Search

Glycine receptors (GlyR) conduct inhibitory glycinergic neurotransmission in the spinal cord and the brainstem. They play an important role in muscle tone, motor coordination, respiration, and pain perception. However, the mechanism underlying GlyR activation remains unclear. There are five potential glycine binding sites in α1 GlyR, and different binding patterns may cause distinct activation or desensitization behaviors. In this study, we investigated the coupling of protein conformational changes and glycine binding events to elucidate the influence of binding patterns on the activation and desensitization processes of α1 GlyRs. Subsequently, we explored the energetic distinctions between the apical and lateral pathways during α1 GlyR conduction to identify the pivotal factors in the ion conduction pathway preference. Moreover, we predicted the mutational effects of the key residues and verified our predictions using electrophysiological experiments. For the mutants that can be activated by glycine, the predictions of the mutational directions were all correct. The strength of the mutational effects was assessed using Pearson’s correlation coefficient, yielding a value of −0.77 between the calculated highest energy barriers and experimental maximum current amplitudes. These findings contribute to our understanding of GlyR activation, identify the key residues of GlyRs, and provide guidance for mechanistic studies on other pLGICs.

Bioluminescence is a fascinating natural phenomenon, wherein organisms produce light through specific biochemical reactions. Among these organisms, Renillaluciferase (RLuc) derived from the sea pansy Renilla reniformisis notable for its blue light emission and has potential applications in bioluminescent tagging. Our study focuses on RLuc8, a variant of RLuc with eight amino acid substitutions. Recent studies have shown that the luminescent emitter coelenteramide can adopt multiple protonation states, which may be influenced by nearby residues at the enzyme’s active site, demonstrating a complex interplay between protein structure and bioluminescence. Herein, using the quantum mechanical consistent force field method and the semimacroscopic protein dipole-Langevin dipole method with linear response approximation, we show that the phenolate state of coelenteramide in RLuc8 is the primary light-emitting species in agreement with experimental results. Our calculations also suggest that the proton transfer (PT) from neutral coelenteramide to Asp162 plays a crucial role in the bioluminescence process. Additionally, we reproduced the observed emission maximum for the amide anion in RLuc8-D120A and the pyrazine anion in the presence of a Na+counterion in RLuc8-D162A, suggesting that these are the primary emitters. Furthermore, our calculations on the neutral emitter in the engineered AncFT-D160A enzyme, structurally akin to RLuc8-D162A but with a considerably blue-shifted emission peak, aligned with the observed data, possibly explaining the variance in emission peaks. Overall, this study demonstrates an effective approach to investigate chromophores’ bimolecular states while incorporating the PT process in emission spectra calculations, contributing valuable insights for future studies of PT in photoproteins.

The dysfunction and defects of ion channels are associated with many human diseases, especially for loss-of-function mutations in ion channels such as cystic fibrosis transmembrane conductance regulator mutations in cystic fibrosis. Understanding ion channels is of great current importance for both medical and fundamental purposes. Such an understanding should include the ability to predict mutational effects and describe functional and mechanistic effects. In this work, we introduce an approach to predict mutational effects based on kinetic information (including reaction barriers and transition state locations) obtained by studying the working mechanism of target proteins. Specifically, we take the Ca2+-activated chloride channel TMEM16A as an example and utilize the computational biology model to predict the mutational effects of key residues. Encouragingly, we verified our predictions through electrophysiological experiments, demonstrating a 94% prediction accuracy regarding mutational directions. The mutational strength assessed by Pearson’s correlation coefficient is −0.80 between our calculations and the experimental results. These findings suggest that the proposed methodology is reliable and can provide valuable guidance for revealing functional mechanisms and identifying key residues of the TMEM16A channel. The proposed approach can be extended to a broad scope of biophysical systems.

ABSTRACTIntroductionCollaborative computing has attracted great interest, enabling researchers worldwide to come together and work seamlessly. Its relevance has never been so apparent as during the recent pandemic given that it allows for the strengthening of scientific collaborations whilst avoiding physical interaction.This technology evaluation reviews the MEDIATE initiative, launched by the Exscalate4Cov consortium, which invites researchers to contribute their virtual screening simulations that are then combined with AI-based consensus approaches to provide robust and method-independent predictions. The best compounds are subsequently tested, and the biological results are then shared with the scientific community.Areas coveredIn this paper, the MEDIATE initiative is described. This shares compounds’ libraries and protein structures prepared to perform standardized virtual screenings. Preliminary analyses are also reported which provide encouraging results emphasizing the MEDIATE initiative’s capacity to identify active compounds.Expert opinionStructure-based virtual screening is well-suited for collaborative projects provided that the participating researchers work on the same input file. Until now, such a strategy was rarely pursued and most initiatives in the field were organized as challenges. The MEDIATE platform is focused on SARS-CoV-2 targets but can be seen as a prototype which can be utilized to perform collaborative virtual screening campaigns in any therapeutic field by sharing the appropriate input files.

