On low-barrier hydrogen bonds and enzyme catalysis.
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Binding Sites↗
Biomedical subjects
A Warshel
Publications and source records attributed to A Warshel.
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↗
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↗
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↗
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↗
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↗
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↗
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↗
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↗
Dipoles localized at helix termini of proteins stabilize charges.
The charge-stabilization effect associated with alpha-helices in proteins has been reexamined by microscopic calculations without any a priori assumptions about the dielectric constant of the protein. The calculations reproduce the observed charge stabilization effect of a helix in two well-defined test cases: a histidine residue situated at the C-terminal end of a helix in barnase and the sulfate ligand located near the N-terminal end of a helix of the sulfate-binding protein. They also show that the effective dielectric constant for helix-charge interactions is much larger than previously assumed and that the stabilizing effect of the helix is not associated with the helix macrodipole but rather with a few localized dipoles confined mostly to the first turn of the helix. It is predicted that mutations at one end of the helix should have very small effects on the stabilization of charges at the opposite terminus. It is pointed out that the relatively short-ranged effect of the helix is essentially similar to other cases in which localized dipoles play key roles in electrostatic stabilization.
Bacterial Proteins↗
Electrostatic energy and macromolecular function.
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Animals↗
Computer simulations of electron-transfer reactions in solution and in photosynthetic reaction centers.
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Computer Simulation↗
Electrostatic control of charge separation in bacterial photosynthesis.
Electrostatic interaction energies of the electron carriers with their surroundings in a photosynthetic bacterial reaction center are calculated. The calculations are based on the detailed crystal structure of reaction centers from Rhodopseu-domonas viridis, and use an iterative, self-consistent procedure to evaluate the effects of induced dipoles in the protein and the surrounding membrane. To obtain the free energies of radical-pair states, the calculated electrostatic interaction energies are combined with the experimentally measured midpoint redox potentials of the electron carriers and of bacteriochlorophyll (BChl) and bacteriopheophytin (BPh) in vitro. The P+HL- radical-pair, in which an electron has moved from the primary electron donor (P) to a BPh on the 'L' side of the reaction center (HL), is found to lie approx. 2.0 kcal/mol below the lowest excited singlet state (P*), when the radical-pair is formed in the static crystallographic structure. The reorganization energy for the subsequent relaxation of P+HL- is calculated to be 5.0 kcal/mol, so that the relaxed radical-pair lies about 7 kcal/mol below P*. The unrelaxed P+BL- radical-pair, in which the electron acceptor is the accessory BChl located between P and HL, appears to be essentially isoenergetic with P*.P+BM-, in which an electron moves to the BChl on the 'M' side, is calculated to lie about 5.5 kcal/mol above P*. These results have an estimated error range of +/- 2.5 kcal/mol. They are shown to be relatively insensitive to various details of the model, including the charge distribution in P+, the atomic charges used for the amino acid residues, the boundaries of the structural region that is considered microscopically and the treatments of the histidyl ligands of P and of potentially ionizable amino acids. The calculated free energies are consistent with rapid electron transfer from P* to HL by way of BL, and with a much slower electron transfer to the pigments on the M side. Tyrosine M208 appears to play a particularly important role in lowering the energy of P+BL-. Electrostatic interactions with the protein favor localization of the positive charge of P+ on PM, one of the two BChl molecules that make up the electron donor.
Bacterial Proteins↗
Dispersed polaron simulations of electron transfer in photosynthetic reaction centers.
A microscopic method for simulating quantum mechanical, nuclear tunneling effects in biological electron transfer reactions is presented and applied to several electron transfer steps in photosynthetic bacterial reaction centers. In this "dispersed polaron" method the fluctuations of the protein and the electron carriers are projected as effective normal modes onto an appropriate reaction coordinate and used to evaluate the quantum mechanical rate constant. The simulations, based on the crystallographic structure of the reaction center from Rhodopseudomonas viridis, focus on electron transfer from a bacteriopheophytin to a quinone and the subsequent back-reaction. The rates of both of these reactions are almost independent of temperature or even increase with decreasing temperature. The simulations reproduce this unusual temperature dependence in a qualitative way, without the use of adjustable parameters for the protein's Franck-Condon factors. The observed dependence of the back-reaction on the free energy of the reaction also is reproduced, including the special behavior in the "inverted region."
