Buffer and Salt Effects in Aqueous Host–Guest Systems: Screening, Competitive Binding, or Both?

There are many open questions regarding the supramolecular properties of ions in water, a fact that has ramifications within any field of study involving buffered solutions. Indeed, as Pielak has noted (Buffers, Especially the Good Kind, Biochemistry, 2021, in press. DOI:10.1021/acs.biochem.1c00200) buffers were conceived of with little regard to their supramolecular properties. But there is a difficulty here; the mathematical models supramolecular chemists use for affinity determinations do not account for screening. As a result, there is uncertainty as to the magnitude of any screening effect and how this compares to competitive salt/buffer binding. Here we use a tetra-cation cavitand to compare halide affinities obtained using a traditional unscreened model and a screened (Debye–Hückel) model. The rule of thumb that emerges is that if ionic strength is changed by >1 order of magnitude—either during a titration or if a comparison is sought between two different buffered solutions—screening should be considered. We also build a competitive mathematical model showing that binding attenuation in buffer is largely due to competitive binding to the host by said buffer. For the system at hand, we find that the effect of competition is approximately twice that of the effect of screening (∼RT at 25 °C). Thus, for strong binders it is less important to account for screening than it is to account for competitive complexation, but for weaker binders both effects should be considered. We anticipate these results will help supramolecular chemists unravel the properties of buffers and so help guide studies of biomacromolecules.

Electron Spray Ionization (ESI) MS sample procedure All samples were prepared as 20 μM concentration solutions in distilled H2O (dH2O). ESI-MS spectra acquisitions were acquired using a Bruker microTOF mass spectrometer in positive mode and generally averaged from 1.0-10.0 minutes. Ions were continuously generated by infusing the aqueous solution samples into the source with a syringe pump at flow rates of 6 µL/min. The parameters were adjusted and were typically as follows: capillary voltage (-4.1 kV); capillary exit voltage (70 V); skimmer voltage (40 V); drying gas temperature (200 °C). The experiments were carried out with a nebulizer gas pressure of 0.3 Bar and a drying gas flow of 4.0 L/min. Nuclear Magnetic Resonance (NMR) Spectroscopy solution preparation procedure All solutions were prepared in unbuffered D2O or phosphate buffered D2O as described in the individual sections. All titrations of host were carried out with ~0.4 mM host solutions prepared from a concentrated stock of ~2 mM; the concentration of the stock solution was determined by titration in triplicate with separate 25 mM sodium ethanesulfonate (SES) solutions, and integration of the methyl peak of ethanesulfonate and the Hm and Hl peak of the host. A concentrated salt solution between 10-500 mM was prepared for use in each titration. The pD of the solutions was uncorrected for titrations in unbuffered D2O and adjusted, if necessary, during dilution for titrations using phosphate buffer. For 1 H NMR spectroscopy titration experiments, 0.5 mL of host solution in an NMR tube was careful titrated with small aliquots of the corresponding sodium salt of the anionic guest.

Errors
Results are expressed as the average, when possible, with the coefficient of variation (CV) expressed as a percentage of the mean when applicable, where s is the sample standard deviation and μ is the sample mean i.e.: 100 %= µ s CV

Reagents and conditions: i) HCl / MeOH
The general synthetic scheme for the synthesis of receptor 1 is shown in Scheme S1. The synthesis and characterization of resorcinarene 2 was reported previously. 1 Subsequent bridging of the phenolic oxygens gives tetra-halide 3 (X = Cl & Br) in ~20 % yield. The yield for this reaction was calculated assuming formation of the dibromo-dichloro cavitand. For this product, 1 H NMR and COSY NMR spectroscopy ( Figure S1 & Figure S2, respectively) revealed two sets of methylene resonances corresponding to the situation whereby the feet/pendant groups are partially brominated or chlorinated. The substitution by bromide is the result of the utilization of bromochloromethane for bridging. Addition of NaBr to the bridging reaction resulted in increased amounts of brominated product, but irrespective of this modification separation of the different chlorinated/brominated products was not possible. The carbon atoms attached to the chlorine or bromine functionality as well as the adjacent carbons could be readily distinguished by 13 C NMR spectroscopy ( Figure S3), while MALDI-TOF MS ( Figure S4 & Figure  S5) analysis of a sample shows the presence of one (m/z = 884), two (m/z = 928), three (m/z = 972), or four (m/z = 1016) bromine atoms in the structure. Integration of the peaks in the 1 H NMR spectrum ( Figure S6) associated with the methylenes one or two bonds adjacent to the halogen substituents revealed there are 3.4 ± 0.1 hydrogens corresponding to a chlorinated terminal atom and 4.6 ± 0.1 hydrogens corresponding to a bromine as the terminal atom. This effectively represents the case whereby there are 1.60 -1.75 chlorine atoms per molecule and 2.25 -2.40 bromines. These numbers were supported by elemental analysis.

