Search PubMed⌕ Search

Biomedical subjects

A Warshel

Publications and source records attributed to A Warshel.

At least 37 records · Page 2Linked to original sources
PubMed1998

The effect of protein relaxation on charge-charge interactions and dielectric constants of proteins.

The effect of the reorganization of the protein polar groups on charge-charge interaction and the corresponding effective dielectric constant (epsilon(eff)) is examined by the semimicroscopic version of the Protein Dipole Langevin Dipoles (PDLD/S) method within the framework of the Linear Response Approximation (LRA). This is done by evaluating the interactions between ionized residues in the reaction center of Rhodobacter sphaeroides, while taking into account the protein reorganization energy. It is found that an explicit consideration of the protein relaxation leads to a significant increase in epsilon(eff) and that semimicroscopic models that do not take this relaxation into account force one to use a large value for the so-called "protein dielectric constant," epsilon(p), of the Poisson-Boltzmann model or for the corresponding epsilon(in) in the PDLD/S model. An additional increase in epsilon(eff) is expected from the reorganization of ionized residues and from changes in the degree of water penetration. This finding provides further support for the idea that epsilon(in) (or epsilon(p)) represents contributions that are not considered explicitly. The present study also provides a systematic illustration of the nature of epsilon(eff), supporting our previously reported view that charge-charge interactions correspond to a large value of this "dielectric constant," even in protein interiors. It is also pointed out that epsilon(eff) for the interaction between ionizable groups in proteins is very different from the effective dielectric constant, epsilon'(eff), that determines the free energy of ion pairs in proteins (epsilon'(eff) reflects the effect of preoriented protein dipoles). Finally, the problems associated with the search for a general epsilon(in) are discussed. It is clarified that the epsilon(in) that reproduces the effect of protein relaxation on charge-charge interaction is not equal to the epsilon(in) that reproduces the corresponding effect upon formation of individual charges. This reflects fundamental inconsistencies in attempts to cast microscopic concepts in a macroscopic model. Thus one should either use a large epsilon(in) for charge-charge interactions and a small epsilon(in) for charge-dipole interactions or consider the protein relaxation microscopically.

Binding Sites↗
PubMed1998

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.

Enzymes↗
PubMed1997

A fast estimate of electrostatic group contributions to the free energy of protein-inhibitor binding.

Dissecting ligand-protein binding free energies in individual contributions of protein residues (which are referred to here as 'group contributions') is of significant importance. For example, such contributions could help in estimating the corresponding mutational effects and in studies of drug resistance problems. However, the meaning of group contributions is not always uniquely defined and the approximations for rapid estimates of such contributions are not well developed. In this paper, the nature of group contributions to binding free energy is examined, focusing particularly on electrostatic contributions which are expected to be well behaved. This analysis examines different definitions of group contributions; the 'relaxed' group contributions that represent the change in binding energy upon mutation of the given residue to glycine, and the 'non-relaxed' group contributions that represent the scaled Coulomb interaction between the given residue and the ligand. Both contributions are defined and evaluated by the linear response approximation (LRA) of the PDLD/ S method. The present analysis considers the binding of pepstatin to endothiapepsin and 23 of its mutants as a test case for a neutral ligand. The 'non-relaxed' group contributions of 15 endothiapepsin residues show significant peaks in the 'electrostatic fingerprint'. The residues that contribute to the electrostatic fingerprint are located in the binding site of endothiapepsin. They include the aspartic dyad (Asp32, Asp215) with adjacent residues and the flap region. Twelve of these 15 residues have a heavy atom distance of <3.75 A to pepstatin. The contributions of 8 (10) of these 12 residues can be reconciled with the calculated 'relaxed' group contributions where one allows the protein and solvent (solvent only) to relax upon mutation of the given residue to glycine. On the other hand, it was found that residues at the second 'solvation shell' can have relaxed contributions that are not captured by the non-relaxed approach. Hence, whereas residues with significant non-relaxed electrostatic contributions are likely to contribute to binding, residues with small non-relaxed contributions may still affect the binding energy. At any rate, it is established here that even in the case of uncharged inhibitors it is possible to use the non-relaxed electrostatic fingerprint to detect 'hot' residues that are responsible for binding. This is significant since some versions of the non-relaxed approximation are faster by several orders of magnitude than more rigorous approaches. The general applicability of this approach is outlined, emphasizing its potential in studies of drug resistance where it is crucial to have a rapid way of anticipating the effect of mutation on both drug binding and catalysis.

