Thermodynamics and energy coupling in the bacteriorhodopsin photocycle

Time-resolved absorption changes of photoexcited bacteriorhodopsin were measured with a gated multichannel analyzer between 100 ns and 100 ms at six temperatures between 5 and 30 degrees C. The energetics of the chromophore reaction cycle were analyzed on the basis of a model containing a single cycle and reversible reactions. The calculated thermodynamic parameters provide insights to general principles of the active transport. They indicate that in this light-driven proton pump the free energy is retained after absorption of the photon as the enthalpy of the pKa shift in the chromophore which allows deprotonation of the Schiff base. Part of the excess free energy is dissipated at the "switch" step where the reaction and transport cycles are coupled, and the rest at the chromophore recovery step. All other reactions take place near equilibrium. The "switch" step is the M1----M2 transition in the reaction cycle [Váró, G., & Lanyi, J. K. (1991) Biochemistry (preceeding paper in this issue)]. It provides for return of the chromophore pKa to its initial value so the Schiff base will become a proton acceptor, for reordering access of the Schiff base from one side of the membrane to the other, and for unidirectionality of the proton transfer. Conformational energy of the protein, acquired during the "switch" step, drives the completion of the photocycle.     

Electrostatic interaction between anions bound to site I and the retinal Schiff base of halorhodopsin

The influence of different anions on the deprotonation of the retinal Schiff base of halorhodopsin in the dark was investigated. We find that a large number of anions cause a significant increase of the pKa of the Schiff base, an effect attributed to binding to "site I" on the protein. The concentration dependencies of the spectroscopic shifts associated with the changes of the pKa yielded dissociation constants (and thus binding energies) for the anions, which were related to the Stokes radii. The data fit the predictions of electrostatic interaction between the anions and the positive charge associated with site I, if the latter is located within a few angstroms from the surface of the protein. The specificity of site I toward various anions is quantitatively explained by the differences in the change of Born energy upon transfer of the anions from water to the binding site. The changes in the deprotonation energy of the Schiff base upon the binding of anions, delta delta Gdeprot, could be calculated from the delta pKa at infinite anion concentration. Unexpectedly, the delta delta Gdeprot values were remarkably close to the energies of binding to site I. Thus, site I and the Schiff base are strongly electrostatically coupled, either because of close proximity or because of the possibility of allosteric energy transfer between them.     

Nanometric design of extraordinary hydrophobic-induced pKa shifts for aspartic acid: Relevance to protein mechanisms

Commonly a key element enabling proteins to function is an amino acid residue or residues with functional side chains having shifted pKa values. This article reports the results on a set of protein-based polymers (model proteins) that exhibit hydrophobic folding and assembly transitions, and that have been designed for the purpose of achieving large hydrophobic-induced pKa shifts by selectively replacing Val residues by Phe residues. The high molecular weight polypentapeptides, actually poly (tricosapeptides) with six varied pentamers in fixed sequence, were designed and synthesized to have the same amino acid compositions but different proximities between a single aspartic acid residue and 5 Phe residues per 30 residues. With the 5 Phe residues distal from the Asp residue, the observed pKa shift was 2.9 when compared to the Val-containing reference. With the 5 Phe residues within 1 nm of the Asp residue, the pKa shift was 6.2. This represents a free energy of interaction of 8 kcal/moles. To our knowledge, this is the largest pKa shift documented for an Asp residue in a polypeptide– or protein–water system. Data are reviewed that do not support the usual electrostatic arguments for pKa shifts of charge–charge repulsion and/or unfavorable ion self-energies arising from displacement of water by hydrophobic moieties, but rather the data are interpreted to indicate the presence of an apolar–polar repulsive free energy of hydration, which results from a potentially highly cooperative competition between apolar and polar species for hydration. © 1994 John Wiley & Sons, Inc.     