Derivation of unscreened and screened (Debye-Hückel) Models
A. Derivation of screened reaction mode Here we describe the derivation of the host/guest binding equilibrium expressions for both the unscreened and screened processes. As thermodynamics mandates, equilibrium is determined by minimization of the Gibbs free energy at constant temperature and pressure. To begin, we consider the partial molar Gibbs free energies of the species dissolved in water from which we can construct the total Gibbs free energy of the system. The partial molar Gibbs free energy of a solute ( ) in dilute solution can be written as: where ̅ ! " is the free energy of the solute measured at the reference concentration " , and RT is the product of the gas constant and absolute temperature. Since this expression neglects added salts, this free energy corresponds to the solute free energy in an ideal unscreened solution. The addition of salts to solutions, however, is known to give rise to screened interactions between ions that leads to nonidealities that lower their free energies even in dilute solution. The dilute solution behavior of salts can be described by the Debye-Hückel limiting law, and modifies the partial molar Gibbs free energy for the screened electrolyte as: where " is the permittivity of free space, is the dielectric constant of the solvent, ! is the charge of , ! is the Born radius (the ion-excluding radius) of , and 0, is the Debye length describing the thickness of the counterion double layer that screens electrostatic interactions. The inverse Debye screening length is defined as: We note that the Debye-Hückel equation only applies below electrolyte concentrations of ~100 mM. Additionally, this theory best describes monovalent ions of similar size. Nevertheless, we expect the theory to semi-quantitively/qualitatively account for the impact of charge screening in host/guest binding. We subsequently use Debye-Hückel theory here to assess the magnitude of the effect of screening on measured binding free energies.
Following from the properties of partial molar thermodynamic quantities, the total Gibbs free energy of a mixture can be expressed as the sum: where is the number of components in the system, and ! is the number of moles of component . In the case of a cationic host ( 8-) / anionic guest ( -) binding event to make the complex :-, the free energy can be written as: where the subscripts and denote the solvent water and non-reacting sodium counterion, the superscript * indicates the initial mole numbers of a specified component, and indicates the extent of reaction in moles. The minus sign in front of for the components 8andis a result of them being 'consumed' during the binding reaction, while the positive sign in front of for :is a result of the complex being a product of the reaction. Minimizing the total Gibbs free energy with respect to yields the condition for reaction equilibrium as: While the partial molar Gibbs free energies are themselves dependent on , the sum of their derivatives (i.e., ∑ ) is zero as a result of the Gibbs-Duhem equation and therefore do not appear in the equilibrium condition above. In the case of the unscreened equilibrium, substituting the expressions for the partial molar Gibbs free energies of each component (Eq. (S1)) into the reaction equilibrium condition (Eq. (S6)) yields: Rearranging this expression, we obtain the unscreened reaction equilibrium product: corresponding to Eq. 5 in the main text. Here < -G," corresponds to the unscreened reaction equilibrium constant measure relative to the reference concentration " . If instead the full screened model expressions (eq. (S2)) for the partial molar Gibbs free energies are substituted into the reaction equilibrium condition (eq. (S6)), we get: Rearranging this expression, we obtain the screened reaction equilibrium product as: corresponding to Eq. (6) in the main text. Similar to the unscreened reaction, < -K," corresponds to the unscreened reaction equilibrium constant measure relative to the reference concentration " , and as such is determined by the same expression as for < -G," above. Screening by added electrolytes in Eq.
