Allosteric Activation Shifts the Rate-Limiting Step in a Short-Form ATP Phosphoribosyltransferase

Short-form ATP phosphoribosyltransferase (ATPPRT) is a hetero-octameric allosteric enzyme comprising four catalytic subunits (HisGS) and four regulatory subunits (HisZ). ATPPRT catalyzes the Mg2+-dependent condensation of ATP and 5-phospho-α-d-ribosyl-1-pyrophosphate (PRPP) to generate N1-(5-phospho-β-d-ribosyl)-ATP (PRATP) and pyrophosphate, the first reaction of histidine biosynthesis. While HisGS is catalytically active on its own, its activity is allosterically enhanced by HisZ in the absence of histidine. In the presence of histidine, HisZ mediates allosteric inhibition of ATPPRT. Here, initial velocity patterns, isothermal titration calorimetry, and differential scanning fluorimetry establish a distinct kinetic mechanism for ATPPRT where PRPP is the first substrate to bind. AMP is an inhibitor of HisGS, but steady-state kinetics and 31P NMR spectroscopy demonstrate that ADP is an alternative substrate. Replacement of Mg2+ by Mn2+ enhances catalysis by HisGS but not by the holoenzyme, suggesting different rate-limiting steps for nonactivated and activated enzyme forms. Density functional theory calculations posit an SN2-like transition state stabilized by two equivalents of the metal ion. Natural bond orbital charge analysis points to Mn2+ increasing HisGS reaction rate via more efficient charge stabilization at the transition state. High solvent viscosity increases HisGS’s catalytic rate, but decreases the hetero-octamer’s, indicating that chemistry and product release are rate-limiting for HisGS and ATPPRT, respectively. This is confirmed by pre-steady-state kinetics, with a burst in product formation observed with the hetero-octamer but not with HisGS. These results are consistent with an activation mechanism whereby HisZ binding leads to a more active conformation of HisGS, accelerating chemistry beyond the product release rate.

A llosteric control of catalysis is a widespread strategy evolved in biosynthetic pathways. 1−4 The modulation of biochemical pathways for synthetic biology applications often requires overcoming or manipulating allosteric regulation. 5,6 Furthermore, allosteric sites provide a more selective avenue for drug design in comparison with active sites, which tend to be more conserved. 3,7,8 Accordingly, the elucidation of allosteric mechanisms in multiprotein enzymatic complexes paves the way for future therapeutic and biotechnological applications.
The allosteric enzyme adenosine 5′-triphosphate phosphoribosyltransferase (ATPPRT) (EC 2.4.2.17), responsible for the first and flux-controlling step in histidine biosynthesis, 9 is a potential drug target in some pathogenic organisms, 8,10−12 the focus of synthetic biology endeavors to harness the histidine biosynthetic pathway for histidine production in bacteria, 6,13,14 and a model system for the study of allosteric regulation of catalysis. 3,8,15,16 ATPPRT catalyzes the Mg 2+ -dependent and reversible nucleophilic substitution of adenosine 5′-triphosphate (ATP) N1 on 5-phospho-α-D-ribosyl-1-pyrophosphate (PRPP) C1 to generate N 1 -(5-phospho-β-D-ribosyl)-ATP (PRATP) and inorganic pyrophosphate (PP i ) (Scheme 1), 9 with the chemical equilibrium highly displaced toward reactants. 17 The metabolic status of the cell regulates ATPPRT activity via allosteric inhibition by histidine 9,18 and orthosteric inhibition by adenosine 5′-monophosphate (AMP). 19 Intriguingly, orthosteric inhibition by adenosine 5′-diphosphate (ADP) is also reported. 19 The hisG gene encodes two forms of ATPPRT. Most histidine-synthesizing organisms possess a long-form of the protein, HisG L , 16,20 a homohexamer with each subunit consisting of two N-terminal catalytic domains and a Cterminal allosteric domain responsible for histidine inhibition. 11 HisG L ATPPRTs operate by a steady-state ordered kinetic mechanism where ATP is the first substrate to bind to, and PRATP the last product to dissociate from, the enzyme. 21,22 Archaea and some eubacteria have instead a short-form of the protein, HisG S , 23,24 a homodimer with each subunit comprising two catalytic domains homologous to HisG L 's, but lacking the C-terminal allosteric domain. 20,25 Thus, HisG S is catalytically active on its own but insensitive to inhibition by histidine. 20,26 HisG S binds HisZ, the product of the hisZ gene, a catalytically inactive paralogue of histidyl-tRNA synthetase, 23 forming the hetero-octameric ATPPRT holoenzyme, where two HisG S dimers flank a HisZ tetramer. 24,26,27 HisZ has two distinct allosteric functions: in the absence of histidine, it activates catalysis by HisG S , and in the presence of histidine, it binds the final product of the pathway and mediates allosteric inhibition of HisG S . 20,24,26,28 The kinetic mechanism of HisG S ATPPRTs has not been investigated, but recent crystal structures suggest that the order of substrate binding may be different from HisG L 's. 29 Moreover, little is known about the kinetics of allosteric activation.
