr.
  Biopolymers (1967), 5 (10), 993-1008CODEN: BIPMAA; ISSN:0006-3525.
  The effects of monovalent counterion concn. upon polynucleotide structural stability under conditions of titrn. of the bases are discussed, based on the previously developed theory (Record (1967)). For any class of transition, the melting temp. Tm at const. pH is a linear function of the log of the monovalent counterion concn., M. At high salt concns., the log of the depression of the melting temp. by pH titrn. is proportional to the pH change, and the stability of the ordered form as measured by its melting temp. at neutral pH is a monotonic function of pHm/pK, where pHm and pK are the pH of melting and the monomer base pK, resp., both measured under similar conditions of temp. and ionic strength. For the transition from double helix to coil, dTm/dlog M, a measure of the neg. of the electrostatic free energy change in the transition, decreases with increasing pH. In acid soln., where the coil is more extensively protonated than the helix, the change in electrostatic free energy in the transition is larger than at neutral pH, whereas in alkali the electrostatic free energy change is smaller than at neutral pH. At sufficiently high pH, dTm/dlog M becomes neg., indicating that the electrostatic free energy change is pos. in the transition of this region. Literature data on the ionic strength dependence of the melting temp. for the acid helices of poly A, poly C, and poly dC are considered theoretically.
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44. 44
  Gray, D. M. (1997) Derivation of nearest-neighbor properties from data on nucleic acid oligomers. I. Simple sets of independent sequences and the influence of absent nearest neighbors Biopolymers 42, 783– 793
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  Derivation of nearest-neighbor properties from data on nucleic acid oligomers. I. Simple sets of independent sequences and the influence of absent nearest neighbors
  Gray, Donald M.
  Biopolymers (1997), 42 (7), 783-793CODEN: BIPMAA; ISSN:0006-3525. (John Wiley & Sons, Inc.)
  The constraints on combinations of nearest neighbors in nucleic acid sequences and the nos. of independent sequences needed to describe nearest-neighbor properties of oligomers and polymers are derived and summarized. It has been pointed out in previous work [D. M. Gray and I. Tinoco, Jr. (1970) Biopolymers, Vol. 9, pp. 223-244; R. F. Goldstein and A. S. Benight (1992) Biopolymers, Vol. 32, pp. 1679-1693] that these constraints restrict the information available from measurements of properties of sequence combinations. The emphasis in this paper is on the properties of oligomer sequences that vary in length, where each nucleotide or base pair at the end of the sequence makes a significant contribution to the measured property by interacting with its boundary of fixed sequence or solvent. In such cases it is not possible to det. values of properties of individual nearest neighbors, except for the like neighbors [e.g., d(A-A), d(G-G), d(T-T), and d(C-C) nucleotide neighbors in single-stranded DNA or d(A-A)/d(T-T) and d(G-G)/d(C-C) base pair neighbors in double-stranded DNA], solely from measurements of properties of different sequences. Even values for properties of the like neighbors cannot be detd. from such oligomeric sequences if the sequences are all of the same length. Nearest-neighbor properties of oligomer sequences that vary in length can be summarized in terms of the values for independent sets of sequences that are nearest neighbors and monomers all with boundaries of the fixed sequence or solvent. Straightforward combinations of the values for the independent sequences will give the values of the property for any dependent sequence, without explicit knowledge of the individual nearest-neighbor values. These considerations have important consequences for the derivation of widely used thermodn. parameters, as discussed in the following paper.
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  Schildkraut, C. and Lifson, S. (1965) Dependence of the melting temperature of DNA on salt concentration Biopolymers 3, 195– 208
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  Dependence of the melting temperature of DNA on salt concentration
  Schildkraut, Carl; Lifson, Shneior
  Biopolymers (1965), 3 (2), 195-208CODEN: BIPMAA; ISSN:0006-3525.
  Data on the decrease of the DNA melting temp. Tm with the salt concn., M, are reported and discussed. The electrostatic free energy change in the helix-coil transition, ΔFe, was related to the potential, ψ, which represented the electrostatic repulsion between the phosphate charges; ψ was calcd. as a function of M and of the distances between the charges of the 2 strands. The Debye-Hueckel approximation was shown to overest. ψ. It was suggested that the high local concn. of the counterions in the immediate vicinity of the fixed charges screened these charges from interacting with other fixed charges, to the extent that the system behaved as if the fixed ions carried a reduced charge. The notion of a reduced charge represented in a single parameter the deviation of the Debye-Hueckel approximation from the true potential. A plot of Tm versus ΔFe gave a straight line as predicted. ΔHo was calcd. from the slope and found to be consistent with exptl. detd. values. The calcns. supported the hypothesis that the change of Tm with salt concn. was due to changes in the screened interactions between the fixed phosphate charges. In analyzing the results of these calens., it was possible on the one hand to indicate some of the limitations of the theoretical model and, on the other hand, draw some conclusions about the order of magnitude of the nonelectrostatic energy of formation of the double helix.
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46. 46
  Tan, Z.-J. and Chen, S.-J. (2007) RNA helix stability in mixed Na⁺/Mg²⁺ solution Biophys. J. 92, 3615– 3632
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  RNA helix stability in mixed Na+/Mg2+ solution
  Tan, Zhi-Jie; Chen, Shi-Jie
  Biophysical Journal (2007), 92 (10), 3615-3632CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