Bacterial Proteins↗
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.
Binding Sites↗
How do serine proteases really work?
Recent advances in genetic engineering have led to a growing acceptance of the fact that enzymes work like other catalysts by reducing the activation barriers of the corresponding reactions. However, the key question about the action of enzymes is not related to the fact that they stabilize transition states but to the question to how they accomplish this task. This work considers the catalytic reaction of serine proteases and demonstrates how one can use a combination of calculations and experimental information to elucidate the key contributions to the catalytic free energy. Recent reports about genetic modifications of the buried aspartic group in serine proteases, which established the large effect of this group (but could not determine its origin), are analyzed. Two independent methods indicate that the buried aspartic group in serine proteases stabilizes the transition state by electrostatic interactions rather than by alternative mechanisms. Simple free energy considerations are used to eliminate the double proton-transfer mechanism (which is depicted in many textbooks as the key catalytic factor in serine proteases). The electrostatic stabilization of the oxyanion side of the transition state is also considered. It is argued that serine proteases and other enzymes work by providing electrostatic complementarity to the changes in charge distribution occurring during the reactions they catalyze.
Kinetics↗
Role of arginine-38 in regulation of the cytochrome c oxidation-reduction equilibrium.
Arg-38 is an internal residue of mitochondrial cytochrome c that is close to heme propionate-7. Previous work comparing the behavior of cytochromes c from several species [Moore, G. R., Harris, D. E., Leitch, F. A., & Pettigrew, G. W. (1984) Biochim. Biophys. Acta 764, 331-342] has suggested that Arg-38 lowers the pKa of this propionate group and thereby accounts for the relative pH independence of the cytochrome c reduction potential from pH 5 to pH 8. The influence of Arg-38 on the oxidation-reduction equilibrium of yeast iso-1-cytochrome c has now been investigated by electrochemical, NMR, and theoretical analysis of six specifically mutated forms of this protein in which Arg has been replaced by Lys, His, Gln, Asn, Leu, or Ala. As the electron-withdrawing character of the residue at position 38 decreases, the reduction potential of the protein also decreases, with the largest decrease (ca. 50 mV) observed for the Ala variant. However, the variation in the reduction potentials of the mutants as a function of pH was similar to that observed for the wild-type protein. The effects of some of these mutations on the pKa values of His-33 and His-39 have been determined by NMR spectroscopy and found to be minimal. Calculations of the electrostatic free energy for the Leu-38 variant predict a decrease in the reduction potential of this mutant that is remarkably close to that observed experimentally. This work establishes that while Arg-38 contributes to the relatively high reduction potential of cytochrome c, this residue does not appear to be the sole functionality responsible for lowering the heme propionate-7 pKa.
Amino Acids↗
Energetics of ion permeation through membrane channels. Solvation of Na+ by gramicidin A.
Calculations of the solvation energetics for a Na+ ion inside the Gramicidin A channel and in water are presented. The protein dipoles Langevin dipoles (PDLD) method is used to obtain an electrostatic free energy profile for ion permeation through the channel. To gauge the quality of the PDLD results the solvation free energy of a Na+ ion in water and in the center of the channel is also calculated using free energy perturbation (FEP) simulations. The effect of the polarisability of the surrounding lipid membrane is taken into account by representing the membrane by a large grid of polarisable point dipoles. The two methods give similar solvation energies in the interior of the channel and these are less than 5 kcal/mol above the solvation free energy for Na+ in water, in good agreement with experimental data on the activation barriers for ion permeation. It appears that the problems associated with previous calculations of energy profiles in membrane channels can be overcome by a consistent treatment of all the relevant electrostatic contributions. In particular, we find that the induced dipoles of the membrane and the protein contributes with approximately 10 kcal/mol to the solvation energy inside the channel and can therefore not be discarded in a realistic description of ion solvation in the Gramicidin channel.
Gramicidin↗