(S10), however, gives rise to < -K falling with increasing salt concentration, that is host/guest binding is weakened by screening. Given that the unscreened model does an excellent job at describing the experimental results, we expect the fitted values of < -K," will tend to be greater than < -G," so that once the screened model is fitted to the data the resultant concentration dependent values of < -K will be comparable to the < -G," . If < -G," and < -K," can be regarded as corresponding the free energies of host/guest binding in the absence of added solutes that can screen interactions, the question follows, by how much do < -G," and < -K," differ?
B. Fitting of screened reaction model to experimental data In difference to the unscreened model, the screened reaction equilibrium model is highly nonlinear as a result of the concentration dependence of the equilibrium constants as described by Eq. (S10). Specifically, since the values of depend on the equilibrium concentrations of all the species in solution (including sodium), an estimate of the distribution of bound and unbound hosts and guests must be made in order to evaluate < -K at every added guest concentration. Here we use an iterative approach to determine the concentrations of the charged species in solution. Our initial guess for these concentrations is made using the unscreened model. We then substitute the host, guest, and complex concentrations predicted by the unscreened model into Eq. (S10) to evaluate the concentration dependent < -K . These yield a new set of estimates for the distribution of reacting species in solution, which in turn can be substituted back into the screened model to evaluate new < -K 's. The procedure is iterated until the distribution of host, guest, and complex species converge to a stable set of concentrations, which subsequently are the equilibrium concentrations. Approximately 5 iterations are required to converge the solution within the accuracy of the Microsoft Excel spreadsheet used to solve these equations.

Analytical Data
A. NMR Titration data All solutions were prepared as described in the solution preparation procedures (Section 1.C). To determine guest affinity for host 1, 1 H NMR spectroscopy titrations were first conducted in unbuffered D2O and were performed on ~0.4 mM host from a concentrated stock of host typically prepared at ~2-4 mM. Dilution of the host solution during all titrations was kept below 10%. a. Determining the affinity of chloride to cavitand 1 Solutions of host 1 showed concentration dependent shifts in the peaks Hj and Hl ( Figure S15); however, this shift was not due to host aggregation. Rather, the 2D Diffusion Oriented Spectroscopy (DOSY) spectra of both a 0.5 mM and a 25 mM solution of 1 in D2O ( Figure S16 and Figure S17) revealed very similar diffusion coefficients: D = 2.79 × 10 -6 (Rh = 0.78 nm) and 2.64 × 10 -6 cm 2 s (Rh = 0.83 nm) respectively. This modest difference is within the expected error of ±10%. Thus, the presumed spherical host is monomeric at both concentrations. It is apposite to note that all 1 H NMR titrations in unbuffered D2O were relative to the tetra-chloride salt of the host. Figure S15 shows the result of an experiment whereby the concentration of host was incrementally increased from 0.25 mM concentration to 16 mM by the addition of aliquots of a concentrated stock solution (50 mM). Since the host remains monomeric during this "titration", the concentration dependent signal shifts observed are the result of increased Clcomplexation at higher concentrations of both species. As confirmation, monitoring the Δδ values for Hl and Hj of host 1 (see Scheme S1) as its concentration was increased gave essentially the same isotherm as titration of host 1 with NaCl (vide infra), when accounting for the concentration of the anion (e.g.  The NMR spectroscopy signal shifts obtained from the titration with NaCl were fitted by nonlinear regression analysis to the 1:1 binding stoichiometry model by Eq. S11 using either the solver in Excel in which Ht and Gt are the total amount of host and guest; fitting the experimentally derived binding isotherm for the change in signal shift Ddobs versus Gt yielded the remaining two unknowns, the binding constant (generic > ) and the maximal shift in the NMR signal (Ddmax). The following assumptions were made: (S12) since (S13) where [Gt] is the total guest concentration, [HG]crown is the concentration of the complex with the anion binding to the crown of four cationic groups of the cavitand, and [HGn]other is the (low) concentration of complexes arising from non-specific binding to the host. However, to accurately determine the affinity of the counterion of the host, one must consider its intrinsic counter anion. Take the case of 1 (counterion, Cl -), for example. Since there are four equivalents of (intrinsic) Clpresent at the start of the