  A recently developed tightly bound ion model can account for the correlation and fluctuation (i.e., different binding modes) of bound ions. However, the model cannot treat mixed ion solns., which are physiol. relevant and biol. significant, and the model was based on B-DNA helixes and thus cannot directly treat RNA helixes. In the present study, we investigate the effects of ion correlation and fluctuation on the thermodn. stability of finite length RNA helixes immersed in a mixed soln. of monovalent and divalent ions. Exptl. comparisons demonstrate that the model gives improved predictions over the Poisson-Boltzmann theory, which has been found to underestimate the roles of multivalent ions such as Mg2+ in stabilizing DNA and RNA helixes. The tightly bound ion model makes quant. predictions on how the Na+-Mg2+ competition dets. helix stability and its helix length-dependence. In addn., the model gives empirical formulas for the thermodn. parameters as functions of Na+/Mg2+ concns. and helix length. Such formulas can be quite useful for practical applications.
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47. 47
  Efron, B. and Tibshirani, R. J. (1993) . An Introduction to the Bootstrap, Chapman & Hall/CRC, Boca Raton, FL.
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  Völker, J., Klump, H. H., Manning, G. S., and Breslauer, K. J. (2001) Counterion association with native and denatured nucleic acids: an experimental approach J. Mol. Biol. 310, 1011– 1025
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  Counterion association with native and denatured nucleic acids: an experimental approach
  Volker, Jens; Klump, Horst H.; Manning, Gerald S.; Breslauer, Kenneth J.
  Journal of Molecular Biology (2001), 310 (5), 1011-1025CODEN: JMOBAK; ISSN:0022-2836. (Academic Press)
  The melting temp. of the poly(dA)·poly(dT) double helix is exquisitely sensitive to salt concn., and the helix-to-coil transition is sharp. Modern calorimetric instrumentation allows this transition to be detected and characterized with high precision at extremely low duplex concns. The authors have taken advantage of these properties to show that this duplex can be used as a sensitive probe to detect and to characterize the influence of other solutes on soln. properties. The authors demonstrate how the temp. assocd. with poly(dA)·poly(dT) melting can be used to define the change in bulk soln. cation concn. imparted by the presence of other duplex and triplex solutes, in both their native and denatured states. The authors use this information to critically evaluate features of counterion condensation theory, as well as to illustrate "crosstalk" between different, noncontacting solute mols. Specifically, the authors probe the melting of a synthetic homopolymer, poly(dA)·poly(dT), in the presence of excess genomic salmon sperm DNA, or in the presence of one of two synthetic RNA polymers (the poly(rA)·poly(rU) duplex or the poly(rU)·poly(rA)·poly(rU) triplex). The authors find that these addns. cause a shift in the melting temp. of poly(dA)·poly(dT), which is proportional to the concn. of the added polymer and dependent on its conformational state (B vs. A, native vs. denatured, and triplex vs. duplex). To a first approxn., the magnitude of the obsd. tm shift does not depend significantly on whether the added polymer is RNA or DNA, but it does depend on the no. of strands making up the helix of the added polymer. The authors ascribe the obsd. changes in melting temp. of poly(dA)·poly(dT) to the increase in ionic strength of the bulk soln. brought about by the presence of the added nucleic acid and its assocd. counterions. The authors refer to this communication between noncontacting biopolymers in soln. as solvent-mediated crosstalk. By comparison with a known std. curve of tm vs. log[Na+] for poly(dA)·poly(dT), the authors est. the magnitude of the apparent change in ionic strength resulting from the presence of the bulk nucleic acid, and the authors compare these results with predictions from theory. The authors find that current theor. considerations correctly predict the direction of the tm shift (the melting temp. increases), while overestimating its magnitude. Specifically, the authors observe an apparent increase in ionic strength equal to 5% of the concn. of the added duplex DNA or RNA (in mol phosphate), and an addnl. apparent increase of about 9.5% of the nucleic acid concn. (mol phosphate) upon denaturation of the added DNA or RNA, yielding a total apparent increase of 14.5%. For the poly(rU)·poly(rA)·poly(rU) triplex, the total apparent increase in ionic strength corresponds to about 13.6% of the amt. of added triplex (moles phosphate). The effect the authors observe is due to coupled equil. between the solute mols. mediated by modulations in cation concn. induced by the presence and/or the transition of one of the solute mols. The authors note that the results are general, so one can use a different solute probe sensitive to proton binding to characterize subtle changes in soln. pH induced by the presence of another solute in soln. The authors discuss some of the broader implications of these measurements/results in terms of nucleic acid melting in multicomponent systems, in terms of probing counterion environments, and in terms of potential regulatory mechanisms. (c) 2001 Academic Press.
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49. 49
  Philips, R. (1966) Adenosine and the adenine nucleotides. Ionization, metal complex formation, and conformation in solution Chem. Rev. 66, 501– 527
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  Sigel, H. (1993) Interactions of metal ions with nucleotides and nucleic acids and their constituents Chem. Soc. Rev. 22, 255– 267
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  Interactions of metal ions with nucleotides and nucleic acids and their constituents
  Sigel, Helmut
  Chemical Society Reviews (1993), 22 (4), 255-67CODEN: CSRVBR; ISSN:0306-0012.
  A review, with 86 refs. Nucleotides, due to their ambivalent properties towards metal ions, are a true challenge to coordination chemists. A metal ion may interact with the phosphate group(s), the sugar moiety, and the base residue of a nucleotide. Moreover, such a base residue itself is already ambivalent; e.g., an adenine residue offers to a metal ion the N-1, N-3, and N-7 sites for binding. It is the aim of this overview briefly to elucidate the binding properties of the various mentioned constituents and to consider 'recognition reactions' of nucleotides and nucleic acids. Which properties govern selectivity in nature.