Aspartic Acid↗
PubMed1996

Energy considerations show that low-barrier hydrogen bonds do not offer a catalytic advantage over ordinary hydrogen bonds.

Low-barrier hydrogen bonds have recently been proposed as a major factor in enzyme catalysis. Here we evaluate the feasibility of transition state (TS) stabilization by low-barrier hydrogen bonds in enzymes. Our analysis focuses on the facts that (i) a low-barrier hydrogen bond is less stable than a regular hydrogen bond in water, (ii) TSs are more stable in the enzyme active sites than in water, and (iii) a nonpolar active site would destabilize the TS relative to its energy in water. Combining these points and other experimental and theoretical facts in a physically consistent frame-work shows that a low-barrier hydrogen bond cannot stabilize the TS more than an ordinary hydrogen bond. The reason for the large catalytic effect of active site hydrogen bonds is that their formation entails a lower reorganization energy than their solution counterparts, due to the preorganized enzyme environment.

Binding Sites↗
PubMed1996

Linear free energy relationships in the intrinsic and GTPase activating protein-stimulated guanosine 5'-triphosphate hydrolysis of p21ras.

Controlling the hydrolysis rate of GTP bound to guanine nucleotide binding proteins is crucial for the right timing of many biological processes. Theoretical, structural, and functional studies have demonstrated that in p21ras the substrate of the reaction, GTP itself, plays a central role by acting as the base catalyst. This substrate-assisted reaction mechanism was analyzed with the help of linear free energy relationships (LFERs). Here we present experimental data that further support the proposed mechanism. We extend the LFER analysis to a wide range of oncogenic as well as nontransforming Ras mutants. It is illustrated that almost all Ras variants follow the observed LFER and thus also the same reaction path. Further, the reduced GTPase reaction rate that characterizes the oncogenic effect of many of the p21 mutants found in human tumors seems to be a consequence of a slightly reduced pKa of the gamma-phosphate group of bound GTP. Factors causing a pKa deviation of just 0.5 unit are enough to slow the intrinsic GTPase reaction rate significantly, and the system may exhibit as a consequence of this an oncogenic potential. Interestingly, we also found oncogenic mutations that do not follow the regular LFER. This suggests that the oncogenic effect of distinct Ras mutants has a different physical origin. The results presented might aid in the design of drugs aimed at reactivating the GTPase reaction of many oncogenic p21ras mutants. We also analyzed the stimulated GTPase reaction of p21ras by the GTPase activating protein (GAP) and the GTPase reaction of Rap1A, a Ras-related GTP binding protein, with similar approaches. The corresponding results indicate that the GAP-stimulated GTPase as well as the Rap1A-catalyzed reaction seem to follow the same substrate-assisted reaction mechanism. However, the correlation coefficient for the GAP-catalyzed reaction is different from the corresponding coefficient for the intrinsic reaction. While the intrinsic reaction exhibits a Brønsted slope of beta = 2.1, the corresponding value for the GAP-activated reaction is beta = 4.9.

Binding Sites↗
PubMed1996

Mechanistic analysis of the observed linear free energy relationships in p21ras and related systems.

Previous studies of the GTPase reaction catalyzed by p21ras have indicated that the logarithm of the observed reaction rate and the pKa of the bound GTP are correlated by the Brønsted relationship log(kcat) = beta pKa + A. While most of the Ras mutants display a Brønsted slope beta of 2.1, a small set of oncogenic mutants exhibit a beta of > > 1. On the other hand, it was found that the corresponding Brønsted slope for the GTPase reaction of p21ras in the presence of GTPase Activating Protein (GAP) is about beta = 4.9. The present work explores the basis for such linear free energy relationships (LFERs) in general and applies these concepts to p21ras and related systems. It is demonstrated that the optimal way to analyze LFER is by using Marcus type parabolas that represent the reactant, intermediate, and product state of the reaction in a relevant energy diagram. The observed LFER is used to analyze the actual free energy surface and reaction path of the intrinsic GTPase reaction in p21ras. From this, a model reaction profile can be constructed that explains how a LFER can arise and also how the different observed Brønsted coefficients can be rationalized. This analysis is augmented by solvent isotope effect studies. It is pointed out that the overall activation barrier reflects the energy of the proton transfer (PT) step, although this step does not include the actual transition state of the hydrolysis reaction. The proposed GTP as a base mechanism is compared to a recently proposed reaction scheme where Gln61 serves as a proton shuttle in a concerted mechanism. It is shown by unique energy considerations that the concerted mechanism is unlikely. Other alternative mechanisms are also considered, and their consistency with the observed LFER and other factors is discussed. Finally, we analyze the observed LFER for the GTPase reaction of p21ras in the presence of GAP and discuss its relevance for the mechanism of GAP activation.