Synergism between coenzyme and alcohol binding to liver alcohol dehydrogenase

Heterotropic cooperativity effects in the binding of alcohols and NAD+ or NADH to liver alcohol dehydrogenase have been examined by equilibrium measurements and stopped-flow kinetic studies. Equilibrium data are reported for benzyl alcohol, 2-chloroethanol, 2,2-dichloroethanol, and trifluoroethanol binding to free enzyme over the pH range 6-10. Binary-complex formation between enzyme and alcohols leads to inner-sphere coordination of the alcohol to catalytic zinc and shows a pH dependence reflecting the ionization states of zinc-bound water and the zinc-bound alcohol. The affinity of the binding protonation state of the enzyme for unionized alcohols increases approximately by a factor of 10 on complex formation between enzyme and NAD+ or NADH. The rate and kinetic cooperativity with coenzyme binding of the alcohol association step indicates that enzyme-bound alcohols participate in hydrogen bonding interactions which affect the rates of alcohol and coenzyme equilibration with the enzyme without providing any pronounced contribution to the net energetics of alcohol binding. The pKa values determined for alcohol deprotonation at the binary-complex level are linearly dependent on those of the free alcohols, and can be readily reconciled with the pKa values attributed to ionization of zinc-bound water. Alcohol coordination to catalytic zinc provides a major contribution to the pKa shift which ensures that the substrate is bound predominantly as an alcoholate ion in the catalytically productive ternary complex at physiological pH. The additional pKa shift contributed by NAD+ binding is less pronounced, but may be of particular mechanistic interest since it increases the acidity of zinc-bound alcohols relatively to that of zinc-bound water.     

Do salt bridges stabilize proteins? A continuum electrostatic analysis

The electrostatic contribution to the free energy of folding was calculated for 21 salt bridges in 9 protein X-ray crystal structures using a continuum electrostatic approach with the DELPHI computer-program package. The majority (17) were found to be electrostatically destabilizing; the average free energy change, which is analogous to mutation of salt bridging side chains to hydrophobic isosteres, was calculated to be 3.5 kcal/mol. This is fundamentally different from stability measurements using pKa shifts, which effectively measure the strength of a salt bridge relative to 1 or more charged hydrogen bonds. The calculated effect was due to a large, unfavorable desolvation contribution that was not fully compensated by favorable interactions within the salt bridge and between salt-bridge partners and other polar and charged groups in the folded protein. Some of the salt bridges were studied in further detail to determine the effect of the choice of values for atomic radii, internal protein dielectric constant, and ionic strength used in the calculations. Increased ionic strength resulted in little or no change in calculated stability for 3 of 4 salt bridges over a range of 0.1-0.9 M. The results suggest that mutation of salt bridges, particularly those that are buried, to "hydrophobic bridges" (that pack at least as well as wild type) can result in proteins with increased stability. Due to the large penalty for burying uncompensated ionizable groups, salt bridges could help to limit the number of low free energy conformations of a molecule or complex and thus play a role in determining specificity (i.e., the uniqueness of a protein fold or protein-ligand binding geometry).     

The conserved, buried aspartic acid in oxidized Escherichia coli thioredoxin has a pKa of 7.5. Its titration produces a related shift in global stability.

Aspartic acid 26 in Escherichia coli thioredoxin is located at the bottom of a hydrophobic cavity, near the redox-active disulfide of the active site. Asp 26 is embedded in the protein except for part of the surface of one carboxyl oxygen. The high degree of evolutionary conversion of Asp 26 suggests that it plays a critical role in thioredoxin function. We have determined the pKa of Asp 26 by a novel electrophoretic method based on the relative electrophoretic mobilities of wild-type thioredoxin and of D26A thioredoxin (with Asp 26 replaced by alanine). The pKa of Asp 26 determined by this technique is 7.5, more than 3 units above the pKa of a solvated carboxyl side chain. The titration of Asp 26 is thermodynamically linked to the stability of thioredoxin. As expected if thioredoxin stability depends on the ionization state of Asp 26, delta Go WT, the free energy of the cooperative denaturation reaction of wild-type thioredoxin by guanidine hydrochloride, varies with pH in a sigmoidal fashion in the vicinity of pH 7.5. Over the same pH range, the free energy for D26A folding, delta Go D26A, is pH independent and D26A is highly stabilized compared to wild type. From the thermodynamic cycle describing the linkage of Asp 26 titration to thioredoxin stability, the difference in free energy between wild-type thioredoxin with protonated Asp 26 and wild-type thioredoxin with deprotonated Asp 26, delta delta Go (COOH----COO-), is calculated to be 4.9 kcal/mol.(ABSTRACT TRUNCATED AT 250 WORDS)     

Effect of pH on the kinetics of the reaction catalyzed by beta-D-hexosaminidase from Halocynthia roretzi]

The analysis of the pH-dependence of Michaelis constant and maximal velocity for the reaction catalyzed by beta-D-hexosaminidase from Halocynthia roretzi revealed two essential ionazable groups of the enzyme. One of them controls substrate binding and has a pKa of 5.5 in free enzyme. The other group (pKa=5.6) is necessary for the occurrence of the catalytic step and appears not to change its pKa on substrate binding.     