titration, the real initial point corresponding to the theoretical 1 H NMR signal from the chloride-free host (δ, ppm) is not known. Under normal circumstances (e.g., a neutral host), the initially observed NMR signal to be monitored (δobs) corresponds to the situation where the guest total Gt = 0. Since in the case here Gt ≠ 0, during titration the resulting maximum shift in the NMR signal (δmax) is lowered and the binding isotherm flattened, i.e., the observed binding constant reduced. Eq. S14 shows the effect the counterion has on δobs, where xH is the mole fraction of the free >> + host, δH is the signal (ppm) of the free host, χHG is the mole fraction of the host-guest complex, and δHG is the corresponding signal of the host-guest complex. If χHG = 0, then δobs = δH. Changes in δobs (Δδobs) are thus the result of changes associated with changes in δHG and are defined by (Eq. S15, the derivations of which have been discussed in more detail by Thordarsson: 5 δobs = χHδH + χHGδHG = (1-χHG)δH + χHGδHG (S14) Δδobs = ΔδHGχHG (S15) Therefore, to determine the binding affinity of Clto the host, the initial observed point of the titration was set to correspond to four equivalents of chloride, and the true (theoretical) δ value for the initial point corresponding to zero equivalents of chloride allowed to float when solving for Δδ in Eq. S11. This led to a binding isotherm that accounts for the presence of stoichiometric Clat the start of the titration, and an obtained value representing the actual affinity. The resulting isotherm from an independent (single peak) fitting of the titration data for Hj and Hl (for proton designations see Scheme S1) using Eq. S11 is shown in Figure S18, where the Δδmax for Hj is significantly larger than for Hl (0.276 vs 0.149 ppm). For both signals, the saturation of the curve and the obtained affinity values (316 M -1 vs 310 M -1 ) were identical and within error. Global (multiple peak) fitting ( Figure S19) was also applied so that large errors, resulting from situations where one or both peaks did not shift significantly (Δδmax < 0.05 ppm), could be mitigated. In the case at hand, as anticipated, global fitting of Hj and Hl was successful and had essentially no effect on the obtained affinity value of Cl -(315 M -1 ). Based on this result, global fitting was applied in all instances, with typically improved errors and reproducibility. 5,7 Data for the titration of sodium chloride to host 1 was collected from multiple experiments to give an average anion affinity of 290 ± 20 M -1 . A representative example titration is shown in Figure S20 and the corresponding BINDFIT isotherm and residuals plot in Figure S21.
An important observation during multiple titrations was that the change in pD of the unbuffered solutions used was less than ~0.4 pD units and fell between the values ~5.6 and ~6.8. As the pD of the solutions was largely unaffected by titration of salts to the host, and as host 1 contains no ionizable groups, the use of a buffer was not strictly necessary.

b. Determining the effect of the cations on chloride binding
To determine what effect the counter-cation had on anion complexation to host 1, titrations were also conducted with the chloride salts of lithium (Li + ), potassium (K + ), cesium (Cs + ) and tetramethyl ammonium ( + N(CH3)4) ( Figure S22-Figure S29). Titrations were conducted in (at least) triplicate. and in each instance data was fitted globally. The results ( %Q -G," , CV%, ΔG) are summarized in Table S1:      . Figure S27. Fit of the data for Hj and Hl from Figure S26    The obtained values for %Q -G," and the corresponding free energy were plotted against thermodynamic parameters of the corresponding chloride salts and are shown graphically in Figure S30. The difference between the enthalpy or free energy of hydration of the respective cation and the chloride anion (Cl -) were selected rather than individual physical or thermodynamic properties of the cations. In this scenario, interactions of the (solvated) cations with (solvated) Clare related to observable changes in the experimental responses (Ka and ΔG), or rather the strongest affinity is observed when the countercation is Na + , and the weakest with Li + . Figure S30. Experimentally determined 56 -7,9 and Δ 56 -7,9 plotted against thermodynamic parameters of the salt. a) plot of the difference in the enthalpy of hydration of cation and chloride anion (ΔHcation -ΔHchloride) against the Ka value obtained for chloride binding to host 1 as the chloride salt of the cation; b) plot of the difference in the free energy of hydration of the cation and chloride anion (ΔGcation -ΔGchloride) against the ΔG value obtained for chloride binding to host 1 with the respective counter-cation. Error bars refer to absolute error from at least three measurements. Thermodynamic parameters of the cations and chloride obtained from reference 9 .