Catalysis↗
PubMed1996

Electrostatic control of GTP and GDP binding in the oncoprotein p21ras.

BACKGROUND: p21ras is one of the GTP-binding proteins that act as intercellular molecular switches. The GTP-bound form of p21ras sends a growth-promoting signal that is terminated once the protein is cycled back into its GDP-bound form. The interaction of guanine-nucleotide-exchange factors (GEFs) with p21ras leads to activation of the protein by promoting GDP --> GTP exchange. Oncogenic mutations of p21ras trap the protein in its biological active GTP-bound form. Other mutations interfere with the activity of GEF. Thus, it is important to explore the structural basis for the action of different mutations. RESULTS: The crystal structures of p21ras are correlated with the binding affinities of GTP and GDP by calculating the relevant electrostatic energies. It is demonstrated that such calculations can provide a road map to the location of 'hot' residues whose mutations are likely to change functional properties of the protein. Furthermore, calculations of the effect of specific mutations on GTP and GDP binding are consistent with those observed. This helps to analyze and locate functionally important parts of the protein. CONCLUSIONS: Our calculations indicate that the protein main chain provides a major contribution to the binding energies of nucleotides and probably plays a key role in relaying the effect of GEF action. Analysis of p21ras mutations in residues that are important for the proper function of GEFs suggests that the region comprising residues 62-67 in p21ras is the major GEF-binding site. This analysis and our computer simulations indicate that the effect of GEF is probably propagated to the P-loop (residues 10-17) through interaction between Gly60 and Gly12. This then reduces the interaction between the main-chain dipoles of the P-loop and the nucleotide. Finally, the results also suggest a possible relationship between the GTP --> GDP structural transition and the catalytic effect of the GTPase-activating protein.

Binding Sites↗
PubMed1996

Ab initio calculations of free energy barriers for chemical reactions in solution: proton transfer in [FHF]-.

This paper describes a hybrid ab initio quantum mechanical/molecular mechanics (QM/MM) method for calculating activation free energies of chemical reactions in solution, using molecular mechanics force fields for the solvent and an ab initio technique that incorporates the potential from the solvent in its Hamiltonian for the solute. The empirical valence bond (EVB) method is used as a reference potential for the ab initio free energy calculation, and drives the reaction along the proper coordinate, thus overcoming problems encountered by direct attempts to use molecular orbital methods in calculations of activation free energies. The utility of our method is illustrated by calculating the activation free energy for proton transfer between fluoride ions in the [FHF]-system, in both polar and nonpolar solution.

Calorimetry↗
PubMed1995

Substrate-assisted catalysis as a mechanism for GTP hydrolysis of p21ras and other GTP-binding proteins.

Despite many advances in understanding the structure and function of GTP-binding proteins the mechanism by which these molecules switch from the GTP-bound on-state to the GDP-bound off-state is still poorly understood. Theoretical studies suggest that the activation of the nucleophilic water which hydrolyzes GTP needs a general base. Such a base could not be located in any of the many GTP-binding proteins. Here we present a unique type of linear free energy relationships that not only supports a mechanism for p21ras in which the substrate GTP itself acts as the catalytic base driving the GTPase reaction but can also help to explain why certain mutants of p21ras are oncogenic and others are not.

Amino Acid Sequence↗
PubMed1994

Calculation of the redox potentials of iron-sulfur proteins: the 2-/3-couple of [Fe4S*4Cys4] clusters in Peptococcus aerogenes ferredoxin, Azotobacter vinelandii ferredoxin I, and Chromatium vinosum high-potential iron protein.