This study analyzes the origin of enzyme catalysis by focusing on the reaction of orotidine 5′-phosphate decarboxylase (ODCase). This reaction involves an enormous catalytic effect of 23 kcal/mol that has been attributed to reactant state destabilization associated with the use of binding energy through the so-called Circe effect. However, our early studies and subsequent key experiments have shown that the presumed effect of the binding energy (namely, the strain exerted by a bond to a phosphate group) does not contribute to the catalysis. In this study, we perform quantitative empirical valence bond calculations that reproduce the catalytic effect of ODCase and the effect of removing the phosphate side chain. The calculations demonstrate that the effect of the phosphate is due to a change in reorganization energy and should not be described as an induced fit effect. Similarly, we show that the overall catalytic effect is due to electrostatic transition state stabilization, which again reflects the smaller reorganization energy in the enzyme than in water. We also elaborate on the problems with the induced fit proposal, including the fact that it does not serve to tell us what the actual origin of the action of the catalytic effect is. In addition to the above points, we use this paper to discuss misconceptions about the meaning of the preorganization effect, as well as other misunderstandings of what is being done in consistent calculations of enzyme catalysis.

A variety of diseases are associated with tyrosine kinase enzymes that activate many proteins via signal transduction cascades. The similar ATP-binding pockets of these tyrosine kinases make it extremely difficult to design selective covalent inhibitors. The present study explores the contribution of the chemical reaction steps to the selectivity of the commercialized inhibitor acalabrutinib over the Bruton’s tyrosine kinase (BTK) and the interleukin-2-inducible T-cell kinase (ITK). Ab initio and empirical valence bond (EVB) simulations of the two kinases indicate that the most favorable reaction path involves a water-assisted mechanism of the 2-butynamide reactive group of acalabrutinib. BTK reacts with acalabrutinib with a substantially lower barrier than ITK, according to our calculated free-energy profile and kinetic simulations. Such a difference is due to the microenvironment of the active site, as further supported by a sequence-based analysis of specificity determinants for several commercialized inhibitors. Our study involves a new approach of simulating directly the IC50 and inactivation efficiency keff, instead of using the standard formulas. This new strategy is particularly important in studies of covalent inhibitors with a very exothermic bonding step. Overall, our results demonstrate the importance of understanding the chemical reaction steps in designing selective covalent inhibitors for tyrosine kinases.

The COVID-19 pandemic has been a public health emergency with continuously evolving deadly variants around the globe. Among many preventive and therapeutic strategies, the design of covalent inhibitors targeting the main protease (Mpro) of SARS-CoV-2 that causes COVID-19 has been one of the hotly pursued areas. Currently, about 30% of marketed drugs that target enzymes are covalent inhibitors. Such inhibitors have been shown in recent years to have many advantages that counteract past reservation of their potential off-target activities, which can be minimized by modulation of the electrophilic warhead and simultaneous optimization of nearby noncovalent interactions. This process can be greatly accelerated by exploration of binding affinities using computational models, which are not well-established yet due to the requirement of capturing the chemical nature of covalent bond formation. Here, we present a robust computational method for effective prediction of absolute binding free energies (ABFEs) of covalent inhibitors. This is done by integrating the protein dipoles Langevin dipoles method (in the PDLD/S-LRA/β version) with quantum mechanical calculations of the energetics of the reaction of the warhead and its amino acid target, in water. This approach evaluates the combined effects of the covalent and noncovalent contributions. The applicability of the method is illustrated by predicting the ABFEs of covalent inhibitors of SARS-CoV-2 Mproand the 20S proteasome. Our results are found to be reliable in predicting ABFEs for cases where the warheads are significantly different. This computational protocol might be a powerful tool for designing effective covalent inhibitors especially for SARS-CoV-2 Mproand for targeted protein degradation.

The cleavage of protein inside cell membranes regulates pathological pathways and is a subject of major interest. Thus, the nature of the coupling between the physical environment and the function of such proteins has recently attracted significant experimental and theoretical efforts. However, it is difficult to determine the nature of this coupling uniquely by experimental and theoretical studies unless one can separate the chemical and the environmental factors. This work describes calculations of the activation barriers of the intramembrane rhomboid protease in neutral and charged lipid bilayers and in detergent micelle, trying to explore the environmental effect. The calculations of the chemical barrier are done using the empirical valence bond (EVB) method. Additionally, the renormalization method captures the energetics and dynamical effects of the conformational change. The simulations indicate that the physical environment around the rhomboid protease is not a major factor in changing the chemical catalysis and that the conformational and substrate dynamics do not exhibit long-time coupling. General issues about the action of membrane-embedded enzymes are also considered.

G-Protein-coupled receptors (GPCRs) belong to an important family of integral membrane receptor proteins that are essential for a variety of transmembrane signaling process, such as vision, olfaction, and hormone responses. They are also involved in many human diseases (Alzheimer’s, heart diseases, etc.) and are therefore common drug targets. Thus, understanding the details of the GPCR activation process is a task of major importance. Various types of crystal structures of GPCRs have been solved either at stable end-point states or at possible intermediate states. However, the detailed mechanism of the activation process is still poorly understood. For example, it is not completely clear when the nucleotide release from the G protein occurs and how the key residues on α5 contribute to the coupling process and further affect the binding specificity. In this work we show by free energy analysis that the guanosine diphosphate (GDP) molecule could be released from the Gsprotein when the binding cavity is half open. This occurs during the transition to the Gsopen state, which is the rate-determining step in the system conformational change. We also account for the experimentally observed slow-down effects by the change of the reaction barriers after mutations. Furthermore, we identify potential key residues on α5 and validated their significance by site-directed mutagenesis, which illustrates that computational works have predictive value even for complex biophysical systems. The methodology of the current work may be applied to other biophysical systems of interest.