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51. 51
  Pecoraro, V. L., Hermes, J. D., and Cleland, W. W. (1984) Stability constants of Mg²⁺ and Cd²⁺ complexes of adenine nucleotides and thionucleotides and rate constants for formation and dissociation of MgATP and MgADP Biochemistry 23, 5262– 5271
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  51
  Stability constants of magnesium and cadmium complexes of adenine nucleotides and thionucleotides and rate constants for formation and dissociation of magnesium-ATP and magnesium-ADP
  Pecoraro, Vincent L.; Hermes, Jeffrey D.; Cleland, W. W.
  Biochemistry (1984), 23 (22), 5262-71CODEN: BICHAW; ISSN:0006-2960.
  Stability consts. for the Mg2+ and Cd2+ complexes of ATP, ADP, ATPαS, ATPβS, and ADPαS (where ATPαS, ATPβS, and ADPαS are nucleotides substituted with S on the indicated phosphate group) were detd. at 30° and μ = 0.1M by 31P NMR. In addn. to being of the utmost importance for detg. species distributions for enzymic studies, these consts. allow an estn. of the dependence of Cd2+ for S vs. O coordination in phosphorothioate complexes. Stability consts. for Mg2+ complexes decrease when S replaces O (log K: ADP, 4.11; ADPαS, 3.66; ATP, 4.70; ATPαS, 4.47; ATPβS, 4.04) because of (1) a statistical factor resulting from the loss of one potential phosphate O ligand and (2) either an alteration in the charge distribution between O and S or destabilization of the chelate ring structure by loss of an internal H-bond between an O of coordinated phosphate and metal-bound H2O. Cd2+ complexes with S-substituted nucleotides are more stable than those without S (log K: ADP, 3.58; ADPαS, 4.95; ATP, 4.36; ATPαS, 4.42; ATPβS, 5.44) because of the preferential binding of Cd3+ to S rather than O, which is estd. to be ∼60 in CdADPαS and CdATPβS. The proportion of tridentate coordination is estd. to be 50-60% in MgATP and MgATPβS, ∼27% in MgATPαS, ∼16% in CdATP or CdATPβS, but ∼75% in CdATPαS. By anal. of the data of E. J. Jaffe and M. Cohn (1979), it is concluded that the preference for O over S coordination to ATPβS is 31,000 for Mg2+, 3100-3900 for Ca2+, and 158-193 for Mn2+. 1H NMR demonstrates that bidentate Cd2+ complexes form intramol. chelates with the N-7 atom of adenine, whereas Mg2+ nucleotides and the tridentate CdATPαS do not. An anal. of the 31P NMR line-widths shows that the rate consts. for dissocn. of MgADP and MgATP are both 7000 s-1, whereas the assocn. rate consts. are 7 × 107 and 4 × 108 M-1 s-1, resp. The obsd. dependence of the line width on nucleotide concn. is best explained by a base-stacking model at nucleotide concns. of >5 mM.
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52. 52
  Hudson, R. H. E., Uddin, A. H., and Damha, M. J. (1995) Association of branched nucleic acids: structural and physicochemical analysis of antiparallel T•AT triple-helical DNA J. Am. Chem. Soc. 117, 12470– 12477
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  Association of branched nucleic acids: structural and physicochemical analysis of antiparallel T·AT triple-helical DNA
  Hudson, Robert H. E.; Uddin, Andre H.; Damha, Masad J.
  Journal of the American Chemical Society (1995), 117 (50), 12470-7CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  The authors report the first example of a stable triple-stranded helix consisting of exclusively T·AT (reverse-Hoogsteen·Watson-Crick) base triplets. The orientation of the third (T) strand in this triplex is anti-parallel with respect to the purine strand of the underlying duplex. Previous studies have examd. the formation of these "antiparallel" T·AT triplets within a G·GC-rich environment; however, the present study demonstrates that G·GC triplets are not a requirement. The approach to induce and stabilize the antiparallel triplex involves the use of a branched oligonucleotide with two parallel dT10 strands joined to riboadenosine via 2'-5' and 3'-5' phosphodiester linkages, i.e., rA[2'-5'-dT10]3'-5'-dT10. This triplex was further stabilized by MgCl2 or NaCl at neutral pH. Triple helix formation by branched oligonucleotide 1 and dA10 was investigated by thermal denaturation anal. and CD spectroscopy. The melting curves at 260 and 284 nm show a single transition from bound to unbound species, indicative of cooperative melting. A linear oligonucleotide with a loop made of four dC residues between two dT10 strands, and with a 5'-5'-phosphodiester linkage at one of the C/T10 junctions, i.e., 3'-dT10C4-5'-5'-dT10-3', did not form a similar triple helical structure. This result shows that the conformational rigidity imparted to the pyrimidine strands, by the branch point in 1, serves to preorganize and stabilize the complex. Potassium ions inhibited triplex helix formation. In accord with what has been demonstrated previously for "parallel" Py·PuPy (Hoogsteen-Watson-Crick) triplexes, the authors show that short oligoadenylates (i.e., dA4 and dA5) can bind cooperatively to the branched oligomer 1. The triplex-inducing capacity of branched oligonucleotides has potentially important implications in the study of intramol. triplexes that occur in vivo.
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53. 53
  Rose, D. M., Bleam, M. L., Record, M. T., Jr., and Bryant, R. G. (1980) ²⁵Mg NMR in DNA solutions: dominance of site binding effects Proc. Natl. Acad. Sci. U.S.A. 77, 6289– 6292
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  Magnesium-25 NMR in DNA solutions: Dominance of site binding effects
  Rose, D. Murk; Bleam, M. L.; Record, M. T., Jr.; Bryant, R. G.
  Proceedings of the National Academy of Sciences of the United States of America (1980), 77 (11), 6289-92CODEN: PNASA6; ISSN:0027-8424.
  25Mg NMR spectroscopy is applied to a study of Mg2+ interactions with DNA, which is considered as a model for a linear polyelectrolyte. The Mg2+ spectrum is complicated by a non-Lorentzian lineshape and is dominated by the effects of chem. exchange with macromol.-binding sites. A distinction is made between specific-site interactions in which Mg2+ loses a H2O mol. from the 1st coordination sphere on binding and those interactions, referred to as territorial binding, in which the ion maintains its 1st coordination sphere complement of solvent. The 1st type of site-binding interactions dominates the 25Mg NMR spectrum, based on a consideration of the magnitudes of the obsd. 25Mg relaxation rates compared with 23Na relaxation rates, the clear contributions of chem. exchange-limited relaxation, and an ion-displacement expt. employing Na+.