Calculations of free energy profiles for the staphylococcal nuclease catalyzed reaction

Calculations of the free energy profile for the first two (rate-limiting) steps of the staphylococcal nuclease catalyzed reaction are reported. The calculations are based on the empirical valence bond method in combination with free energy perturbation molecular dynamics simulations. The calculated activation free energy is in good agreement with experimental kinetic data, and the catalytic effect of the enzyme is reproduced without any arbitrary adjustment of parameters. The enormous reduction of the activation barrier (relative to the reference reaction in water) appears to be largely associated with the strong electrostatic effect of the Ca2+ ion and the two arginine residues in the active site. This favorable electrostatic environment reduces the cost of the general-base catalysis step by almost 15 kcal/mol (by stabilizing the OH- nucleophile) and then stabilizes the developing negative charge on the 5'-phosphate group in the second step of the reaction by about 19 kcal/mol. The basic features of the originally postulated enzyme mechanism (Cotton et al., 1979) are found to be compatible with the observed activation free energy. However, the proposed modification of the mechanism (Sepersu et al., 1987), in which Arg 87 interacts only with the pentacoordinated transition state, is supported by the simulations. Further calculations on the D21E mutant also give results in good agreement with kinetic data.     

Apparent pKa shifts of titratable residues at high denaturant concentration and the impact on protein stability

Urea and guanidine-hydrochloride (GdnHCl) are frequently used for protein denaturation in order to determine the Gibbs free energy of folding and kinetic folding/unfolding parameters. Constant pH value is applied in the folding/unfolding experiments at different denaturant concentrations and steady protonation state of titratable groups is assumed in the folded and unfolded protein, respectively. The apparent side-chain pKa values of Asp, Glu, His and Lys in the absence and presence of 6 M urea and GdnHCl, respectively, have been determined by 1H-NMR. pKa values of all four residues are up-shifted by 0.3-0.5 pH units in presence of 6 M urea by comparison with pKa values of the residues dissolved in water. In the presence of 6 M GdnHCl, pKa values are down-shifted by 0.2-0.3 pH units in the case of acidic and up-shifted by 0.3-0.5 pH units in the case of basic residues. Shifted pKa values in the presence of denaturant may have a pronounced effect on the outcome of the protein stability obtained from denaturant unfolding experiments.     

Zinc and cadmium 5-aminolevulinate dehydratase. Metal-dependent pH profiles

Native 5-aminolevulinic acid dehydratase contains zinc ions, which are essential for the enzymatic activity. Replacement of zinc by cadmium yielded an active enzyme whose kinetic parameters (kkat and Km) are similar to those of the zinc enzyme in the neutral pH range. However, the pH profiles of kcat and Km were different due to different pKa values. Two groups both with pKa values of 6.5 in the free zinc enzyme, but with pKa values of 7.0 in the cadmium enzyme were calculated from plots of log (kcat/Km) versus pH. On the other hand, the enzyme-substrate complex is controlled by one acidic group (zinc pKa = 6.0, cadmium pKa = 6.4) and one basis group (zinc pKa = 8.2, cadmium pKa = 7.7) as calculated from plots of log kcat versus pH. The Arrhenius plots for kcat of the two enzymes show no significant difference, the free energies of activation are 77.1 kJ/mol for the zinc and 76.8 kJ/mol for the cadmium enzyme. From this and from previous work it is concluded that the metal ions are located near the active site and influence the ionisations of essential amino acid residues. From the pH profiles of the modifying reaction and inhibition by diethylpyrocarbonate a histidinyl residue is inferred as one of the ionisable groups of the active site.     