Cysteine proteases play a major role in many life processes and are the target of key drugs. The reaction mechanism of these enzymes is a complex process, which involves several steps that are divided into two main groups: acylation and deacylation. In this work, we studied the energy profile for the acylation and a part of the deacylation reaction of three different enzymes, cruzain, papain, and the Q19A-mutated papain with the benzyloxycarbonyl-phenylalanylarginine-4-methylcoumaryl-7-amide (CBZ-FR-AMC) substrate. The calculations were performed using the EVB and PDLD/S-LRA methods. The overall agreement between the calculated and observed results is encouraging and indicates that we captured the correct reaction mechanism. Finally, our finding indicates that the minimum of the reaction profile, between the acylation and deacylation steps, should provide an excellent state for the binding of covalent inhibitors.

The development of reliable ways of predicting the binding free energies of covalent inhibitors is a challenge for computer-aided drug design. Such development is important, for example, in the fight against the SARS-CoV-2 virus, in which covalent inhibitors can provide a promising tool for blocking Mpro, the main protease of the virus. This work develops a reliable and practical protocol for evaluating the binding free energy of covalent inhibitors. Our protocol presents a major advance over other approaches that do not consider the chemical contribution of the binding free energy. Our strategy combines the empirical valence bond method for evaluating the reaction energy profile and the PDLD/S-LRA/β method for evaluating the noncovalent part of the binding process. This protocol has been used in the calculations of the binding free energy of an α-ketoamide inhibitor of Mpro. Encouragingly, our approach reproduces the observed binding free energy. Our study of covalent inhibitors of cysteine proteases indicates that in the choice of an effective warhead it is crucial to focus on the exothermicity of the point on the free energy surface of a peptide cleavage that connects the acylation and deacylation steps. Overall, we believe that our approach should provide a powerful and effective method for in silicodesign of covalent drugs.

The ATPase-catalysed conversion of ATP to ADP is a fundamental process in biology. During the hydrolysis of ATP, the a3ß3domain undergoes conformational changes while the central stalk (?/D) rotates unidirectionally. Experimental studies have suggested that different catalytic mechanisms operate depending on the type of ATPase, but the structural and energetic basis of these mechanisms remains unclear. In particular, it is not clear how the positions of the catalytic dwells influence the energy transduction. Here we show that the observed dwell positions, unidirectional rotation and movement against the applied torque are reflections of the free-energy surface of the systems. Instructively, we determine that the dwell positions do not substantially affect the stopping torque. Our results suggest that the three resting states and the pathways that connect them should not be treated equally. The current work demonstrates how the free-energy landscape determines the behaviour of different types of ATPases.

The COVID-19 caused by SARS-CoV-2 has spread globally and caused tremendous loss of lives and properties, and it is of utmost urgency to understand its propagation process and to find ways to slow down the epidemic. In this work, we used a coarse-grained model to calculate the binding free energy of SARS-CoV-2 or SARS-CoV to their human receptor ACE2. The investigation of the free energy contribution of the interacting residues indicates that the residues located outside the receptor binding domain are the source of the stronger binding of the novel virus. Thus, the current results suggest that the essential evolution of SARS-CoV-2 happens remotely from the binding domain at the spike protein trimeric body. Such evolution may facilitate the conformational change and the infection process that occurs after the virus is bound to ACE2. By studying the binding pattern between SARS-CoV antibody m396 and SARS-CoV-2, it is found that the remote energetic contribution is missing, which might explain the absence of cross-reactivity of such antibodies.

The proteasome is a key protease in the eukaryotic cells which is responsible for various important cellular processes such as the control of the cell cycle, immune responses, protein homeostasis, inflammation, apoptosis, and the response to proteotoxic stress. Acting as a major molecular machine for protein degradation, proteasome first identifies damaged or obsolete regulatory proteins by attaching ubiquitin chains and subsequently utilizes conserved pore loops of the heterohexameric ring of AAA+ (ATPases associated with diverse cellular activities) to pull and mechanically unfold and translocate the misfolded protein to the active site for proteolysis. A detailed knowledge of the reaction mechanism for this proteasomal proteolysis is of central importance, both for fundamental understanding and for drug discovery. The present study investigates the mechanism of the proteolysis by the proteasome with full consideration of the protein’s flexibility and its impact on the reaction free energy. Major attention is paid to the role of the protein electrostatics in determining the activation barriers. The reaction mechanism is studied by considering a small artificial fluorogenic peptide substrate (Suc-LLVY-AMC) and evaluating the activation barriers and reaction free energies for the acylation and deacylation steps, by using the empirical valence bond method. Our results shed light on the proteolysis mechanism and thus should be important for further studies of the proteasome action.

Simulating the nature of voltage-activated systems is a problem of major current interest, ranging from the action of voltage-gated ion channels to energy storage batteries. However, fully microscopic converging molecular simulations of external voltage effects present a major challenge, and macroscopic models are associated with major uncertainties about the dielectric treatment and the underlying physical basis. Recently we developed a coarse-grained (CG) model that represents explicitly the electrodes, the electrolytes, and the membrane/protein system. The CG model provides a semimacroscopic way of capturing the microscopic physics of voltage-activated systems. Our method was originally validated by reproducing macroscopic and analytical results for key test cases and then used in modeling voltage-activated ion channels and related problems. In this work, we further establish the reliability of the CG voltage model by comparing it to the results of Monte Carlo (MC) simulations with a microscopic electrolyte model. The comparison explores different aspects of membrane, electrolyte, and electrode systems ranging from the Gouy–Chapman model to the determination of the electrolyte charge distribution in the solution between two electrodes (without and with a separating membrane), as well as the evaluation of gating charges. Overall the agreement is very impressive. This provides confidence in the CG model and also shows that the MC model can be used in realistic simulation of voltage activation of membrane proteins with sufficient computer time.