We recently reported several crystal structures of the psychrophilic bacterium Psychrobacter arcticus dimeric HisG S (PaHisG S ) and hetero-octameric ATPPRT holoenzyme (PaATPPRT), 26,29 from which an activation mechanism was inferred that involves tightening of the PaHisG S dimer in the hetero-octamer when both substrates are bound (Figure 1), which facilitates leaving group stabilization at the transition state. 29 Here we employ initial rate studies, isothermal titration calorimetry (ITC), differential scanning fluorimetry (DSF), 31 P nuclear magnetic resonance ( 31 P NMR), liquid chromatog-raphy−mass spectrometry (LC-MS), density functional theory, solvent viscosity effects, and pre-steady-state kinetics to unveil a distinct kinetic mechanism for PaATPPRT, the role of ADP as a substrate instead of an inhibitor, the basis for chargestabilization at the transition state, and a shift in the rate-liming step upon allosteric activation of the enzyme.

■ MATERIALS AND METHODS
Materials. ATP, PRPP, PP i , AMP, ADP, MgCl 2 , MnCl 2 , D 2 O (99.9 atom % deuterium), tricine, dithiothreitol (DTT), and glycerol were purchased from Sigma-Aldrich. All other chemicals were purchased from readily available commercial sources, and all chemicals were used without further purification. PaHisG S , PaHisZ, Mycobacterium tuberculosis pyrophosphatase (MtPPase), and tobacco etch virus protease were obtained as previously published. 26 PRATP was produced as previously described. 29 PaHisG S and PaATPPRT Activity Assay. All assays were performed under initial rate conditions in the forward direction at 20°C as previously described 26 by monitoring the increase in absorbance at 290 nm due to formation of PRATP (ε 290 nm = 3600 M −1 cm −1 ) 30 in 1 cm path length quartz cuvettes (Hellma) in a Shimadzu UV-2600 spectrophotometer. Unless stated otherwise, for PaHisG S activity, PaHisG S concentration was 2.2 μM, and for PaATPPRT activity, PaHisG S and PaHisZ concentrations were 0.38 and 15 μM, respectively. Reactions were started by addition of PRPP. Control reactions lacked either ATP, PRPP, PaHisG S , or PaHisZ. In all kinetic experiments under the various different conditions described below, controls were carried out to ensure that the rate did not depend on MtPPase. Kinetic measurements were performed at least in duplicates unless stated otherwise.
PaATPPRT Equilibrium Dissociation Constant (K D ) in Glycerol. Initial velocities were measured in the presence of 5.6 mM ATP, 2 mM PRPP, 0.38 μM PaHisG S , and varying concentrations of PaHisZ (0.9−8.5 μM) in 0%, (0.5−16.3 μM) in 18% and 27% glycerol (v/v). PaHisZ-PaHisG S K D values were obtained by fitting initial rate data to a kinetic equation (vide infra) as previously reported. 26 PaATPPRT and PaHisG S Saturation Kinetics with ATP and PRPP. PaATPPRT initial rates were measured at saturating concentrations of one substrate and varying concentrations of the other, either ATP (0.4−5.6 mM) or PRPP (0.1−2.0 mM). Initial rates for PaHisG S were determined at saturating concentrations of one substrate and varying concentrations of the other, either ATP (either 0.  and control reactions lacked PaHisG S . LC-MS analysis of the protein-free reaction mixtures was performed on an EC250/4.6 Nucleodur 100−10 C18 ec HPLC column (10 μm × 4.6 mm × 250 mm) (Macherey-Nagel) in a 1260 infinity HPLC system coupled to a G6130B Single Quadrupole mass spectrometer (Agilent Technologies). Separation of PRATP and ATP was carried out in (A) 50 mM triethylamine-acetic acid pH 7.4 and (B) methanol as a mobile phase in the following sequence: 0− 3 min 100% A, 3−3.1 min 90% A and 10% B, 3.1−12 min 80% A and 20% B at a flow rate of 1 mL min −1 , with UV absorbance monitored at 260 and 290 nm. Electrospray ionization-mass spectrometry (ESI-MS) data were acquired in negative mode with a capillary voltage of 4500 V.
PaATPPRT and PaHisG S Saturation Kinetics in Glycerol. PaATPPRT and PaHisG S initial rates were measured at saturating concentrations of one substrate and varying concentrations of the other, either ATP (0.4−5.6 mM) or PRPP (0.1−2.0 mM), in the presence of 0%, 18%, and 27% glycerol (v/v).