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54. 54
  Ma, C. and Bloomfield, V. A. (1995) Gel electrophoresis measurement of counterion condensation on DNA Biopolymers 35, 211– 216
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  Gel electrophoresis measurement of counterion condensation on DNA
  Ma, Chenglie; Bloomfield, Victor A.
  Biopolymers (1995), 35 (2), 211-16CODEN: BIPMAA; ISSN:0006-3525. (Wiley)
  We used agarose gel electrophoresis to measure the effective charge neutralization of DNA of counterions of different structure and valence, including Na+, Mg2+, Co(NH3)63+ and spermidine3+, which competed for binding with an excess of Tris acetate buffer. Linear DNA molecules ranged in size from 1 to 5 kilobases, and supercoiled plasmid pUC18 was also measured. In all cases, the results were in good agreement with theor. predictions from counterion condensation theory for two-counterion mixts.
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55. 55
  Cowan, J. A., Huang, H.-W., and Hsu, L. Y. (1993) Sequence selective coordination of Mg²⁺(aq) to DNA J. Inorg. Biochem. 52, 121– 129
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  Sequence selective coordination of magnesium (aq) to DNA
  Cowan, J. A.; Huang, H. W.; Hsu, L. Y.
  Journal of Inorganic Biochemistry (1993), 52 (2), 121-9CODEN: JIBIDJ; ISSN:0162-0134.
  Thermodn. parameters for magnesium binding to a series of DNA mols. of defined sequence have been evaluated by 25Mg NMR spectroscopy. These results demonstrate that G/C-DNA binds Mg2+ (aq) up to 40 to 100-fold more strongly than A/T-DNA, i.e., coordination of Mg2+(aq) to G/C-DNA is ca. 2.1-2.7 kcal (mole Mg2+)-1 more stable relative to A/T-DNA. Activation free energies [ΔG* ∼(12.7-13.3) × 103 kcal] and exchange rates [kex ∼(0.5-3.0) × 103s-1] were estd. by variable temp. expts. The low value of the quadrupole coupling consts. (χB = 0.2-0.6 MHz) is indicative of outer-sphere coordination by Mg(H2O)62+.
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56. 56
  Buckin, V. A., Kankiya, B. I., Rentzeperis, D., and Marky, L. A. (1994) Mg²⁺ recognizes the sequence of DNA through its hydration shell J. Am. Chem. Soc. 116, 9423– 9429
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  Mg2+ recognizes the sequence of DNA through its hydration shell
  Buckin, Vitaly A.; Kankiya, B. I.; Rentzeperis, Dionisios; Marky, Luis A.
  Journal of the American Chemical Society (1994), 116 (21), 9423-9CODEN: JACSAT; ISSN:0002-7863.
  The authors have studied the interaction of Mg2+ with six deoxyoctanucleotide duplexes of known sequence. Specifically, the authors have measured the resulting hydration changes by following the change in the concn. increment of ultrasonic velocity, δA, of each of these six duplexes, in their Cs+ salt at 1.2°, during a course of a titrn. with Mg2+. The addn. of Mg2+ results in the initial lowering of δA that levels off at [Mg2+]/[Pi] molar ratios ranging from 12 to 30, depending on the duplex, and corresponds to a dehydration event from the exchange of Cs+ counterions by Mg2+ in the ionic atm. of the duplexes. This is followed by a further lowering of δA at higher [Mg2+]/[Pi] ratios that may result from DNA aggregation and/or conformational change. The authors obtained a change in the molar concn. increment of ultrasonic velocity per mol of bound Mg2+, ΔAMg2+, and binding affinities, Kapp, ranging from -4.4 cm3 mol-1 and 150 M-1 for d(A)8·d(T)8 and -18 cm3 mol-1 and 40 M-1 for [d(CG)4]2, resp., by fitting the first portion of each titrn. curve and assuming an overall binding of 0.5 Mg2+ per phosphate. Thus, the overall magnitude of the dehydration effect, which is detd. by the structure of the Mg2+-DNA complex, and the Kapp are functions of the DNA sequence. Furthermore, the dehydration effect of Mg2+ binding correlates with the hydration state of the DNA: the higher its hydration state, the lower the dehydration effect of Mg2+ binding is. Mg2+ recognizes the sequence of DNA through its overall hydration state, probably by forming mostly outer-sphere complexes with oligomers contg. exclusively dA·dT base pairs and inner-sphere complexes with dG·dC oligomers.
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57. 57
  Black, C. B. and Cowan, J. A. (1994) Quantitative evaluation of electrostatic and hydrogen-bonding contributions to metal cofactor binding to nucleic acids J. Am. Chem. Soc. 116, 1174– 1178
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  Quantitative Evaluation of Electrostatic and Hydrogen-Bonding Contributions to Metal Cofactor Binding to Nucleic Acids
  Black, C. B.; Cowan, J. A.
  Journal of the American Chemical Society (1994), 116 (4), 1174-8CODEN: JACSAT; ISSN:0002-7863.
  The binding free energy (ΔGb) of a hydrated alkali or alk. earth ion to double-strand nucleic acids is dominated by electrostatic (ΔGes) and hydrogen-bonding (ΔGhb) contributions. The authors have estd. the relative magnitudes of these two terms by use of metal complexes of defined charge and hydrogen-bonding capability. A strategy is described where ΔGb for Mn+(aq) is compared with values obtained from substitutionally-inert cobaltic-ammine complexes of similar charge ([Co(NH3)6-zXz]n+, X = NH3, NO2-). Values for the latter are dominated by the electrostatic term, and so ΔGhb can be detd. by direct comparison with the hydrated Mg2+(aq) or Na+(aq) ion of equiv. charge. Apparent binding affinities (Ka, M-1) for a series of aquated metal ions (Mg2+(aq), Na+(aq)) and cobalt coordination complexes (Co(NH3)63+, [Co(NH3)5NO2]2+, [Co(NH3)4(NO2)2]+) to B- and A-configuration nucleic acids have been detd. in 20 mM Tris (pH 7.0) by NMR line-shape anal. and the neighbor exclusion model of McGhee-von Hippel. B-conformer nucleic acids: [Co(NH3)6]3+, 14 800 M-1; [Co(NH3)5NO2]2+, 1500 M-1; [Co(NH3)4(NO2)2]+, 20 M-1; Mg2+(aq), 12 800 M-1; Na+(aq), 150 M-1. A-conformer nucleic acids: [Co(NH3)6]3+, 4200 M-1; [Co(NH3)5NO2]2+, 250 M-1; [Co(NH3)4(NO2)2]+, undetd.; Mg2+(aq), 2500 M-1; Na+(aq), 8 M-1. Individual contributions from electrostatic attraction and hydrogen bonding have been evaluated and found to be additive for each specific configuration. The results are consistent with the expectations of polyelectrolyte theory. Stronger binding to B-conformers results from electrostatic terms, while the contribution from hydrogen bonding is apparently conformation independent. Variable temp. expts. demonstrate that the main factor dictating the exchange region for bound and free metal species derives from extensive hydrogen bonding to the polynucleotide.