Enzymes, as paramount protein catalysts, occupy a central role in fostering remarkable progress across numerous fields. However, the intricacy of sequence-function relationships continues to obscure our grasp of enzyme behaviors and curtails our capabilities in rational enzyme engineering. Generative artificial intelligence (AI), known for its proficiency in handling intricate data distributions, holds the potential to offer novel perspectives in enzyme research. Generative models could discern elusive patterns within the vast sequence space and uncover new functional enzyme sequences. This review highlights the recent advancements in employing generative AI for enzyme sequence analysis. We delve into the impact of generative AI in predicting mutation effects on enzyme fitness, catalytic activity and stability, rationalizing the laboratory evolution of de novoenzymes, and decoding protein sequence semantics and their application in enzyme engineering. Notably, the prediction of catalytic activity and stability of enzymes using natural protein sequences serves as a vital link, indicating how enzyme catalysis shapes enzyme evolution. Overall, we foresee that the integration of generative AI into enzyme studies will remarkably enhance our knowledge of enzymes and expedite the creation of superior biocatalysts.This Review underscores the latest advances in applying generative AI to the analysis of enzyme sequences, which has deepened our insight into enzyme evolution and catalysis, thereby advancing enzyme engineering.

Increasing the accuracy of the evaluation of ligand-binding energies is one of the most important tasks of current computational biology. Here we explore the accuracy of free energy perturbation (FEP) approaches by comparing the performance of a “regular” FEP method to the one using replica exchange to enhance the sampling on a well-defined benchmark. The examination was limited to the so-called alchemical perturbations which are restricted to a fragment of the drug, and therefore, the calculation is a relative one rather than the absolute binding energy of the drug. Overall, our calculations reach the 1 kcal/mol accuracy limit. It is also shown that the accurate prediction of the position of water molecules around the binding pocket is important for FEP calculations. Interestingly, the replica exchange method does not significantly improve the accuracy of binding energies, suggesting that we reach the limit where the force field quality is a critical factor for accurate calculations.

SARS-CoV-2 is the virus that causes the global pandemic of COVID-19. The main protease (Mpro) of SARS-CoV-2 is essential for viral infection and is one of the major therapeutic targets for COVID-19. Here, we report the design, synthesis, and biological characterization of a novel heterobifunctional small molecule that could effectively induce the degradation of SARS-CoV-2 Mproand its drug-resistant mutants in HEK 293T cells, thus demonstrating a new alternative strategy for intervening with proteins important for this novel coronavirus.

Understanding the relationship between the adiabatic free energy profiles of chemical reactions and the underlining diabatic states is central to the description of chemical reactivity. The diabatic states form the theoretical basis of linear free energy relationships (LFERs) and thus play a major role in physical organic chemistry and related fields. However, the theoretical justification for some of the implicit LFER assumptions has not been fully established by quantum mechanical studies. This study follows our earlier works(1, 2) and uses the ab initio frozen density functional theory (FDFT) method(3) to evaluate both the diabatic and the adiabatic free energy surfaces and to determine the corresponding off-diagonal coupling matrix elements for a series of SN2 reactions. It is found that the off-diagonal coupling matrix elements are almost the same regardless of the nucleophile and the leaving group but change upon changing the central group. Furthermore, it is also found that the off-diagonal elements are basically the same in gas phase and in solution, even when the solvent is explicitly included in the ab initio calculations. Furthermore, our study establishes that the FDFT diabatic profiles are parabolic to a good approximation, thus providing a first-principles support to the origin of LFER. These findings further support the basic approximation of the empirical valence bond treatment.

No Abstract

No Abstract

A consistent treatment of electrostatic energies is arguably the most important requirement for the realistic modeling of biological systems. An important part of electrostatic modeling is the ability to account for the polarizability of the simulated system. This can be done both macroscopically and microscopically, but the use of macroscopic models may lead to conceptual traps, which do not exist in the microscopic treatments. The present work describes the development of microscopic polarizable force fields starting with the introduction of these powerful tools and following some of the subsequent developments in the field. Special effort has been made to review a wide range of applications and emphasize cases when the use of polarizable force fields is important. Finally, a brief perspective is given on the future of this rapidly growing field.