PaHisG S Inhibition by AMP. The half-maximal inhibitory concentration of AMP was determined by measuring initial rates for PaHisG S (4.5 μM) in the presence of 5.6 mM ATP, 2 mM PRPP, and varying concentrations of AMP (0−0.8 mM). The inhibition mechanism was investigated by measuring initial rates for PaHisG S (4. . PaHisG S concentration was more than 4-fold higher than the lowest AMP concentration used, and pseudo-first-order approximation was assumed. PaHisG S Saturation Kinetics with ADP and PRPP. Initial rates for PaHisG S were determined at saturating concentrations of one substrate and varying concentrations of the other, either ADP (0.4−5.6 mM) or PRPP (0.1−2.0 mM).
Comparison of PaHisG S Reactions with ADP and ATP by 31 P NMR Spectroscopy. Analysis of PaHisG S reactions by 31 P NMR spectroscopy was carried out as previously described, 26 except that PaHisG S concentration was 10.3 μM and ADP replaced ATP in half of the reactions. All reactions were run in duplicate, and control reactions lacked PaHisG S .
PaATPPRT and PaHisG S Initial Velocity Patterns. Initial rates for PaATPPRT were measured in the presence of varying ATP (0.4−5.6 mM) and PRPP (0.1−2.0 mM), with 1 μM PaHisG S and 20 μM PaHisZ. Initial rates for PaHisG S were determined in the presence of varying ATP (0.2−2.8 mM) and PRPP (0.1−2.0 mM). Measurements were performed in quadruplicates.
PaHisG S Binding by ITC. ITC measurements were carried out at 20°C in a MicroCal PEAQ-ITC calorimeter (Malvern Instruments). Protein and ligand were solubilized in the same ATPPRT assay buffer. After a small injection of 0.4 μL, 18 successive injections of 2 μL of ligand (either 0.8 mM PRPP or 10 mM ATP) were made into 300 μL of 50 μM PaHisG S , with 150-s intervals between successive injections and a reference power of 10 μcal s −1 . Heat of dilution for each experiment was measured by titrating ligand into assay buffer, and subtracted from the corresponding binding curve. All measurements were performed in duplicate. Data for PRPP binding were fitted to a single-site binding model as implemented in the PEAQ-ITC analysis software (Malvern Instruments). PaHisG S Thermal Denaturation by DSF. DSF measurements (λ ex = 490 nm, λ em 610 nm) were performed in 96-well plates on a Stratagene Mx3005p instrument. Thermal denaturation assays (50 μL) for 7.5 μM PaHisG S were measured in the presence and absence of ligands (6 mM ATP, 2 mM PRPP, 208 μM PRATP, 3.6 mM PP i ), with or without 22% glycerol (v/v) (apoenzyme) in 100 mM tricine, 100 mM KCl, 4 mM DTT and 15 mM MgCl 2 pH 8.5. The assay for apoenzyme was also performed in 10 mM KH 2 PO 4 , 10 mM KF pH 8.0. Sypro Orange (5×) (Invitrogen) was added to all wells. Thermal denaturation curves were recorded over a temperature range from 25−93°C with 1°C min −1 increments. Control curves lacked enzyme and were subtracted from curves containing enzyme. All measurements were carried out in triplicate.
Density Functional Theory Calculations. Theoretical structures were derived from B3LYP calculations using a 6-31G* basis set with a Lanl2DZ basis set on Mg 2+ and Mn 2+ and a Lanl2DZ pseudopotential added to Mg 2+ and Mn 2+ as implemented in Gaussian 09. 31 A model system was chosen by including all residues within 5 Å of ADP and PRPP in the crystallographic dimer of the PaHisG S -PRPP-Mg-ADP complex crystal structure 29 and by flipping the adenine ring from its crystal structure orientation to bring N1 in proximity to PRPP. The system was further paired down to include only functional groups, metal ions and water molecules within the 5-Å cutoff that were essential for stabilization of the transition structure. In addition to the divalent metal found in the crystal structure, a second divalent metal had to be included in the system for a transition structure to be located. Initial searches exploring structures with fixed distances along the reaction coordinate were located by performing an optimization of an input structure with the key bond-forming or bond-breaking distances held constant, and frequency calculations resulted in only one imaginary frequency along the reaction coordinate. Final transition structures for the system complexed with either Mg 2+ or Mn 2+ were located as stationary points with no geometrical constrains and exhibit only one imaginary frequency along the reaction coordinate. Coordinates for all optimized structures are available in the Supporting Information.