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  Gessner, R. V., Quigley, G. J., Wang, A. H.-J., van der Marel, G. A., van Boom, J. H., and Rich, A. (1985) Structural basis for stabilization of Z-DNA by cobalt hexaammine and magnesium cations Biochemistry 24, 237– 240
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  Structural basis for stabilization of Z-DNA by cobalt hexaammine and magnesium cations
  Gessner, Reinhard V.; Quigley, Gary J.; Wang, Andrew H. J.; Van der Marel, Gijs A.; Van Boom, Jacques H.; Rich, Alexander
  Biochemistry (1985), 24 (2), 237-40CODEN: BICHAW; ISSN:0006-2960.
  In the equil. between B-DNA and Z-DNA in poly(dC-dG), [Co(NH3)6]3+ stabilizes the Z form 4 orders of magnitude more effectively than does Mg2+. The structural basis of this difference is revealed in Z-DNA crystal structures of d(CpGpCpGpCpG) stabilized by either Na+/Mg2+ or Na+/Mg2+ plus [Co(NH3)6]3+. The crystals diffract x-rays to high resoln., and the structures were refined at 1.25 Å. [Co(NH3)6]3+ forms 5 H bonds on the surface of Z-DNA, bonding to a guanine O6 and N7 as well as to a phosphate group in the ZII conformation. The Mg2+ ion binds through its hydration shell with ≤3 H bonds to guanine N7 and O6. Higher charge, specific fitting of more H bonds, and a more stable complex all contribute to the great effectiveness of [Co(NH3)6]3+ in stabilizing Z-DNA.
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  Sines, C. C., McFail-Isom, L., Howerton, S. B., VanDerveer, D., and Willimas, L. D. (2000) Cation mediate B-DNA conformational heterogeneity J. Am. Chem. Soc. 122, 11048– 11056
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  Cations Mediate B-DNA Conformational Heterogeneity
  Sines, Chad C.; McFail-Isom, Lori; Howerton, Shelley B.; VanDerveer, Don; Williams, Loren Dean
  Journal of the American Chemical Society (2000), 122 (45), 11048-11056CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  We demonstrate that DNA conformation is sensitive to cationic environment. We describe a high resoln. (1.2 Å) potassium form of CGCGAATTCGCG, detd. from crystals grown in the presence of spermine and magnesium, along with potassium. The structure was refined with anisotropic displacement-factors by SHELX-97 to an R-factor of 13.9%. A comparison of this structure with others, reveals that the conformation of CGCGAATTCGCG varies in direct response to cation type and position. The DNA conformation in the presence of excess magnesium differs from the conformation in the presence of excess spermine. Divalent cations near the minor groove sequester into the lip, which is the region between opposing phosphate groups. Minor groove width is sensitive to, and can be predicted by, cation positions. It appears that minor groove narrowing is facilitated by interactions of cations with opposing phosphate groups.
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  Blagoi, Y. U. P., Sorokin, V. A., Valeyev, V. A., Khomenko, S. A., and Gladchenko, G. O. (1978) Magnesium ion effect on the helix-coil transition of DNA Biopolymers 17, 1103– 1118
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  Magnesium ion effect on the helix-coil transition of DNA
  Blagoi, Yu. P.; Sorokin, V. A.; Valeev, V. A.; Khomenko, S. A.; Gladchenko, G. O.
  Biopolymers (1978), 17 (5), 1103-18CODEN: BIPMAA; ISSN:0006-3525.
  The effect of Mg2+ on the parameters of the DNA helix-coil transition was studied for the concn. range 10-6-10-1M at an ionic strength of 10-3M Na+. Binding with Mg2+ increased the DNA stability, the effect being obsd. mainly in the concn. range 10-6-10-4M. At a Mg2+ concn. of >10-2M the thermal stability of DNA started to decrease. The melting range extended to concns. ∼10-5M and then decreased to 7-8° at the ion content of 10-3M. Asymmetry of the melting curves was obsd. at low ionic strengths ([Na+] = 10-3M and [Mg2+] ≤10-5M). The results, analyzed in terms of the statistical thermodn. theory of double-stranded homopolymers melting in the presence of ligands, suggest that the effects obsd. might be due to the ion redistribution from denatured to native DNA. An exptl. DNA-Mg2+ phase diagram was obtained which is in good agreement with the theory. Thermal denaturation of the system may be an efficient method for detg. the ion-binding consts. for both native and denatured DNA.
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  Annual Review of Physical Chemistry (1995), 46 (), 657-700CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews)
  A review, with 151 refs. Coulombic interactions of salt ions with polymeric and oligomeric nucleic acids in soln. have large and distinctive effects on ion distributions, on thermodn. coeffs., and hence on equil. processes involving nucleic acids, such as their conformational transitions and binding interactions. In exptl. or theor. studies where an oligonucleotide is taken to represent the corresponding polynucleotide, the impact of Coulombic end effects on mol. and thermodn. properties. must be taken into account. Observable consequences of Coulombic interactions in nucleic acid solns. have been calcd. by using models with varying degrees of detail and methods formulated at varying levels of rigor. From comparisons of exptl. results with predictions of the prevalent methods have proved capable of accounting for thermodn. (and some mol.) consequences of Coulombic interactions with a minimal no. of preaveraged parameters that represent the most important structural features of the nucleic acid soln.
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  Shkel, I. A. and Record, M. T., Jr (2004) Effect of the number of nucleic acid oligomer charges on the salt dependence of stability (ΔG°₃₇) and melting temperature (T_m): NLPB analysis of experimental data Biochemistry 43, 7090– 7101
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  Effect of the Number of Nucleic Acid Oligomer Charges on the Salt Dependence of Stability (ΔG°37) and Melting Temperature (Tm): NLPB Analysis of Experimental Data
  Shkel, Irina A.; Record, M. Thomas, Jr.
  Biochemistry (2004), 43 (22), 7090-7101CODEN: BICHAW; ISSN:0006-2960. (American Chemical Society)