pKa values and the pH dependent stability of the N-terminal domain of L9 as probes of electrostatic interactions in the denatured state. Differentiation between local and nonlocal interactions

pKa values were measured for the 6 carboxylates in the N-terminal domain of L9 (NTL9) by following NMR chemical shifts as a function of pH. The contribution of each carboxylate to the pH dependent stability of NTL9 was estimated by comparing the pKa values for the native and denatured state of the protein. A set of peptides with sequences derived from NTL9 were used to model the denatured state. In the protein fragments, the pKa values measured for the aspartates varied between 3.8 and 4.1 and the pKa values measured for the glutamates varied between 4.1 and 4.6. These results indicate that the local sequence can significantly influence pKa values in the denatured state and highlight the difficulties in using standard pKa values derived from small compounds. Calculations based on the measured pKa values suggest that the free energy of unfolding of NTL9 should decrease by 4.4 kcal mol-1 when the pH is lowered from 6 to 2. In contrast, urea and thermal denaturation experiments indicate that the stability of the protein decreases by only 2.6 kcal mol-1 when the carboxylates are protonated. This discrepancy indicates that the protein fragments are not a complete representation of the denatured state and that nonlocal sequence effects perturb the pKa's in the denatured state. Increasing the salt concentration from 100 to 750 mM NaCl removes the discrepancy between the stabilities derived from denaturation experiments and the stability changes calculated from the pKa values. At high concentrations of salt there is also less variation of the pKa values measured in the protein fragments. Our results argue that in the denatured state of NTL9 there are electrostatic interactions between groups both local and nonlocal in primary sequence.     

Semiquantitative calculations of catalytic free energies in genetically modified enzymes

The catalytic free energy and binding free energies of the native and the Asn-155----Thr, Asn-155----Leu, and Asn-155----Ala mutants of subtilisin are calculated by the empirical valence bond method and a free energy perturbation method. Two simple procedures are used; one "mutates" the substrate, and the other "mutates" the enzyme. The calculated changes in free energies (delta delta G not equal to cat and delta delta Gbind) between the mutant and native enzymes are within 1 kcal/mol of the corresponding observed values. This indicates that we are approaching a quantitative structure-function correlation. The calculated changes in catalytic free energies are almost entirely due to the electrostatic interaction between the enzyme-water system and the charges of the reacting system. This supports the idea that the electrostatic free energy associated with the changes of charges of the reacting system is the key factor in enzyme catalysis.     

Acylation of subtilisin Carlsberg by phenyl esters.

Approximate Hammett reaction constants rho calculated from k2/K8 values of several phenyl esters of N-acetyl-L-phenylalanine, hippuric acid, and beta-phenylpropionic acid are 0.0, 0.4, and 1.0 respectively. To determine whether the lack of substituent effect of k2/K8 with the N-acetyl-L-phenylalanine esters is a result of substituent-insensitive k2 or rate-limiting association of enzyme and substrate, pH-k2/K8 deependences and solvent deuterium isotope effects were determined for certain of the substrates and compared with those found with the corresponding hippurates and beta-phenylpropionates. In the pH range 5 to 8, k2/K8 of the phenyl and 4-nitrophenyl esters of each series is dependent upon the unprotonated form of an enzymatic base of apparent pKa approximately 7.4, identical with the pKa found for the free enzyme. With the phenyl esters of each substrate class, k2/K8 decreased by 2 to 3 times in deuterium oxide compared with water. The results suggest that a step involving a general base-catalyzed proton transfer, almost certainly k2, is rate-limiting with the N-acetyl-L-phenylalaninates, as well as the hippurates and beta-phenylpropionates. Attack by the protein on the latter substrates is prediminantly nucleophilic, judged by the similarity of rho in the enzymatic and reference hydroxide ion-catalyzed hydrolyses. The power rho values for the N-acetyl-L-phenylalaninates and hippurates could result from an electrophilic component in their hydrolytic mechanisms.     

Electrostatic contributions to the binding free energy of the lambdacI repressor to DNA.