Pre-Steady-State Kinetics. Approach to steady-state in PaHisG S and PaATPPRT reactions was investigated under multiple-turnover conditions by monitoring the increase in absorbance at 290 nm upon PRATP formation at 20°C in an Applied Photophysics SX-20 stopped-flow spectrophotometer outfitted with a 5 μL mixing cell (0.5 cm path length and 0.9 ms dead-time). Each syringe contained 100 mM tricine pH 8.5, 100 mM KCl, 4 mM DTT, 15 mM MgCl 2 , and 20 μM MtPPase. In addition, one syringe carried 40 μM PaHisG S (with or without 100 μM PaHisZ) and 4 mM PRPP, while the other carried 11.2 mM ATP. Reaction was triggered by rapidly mixing 55 μL from each syringe. Absorbance increase with PaHisG S was monitored in a linear-time base for 5 s with 5000 data points collected, and with PaATPPRT, in a split-time base for 2 s, with 4000 data points collected in the first 0.2 s and 4000 in the following 1.8 s. At least 8 traces were acquired for each enzyme, and controls lacked PRPP.
Data Analysis of Kinetics and Thermal Denaturation. Kinetic and DSF data were analyzed by the nonlinear regression function of SigmaPlot 13 (SPSS Inc.). Data points and error bars in graphs are represented as mean ± standard error, and kinetic and equilibrium constants are presented as Biochemistry Article mean ± fitting error. Initial rate data with varying concentrations of PaHisZ were fitted to eq 1. The concentration of PaATPPRT at any concentration of PaHisG S and PaHisZ was calculated according to eq 2. Substrate saturation data were fitted to eq 3. Inhibition data at fixed substrate concentrations were fitted to eq 4, and competitive inhibition data were fitted to eq 5. Initial velocity patterns were fitted to eq 6, and pre-steady-state kinetics under multipleturnover conditions was fitted to eq 7. In eqs 1−7, v is the initial rate, V max is the maximal velocity, G is the concentration of PaHisG S , Z is the concentration of PaHisZ, K D is the equilibrium dissociation constant, PaATPPRT is the concentration of PaHisG S -PaHisZ complex, S is the concentration of the varying substrate, k cat is the steady-state turnover number, K M is the apparent Michaelis constant, E T is total enzyme concentration, v i is the initial rate in the presence of inhibitor, IC 50 is the half-maximal inhibitory concentration, K i is the inhibitor dissociation constant, A and B are the first and second substrates to bind to the enzyme, respectively, K a and K b are their respective Michaelis constants, K ia is the apparent dissociation constant for the complex between enzyme and substrate A when the concentration of B approaches zero, t is time, P(t) is product concentration at time t, A 0 is the amplitude of the burst phase, and k burst is the first-order rate constant of product formation in the burst phase. DSF thermal denaturation data were fitted to eq 8, 32 where F U is fraction unfolded, T is the temperature in°C, T m is the melting temperature, c is the slope of the transition region, and LL and UL are folded and unfolded baselines, respectively.
■ RESULTS AND DISCUSSION PaHisG S and PaATPPRT Kinetic Mechanism. A steadystate ordered kinetic mechanism in which ATP is the first substrate to bind to the enzyme, and PRATP is the last product to dissociate from it, has long been demonstrated for HisG L ATPPRTs. 21,22 This mechanism has been supported by several structures of Campylobacter jejuni and M. tuberculosis ATPPRT-ATP binary complexes, 10,16 and by the recent structure of the C. jejuni ATPPRT catalytic core in complex with PRPP, where despite being able to bind to the free enzyme, PRPP drifts into the ATP binding site, which would lead to a dead-end complex. 33 The kinetic mechanism of HisG S ATPPRTs, on the other hand, has not been explored. We recently published the crystal structures of PaHisG S and PaATPPRT in binary complexes with PRPP and PRATP, and in ternary complexes with PRPP-ATP, but were unable to obtain structures of enzyme-ATP binary complexes, suggesting a reverse order of substrate binding in comparison with HisG L ATPPRTs. 29 To test this hypothesis, the kinetic mechanism of PaHisG S and PaATPPRT was investigated. Intersecting patterns of double-reciprocal plots with both ATP and PRPP in initial velocity studies were determined for PaATPPRT ( Figure  2A,B) and PaHisG S ( Figure 2C,D), indicating a ternary complex is formed in a sequential mechanism. The doublereciprocal plots intersecting to the left of the y-axes rule out a rapid equilibrium ordered mechanism. 34 Fitting the data to eq 6 ( Figure 2E,F) yielded steady-state kinetic parameters summarized in Table S1.
