On catalytic preorganization in oxyanion holes: highlighting the problems with the gas-phase modeling of oxyanion holes and illustrating the need for complete enzyme models.

Oxyanion holes play a major role in catalyzing enzymatic reactions, yet the corresponding energetics is frequently misunderstood. The main problem may be associated with the nontrivial nature of the electrostatic preorganization effect, without following the relevant formulation. That is, although the energetics of oxyanion holes have been fully quantified in early studies (which include both the enzymatic and reference solution reactions), the findings of these studies are sometimes overlooked, and, in some cases, it is assumed that gas-phase calculations with a fixed model of an oxyanion hole are sufficient for assessing the corresponding effect in the protein. Herein, we present a systematic analysis of this issue, clarifying the problems associated with modeling oxyanions by means of two fixed water molecules (or related constructs). We then re-emphasize the point that the effect of the oxyanion hole is mainly due to the fact that the relevant dipoles are already set in an orientation that stabilizes the TS charges, whereas the corresponding dipoles in solution are randomly oriented, resulting in the need to pay a very large reorganization energy. Simply calculating interaction energies with relatively fixed species cannot capture this crucial point, and considering it may help in advancing rational enzyme design.

Examining the case for the effect of barrier compression on tunneling, vibrationally enhanced catalysis, catalytic entropy and related issues.

The idea that tunneling is enhanced by the compression of the donor-acceptor distance has attracted significant interest. In particular, recent studies argued that this proposal is consistent with pressure effects on enzymatic reactions, and that the observed pressure effects support the idea of vibrationally enhanced catalysis. However, a careful analysis of the current works reveals serious inconsistencies in the evidence presented to support these hypotheses. Apparently, tunneling decreases upon compression, and external pressure does not lead to the applicable compression of the free energy surface. Additionally, pressure experiments do not provide actual evidence for vibrationally enhanced catalysis. Finally, the temperature dependence of the entropy change in hydride transfer reactions is shown to reflect simple electrostatic effects.

A computational study of the hydrolysis of dGTP analogues with halomethylene-modified leaving groups in solution: implications for the mechanism of DNA polymerases.

DNA polymerases make up a family of enzymes responsible for regulating DNA replication and repair, which in turn maintains the integrity of the genome. However, despite intensive kinetic, crystallographic, and computational studies, elucidation of the detailed enzymatic mechanism still presents a significant challenge. We recently developed an alternative strategy for exploring the fidelity and mechanism of DNA polymerases, by probing leaving group effects on nucleotidyl transfer using a series of dGTP bisphosphonate analogues in which the beta,gamma-bridging oxygen was replaced by a series of substituted methylene groups (X = CYZ, where Y and Z = H, halogen, or another substituent). Pre-steady state kinetic measurements of DNA polymerase-catalyzed incorporation of correctly base paired (R) and mispaired (W) analogues demonstrated a strong linear free energy relationship (LFER) between the polymerase rate constant (k(pol)) and the highest pK(a) of the free bisphosphonic acid corresponding to the leaving group. However, unexpectedly, the data segregated into two distinctly different linear correlations depending on the nature of the substituent. The discrepancy between the two lines was considerably greater when the dGTP analogue formed an incorrect (G.T) rather than a correct (G.C) base pair, although the reason for this phenomenon remains unexplained. Here, we have evaluated the complete free energy surfaces for bisphosphonate hydrolysis in aqueous solution and evaluated the corresponding LFER. Our study, which employs several alternative solvation models, finds a split of the calculated LFER for the mono- and dihalogen compounds into two parallel lines, reflecting their behavior in the polymerase-catalyzed condensation reaction. We suggest that the division into two linear subsets may be a generalized solvation phenomenon involving the overall electrostatic interaction between the substrates and their surroundings and would also be observed in polar solvents in the absence of the enzyme, if the reaction in solvent is in fact identical to that of the enzyme. However, the amplified differences between the LFER lines for the incorporation of matched and mismatched deoxynucleotides probably reflects the differences in the electrostatic interaction between the TS charges in the polymerase active site. An understanding of the mechanism of this reaction in solution could thereby provide a steppingstone for understanding the factors governing the fidelity of DNA polymerases.

Simulations of ion current in realistic models of ion channels: the KcsA potassium channel.