Calculations of the redox potentials of the 2-/3-couples of [Fe4S*4Cys4] clusters in the iron-sulfur proteins Peptococcus aerogenes ferredoxin (PaFd), Azotobacter vinelandii ferredoxin I (AvFdI) and Chromatium vinosum high potential iron protein (CvHiPIP) based on the Protein Dipoles Langevin Dipoles (PDLD) method are reported. The structures of these proteins have been determined by X-ray crystallography; in the case of PaFd the structure has recently been revised due to a change in the sequence close to Cluster II. The large differences between the potentials of the [Fe4S*4Cys4] clusters of PaFd and AvFdI and the potential of the [Fe4S*4Cys4] cluster of CvHiPIP are successfully modeled and originate principally in differences in the configuration of main-chain amide groups near the clusters. The small difference between the potentials of PaFd and AvFdI is also satisfactorily modeled in the case of Cluster I of PaFd. Solvent dipoles close to the cluster in PaFd are an important contributor to its higher potential. The two X-ray structures of PaFd yield similar results for Cluster I of PaFd. In contrast, the results for Cluster II differ substantially; for reasons not yet clear, the recently revised structure leads to results in worse agreement with experiment.

Amino Acid Sequence↗
PubMed1994

Why have mutagenesis studies not located the general base in ras p21.

Ras p21 plays a major role in the control of cell growth, and oncogenic mutations of this protein have been found in human cancers. Unfortunately, the detailed mode of action of Ras p21 is still unclear, in spite of the great interest in this protein and the availability of its X-ray crystal structure. In particular, mutagenesis studies of different active site residues could not identify the general base for GTP hydrolysis. Here we tackle this question using a computer simulation approach with clear and reliable energy considerations and conclude that the most likely general base is the bound GTP itself. Obviously, the identification of such a general base cannot be easily accomplished by mutagenesis experiments.

Binding Sites↗
PubMed1992

Protein control of iron-sulfur cluster redox potentials.

The relationship between the three-dimensional structures of iron-sulfur proteins and the redox potentials of their iron-sulfur clusters is of fundamental importance. We report calculations of the redox potentials of the [Fe4S4(S-cys)4]-2/-3 couple in four crystallographically characterized proteins: Azotobacter vinelandii ferredoxin I, Peptococcus aerogenes ferredoxin, Bacillus thermoproteolyticus ferredoxin, and Chromatium vinosum high potential iron protein (HiPIP). Our calculations use the "protein dipoles Langevin dipoles" microscopic electrostatic model, which includes both protein and solvent water. The variations in calculated redox potentials are in excellent agreement with experimental data. In particular, our results confirm the important role of amide groups close to the cluster in separating the potential of C. vinosum HiPIP from those of the other three proteins. However, the potentials of these latter exhibit a substantial range despite extremely similar amide group environments of their clusters. Our results show that the potentials in these proteins are tuned in part by varying the access of solvent water to the neighborhood of the cluster. Our calculations provide the first successful quantitative modeling of the protein control of iron-sulfur cluster redox potentials.

Azotobacter vinelandii↗
PubMed1992

On the mechanism of guanosine triphosphate hydrolysis in ras p21 proteins.

The residue Gln61 is assumed to play a major role in the mechanism of ras p21, and mutations of this residue are often found in human tumors. Such mutations lead to a major reduction in the rate of GTP hydrolysis by the complex of ras p21 and the GTPase activating protein (GAP) and lock the protein in a growth-promoting state. This work examines the role of Gln61 in ras p21 by using computer simulation approaches to correlate the structure and energetics of this system. Free energy perturbation calculations and simpler electrostatic considerations demonstrate that Gln61 is unlikely to serve as the general base in the intrinsic GAP-independent reaction of p21. Glutamine is already a very weak base in water, and surprisingly the GlnH+ OH-reaction intermediate is even less stable in the protein active site than in the corresponding reaction in water. The electrostatic field of Glu63, which could in principle stabilize the protonated Gln61, is found to be largely shielded by the surrounding solvent. However, it is still possible that Gln61 is a general base in the GAP/ras p21 complex since this system could enhance the electrostatic effect of Glu63. It is also possible that the gamma-phosphate acts as general base and that Gln61 accelerates the reaction by stabilizing the OH- nucleophile. If such a mechanism is operative, then GAP may enhance the effect of Gln61 by preorienting its hydrogen bonds in the transition-state configuration.

GTP-Binding Proteins↗
PubMed1992

Effect of the Asn52----Ile mutation on the redox potential of yeast cytochrome c. Theory and experiment.