Binding studies were performed with PaHisG S to elucidate the substrate binding order. Binding of PRPP to PaHisG S was detected by ITC ( Figure S1), and fitting the data from two independent experiments to a single-site binding model (stoichiometry of 1:1 and no cooperativity) resulted in K D 's of 15.4 ± 0.2 and 8.3 ± 0.1 μM (one from each experiment, yielding a mean ± SE of 12 ± 2 μM). ATP binding to PaHisG S , on the other hand, could not be detected, as no signal was observed beyond heat of dilution ( Figure S2). This Three-dimensional plot of (E) PaATPPRT and (F) PaHisG S initial rate data, where lines are data fitting to eq 6.

Biochemistry
Article corroborates the hypothesis that PRPP can bind to the free enzyme, while ATP cannot.
To confirm and expand these results, PaHisG S thermal denaturation curves in the presence and absence of substrates and products were determined by DSF (Figure 3), and data fitting to eq 8 produced T m 's shown in Table S2. PRPP and PRATP increased PaHisG S T m by 6 and 5°C, respectively, indicating that these molecules can bind to the free enzyme. Conversely, ATP and PP i did not alter PaHisG S T m . The latter observation alone does not necessarily rule out the possibility that ATP and PP i can bind to the free enzyme, but the integration of crystallography, 29 initial velocity patterns, ITC, and DSF data supports a steady-state ordered mechanism where PRPP is the first substrate to bind to PaHisG S and PRATP is the last product to dissociate from it. The strong parallels in corresponding binding modes seen in the PaHisG S and PaATPPRT crystal structures 29 suggest that PaATPPRT follows the same mechanism. Moreover, given the conservation of PRPP position in PaATPPRT 29 and Lactococcus lactis ATPPRT binary complexes, 27 this mechanism may be valid for other HisG S ATPPRTs.
AMP Is an Inhibitor of PaHisG S . AMP is a competitive inhibitor of HisG L ATPPRTs against both substrates, 16,19 which is explained structurally by the simultaneous partial occupation of the PRPP and ATP binding sites by AMP's phosphoribosyl and adenine moieties, respectively. 11,16,35 AMP is also a competitive inhibitor against PRPP in L. lactis ATPPRT, 28 and the recent crystal structure of the PaHisG S -AMP complex shows a similar binding mode as in HisG L ATPPRTs. 11,16,29,35 AMP inhibits PaHisG S with an IC 50 of 79 ± 6 μM ( Figure S3A), and inhibition is competitive against both PRPP and ATP, with K i 's of 25 ± 5 and 52 ± 8 μM, respectively ( Figure S3B,C). These values are on average ca. 7and 10-fold lower than those for HisG L ATPPRTs, 16,19 and over 27-fold lower than that for L. lactis ATPPRT, 28 suggesting PaHisG S activity is more stringently regulated by this metabolite.
ADP Is a Substrate for PaHisG S . ADP has been shown to be an inhibitor of HisG L ATPPRTs. 19 However, crystal structures of PaHisG S and PaATPPRT in complex with PRPP-ADP reveal that ADP binds in the same manner as ATP. 29 In order to evaluate the ability of PaHisG S to use ADP as a substrate, we compared the reactions with ADP and ATP by 31 P NMR spectroscopy ( Figure S4). The spectra of reactions containing ADP ( Figure S4A) and ATP ( Figure  S4C) are similar except for the peak at −19.2 to −19.4 corresponding to the γ-PO 4 2− phosphorus of ATP and PRATP, since this group is absent in ADP and N 1 -(5-phospho-β-D-ribosyl)-ADP (PRADP). Spectra for both reactions differ from the controls lacking PaHisG S (Figure S4B,D). The characteristic peak at ca. 3.3 ppm corresponding to the phosphorus in the N 1 -5-phospho-β-D-ribose moiety of the product 26 is present in the reaction spectra with ADP ( Figure S4A, inset) and ATP ( Figure S4C, inset), and absent in the controls ( Figure S4B,D, insets), establishing that ADP can replace ATP as a substrate for PaHisG S .
For a quantitative comparison of the reactions with ATP and ADP, steady-state kinetic analysis of the reaction with either substrate was carried out (Figure 4) and kinetic parameters are summarized in Table S3. Values of k cat are the same within error with either ATP or ADP as a substrate, indicating that once saturated PaHisG S turns over ATP and ADP just as effectively. The main difference is in the K M for ADP, which is over 3-fold that for ATP, suggesting some small loss of affinity for the steady-state with ADP.
PaHisG S and PaATPPRT Kinetics with Mn 2+ . Replacement of Mg 2+ by Mn 2+ is a common strategy in enzymology, 36 having been employed to uncover rate-limiting steps in reactions involving stabilization of phosphate groups. 37 HisG L ATPPRTs have been reported to have their activities either unaltered or decreased by changing the divalent metal in the reaction from the physiological Mg 2+ to Mn 2+ , but no mechanistic inference has been drawn. 17,38 To evaluate the effect of Mn 2+ on a HisG S enzyme, saturation curves for PaHisG S and PaATPPRT with either divalent metal were determined ( Figure 5), and kinetic constants are displayed in Table S4. Mn 2+ led to 2.6-and 11-fold increases in PaHisG S k cat and k cat /K M ATP , respectively, as compared with Mg 2+ . The change in k cat /K M ATP was driven in large part by a reduction in K M ATP . LC-MS analysis of the PaHisG S reaction with Mn 2+ confirmed the same product, PRATP, was being formed ( Figure S5).