  For nucleic acid oligomers with variable chain lengths, the salt concn. ([salt]) dependences of the denaturation temp. (Tm) and of the free energy of helix formation at 37° (ΔG°37) are predicted using nonlinear Poisson-Boltzmann (NLPB) calcns. Anal. of exptl. data reveals that the ratio of the [salt] deriv. of melting temp. (STm = dTm/d log[salt]) to the value for a polymer with the same base compn. (STm/STm,∞) is independent of base compn. but strongly dependent on the no. of DNA charges (|Z|) below ∼8 bp for two-strand helixes (formed from assocn. of two complementary strands) and below ∼18 bp for hairpin helixes (formed from folding of one self-complementary strand). The authors interpret these STm/STm,∞ ratios in terms of the ratio of thermodn. ion release from the oligomer (Δnu, per charge) to that from the same oligomer embedded in polymeric DNA (Δnu,∞, per charge). Exptl. values of STm/STm,∞ and its dependence on |Z| are in good agreement with NLPB predictions for a preaveraged (essential structural) model of DNA. In particular, the NLPB calcns. describe the stronger |Z| dependence of STm obsd. for melting of oligomeric hairpin helixes than for melting of two-strand helixes. These calcns. predict an exptl. detectable (≥ 10%) difference between STm and STm,∞ which increases strongly with decreasing length for two-strand helix lengths of <15 bp and for hairpin helix lengths of <30 bp. From NLPB values of Δnu/Δnu,∞, the authors predict ΔG°37 as a function of [salt] and |Z|. Predictions of thermodn. and thermal stabilities of oligomeric helixes as functions of length and [salt] are consistent with and represent a significant refinement of the av. oligomer salt effect currently in use in nearest neighbor stability predictions.
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  Elson, E. L., Scheffler, I. E., and Baldwin, R. L. (1970) Helix formation by d(TA) oligomers. III. Electrostatic effects J. Mol. Biol. 54, 401– 415
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  Elson, Elliot L.; Scheffler, Immo E.; Baldwin, Robert L.
  Journal of Molecular Biology (1970), 54 (3), 401-15CODEN: JMOBAK; ISSN:0022-2836.
  Expts. with d(TA)n hairpin helices are reported which contradict the simple Ising (or nearest-neighbor interactions) model for the DNA helix-coil transition at low or moderate counterion concns. First the dependence of Tm(n) on lot M (where M is monovalent counterion molarity) falls off sharply with decreasing n in the range 8 ≤ n ≤ 22, so that the set of melting curves is compressed into a narrow temp. range at low M. At M = 0.0028, d(TA)20 has a higher Tm than poly d(AT) and the Tm of d(TA)9 is only slightly lower. Electrostatic interactions have a relatively small effect on the breadths of these melting curves: the curves for all oligomers sharpen slightly as the counterion concn. is reduced. Where zp is the effective charge per phosphate group and D is the effective dielec. const., the melting curves for all oligomers can be represented for all values of M by a single value of zp2/D; it is necessary to count interactions between charges both in the helix and in adjoining nonhelical segments.
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  Rouzina, I. and Bloomfield, V. A. (1997) Competitive electrostatic binding of charged ligands to polyelectrolytes: practical approach using the non-linear Poisson-Boltzmann equation Biophys. Chem. 64, 139– 155
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  Rouzina, Ioulia; Bloomfield, Victor A.
  Biophysical Chemistry (1997), 64 (1-3), 139-155CODEN: BICIAZ; ISSN:0301-4622. (Elsevier)
  We have developed a practical anal. treatment of the non-linear Poisson-Boltzmann (P-B) equation to characterize the strong but non-specific binding of charged ligands to DNA and other highly charged macromols. These reactions are notable for their strong salt dependence and anti-cooperativity, features which the theory fully explains. We summarize anal. results for concn. profiles and ion binding in various regimes of surface curvature and ionic strength, and show how counterion size and charge distribution may influence competitive binding. We present several practical applications of the formalism, showing how to est. the ligand concn. needed to effectively compete with a given buffer salt, and how to calc. the amts. of counterion species bound at various distances from the DNA surface under given bulk soln. conditions. We cast our results into the form of a Scatchard binding isotherm, showing how the apparent binding const. Kobs and S = -d log Kobs/d log [M+] can be predicted from the basic theory. Anti-cooperativity arises naturally without steric repulsion, and binding curves can be fitted with Kobs and effective charge as the only free parameters. We extend the anal. P-B anal. to an arbitrary no. of counterion species, and apply the results to fit and predict three-ion competition data.
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  Bacquet, R. J. and Rossky, P. J. (1988) Ionic distributions and competitive association in DNA/mixed salt solutions J. Phys. Chem. 92, 3604– 3612
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  Ionic distributions and competitive association in DNA/mixed salt solutions
  Bacquet, Russell J.; Rossky, Peter J.
  Journal of Physical Chemistry (1988), 92 (12), 3604-12CODEN: JPCHAX; ISSN:0022-3654.
  The hypernetted chain integral equation is used to study ionic distributions near a simple model of DNA in aq. mixts. of NaCl and MgCl2. A wide range of both relative and abs. concns. of the salts is considered, including cases where only one salt is present. In dil. systems (low ionic strength), the soln. compn. near the polyion is more responsive to changes in the bulk soln. compn., and competition by the divalent counterions is more effective. It is found that for reasonable definitions of the polyion vicinity the displacement of Na+ by Mg2+ in this region is approx. 1 for 1, with a corresponding increase in the degree of polyion neutralization at short range, with increasing Mg2+ concn. in the bulk. Calcd. ests. of mean-square elec. field gradients experienced by Na nuclei in these solns. manifest a very good correlation with measured NMR line width, indicating that the obsd. structural phenomena are realistically described.
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  SantaLucia, J., Jr (1998) A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics Proc. Natl. Acad. Sci. U.S.A. 95, 1460– 1465