Realistic studies of ion current in biologic channels present a major challenge for computer simulation approaches. All-atom molecular dynamics simulations involve serious time limitations that prevent their use in direct evaluation of ion current in channels with significant barriers. The alternative use of Brownian dynamics (BD) simulations can provide the current for simplified macroscopic models. However, the time needed for accurate calculations of electrostatic energies can make BD simulations of ion current expensive. The present work develops an approach that overcomes some of the above challenges and allows one to simulate ion currents in models of biologic channels. Our method provides a fast and reliable estimate of the energetics of the system by combining semimacroscopic calculations of the self-energy of each ion and an implicit treatment of the interactions between the ions, as well as the interactions between the ions and the protein-ionizable groups. This treatment involves the use of the semimacroscopic version of the protein dipole Langevin dipole (PDLD/S) model in its linear response approximation (LRA) implementation, which reduces the uncertainties about the value of the protein "dielectric constant." The resulting free energy surface is used to generate the forces for on-the-fly BD simulations of the corresponding ion currents. Our model is examined in a preliminary simulation of the ion current in the KcsA potassium channel. The complete free energy profile for a single ion transport reflects reasonable energetics and captures the effect of the protein-ionized groups. This calculated profile indicates that we are dealing with the channel in its closed state. Reducing the barrier at the gate region allows us to simulate the ion current in a reasonable computational time. Several limiting cases are examined, including those that reproduce the observed current, and the nature of the productive trajectories is considered. The ability to simulate the current in realistic models of ion channels should provide a powerful tool for studies of the biologic function of such systems, including the analysis of the effect of mutations, pH, and electric potentials.

How much do enzymes really gain by restraining their reacting fragments?

The steric effect, exerted by enzymes on their reacting substrates, has been considered as a major factor in enzyme catalysis. In particular, it has been proposed that enzymes catalyze their reactions by pushing their reacting fragments to a catalytic configuration which is sometimes called near attack configuration (NAC). This work uses computer simulation approaches to determine the relative importance of the steric contribution to enzyme catalysis. The steric proposal is expressed in terms of well defined thermodynamic cycles that compare the reaction in the enzyme to the corresponding reaction in water. The S(N)2 reaction of haloalkane dehalogenase from Xanthobacter autotrophicus GJ10, which was used in previous studies to support the strain concept is chosen as a test case for this proposal. The empirical valence bond (EVB) method provides the reaction potential surfaces in our studies. The reliability and efficiency of this method make it possible to obtain stable results for the steric free energy. Two independent strategies are used to evaluate the actual magnitude of the steric effect. The first applies restraints on the substrate coordinates in water in a way that mimics the steric effect of the protein active site. These restraints are then released and the free energy associated with the release process provides the desired estimate of the steric effect. The second approach eliminates the electrostatic interactions between the substrate and the surrounding in the enzyme and in water, and compares the corresponding reaction profiles. The difference between the resulting profiles provides a direct estimate of the nonelectrostatic contribution to catalysis and the corresponding steric effect. It is found that the nonelectrostatic contribution is about -0.7 kcal/mol while the full "apparent steric contribution" is about -2.2 kcal/mol. The apparent steric effect includes about -1.5 kcal/mol electrostatic contribution. The total electrostatic contribution is found to account for almost all the observed catalytic effect ( approximately -6.1 kcal/mol of the -6.8 calculated total catalytic effect). Thus, it is concluded that the steric effect is not the major source of the catalytic power of haloalkane dehalogenase. Furthermore, it is found that the largest component of the apparent steric effect is associated with the solvent reorganization energy. This solvent-induced effect is quite different from the traditional picture of balance between the repulsive interaction of the reactive fragments and the steric force of the protein.

What are the dielectric "constants" of proteins and how to validate electrostatic models?