In contrast to PaHisG S , steady-state constants for PaATPPRT were unchanged by Mn 2+ , except for a 2.9-fold increase in k cat /K M ATP owing to a reduction in K M ATP . These results raise the possibility that PaHisG S and PaATPPRT reactions have distinct rate-limiting steps. Crystal structures of PaHisG S and PaATPPRT with various ligands do not depict any specific interaction between Mg 2+ and the enzyme, 29 raising the possibility the off-rates of products from the active site might not be affected by the nature of the metal ion. It is possible, nonetheless, that a solution metal stabilizes charges of either PRATP or PP i concomitantly with product release from the enzyme. The metal ion seen in the structures acts as a Lewis acid to stabilize negative charges in the Michaelis complex upon binding of ATP, with a putative second metal

Biochemistry
Article ion likely present at the transition state to facilitate departure of the PP i leaving group. 29 Thus, one might expect Mn 2+ to increase the reaction rate if rate-limiting steps are located between ATP binding to the enzyme-PRPP complex and product formation, since a stronger Lewis acid would facilitate catalysis by stabilizing charges more efficiently. The kinetic constants affected would be k cat and k cat /K M ATP , which is exactly what is observed with PaHisG S . If, on the other hand, ternary complex formation played a minor role in limiting the reaction rate, chemistry was fast, and product release was the slowest step, a modest increase in k cat /K M ATP only would be expected, which is the case with PaATPPRT.
A Transition-State Hypothesis for the PaHisG S Reaction. An S N 1-like, D N *A N ‡39,40 transition-state structure has recently been proposed for C. jejuni and M. tuberculosis (HisG L ) and L. lactis (HisG S ) ATPPRT-catalyzed reaction based on kinetic isotope effects and computational chemistry, using a simplified model of the reaction for density functional theory calculations. 10 Having established that PaHisG S utilizes ADP as a substrate with a similar k cat as it does ATP (Table  S3), the crystal structure of the PaHisG S -PRPP-Mg-ADP Michaelis complex 29 served as a starting point for density functional theory calculations in order to find a theoretical transition state for the reaction that includes not only the full substrates but also several active-site residue side-chain surrogates and water molecules essential to stabilize the system, with either Mg 2+ or Mn 2+ as the metal ion ( Figure 6). Transition structures were located as stationary points (i.e., without any constraints on distances or dihedral angles) and possess only one imaginary frequency reflecting vibration along the N1−C1−O1 axis. Inclusion of a second equivalent of the divalent metal ion to stabilize the departing PP i leaving group was essential to locate transition structures, lending support to a recent proposal based on the crystal structures of PaHisG S and PaATPPRT Michaelis complexes 29 and the transition structures of other phosphoribosyltransferases. 41 The optimized structures indicate an S N 2-like, almost synchronous A N D N transition state is possible for the PaHisG S -catalyzed reaction with either Mg 2+ ( Figure 6A) or Mn 2+ ( Figure 6B) as a Lewis acid. The 6-NH 2 group of ADP is protonated in all transition structures and is likely to lose a proton to form the 6-NH group of PRADP only after the nucleophilic substitution is complete, as recently hypothesized. 29 Nucleophilic attack occurs from the charge-neutral resonance structure of adenine in which N1 has transiently a negative charge due to electron donation from N6. This natural resonance structure represents 6.64% of the distribu-  Substrates are represented as stick models, side-chain mimics as wireframe, and metal ions and water oxygens as spheres. Carbon is in either cyan or yellow for substrates and in gray for side-chain mimics, with oxygen in red, nitrogen in blue, phosphorus in orange, magnesium in green, and manganese in purple. Hydrogens are omitted for simplicity. Partial bonds and metal ion coordination bonds are represented by dashed lines. Distances are shown for the N1−C1 and the C1−O1 bonds. Key residue side-chain mimics are labeled, and the prime denotes a residue of the adjacent subunit in the PaHisG S dimer. 29 Biochemistry Article tion of adenine resonances. 42 The A N D N transition state located here contrasts with the D N *A N ‡ one proposed for HisG L and HisG S ATPPRT reaction. 10 This would mean that different orthologues of ATPPRT catalyze the same reaction via different transition states, which is not uncommon in ribosyl-transfer reactions. For instance, distinct transition-state models based on kinetic isotope effects and density functional theory have been suggested for bovine and human purine nucleoside phosphorylases, 43,44 and for wild-type and mutant human purine nucleoside phosphorylases. 43,45 Kinetic isotope effect measurements for PaHisG S could test the A N D N transition-state hypothesis put forth in this work.