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  A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics
  Santalucia, John, Jr.
  Proceedings of the National Academy of Sciences of the United States of America (1998), 95 (4), 1460-1465CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
  A unified view of polymer, dumbbell, and oligonucleotide nearest-neighbor (NN) thermodn. is presented. DNA NN ΔG37° parameters from seven labs. are presented in the same format so that careful comparisons can be made. The seven studies used data from natural polymers, synthetic polymers, oligonucleotide dumbbells, and oligonucleotide duplexes to derive NN parameters; used different methods of data anal.; used different salt concns.; and presented the NN thermodn. in different formats. As a result of these differences, there has been much confusion regarding the NN thermodn. of DNA polymers and oligomers. Herein I show that six of the studies are actually in remarkable agreement with one another and explanations are provided in cases where discrepancies remain. Further, a single set of parameters, derived from 108 oligonucleotide duplexes, adequately describes polymer and oligomer thermodn. Empirical salt dependencies are also derived for oligonucleotides and polymers.
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67. 67
  Stellwagen, E., Dong, Q., and Stellwagen, N. C. (2007) Quantitative analysis of monovalent counterion binding to random-sequence, double-stranded DNA using the replacement ion method Biochemistry 46, 2050– 2058
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  Quantitative Analysis of Monovalent Counterion Binding to Random-Sequence, Double-Stranded DNA Using the Replacement Ion Method
  Stellwagen, Earle; Dong, Qian; Stellwagen, Nancy C.
  Biochemistry (2007), 46 (7), 2050-2058CODEN: BICHAW; ISSN:0006-2960. (American Chemical Society)
  A variation of affinity capillary electrophoresis, called the replacement ion (RI) method, has been developed to measure the binding of monovalent cations to random sequence, double-stranded (ds) DNA. In this method, the ionic strength is kept const. by gradually replacing a nonbinding ion in the soln. with a binding ion and measuring the mobility of binding and nonbinding analytes as a function of binding ion concn. The method was validated by measuring the binding of Li+ ions to adenosine nucleotides; the apparent dissocn. consts. obtained by the RI method are comparable to literature values obtained by other methods. The binding of Tris+, NH4+, Li+, Na+, and K+ to dsDNA was then investigated. The apparent dissocn. consts. obsd. for counterion binding to a random-sequence 26-base pair (bp) oligomer ranged from 71 mM for Tris+ to 173 mM for Na+ and K+. Hence, pos. charged Tris buffer ions will compete with other monovalent cations in Tris-buffered solns. The bound cations identified in this study may correspond to the strongly correlated, tightly bound ions recently postulated to exist as a class of ions near the surface of dsDNA (Tan, Z.-J., and Chen, S.-J., 2006). Monovalent cation binding to random-sequence dsDNA would be expected to occur in addn. to any site-specific binding of cations to A-tracts or other DNA sequence motifs. Single-stranded DNA oligomers do not bind the five tested cations under the conditions investigated here.
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68. 68
  Bai, Y., Greenfeld, M., Travers, K. J., Chu, V. B., Lipfert, J., Doniach, S., and Herschlag, D. (2007) Quantitative and comprehensive decomposition of the ion atmosphere around nucleic acids J. Am. Chem. Soc. 129, 14981– 14988
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  68
  Quantitative and Comprehensive Decomposition of the Ion Atmosphere around Nucleic Acids
  Bai, Yu; Greenfeld, Max; Travers, Kevin J.; Chu, Vincent B.; Lipfert, Jan; Doniach, Sebastian; Herschlag, Daniel
  Journal of the American Chemical Society (2007), 129 (48), 14981-14988CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  The ion atm. around nucleic acids critically affects biol. and phys. processes such as chromosome packing, RNA folding, and mol. recognition. However, the dynamic nature of the ion atm. renders it difficult to characterize. The basic thermodn. description of this atm., a full accounting of the type and no. of assocd. ions, has remained elusive. Here we provide the first complete accounting of the ion atm., using buffer equilibration and at. emission spectroscopy (BE-AES) to accurately quantitate the cation assocn. and anion depletion. We have examd. the influence of ion size and charge on ion occupancy around simple, well-defined DNA mols. The relative affinity of monovalent and divalent cations correlates inversely with their size. Divalent cations assoc. preferentially over monovalent cations; e.g., with Na+ in 4-fold excess of Mg2+ (20 vs. 5 mM), the ion atm. nevertheless has 3-fold more Mg2+ than Na+. Further, the dicationic polyamine putrescine2+ does not compete effectively for assocn. relative to divalent metal ions, presumably because of its lower charge d. These and other BE-AES results can be used to evaluate and guide the improvement of electrostatic treatments. As a first step, we compare the BE-AES results to predictions from the widely used nonlinear Poisson Boltzmann (NLPB) theory and assess the applicability and precision of this theory. In the future, BE-AES in conjunction with improved theor. models, can be applied to complex binding and folding equil. of nucleic acids and their complexes, to parse the electrostatic contribution from the overall thermodn. of important biol. processes.
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Additional sets of T_m values used to develop and validate new magnesium correction, results of DSC and CD experiments, nearest-neighbor model of T_m magnesium correction and Δn calculations for duplexes that melt in non-two-state fashion. This material is available free of charge via the Internet at http://pubs.acs.org. Further, the database of average melting profiles, fraction of melted base pairs versus temperature, is available at http://biophysics.idtdna.com/Paper7/Abstract7.html.
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Predicting Stability of DNA Duplexes in Solutions Containing Magnesium and Monovalent Cations