Theoretical methods for correlation of sequence changes and redox potential of electron transport proteins are examined using the Asn52----Ile mutation in cytochrome c as a test case. The first approach uses the protein dipoles Langevin dipoles (PDLD) method and the high resolution X-ray structures of the native and the mutant proteins. This approach is found to give reliable results where all the solvent molecules are represented by Langevin dipoles and also when some bound water molecules are represented explicitly. A free energy perturbation method is also found to give reasonable results but at the expense of much more computer time. Finally, an approach that generates mutant structures from the native structure by molecular dynamics simulation and then uses these configurations in PDLD calculations is found to give a reasonable estimate of the effect of the mutation on the corresponding redox potential. The encouraging results obtained here and in a preliminary test case of the Phe82----Ser mutation indicates that the present strategies can provide a useful tool for structure-redox and sequence-redox correlation in proteins.

Amino Acid Sequence↗
PubMed1992

Computer simulation of the initial proton transfer step in human carbonic anhydrase I.

The initial water proteolysis step in the proton transfer "half-reaction" of human carbonic anhydrase I is simulated using the empirical valence bond method in combination with free energy perturbation molecular dynamics calculations. A free energy profile for the enzyme catalysed reaction and the corresponding pKa associated with ionization of the zinc-bound water is calculated. The obtained pKa value of 7 to 8 appears to be in good agreement with experimental observations and the calculated rate constant for this step is also compatible with kinetic data. The simulations clearly emphasize the important electrostatic effect associated with the catalytic zinc ion.

Carbonic Anhydrases↗
PubMed1992

Computer simulations of enzymatic reactions: examination of linear free-energy relationships and quantum-mechanical corrections in the initial proton-transfer step of carbonic anhydrase.

Computer simulation approaches can provide a powerful tool for correlating the structure of enzymes with their catalytic activity. One of the most effective ways of simulating enzymatic reactions is provided by the empirical valence bond method. The general applicability of this method has been demonstrated in several enzymatic reactions and it is reexamined here in a study of the initial proton-transfer step in the catalytic reaction of carbonic anhydrase. The simulations produce a rate constant which is in agreement with the observed kinetic data and emphasizes the importance of the electrostatic effect associated with the catalytic zinc ion. The calculations are also used to examine the validity of linear free-energy relationships (LFERs) in enzyme catalysis and to evaluate quantum-mechanical corrections of the calculated rate constant. It is found that LFERs are valid in the present case and it is argued that this reflects the fact that the protein responds linearly to the development of electrostatic forces during the reaction. It is concluded that the present approach can be used to augment experimental studies in establishing the general validity of LFERs. It is noted, however, that such relationships are much more valid for transitions between different resonance structures than for transitions between reactants and product states.

Carbonic Anhydrases↗
PubMed1992

Calculations of antibody-antigen interactions: microscopic and semi-microscopic evaluation of the free energies of binding of phosphorylcholine analogs to McPC603.

The study of antibody-antigen interactions should greatly benefit from the development of quantitative models for the evaluation of binding free energies in proteins. The present work addresses this challenge by considering the test case of the binding free energies of phosphorylcholine analogs to the murine myeloma protein McPC603. This includes the evaluation of the differential binding energy as well as the absolute binding energies and their corresponding electrostatic contributions. Four different approaches are examined: the Protein Dipoles Langevin Dipoles (PDLD) method, the semi-microscopic PDLD (PDLD/S) method, a free energy perturbation (FEP) method based on an adiabatic charging procedure and a linear response approximation that accelerates the FEP calculation. The PDLD electrostatic calculations are augmented by estimates of the relevant hydrophobic and steric contributions. The determination of the hydrophobic energy involves an approach which considers the modification of the effective surface area of the solute by local field effects. The steric contributions are analyzed in terms of the corresponding reorganization energies. This treatment, which considers the protein as a harmonic system, views the steric forces as the restoring forces for the electrostatic interactions. The FEP method is found to give unreliable results with regular cut-off radii and starts to give quantitative results only in very expensive treatment with very large cut-off radii. The PDLD and PDLD/S methods are much faster than the FEP approach and give reasonable results for both the relative and absolute binding energies. The speed and simplicity of the PDLD/S method make it an effective strategy for interactive docking studies and indeed such an option is incorporated in the program MOLARIS. A component analysis of the different energy contributions of the FEP treatment and a similar PDLD analysis indicate that electrostatic effects provide the largest contribution to the differential binding energy, while the hydrophobic and steric contributions are much smaller. This finding lends further support to the idea that electrostatic interactions play a major role in determining the antigen specificity of McPC603.

Animals↗