Overlay of the transition structures with Mg 2+ and Mn 2+ demonstrates an almost identical arrangement ( Figure 6C), indicating transition-state geometry cannot explain the discrimination in PaHisG S reactivity between the metal ions. Natural bond orbital (NBO) analysis of the transition structures, however, revealed significant differences in charge distribution in the metal ions and the PP i at the transition state depending on which metal is included (Table S5). Most atoms have very similar charges in the two transition structures, except for the metal ions and PP i oxygens. The average charge of the two magnesium ions at the transition state is 1.439, over 2-fold higher than the average charge of the manganese ions, 0.649. This is due to more efficient attenuation of the negative charge of the PP i leaving group by Mn 2+ through d-orbital bonding to coordinating oxygens, as shown by orbital population analysis. As compared with Mg 2+ , therefore, Mn 2+ improves catalysis in the PaHisG S reaction by more effectively stabilizing the negatively charged leaving group at the transition state.
Solvent Viscosity Effects on PaHisG S and PaATPPRT Kinetics. In order to probe further the distinct rate-limiting steps governing PaHisG S and PaATPPRT catalyses, the effect of solvent viscosity on reaction rates was evaluated (Figure 7), and the data are summarized in Tables S6 and S7. Increasing solvent viscosity by increasing glycerol concentration 46 slows down diffusional steps such as substrate binding and release and product release, and values of kinetic constants will be reduced if such steps are rate-limiting. 47−49 PaHisG S rate constants did not decrease with increasing glycerol concentration (Table S6), consistent with diffusional steps not contributing to limit the reaction rate. Instead, as shown in Figure 7A and Table S6, glycerol led to an increase in PaHisG S k cat and k cat /K M PRPP of up to 2.7-and 2.4-fold, respectively, while k cat /K M ATP was only marginally affected. Inverse solvent viscosity effects generally suggest that a more active dynamic conformation of the enzyme or the Michaelis complex is favored at high viscosity. 47−49 To rule out the possibility that glycerol might be affecting the overall stability of the enzyme, a thermal denaturation curve was determined by DSF in 22% glycerol ( Figure S6), and no difference in T m was observed in comparison with that determined without glycerol (Table S2). Crystal structures of PaHisG S apoenzyme and PaHisG S -PRPP-ATP were also obtained with and without soaking crystals in glycerol, and no electron density for glycerol was visualized in any of the structures. 29 This suggests that glycerol is acting as part of bulk solvent, not as a ligand, but with the caveat that crystal lattice might have prevented binding.
To assess the effect of solvent viscosity on PaATPPRT, first the K D for the PaHisG S -PaHisZ complex had to be measured in glycerol ( Figure S7), and data fitting to eq 1 yielded K D 's of 1.3 ± 0.1, 1.1 ± 0.2, and 0.5 ± 0.1 μM in 0%, 18%, and 27% glycerol, respectively. Knowledge of the K D 's allowed calculation, using eq 2, of PaATPPRT concentrations at different glycerol concentrations for measurement of k cat . In contrast to the effect on PaHisG S , increasing solvent viscosity resulted in a decrease of up to 2.5-fold in PaATPPRT k cat , with negligible effects on k cat /K M for either substrate, as shown in Figure 7B and Table S7. This points to product dissociation from PaATPPRT as the rate-limiting step in the reaction, as is the case with HisG L ATPPRTs. 8,50 Burst in Product Formation by PaATPPRT. To glean additional support for distinct rate-limiting steps controlling nonactivated and activated PaHisG S reactions, product formation time courses were monitored under pre-steadystate conditions for PaHisG S and PaATPPRT (Figure 8). PRATP formation with PaHisG S varies linearly with time with a steady-state rate constant of 0.091 ± 0.001 s −1 , in reasonable agreement with k cat (Tables S3, S4, S6). This rules out a slow step after formation of enzyme-bound products 51 and suggests interconversion between ternary complexes (k 5 + k 6 in Scheme 2) is rate-limiting.