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Abstract

Materials and Methods

DNA Oligonucleotides

UV Melting Studies

Differential Scanning Calorimetry (DSC)

Statistical Analysis of Tm Predictions

Results

Effects of Buffer pH on Melting Temperature

Figure 1

Comparison of DNA Duplex Stability in Na+ and K+ buffers

Figure 2

Previously Published Tm Magnesium Corrections

Figure 3

Magnesium Ions and DNA Melting Temperatures

Figure 4

Figure 5

Figure 6

Accuracy and Limitations of the New Tm Magnesium Correction

Deoxynucleoside Triphosphates Decrease Effects of Magnesium Ions

Figure 7

Competition between Magnesium and Monovalent Ions in Duplex Stabilization

Figure 8

Figure 9

Example of Calculations Using the New Tm Magnesium Correction

Discussion

Binding of Magnesium Cations to Single Stranded versus Double Stranded DNA

Figure 10

Competitive Behavior of Monovalent and Magnesium Cations

Effects of Magnesium Ions on Transition Enthalpies, Entropies and Free Energies

Implications for PCR and DNA Sequencing

Supporting Information

Terms & Conditions

Acknowledgment

References

Cited By

Abstract

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

References

Supporting Information

Supporting Information

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Statistical Analysis of T_m Predictions

Comparison of DNA Duplex Stability in Na⁺ and K⁺ buffers

Previously Published T_m Magnesium Corrections

Accuracy and Limitations of the New T_m Magnesium Correction

Example of Calculations Using the New T_m Magnesium Correction