Implicit models for evaluation of electrostatic energies in proteins include dielectric constants that represent effect of the protein environment. Unfortunately, the results obtained by such models are very sensitive to the value used for the dielectric constant. Furthermore, the factors that determine the optimal value of these constants are far from being obvious. This review considers the meaning of the protein dielectric constants and the ways to determine their optimal values. It is pointed out that typical benchmarks for validation of electrostatic models cannot discriminate between consistent and inconsistent models. In particular, the observed pK(a) values of surface groups can be reproduced correctly by models with entirely incorrect physical features. Thus, we introduce a discriminative benchmark that only includes residues whose pK(a) values are shifted significantly from their values in water. We also use the semimacroscopic version of the protein dipole Langevin dipole (PDLD/S) formulation to generate a series of models that move gradually from microscopic to fully macroscopic models. These include the linear response version of the PDLD/S models, Poisson Boltzmann (PB)-type models, and Tanford Kirkwwod (TK)-type models. Using our different models and the discriminative benchmark, we show that the protein dielectric constant, epsilon(p), is not a universal constant but simply a parameter that depends on the model used. It is also shown in agreement with our previous works that epsilon(p) represents the factors that are not considered explicitly. The use of a discriminative benchmark appears to help not only in identifying nonphysical models but also in analyzing effects that are not reproduced in an accurate way by consistent models. These include the effect of water penetration and the effect of the protein reorganization. Finally, we show that the optimal dielectric constant for self-energies is not the optimal constant for charge-charge interactions.

Remarkable rate enhancement of orotidine 5'-monophosphate decarboxylase is due to transition-state stabilization rather than to ground-state destabilization.

The remarkable rate enhancement of orotidine 5'-phosphate decarboxylase (ODCase) has been attributed to ground-state destabilization (GSD) by desolvation and more recently to GSD by electrostatic stress. Here we reiterate our previous arguments that the GSD mechanisms are not likely to play a major role in enzyme catalysis and analyze quantitatively the origin of the rate enhancement of ODCase. This analysis involves energy considerations and computer simulations. Our energy considerations show that (i) the previously proposed desolvation mechanism is based on an improper reference state; (ii) a nonpolar active site cannot account for the catalytic effect of the enzyme; (iii) the focus on the role of the negatively charged protein residues in the electrostatic stress GSD mechanism overlooks the fact that the positively charged Lys72 strongly stabilizes the substrate; (iv) although the previous calculation of the actual enzymatic reaction correctly reproduced the observed rate enhancement, it could not obtain this rate enhancement from the calculated binding energies (which are the relevant quantities for determining GSD effects); (v) the GSD mechanism is inconsistent with the observed binding energy of the phosphoribosyl part of the substrate; and (vi) the presumably unstable substrate (orotate) can be stabilized, at equilibrium, by accepting a proton from the solvent. Our computer simulation studies involve two set of calculations. First, we study the catalytic reaction by using an empirical valence bond potential surface calibrated by ab initio calculations of the reference solution reaction. This calculation reproduces the observed catalytic effect of the enzyme. Next, we use free-energy perturbation calculations and evaluated the electrostatic contributions to the binding energies of the ground state and transition state (TS). These calculations show that the rate enhancement in ODCase is due to the TS stabilization rather than to GSD. The differences between our own and the previous theoretical analyses stem from both the selection of the reacting system and the treatment of the long-range electrostatic contributions to the binding energy. The reacting system was previously assumed to encompass only the orotate. However, this selection does not allow proper description of the reaction catalyzed by the enzyme (i.e., [Orotate(-) + LysH(+)] if [uracil + Lys + CO(2)]). Therefore, the reacting system should include both orotate and the general acid in the form of the protonated Lys72 protein residue. This selection leads to a simple and consistent interpretation of the catalytic effect where the electrostatic stabilization of the transition state is due to the fact that the two negatively charged aspartic residues are already placed near the reactive lysine so that they do not have to reorganize significantly during the reaction. Interestingly, even calculations with only orotate(-) as the reacting system do not produce sufficient destabilization to account for a GSD mechanism. In summary, we conclude, in agreement with previous workers, that ODCase catalyzes its reaction by electrostatic effects. However, we show that these effects are associated with TS stabilization due to a reduction in the protein-protein reorganization energy and not with protein-substrate destabilization effects.

How important are entropic contributions to enzyme catalysis?