On the other hand, a burst in PRATP formation precedes the steady-state with PaATPPRT, and data fitting to eq 7 yielded a k burst of 80 ± 1 s −1 , a steady-state rate constant of PaATPPRT saturation curves (top) and steady-state constants (bottom) dependence on glycerol concentration. Data represent either mean ± SE (scatter plots) or value ± fitting error (bar plots). Lines are data fitting to eq 3. Biochemistry Article 1.11 ± 0.01 s −1 , and an A 0 of 4.3 μM. This is consistent with a step after chemistry, likely product release (k′ 7 in Scheme 2), limiting the reaction rate, 51,52 in agreement with the conclusion drawn from solvent viscosity effects. M. tuberculosis HisG L ATPPRT also displays a burst in product formation with a k burst of 0.67 s −1 at 25°C. 8 Thus, PaATPPRT k burst at 20°C is over 119-fold higher than M. tuberculosis HisG L ATPPRT's at 25°C, which may be a feature of HisG S ATPPRTs and/or a consequence of PaATPPRT being psychrophilic. 26 The amplitude of the burst phase (A 0 ) generally reflects the concentration of the Michaelis complex, which at saturating substrate concentrations could be as high as the concentration of enzyme. 53 The A 0 of 4.3 μM is over 4.4-fold lower than the concentration of PaATPPRT used in the experiment (19 μM). Two main reasons may account, separately or in combination, for this result without invoking the unlikely scenario where ca. 75% of enzyme molecules are inactive. First, the enzyme might not be fully saturated by one or both substrates, which would also explain the steady-state rate constant being slightly smaller than the k cat values extrapolated from substrate saturation curves. This may be the case with the PaHisG S steady-state rate constant as well. Second, chemical reversibility decreases A 0 . Both k burst and A 0 are dependent on all rate constants depicted in Scheme 2, the forward and reverse rate constants for interconversion between enzyme-bound substrates and products, k 5 and k 6 , respectively, and the net rate constant for release of products from the enzyme, k′ 7 , according to eqs 9 and 10. 51 Upon inspection of eqs 9 and 10, one must conclude that under the most favorable conditions, full expression of A 0 can only occur when chemistry is irreversible (k 6 = 0) and much faster than product release (k 5 ≫ k′ 7 ). Internal reversibility, described by the magnitude of k 6 , will increase k burst while decreasing A 0 . Equilibrium in the ATPPRT reaction strongly favors the reactants, 17 making it possible for the crystal structure of the PaATPPRT-PRPP-ATP ternary-complex to be attained with wild-type enzyme. 29 Hence, k 6 is likely to be much larger than k 5 , making k 6 the main contributor to k burst and significantly reducing A 0 from its theoretical upper limit of 19 μM. Relative contributions of k 5 and k 6 to k burst and A 0 notwithstanding, it is clear that activation of PaHisG S by PaHisZ switches the rate-limiting step of the reaction from interconversion between the ternary complexes to product release.
PaHisZ-Induced Shift in the Rate-Limiting Step. The results presented here demonstrate that two long-established mechanistic features of HisG L ATPPRTs, namely, ATP as the first substrate to bind to the enzyme and ADP as an

Biochemistry
Article inhibitor, 16,19,21,22,33 do not apply to PaHisG S , and possibly other HisG S ATPPRTs. Providing functional data to support hypotheses proposed based on extensive crystallography work on PaHisG S and PaATPPRT, 29 PaHisG S is shown to be able to replace ATP for ADP as a substrate and to operate by a steadystate ordered mechanism where PRPP is the first substrate to bind to the enzyme (Scheme 3). PaHisG S k cat increases when Mn 2+ replaces Mg 2+ , which can be accounted for owing to more efficient charge stabilization by Mn 2+ upon leaving group departure at the transition state. The observation that PaATPPRT steady-state kinetics is unaltered with Mn 2+ raises the possibility of k cat 's for the activated and nonactivated enzyme forms reporting on distinct steps. This is confirmed by solvent viscosity effects on steady-state parameters and by presteady-state kinetics under multiple-turnover conditions, which indicate that interconversion between PaHisG S −PRPP-ATP and PaHisG S −PRATP-PP i complexes limits the reaction rate for the nonactivated enzyme, likely with a significant contribution from chemistry given the effect of Mn 2+ . However, allosteric activation by PaHisZ accelerates this interconversion well beyond the steady-state rate, which now reflects the off-rate of either PP i from the PaATPPRT− PRATP-PP i ternary complex or PRATP from the PaATPPRT−PRATP binary complex (Scheme 3). This provides fundamental insight into the allosteric regulation of a complex multiprotein enzyme.

* S Supporting Information
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.biochem.8b00559.
ITC curves, PaHisG S inhibition by AMP, spectra, DSFbased thermal denaturation of PaHisG S , determination of equilibrium dissociation, PaATPPRT and PaHisG S steady-state parameters from initial velocity patterns, PaHisG S T m 's by DSF in the presence and absence of ligands, steady-state kinetic constants, effect of Mn 2+ on PaATPPRT and PaHisG S steady-state kinetic parameters, NBO charge distribution, solvent viscosity effects, and coordinates for all transition structures (PDF)