The idea that enzyme catalysis involves special factors such as coherent fluctuations, quantum mechanical tunnelling and non-equilibrium solvation (NES) effects has gained popularity in recent years. It has also been suggested that transition state theory (TST) cannot be used in studies of enzyme catalysis. The present work uses reliable state of the art simulation approaches to examine the above ideas. We start by demonstrating that we are able to simulate any of the present catalytic proposals using the empirical valence bond (EVB) potential energy surfaces, the dispersed polaron model and the quantized classical path (QCP) approach, as well as the approximate vibronic method. These approaches do not treat the catalytic effects by phenomenological treatments and thus can be considered as first principles approaches (at least their ability to compare enzymatic reaction to the corresponding solution reactions). This work will consider the lipoxygenase reaction, and to lesser extent other enzymes, for specific demonstration. It will be pointed out that our study of the lipoxygenase reaction reproduces the very large observed isotope effect and the observed rate constant while obtaining no catalytic contribution from nuclear quantum mechanical (NQM) effects. Furthermore, it will be clarified that our studies established that the NQM effect decreases rather than increases when the donor–acceptor distance is compressed. The consequences of these findings in terms of the temperature dependence of the kinetic isotope effect and in terms of different catalytic proposals will be discussed.This paper will also consider briefly the dynamical effects and conclude that such effects do not contribute in a significant way to enzyme catalysis. Furthermore, it will be pointed out that, in contrast to recent suggestions, NES effects are not dynamical effects and should therefore be part of the activation free energy rather than the transmission factor. In view of findings of the present work and our earlier works, it seems that TST provides a quantitative tool for studies of enzyme catalysis and that the key open questions are related to the nature of the factors that lead to transition state stabilization.

Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.

Proton transport (PTR) processes play a major role in bioenergetics and thus it is important to gain a molecular understanding of these processes. At present the detailed description of PTR in proteins is somewhat unclear and it is important to examine different models by using well-defined experimental systems. One of the best benchmarks is provided by carbonic anhydrase III (CA III), because this is one of the few systems where we have a clear molecular knowledge of the rate constant of the PTR process and its variation upon mutations. Furthermore, this system transfers a proton between several water molecules, thus making it highly relevant to a careful examination of the “proton wire” concept. Obtaining a correlation between the structure of this protein and the rate of the PTR process should help to discriminate between alternative models and to give useful clues about PTR processes in other systems. Obviously, obtaining such a correlation requires a correct representation of the “chemistry” of PTR between different donors and acceptors, as well as the ability to evaluate the free energy barriers of charge transfer in proteins, and to simulate long-time kinetic processes. The microscopic empirical valence bond (Warshel, A., and R. M. Weiss. 1980. J. Am. Chem. Soc. 102:6218–6226; and Åqvist, J., and A. Warshel. 1993. Chem. Rev. 93:2523–2544) provides a powerful way for representing the chemistry and evaluating the free energy barriers, but it cannot be used with the currently available computer times in direct simulation of PTR with significant activation barriers. Alternatively, one can reduce the empirical valence bond (EVB) to the modified Marcus’ relationship and use semimacroscopic electrostatic calculations plus a master equation to determine the PTR kinetics (Sham, Y., I. Muegge, and A. Warshel. 1999. Proteins. 36:484–500). However, such an approximation does not provide a rigorous multisite kinetic treatment. Here we combine the useful ingredients of both approaches and develop a simplified EVB effective potential that treats explicitly the chain of donors and acceptors while considering implicitly the rest of the protein/solvent system. This approach can be used in Langevin dynamics simulations of long-time PTR processes. The validity of our new simplified approach is demonstrated first by comparing its Langevin dynamics results for a PTR along a chain of water molecules in water to the corresponding molecular dynamics simulations of the fully microscopic EVB model. This study examines dynamics of both models in cases of low activation barriers and the dependence of the rate on the energetics for cases with moderate barriers. The study of the dependence on the activation barrier is next extended to the range of higher barriers, demonstrating a clear correlation between the barrier height and the rate constant. The simplified EVB model is then examined in studies of the PTR in carbonic anhydrase III, where it reproduces the relevant experimental results without the use of any parameter that is specifically adjusted to fit the energetics or dynamics of the reaction in the protein. We also validate the conclusions obtained previously from the EVB-based modified Marcus’ relationship. It is concluded that this approach and the EVB-based model provide a reliable, effective, and general tool for studies of PTR in proteins. Finally in view of the behavior of the simulated result, in both water and the CA III, we conclude that the rate of PTR in proteins is determined by the electrostatic energy of the transferred proton as long as this energy is higher than a few kcal/mol.

The nature of the control of water/proton selectivity in biological channels is a problem of a fundamental importance. Most studies of this issue have proposed that an interference with the orientational requirements of the so-called proton wire is the source of selectivity. The elucidation of the structures of aquaporins, which have evolved to prevent proton transfer (PT), provided a clear benchmark for exploring the selectivity problem. Previous simulations of this system have not examined, however, the actual issue of PT, but only considered the much simpler task of the transfer of water molecules. Here we take aquaporin as a benchmark and quantify the origin of the water/proton selectivity in this and related systems. This is done by evaluating in a consistent way the free energy profile for transferring a proton along the channel and relating this profile to the relevant PT rate constants. It is found that the water/proton selectivity is controlled by the change in solvation free energy upon moving the charged proton from water to the channel. The reason for the focus on the elegant concept of the proton wire and the related Grotthuss-type mechanism is also considered. It is concluded that these mechanisms are clearly important in cases with flat free energy surfaces (e.g., in bulk water, in gas phase water chains, and in infinitely long channels). However, in cases of biological channels, the actual PT mechanism is much less important than the energetics of transferring the proton charge from water to different regions in the channels.