The idea that enzymes accelerate their reactions by entropic effects has played a major role in many prominent proposals about the origin of enzyme catalysis. This idea implies that the binding to an enzyme active site freezes the motion of the reacting fragments and eliminates their entropic contributions, (delta S(cat)(double dagger))', to the activation energy. It is also implied that the binding entropy is equal to the activation entropy, (delta S(w)(double dagger))', of the corresponding solution reaction. It is, however, difficult to examine this idea by experimental approaches. The present paper defines the entropic proposal in a rigorous way and develops a computer simulation approach that determines (delta S(double dagger))'. This approach allows us to evaluate the differences between (delta S(double dagger))' of an enzymatic reaction and of the corresponding reference reaction in solution. Our approach is used in a study of the entropic contribution to the catalytic reaction of subtilisin. It is found that this contribution is much smaller than previously thought. This result is due to the following: (i) Many of the motions that are free in the reactants state of the reference solution reaction are also free at the transition state. (ii) The binding to the enzyme does not completely freeze the motion of the reacting fragments so that (delta S(double dagger))' in the enzymes is not zero. (iii) The binding entropy is not necessarily equal to (delta S(w)(double dagger))'.

How does GAP catalyze the GTPase reaction of Ras? A computer simulation study.

The formation of a complex between p21(ras) and GAP accelerates the GTPase reaction of p21(ras) and terminates the signal for cell proliferation. The understanding of this rate acceleration is important for the elucidation of the role of Ras mutants in tumor formation. In principle there are two main options for the origin of the effect of GAP. One is a direct electrostatic interaction between the residues of GAP and the transition state of the Ras-GAP complex and the other is a GAP-induced shift of the structure of Ras to a configuration that increases the stabilization of the transition state. This work examines the relative importance of these options by computer simulations of the catalytic effect of Ras. The simulations use the empirical valence bond (EVB) method to study the GTPase reaction along the alternative associative and dissociative paths. This approach reproduces the trend in the overall experimentally observed catalytic effect of GAP: the calculated effect is 7 +/- 3 kcal/mol as compared to the observed effect of approximately 6.6 kcal/mol. Furthermore, the calculated effect of mutating Arg789 to a nonpolar residue is 3-4 kcal/mol as compared to the observed effect of 4.5 kcal/mol for the Arg789Ala mutation. It is concluded, in agreement with previous proposals, that the effect of Arg789 is associated with its direct interaction with the transition state charge distribution. However, calculations that use the coordinates of Ras from the Ras-GAP complex (referred to here as Ras') reproduce a significant catalytic effect relative to the Ras coordinates. This indicates that part of the effect of GAP involves a stabilization of a catalytic configuration of Ras. This configuration increases the positive electrostatic potential on the beta-phosphate (relative to the corresponding situation in the free Ras). In other words, GAP stabilizes the GDP bound configuration of Ras relative to that of the GTP-bound conformation. The elusive oncogenic effect of mutating Gln61 is also explored. The calculated effect of such mutations in the Ras-GAP complex are found to be small, while the observed effect is very large (8.7 kcal/mol). Since the Ras is locked in its Ras-GAP configuration in our simulations, we conclude that the oncogenic effect of mutation of Gln61 is indirect and is associated most probably with the structural changes of Ras upon forming the Ras-GAP complex. In view of these and the results for the Ras' we conclude that GAP activates Ras by both direct electrostatic stabilization of the transition state and an indirect allosteric effect that stabilizes the GDP-bound form. The present study also explored the feasibility of the associative and dissociative mechanism in the GTPase reaction of Ras. It is concluded that the reaction is most likely to involve an associative mechanism.

Examining methods for calculations of binding free energies: LRA, LIE, PDLD-LRA, and PDLD/S-LRA calculations of ligands binding to an HIV protease.