c. Other halide affinity determinations to cavitand 1 When determining the affinity of other halides to the chloride salt of host 1, it needs to be noted that the titrating anion is in competition with the four intrinsic equivalents of chloride ions ( %Q -G," = 290 M -1 determined using NaCl). In these experiments titration with bromide (Br -), and iodide (I -) salts generally lead to large signal shifts (δmax) in Hj or Hl (Scheme S1) of the host. Smaller shifts were observed for fluoride (F -). A representative titration and binding isotherm for host 1 titrated with each of the halides (unbuffered D2O) is shown in Figure S31 - Figure S36.      For a competing (titrating) guest (X -) and the intrinsic chloride (Cl -) the mass balance for the competitive complexation model is defined by the total host concentration ([Ht]) and the total concentration of each of the guests ([X -]t and [Cl -]t), i.e., Eq. S16-S18: Where: The cubic function (Eq. S19) was solved trigonometrically for the smallest, real, positive number to give the free host concentration [ ]. Thus, [ ] can be used to relate the concentration of free host to the total concentration of host and guest and was used in non-linear curve fitting by applying an equation defining the NMR binding isotherm. 11,12 This was used to determine Kx-for each of the halides based on %Q -G," = 290 M -1 for Cl -. The data obtained ( < -G," , CV%, and ΔG) is summarized in Table S2.  To confirm the results of this method, the tetrabromide salt of host 1 was also prepared, and KBrdetermined by titrating with NaBr. Again, because there are four equivalents of (intrinsic) Brpresent at the start of the titration, the real initial point corresponding to the theoretical 1 H NMR signal from the bromide-free host (δ, ppm) is not known. Therefore, to determine the binding affinity of Brto the host, the initial observed point of the titration was set to correspond to four equivalents of bromide, and the true (theoretical) δ value for the initial point corresponding to zero equivalents of bromide allowed to float when solving for Δδ in Eq. S11. Titration of the tetrabromide host with NaBr ( Figure S37 -Figure S38) gave 1890 ± 254 M -1 , in very good agreement with the data obtained from titration of the tetra-chloride salt of 1 with Br - (Table S2, YZ -G," = 1860 ± 237 M -1 ). This value for Braffinity was also used with the competitive complexation model (Eq. S19) to determine the affinity of iodide towards the tetra-bromide salt of 1 ( Figure S39 - Figure S40). This gave KI-= 12,400 ± 1410 M -1 , again within statistical agreement from that obtained with the chloride salt (Table S2, [ -G," = 12,800 ± 1450 M -1 ). Changes in Δδmax were too small under these conditions to accurately determine the affinity of Fand Clusing the bromide salt of 1.

d. Buffer complexation determinations
Phosphate buffer is routinely used to prepare buffer solutions because it has three distinct regions in which the acid is in equilibrium with its conjugate base and therefore can provide efficient buffering capacity across several broad pH ranges. Nominally, they are pH: 0-4; 5-9; and 10-14 ( Figure S41). The competitive complexation model (Eq. S19) was used to determine the affinity of hydrogen phosphate (HPO4 2-) and dihydrogen phosphate (H2PO4 -) binding to the chloride salt of host 1. Representative titrations (details given below) and isotherms for each anion are shown in Figure S42- Figure S45. Note that the HPO4 2and H2PO4anions are the predominate phosphate species for the preparation of buffer solutions at acidic to slightly basic pH (e.g. biologically relevant buffers). Trivalent phosphate (PO4 3-) was not investigated because the major species below pH = 12.7 is hydrogen phosphate (HPO4 2-) and -OH; having four major species in solution precludes an accurate determination of the affinity of PO4 3using Eq. S19. Note that solutions of HPO4 2inevitably contain varying amounts of H2PO4and -OH (from the reaction of HPO4 2with water). During the titration with HPO4 2-, the pD varied from ~8.4 (after the first aliquot of salt) to ~9.6. Thus, over this range the [ -OH] was ~0.003-0.04 mM (<0.01-0.1 mol%), and the concentration of HPO4 2varied from 94 to >99%. As a result, the data from this titration fitted the competitive complexation model (intrinsic Cland HPO4 2in competition for host) well. The corresponding titration with H2PO4falls within a narrower range for anion-speciation. In this titration the pH varied from ~5.5 to ~4.6 and thus, the concentration of H2PO4was always >98%. Thus, within this range the hydronium ion concentration is both negligible (0.003-0.03 mM) and irrelevant to binding. Again, the data fitted the competitive complexation model well.    Fitting the data from the titration of the host with the corresponding sodium phosphate salts to the competitive model gave the association constants shown in Table S3.