A model based on the nonlinear Poisson-Boltzmann (NLPB) equation is used to study the electrostatic contribution to the binding free energy of the lambdacI repressor to its operator DNA. In particular, we use the Poisson-Boltzmann model to calculate the pKa shift of individual ionizable amino acids upon binding. We find that three residues on each monomer, Glu34, Glu83, and the amino terminus, have significant changes in their pKa and titrate between pH 4 and 9. This information is then used to calculate the pH dependence of the binding free energy. We find that the calculated pH dependence of binding accurately reproduces the available experimental data over a range of physiological pH values. The NLPB equation is then used to develop an overall picture of the electrostatics of the lambdacI repressor-operator interaction. We find that long-range Coulombic forces associated with the highly charged nucleic acid provide a strong driving force for the interaction of the protein with the DNA. These favorable electrostatic interactions are opposed, however, by unfavorable changes in the solvation of both the protein and the DNA upon binding. Specifically, the formation of a protein-DNA complex removes both charged and polar groups at the binding interface from solvent while it displaces salt from around the nucleic acid. As a result, the electrostatic contribution to the lambdacI repressor-operator interaction opposes binding by approximately 73 kcal/mol at physiological salt concentrations and neutral pH. A variety of entropic terms also oppose binding. The major force driving the binding process appears to be release of interfacial water from the protein and DNA surfaces upon complexation and, possibly, enhanced packing interactions between the protein and DNA in the interface. When the various nonelectrostatic terms are described with simple models that have been applied previously to other binding processes, a general picture of protein/DNA association emerges in which binding is driven by the nonpolar interactions, whereas specificity results from electrostatic interactions that weaken binding but are necessary components of any protein/DNA complex.     

Quantum chemical modeling of enzymatic reactions: the case of 4-oxalocrotonate tautomerase

The reaction mechanism of 4-oxalocrotonate tautomerase (4-OT) is studied using the density functional theory method B3LYP. This enzyme catalyzes the isomerisation of unconjugated alpha-keto acids to their conjugated isomers. Two different quantum chemical models of the active site are devised and the potential energy curves for the reaction are computed. The calculations support the proposed reaction mechanism in which Pro-1 acts as a base to shuttle a proton from the C3 to the C5 position of the substrate. The first step (proton transfer from C3 to proline) is shown to be the rate-limiting step. The energy of the charge-separated intermediate (protonated proline-deprotonated substrate) is calculated to be quite low, in accordance with measured pKa values. The results of the two models are used to evaluate the methodology employed in modeling enzyme active sites using quantum chemical cluster models.     

Electrostatic forces in two lysozymes: calculations and measurements of histidine pKa values.

In order to examine the electrostatic forces in globular proteins, pKa values and their ionic strength dependence of His residues of hen egg white lysozyme (HEWL) and human lysozyme (HUML) were measured, and they were compared with those calculated numerically. pKa values of His residues in HEWL, HUML, and short oligopeptides were determined from chemical shift changes of His side chains by 1H-nmr measurements. The associated changes in pKa values in HEWL and HUML were calculated by solving the Poisson-Boltzmann equations numerically for macroscopic dielectric models. The calculated pKa changes and their ionic strength dependence agreed fairly well with the observed ones. The contribution from each residue of each alpha-helix dipole to the pKa values and their ionic strength dependence was analyzed using Green's reciprocity theorem. The results indicate that (1) the pKa of His residues are largely affected by surrounding ionized and polar groups; (2) the ionic strength dependence of the pKa values is determined by the overall charge distributions and their accessibilities to solvent; and (3) alpha-helix dipoles make a significant contribution to the pKa, when the His residue is close to the helix terminus and not fully exposed to the solvent.     

The binding of physiologically significant protons to 2,3-diphosphoglycerate

The intrinsic pKa values of protons of 2,3-diphosphoglycerate (DPG) which titrate in the physiologically significant range (i.e., pH 6.8-7.8) have been determined by measuring the changes in chemical shifts of the two phosphate resonances of the molecule as a function of pH using 31P-NMR spectroscopy. While conventional acid-base titration techniques resulted in apparent pKa values of 6.39 and 7.39 for these protons, analysis of the 31P-NMR data by statistical thermodynamic methods yielded intrinsic pKa values of 6.99 +/- 0.07 and 7.28 +/- 0.04, for protons associated with the phosphates bound to carbon-3 (C-3) and carbon-2 (C-2), respectively, with an interaction energy of +0.77 kcal/mol. The free energies for the binding of protons to the C-2 and C-3 phosphates and the associated interaction energies determined by 31P-NMR were used to generate a theoretical titration curve which was essentially identical to that determined by conventional acid-base titration. The physiological implications of this work are briefly discussed.     