Several strategies for evaluation of the protein-ligand binding free energies are examined. Particular emphasis is placed on the Linear Response Approximation (LRA) (Lee et. al., Prot Eng 1992;5:215-228) and the Linear Interaction Energy (LIE) method (Aqvist et. al., Prot Eng 1994;7:385-391). The performance of the Protein Dipoles Langevin Dipoles (PDLD) method and its semi-microscopic version (the PDLD/S method) is also considered. The examination is done by using these methods in the evaluating of the binding free energies of neutral C2-symmetric cyclic urea-based molecules to Human Immunodeficiency Virus (HIV) protease. Our starting point is the introduction of a thermodynamic cycle that decomposes the total binding free energy to electrostatic and non-electrostatic contributions. This cycle is closely related to the cycle introduced in our original LRA study (Lee et. al., Prot Eng 1992;5:215-228). The electrostatic contribution is evaluated within the LRA formulation by averaging the protein-ligand (and/or solvent-ligand) electrostatic energy over trajectories that are propagated on the potentials of both the polar and non-polar (where all residual charges are set to zero) states of the ligand. This average involves a scaling factor of 0.5 for the contributions from each state and this factor is being used in both the LRA and LIE methods. The difference is, however, that the LIE method neglects the contribution from trajectories over the potential of the non-polar state. This approximation is entirely valid in studies of ligands in water but not necessarily in active sites of proteins. It is found in the present case that the contribution from the non-polar states to the protein-ligand binding energy is rather small. Nevertheless, it is clearly expected that this term is not negligible in cases where the protein provides preorganized environment to stabilize the residual charges of the ligand. This contribution can be particularly important in cases of charged ligands. The analysis of the non-electrostatic term is much more complex. It is concluded that within the LRA method one has to complete the relevant thermodynamic cycle by evaluating the binding free energy of the "non-polar" ligand, l;, where all the residual charges are set to zero. It is shown that the LIE term, which involves the scaling of the van der Waals interaction by a constant beta (usually in the order of 0.15 to 0.25), corresponds to this part of the cycle. In order to elucidate the nature of this non-electrostatic term and the origin of the scaling constant beta, it is important to evaluate explicitly the different contributions to the binding energy of the non-polar ligand, DeltaG(bind,l;). Since this cannot be done at present (for relatively large ligands) by rigorous free energy perturbation approaches, we evaluate DeltaG(bind,l;) by the PDLD approach, augmented by microscopic calculations of the change in configurational entropy upon binding. This evaluation takes into account the van der Waals, hydrophobic, water penetration and entropic contributions, which are the most important free energy contributions that make up the total DeltaG(bind,l;). The sum of these contributions is scaled by a factor straight theta and it is argued that obtaining a quantitative balance between these contributions should result in straight theta = 1. By doing so we should have a reliable estimate of the value of the LIE beta and a way to understand its origin. The present approach gives straight theta values between 0.5 and 0.73, depending on the approximation used. This is encouraging but still not satisfying. Nevertheless, one might be able to use our PDLD approach to estimate the change of the LIE straight theta between different protein active sites. It is pointed out that the LIE method is quite similar to our original approach where the electrostatic term was evaluated by the LRA method and the non-electrostatic term by the PDLD method (with its vdw, solvation,

Simulating proton translocations in proteins: probing proton transfer pathways in the Rhodobacter sphaeroides reaction center.

A general method for simulating proton translocations in proteins and for exploring the role of different proton transfer pathways is developed and examined. The method evaluates the rate constants for proton transfer processes using the energetics of the relevant proton configurations. The energies (DeltaG((m))) of the different protonation states are evaluated in two steps. First, the semimicroscopic version of the protein dipole Langevin dipole (PDLD/S) method is used to evaluate the intrinsic energy of bringing the protons to their protein sites, when the charges of all protein ionized residues are set to zero. Second, the interactions between the charged groups are evaluated by using a Coulomb's Law with an effective dielectric constant. This approach, which was introduced in an earlier study by one of the authors of the current report, allows for a very fast determination of any DeltaG((m)) and for practical evaluation of the time-dependent proton population: That is, the rate constants for proton transfer processes are evaluated by using the corresponding DeltaG((m)) values and a Marcus type relationship. These rate constants are then used to construct a master equation, the integration of which by a fourth-order Runge-Kutta method yields the proton population as a function of time. The integration evaluates, 'on the fly,' the changes of the rate constants as a result of the time-dependent changes in charge-charge interaction, and this feature benefits from the fast determination of DeltaG((m)). The method is demonstrated in a preliminary study of proton translocation processes in the reaction center of Rhodobacter sphaeroides. It is found that proton transfer across water chains involves significant activation barriers and that ionized protein residues probably are involved in the proton transfer pathways. The potential of the present method in analyzing mutation experiments is discussed briefly and illustrated. The present study also examines different views of the nature of proton translocations in proteins. It is shown that such processes are controlled mainly by the electrostatic interaction between the proton site and its surroundings rather than by the local bond rearrangements of water molecules that are involved in the proton pathways. Thus, the overall rate of proton transport frequently is controlled by the highest barrier along the conduction pathway. Proteins 1999;36:484-500.