Computer simulations can provide in principle quantitative correlation between the structures of DNA polymerases and the replication fidelity. This paper describes our progress in this direction. Using several theoretical approaches, including the free energy perturbation (FEP), linear response approximation (LRA), and the empirical valence bond (EVB) methods, we examined the stability of several mismatched base pairs in DNA duplex in aqueous solution, the contribution of binding energy to the fidelity of DNA polymerases β and T7, and the mechanism and energetics of the polymerization reaction catalyzed by T7 DNA polymerase. © 2003 Wiley Periodicals, Inc. Biopolymers 68: 286–299, 2003

1. Introduction 563 2. Obtaining rate constants from molecular-dynamics simulations 564 2.1 General relationships between quantum electronic structures and reaction rates 564 2.2 The transition-state theory (TST) 569 2.3 The transmission coefficient 572 3. Simulating biological electron-transfer reactions 575 3.1 Semi-classical surface-hopping and the Marcus equation 575 3.2 Treating quantum mechanical nuclear tunneling by the dispersed-polaron/spin-boson method 580 3.3 Density-matrix treatments 583 3.4 Charge separation in photosynthetic bacterial reaction centers 584 4. Light-induced photoisomerizations in rhodopsin and bacteriorhodopsin 596 5. Energetics and dynamics of enzyme reactions 614 5.1 The empirical-valence-bond treatment and free-energy perturbation methods 614 5.2 Activation energies are decreased in enzymes relative to solution, often by electrostatic effects that stabilize the transition state 620 5.3 Entropic effects in enzyme catalysis 627 5.4 What is meant by dynamical contributions to catalysis? 634 5.5 Transmission coefficients are similar for corresponding reactions in enzymes and water 636 5.6 Non-equilibrium solvation effects contribute to catalysis mainly through Δg‡, not the transmission coefficient 641 5.7 Vibrationally assisted nuclear tunneling in enzyme catalysis 648 5.8 Diffusive processes in enzyme reactions and transmembrane channels 651 6. Concluding remarks 658 7. Acknowledgements 658 8. References 658 Obtaining a detailed understanding of the dynamics of a biochemical reaction is a formidable challenge. Indeed, it might appear at first sight that reactions in proteins are too complex to analyze microscopically. At room temperature, even a relatively small protein can have as many as 1034 accessible conformational states (Dill, 1985). In many cases, however, we have detailed structural information about the active site of an enzyme, whereas such information is missing for corresponding chemical systems in solution. The atomic coordinates of the chromophore in bacteriorhodopsin, for example, are known to a resolution of 1–2 Å. In addition, experimental studies of biological processes such as photoisomerization and electron transfer have provided a wealth of detailed information that eventually may make some of these processes classical problems in chemical physics as well as biology.

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 pKavalues 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 pKavalues 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, εp, 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 εprepresents 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. Proteins 2001;44:400–417. © 2001 Wiley‐Liss, Inc.

Q‐Chem 2.0 is a new release of an electronic structure program package, capable of performing first principles calculations on the ground and excited states of molecules using both density functional theory and wave function‐based methods. A review of the technical features contained within Q‐Chem 2.0 is presented. This article contains brief descriptive discussions of the key physical features of all new algorithms and theoretical models, together with sample calculations that illustrate their performance. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1532–1548, 2000

The use of hybrid ab initioQM/MM methods in studies of metalloenzymes and related systems presents a major challenge to computational chemists. Methods that include the metal ion in the quantum mechanical region should also include the ligands of the metal in this region. Such a treatment, however, should be very demanding if one is interested in performing the configurational averaging needed for proper calculations of activation free energies. In the present work we examine the ability of the frozen DFT (FDFT) and the constrained DFT (CDFT) approaches to be used in ab initiostudies of metal‐catalyzed reactions, while allowing for an effective QM (rather than a QM/MM) treatment of the reacting complex. These approaches allow one to treat the entire enzyme by ab initioDFT methods, while confining the SCF calculations to a relatively small subsystem and keeping the electron density of the rest of the system frozen (or constrained). It is found that the FDFT and CDFT models can reproduce the trend obtained by a full DFT calculation of a proton transfer between two water molecules in a (Im)3Zn2+(H2O)2system. This and related test cases indicate that our approximated models should be capable of providing a reliable representation of the energetics of metalloenzymes. The reasons for the special efficiency of the FDFT approach are clarified, and the strategies that can be used in FDFT studies of metalloenzymes are outlined. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1554–1561, 2000

Q-Chem 2.0 is a new release of an electronic structure program package, capable of performing first principles calculations on the ground and excited states of molecules using both density functional theory and wave function-based methods. A review of the technical features contained within Q-Chem 2.0 is presented. This article contains brief descriptive discussions of the key physical features of all new algorithms and theoretical models, together with sample calculations that illustrate their performance. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1532–1548, 2000

A general methodology for the study of chemical catalysis is presented and demonstrated in a study of Friedel–Crafts‐type alkylation reactions that are constrained to collinear configurations. Ab initiopotential energy surfaces in solution and relevant experimental results are used to calibrate general empirical valence bond (EVB) potential surfaces for studies of such reactions. The EVB surfaces allow one to interpolate the ab initioresults to studies of the effect of different solvents, substituents, and catalysts on the alkylation reactions. This implicit approach introduces such effects by shifting the diagonal energies of the corresponding resonance structures. Such an EVB/shift approach appears valuable for assessing the effects of different catalysts and solvents on complex chemical reactions. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 607–625, 2000

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 (Åqvist 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 β (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 β, it is important to evaluate explicitly the different contributions to the binding energy of the non‐polar ligand, ΔGbind,ℓ`. Since this cannot be done at present (for relatively large ligands) by rigorous free energy perturbation approaches, we evaluate ΔGbind,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 ΔGbind,ℓ`. The sum of these contributions is scaled by a factor θ and it is argued that obtaining a quantitative balance between these contributions should result in θ = 1. By doing so we should have a reliable estimate of the value of the LIE β and a way to understand its origin. The present approach gives θ 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 θ between different protein active sites.