Modifying the beta,gamma leaving-group bridging oxygen alters nucleotide incorporation efficiency, fidelity, and the catalytic mechanism of DNA polymerase beta

DNA polymerase catalysis and fidelity studies typically compare incorporation of "right" versus "wrong" nucleotide bases where the leaving group is pyrophosphate. Here we use dGTP analogues replacing the beta,gamma-bridging O with CH2, CHF, CF2, or CCl2 to explore leaving-group effects on the nucleotidyl transfer mechanism and fidelity of DNA polymerase (pol) beta. T.G mismatches occur with fidelities similar to dGTP with the exception of the CH2 analogue, which is incorporated with 5-fold higher fidelity. All analogues are observed to bind opposite template C with Kds between 1 and 4 microM, and structural evidence suggests that the analogues bind in essentially the native conformation, making them suitable substrates for probing linear free energy relationships (LFERs) in transient-kinetics experiments. Importantly, Brnsted correlations of log(kpol) versus leaving-group pKa for both right and wrong base incorporation reveal similar sensitivities (betalg approximately -0.8) followed by departures from linearity, suggesting that a chemical step rather than enzyme conformational change is rate-limiting for either process. The location of the breaks relative to pKas of CF2, O, and the sterically bulky CCl2-bridging compounds suggests a modification-induced change in the mechanism by stabilization of leaving-group elimination. The results are addressed theoretically in terms of the energetics of successive primer 3'-O addition (bond forming) and pyrophosphate analogue elimination (bond breaking) reaction energy barriers.     

Determinants of conductance of a bacterial voltage-gated sodium channel

Through molecular dynamics (MD) and free energy simulations in electric fields, we examine the factors influencing conductance of bacterial voltage-gated sodium channel Na_vMs. The channel utilizes four glutamic acid residues in the selectivity filter (SF). Previously, we have shown, through constant pH and free energy calculations of pKa values, that fully deprotonated, singly protonated, and doubly protonated states are all feasible at physiological pH, depending on how many ions are bound in the SF. With 173 MD simulations of 450 or 500 ns and additional free energy simulations, we determine that the conductance is highest for the deprotonated state and decreases with each additional proton bound. We also determine that the pKa value of the four glutamic residues for the transition between deprotonated and singly protonated states is close to the physiological pH and that there is a small voltage dependence. The pKa value and conductance trends are in agreement with experimental work on bacterial Na_v channels, which show a decrease in maximal conductance with lowering of pH, with pKa in the physiological range. We examine binding sites for Na⁺ in the SF, compare with previous work, and note a dependence on starting structures. We find that narrowing of the gate backbone to values lower than the crystal structure's backbone radius reduces the conductance, whereas increasing the gate radius further does not affect the conductance. Simulations with some amount of negatively charged lipids as opposed to purely neutral lipids increases the conductance, as do simulations at higher voltages.     

Electrostatic calculations of amino acid titration and electron transfer, Q-AQB-->QAQ-B, in the reaction center.

The titration of amino acids and the energetics of electron transfer from the primary electron acceptor (QA) to the secondary electron acceptor (QB) in the photosynthetic reaction center of Rhodobacter sphaeroides are calculated using a continuum electrostatic model. Strong electrostatic interactions between titrating sites give rise to complex titration curves. Glu L212 is calculated to have an anomalously broad titration curve, which explains the seemingly contradictory experimental results concerning its pKa. The electrostatic field following electron transfer shifts the average protonation of amino acids near the quinones. The pH dependence of the free energy between Q-AQB and QAQ-B calculated from these shifts is in good agreement with experiment. However, the calculated absolute free energy difference is in severe disagreement (by approximately 230 meV) with the observed experimental value, i.e., electron transfer from Q-A to QB is calculated to be unfavorable. The large stabilization energy of the Q-A state arises from the predominantly positively charged residues in the vicinity of QA in contrast to the predominantly negatively charged residues near QB. The discrepancy between calculated and experimental values for delta G(Q-AQB-->QAQ-B) points to limitations of the continuum electrostatic model. Inclusion of other contributions to the energetics (e.g., protein motion following quinone reduction) that may improve the agreement between theory and experiment are discussed.