Role of active site residues in the glycosylase step of T4 endonuclease V. Computer simulation studies on ionization states.

T4 Endonuclease V (EndoV) is a base excision repair enzyme that removes thymine dimers (TD) from damaged DNA. To elucidate the role of the active site residues in catalysis, their pK(a)'s were evaluated using the semimicroscopic version of the protein dipoles-Langevin dipoles method (PDLD/S). Contributions of different effects to the pK(a) such as charge-charge interactions, conformational rearrangement, protein relaxation, and DNA binding were analyzed in detail. Charging of the active site residues was found to be less favorable in the complex than in the free enzyme. The pK(a) of the N-terminus decreased from 8.01 in the free enzyme to 6.52 in the complex, while the pK(a) of Glu-23 increased from 1. 52 to 7.82, which indicates that the key residues are neutral in the reactant state of the glycosylase step. These pK(a)'s are in agreement with the optimal pH range of the reaction and support the N-terminus acting as a nucleophile. The Glu-23 in its protonated form is hydrogen bonded to O4' of the sugar of 5' TD and can play a role in increasing the positive charge of C1' and, hence, accelerating the nucleophilic substitution. Furthermore, the neutral Glu-23 is a likely candidate to protonate O4' to induce ring opening required to complete the glycosylase step of EndoV. The positively charged Arg-22 and Arg-26 provide an electrostatically favorable environment for the leaving base. To distinguish between S(N)1 and S(N)2 mechanisms of the glycosylase step the energetics of protonating O2 of 5' TD was calculated. The enzyme was found to stabilize the neutral thymine by approximately 3.6 kcal/mol, whereas it destabilizes the protonated thymine by approximately 6.6 kcal/mol with respect to an aqueous environment. Consequently, the formation of a protonated thymine intermediate is unlikely, indicating an S(N)2 reaction mechanism for the glycosylase step.

Mechanistic alternatives in phosphate monoester hydrolysis: what conclusions can be drawn from available experimental data?

Phosphate monoester hydrolysis reactions in enzymes and solution are often discussed in terms of whether the reaction pathway is associative or dissociative. Although experimental results for solution reactions have usually been considered as evidence for the second alternative, a closer thermodynamic analysis of observed linear free energy relationships shows that experimental information is consistent with the associative, concerted and dissociative alternatives.

Electrostatic effects in macromolecules: fundamental concepts and practical modeling.

The past few years have seen an exponential growth in the calculations of electrostatic energies of macromolecules and an increased recognition of the crucial role of electrostatic effects. This review considers the current state of the field. Focus is placed on calculations of pKas, redox potentials and binding energies in macromolecules and clarification of the fact that the value of the dielectric 'constant' of a protein depends on its definition and that small dielectric constants should not be used in describing charge-charge interactions by current continuum models.

Computer simulations of enzyme catalysis: finding out what has been optimized by evolution.

The origin of the catalytic power of enzymes is discussed, paying attention to evolutionary constraints. It is pointed out that enzyme catalysis reflects energy contributions that cannot be determined uniquely by current experimental approaches without augmenting the analysis by computer simulation studies. The use of energy considerations and computer simulations allows one to exclude many of the popular proposals for the way enzymes work. It appears that the standard approaches used by organic chemists to catalyze reactions in solutions are not used by enzymes. This point is illustrated by considering the desolvation hypothesis and showing that it cannot account for a large increase in kcat relative to the corresponding kcage for the reference reaction in a solvent cage. The problems associated with other frequently invoked mechanisms also are outlined. Furthermore, it is pointed out that mutation studies are inconsistent with ground state destabilization mechanisms. After considering factors that were not optimized by evolution, we review computer simulation studies that reproduced the overall catalytic effect of different enzymes. These studies pointed toward electrostatic effects as the most important catalytic contributions. The nature of this electrostatic stabilization mechanism is far from being obvious because the electrostatic interaction between the reacting system and the surrounding area is similar in enzymes and in solution. However, the difference is that enzymes have a preorganized dipolar environment that does not have to pay the reorganization energy for stabilizing the relevant transition states. Apparently, the catalytic power of enzymes is stored in their folding energy in the form of the preorganized polar environment.