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 (Åqvist 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 β (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 β, it is important to evaluate explicitly the different contributions to the binding energy of the non-polar ligand, ΔGbind,ℓ`. Since this cannot be done at present (for relatively large ligands) by rigorous free energy perturbation approaches, we evaluate ΔGbind,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 ΔGbind,ℓ`. The sum of these contributions is scaled by a factor θ and it is argued that obtaining a quantitative balance between these contributions should result in θ = 1. By doing so we should have a reliable estimate of the value of the LIE β and a way to understand its origin. The present approach gives θ 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 θ 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, and hydrophobic contributions). The practical difference is that the LIE method approximates the non-electrostatic term by the average of the van der Waals interaction, while our LRA method evaluates this term by the PDLD method. This point is illustrated by the fact that our LRA approach gives results of similar quality to those obtained by the LIE approach. Finally it is found that results of similar quality are obtained by the PDLD/S method and the LRA method. This is significant since the PDLD/S method is much faster than the LRA and LIE methods. However, more studies of the relative accuracy on other systems are needed in order to establish their relative merits. Proteins 2000;39:393–407. © 2000 Wiley-Liss, Inc.

A systematic ab initio study of the reactions of amides with alcohols and thiols in aqueous solution is presented. This study is aimed at providing well-defined reference free-energy surfaces for the corresponding studies of the catalytic power of serine and cysteine protease. The applied methodology consists of the combined ab initio and Langevine dipoles (LD) solvent model, and a systematic calibration using the available experiments. The study of the base-catalyzed and general-base-catalyzed methanolysis of formamide, which serves as a reference reaction of serine protease, indicates that when a water molecule is the base the initial proton transfer is concerted with the RO⁻ nucleophilic attack. However, with histidine as a general base this reaction is a stepwise process with a shallow surface that can allow also for a concerted path. It is also found that the protonation of the nitrogen of the oxyanion leads to breaking of the CN bond. The study of a reference reaction of cysteine protease indicates that the initial proton transfer to the general base occurs before the RS⁻ attack on the amide. The nucleophilic attack may be concerted with the protonation of the amide nitrogen, but a stepwise process where the protonation occurs after the formation of the tetrahedral intermediate is also possible. The CN bond cleavage appears to be the last step of the reaction. The common belief that thiols have greater tendency to add to carbonyl groups than alcohols is revisited. It is found that this is probably true because the reactivity of thiols can involve unassisted proton transfer to the nitrogen or oxygen of the amide concerted with the nucleophilic attack. The possibility that thiolysis of amides in solution circumvents the general-base catalysis mechanism should thus be taken into account in comparing enzymatic reactions to uncatalyzed solution reactions. Having relatively reliable potential surfaces for the reference reactions of serine and cysteine proteases should allow one to calibrate potential surfaces for the corresponding enzymatic reactions. This can be very useful for calibrating empirical valence bond (EVB) potential surfaces or other hybrid quantum mechanical/molecular mechanical (QM/MM) semiempirical potential surfaces. In addition, our results will be useful for ab initio studies that use the EVB surfaces as reference potentials. Furthermore, any attempts to study these enzymatic reactions by quantum mechanical approaches should be validated by examining the corresponding solution reactions and the present study should be helpful in such validation studies. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 44–53, 2000

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 (ΔG(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 ΔG(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 ΔG(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 ΔG(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. © 1999 Wiley‐Liss, Inc.

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.

The interpretation of a large number of experiments that are generally considered to support the dissociative or metaphosphate mechanism of phosphate monoesters in aqueous solution is scrutinized using results of ab initio quantum chemical calculations. It is concluded that while it is currently not clear whether the associative or dissociative mechanism of phosphate monoester hydrolysis is operating in aqueous solution, the associative transition state can be better stabilized by the interaction between the equatorial oxygens and the proton donor groups in the enzyme active sites.

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 (ΔG^(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 ΔG^(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 ΔG^(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 ΔG^(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. © 1999 Wiley-Liss, Inc.

The efficiency of light induced electron transfer across membranes is examined on a molecular level. The activation energies that determine this efficiency are evaluated by pure electrostatic considerations in terms of the membrane dielectric and the relaxation of the dielectric at the sites of the electron donors and acceptors. These considerations allow one, for the first time, to assess the efficiency of photosynthetic systems in terms of their molecular components. It is demonstrated that a conduction chain of stacked acceptors immersed in a low dielectric membrane cannot be expected to provide an efficient photosynthetic system. On the other hand, efficient photosynthetic systems can be obtained when the acceptors are placed in polar active sites of proteins and arranged in order of increasing redox potentials.

The reorganization energy (λ) for electron transfer from the primary electron donor (P*) to the adjacent bacteriochlorophyll (B) in photosynthetic bacterial reaction centers is explored by molecular-dynamics simulations. Relatively long (40ps) molecular-dynamics trajectories are used, rather than free energy perturbation techniques. When the surroundings of the reaction center are modeled as a membrane, λ for P*B → P+B− is found to be ∼1.6 kcal/mol. The results are not sensitive to the treatment of the protein's ionizable groups, but surrounding the reaction center with water gives higher values of λ (∼6.5 kcal/mol). In light of the evidence that P+B− lies slightly below P* in energy, the small λ obtained with the membrane model is consistent with the speed and temperature independence of photochemical charge separation. The calculated reorganization energy is smaller than would be expected if the molecular dynamics trajectories had sampled the full conformational space of the system. Because the system does not relax completely on the time scale of electron transfer, the λ obtained here probably is more pertinent than the larger value that would be obtained for a fully equilibrated system.