e. Determination of binding constants in buffered systems
To determine if the buffers attenuate the affinity of the halide guests, halide ion affinity determinations using 1 were performed under three different buffered solutions: 1) 10 mM phosphate pH 7.3 (45% H2PO4 -, 55% HPO4 2-, I = 21.0 mM); 2) 23.8 mM phosphate buffer at pH 3.0 (12% H3PO4, 88% H2PO4 -, I = 21.0 mM) at same ionic strength of 1), and; 3) 10 mM phosphate buffer at pH = 3.0 (12% H3PO4, 88% H2PO4 -, I = 8.8 mM) maintaining the buffer concentration of 1), but at reduced ionic strength. In the latter two cases, neutral H3PO4 was assumed not to bind to the cationic host. The average initial and final I value for each titration is shown in Table S4. c c a) Ionic strength value reported as (initial | final) and includes contributions from the host, counterions, buffer, and guest. b) although the titration was performed up to this value the measured binding was too weak to determine accurately. c) Not determined. Table S5 shows the observed binding constants ( LMN G," ), obtained when the host 1.4Xwas titrated with NaX in the three different solution conditions We highlight one example here with the data for Case 1 shown below for the titration of NaCl into a solution in 1.4Clin 10 mM phosphate buffer, pH = 7.3. The LMN G," for chloride was found to be 135 ± 3 M -1 ( Figure S46 & Figure S47). In this case (titration of 1.4Clwith Cl -), the affinity constant was attained by fitting the data to a 1:1 model and floating the initial point. For the remaining halides the titration data was fit with Eq. S19 using the obtained LMN G," for Cl Average values base on at least three determinations. b) 10 mM sodium phosphate buffer, pH 7.3 (I = 21 mM) c) 23.8 mM sodium phosphate buffer, pH 3.0 (I = 21 mM) d) 10 mM phosphate buffer, pH = 3.0 (I = 8.8 mM) e) >?@ 7,9 value for Xobtained by competitive complexation model (Eq. S19) using >?@ 7,9 for Cl -.
f) >?@ 7,9 value obtained by accounting for four equiv. of Cland floating initial point. g) The measured binding was too weak to determine accurately h) Not determined.  f. Predicting binding constants in complex mixtures Determining = " 7,9 values in a straightforward competition system, for example of a halide or buffer to the host (sections c. and d.), involves a cubic equation that can be solved trigonometrically (Eq. S19). However, this is not the case when dealing with a more complex system, such as determining the binding constants for each species when the host is in a two-component buffer, or when titrating the host with a (second) halide in the presence of a one-component buffer. In these situations, the base mathematics is a quartic equation (or higher polynomial for more complex situations still) and it is not usually possible to determine each = " 7,9 value in question de novo, either trigonometrically or by iterative fitting. However, as we show here, when selected association constants are known, it is possible to calculate/predict guest affinities ( DEFG 7,9 ) in such complex systems. This ability to predict informs us that the mathematics used - Take, by way of example, the titration of any halide 0 into a solution containing the tetrachloride salt of host 1 ( 8- decreases during the (simulated) titration; specifically, [ ] V = 4 × [ 8-] V for host 1, which is incrementally adjusted due to dilution upon the (simulated) addition of the (buffered) guest solution. In each calculation the iterative process was carried out until the maximal change was < 0.0001.
From the calculated free guest concentrations using Eq. S21, the concentration of each hostguest complex was determined (e.g. [ ] V − [ ] = [ ]). The mole fraction definition (Eq. S15) was then used to generate population distributions of the host-guest complexes, which was used in concert with the observed δmax from individual titrations of each guest (Section 4.A.c-e) to generate calculated Δδ values (Δδcalc) of the guest, 0 , in the presence of 0 , 0 and 0 . Excel's Solver function was then used to solve Eq. S20 by nonlinear regression and generate the least-squares best fit isotherm for DEFG 7,9 based on Δδcalc. Error estimates were determined using Eq. S22, where % < 0 is the individually determined error of the respective anion, and ƇƲ% is the combined (propagated) estimated (relative) error from each included anion.