The “dispersed polaron” version of the semiclassical trajectory approach is used to evaluate the quantum mechanical nuclear tunneling effects in the charge recombination reaction, P+Q-?PQ, in photosynthetic bacterial reaction centers, The cclculations are based on the crystallographic structure of reaction centers from Rhodopseudomonas viridis. They succeed in capturing the temperature dependence of the rate constant without using adjustable parameters. This provides the first example of a microscopic simulation of quantum mechanical nuclear tunneling in a biological system.

The interactions between biologically important enzymes and drugs are of great interest. In order to address some aspects of these interactions we have initiated a program to investigate enzymedrug interactions. Specifically, the interactions between one of the isozymes of carbonic anhydrase and a family of drugs known as sulfonamides have been studied using computational methods. In particular the electrostatic free energy of binding of carbonic anhydrase II with acetazolamide, methazolamide,p-chlorobenzenesulfonamide,p-aminobenzenesulfonamide and three new compounds (MK1, MK2, and MK3) has been computed using finite-difference Poisson-Boltzmann (FDPB) [1] method and the semimacroscopic version [2, 3] of the protein dipole Langevin dipole (PDLD) method [4]. Both methods, FDPB and PDLD, give similar results for the electrostatic free energy of binding even though different charges and different treatments were used for the protein. The calculated electrostatic binding free energies are in reasonable agreement with the experimental data. The potential and the limitation of electrostatic models for studies of binding energies are discussed.

The challenge of evaluating absolute binding free energies of protein–protein complexes is addressed using the scaled Protein Dipoles Langevin Dipoles (PDLD/S) model in combination with the Linear Response Approximation (LRA). This is done by taking the complex between Rap1A (Rap) and the p21^ras binding domain of c-Raf (Raf-RBD) (Nassar et al., Nature 375:554–560, 1995) as a model system. Several formulations and different thermodynamic cycles are explored taking advantage of the LRA method and considering the protein reorganization during complex formation. The performance of different approximations is examined by comparing the calculated and observed absolute binding energies for the native complex and some of its mutants. The evaluation of the contributions of individual residues to the binding free energy, which is referred to here as group contributions is also examined. Special attention is paid to the role of the “dielectric constant,” εin which is in fact a scaling factor that represents the contributions that are treated implicitly. It is found that explicit consideration of protein relaxation is crucial for obtaining reasonable results with small values of εin, but it is also found that such a treatment of protein–protein interactions is very challenging and does not always give stable results. This indicates that more advanced explicit calculations should be based on experimentally determined structures of both the complex and the isolated proteins. Nevertheless, it is demonstrated that the qualitative trend of the effect of mutations can be reproduced by considering the effect of protein reorganization implicitly, using εin ˜25 for ionized residues and εin ˜4 for polar residues. Thus, it is concluded that an explicit treatment of solvent relaxation (which is common to current continuum models) does not provide sufficient compensation for turning off the charges of ionized residues on the interaction surface of the Raf-RBD/Rap complex. Representing the missing contribution by large εin can, of course, reproduce the observed effect of ionized residues, but now the contribution of uncharged residues will be largely underestimated. Regardless of these conceptual problems, it is established that a very simple nonrelaxed approach, where the relaxation of both the protein and the solvent are considered implicitly, can provide an effective qualitative way for evaluating group contributions, using large and small values for εin of ionized and neutral residues, respectively. As much as the actual system studied is concerned we find that more residues than generally assumed play a role in Raf-RBD/Rap interaction. This includes residues that are not located at the protein–protein interaction surface. These residues contribute to the binding energy through direct charge–charge interaction without leading to drastic structural changes. The overall contribution of the surface residues is quite significant since Raf and Rap are positively and negatively charged, respectively, and their charges are distributed along the interaction site between the two proteins. Proteins 30:407–423, 1998. © 1998 Wiley-Liss, Inc.

A new and very simple representation of protein conformations has been used together with energy minimisation and thermalisation to simulate protein folding. Under certain conditions, the method succeeds in ‘renaturing’ bovine pancreatic trypsin inhibitor from an open-chain conformation into a folded conformation close to that of the native molecule.

The effect of the reorganization of the protein polar groups on charge-charge interaction and the corresponding effective dielectric constant (∈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 ∈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,” ∈p, of the Poisson-Boltzmann model or for the corresponding ∈in in the PDLD/S model. An additional increase in ∈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 ∈in (or ∈p) represents contributions that are not considered explicitly. The present study also provides a systematic illustration of the nature of ∈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 ∈eff for the interaction between ionizable groups in proteins is very different from the effective dielectric constant, ∈′eff, that determines the free energy of ion pairs in proteins (∈′eff reflects the effect of preoriented protein dipoles). Finally, the problems associated with the search for a general ∈in are discussed. It is clarified that the ∈in that reproduces the effect of protein relaxation on charge-charge interaction is not equal to the ∈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 ∈in for charge-charge interactions and a small ∈in for charge-dipole interactions or consider the protein relaxation microscopically.