Effect of mutations on the thermostability of Aspergillus aculeatus ß-1,4-galactanase.

New variants of ß-1,4-galactanase from the mesophilic organism Aspergillus aculeatus were designed using the structure of ß-1,4-galactanase from the thermophile organism Myceliophthora thermophila as a template. Some of the variants were generated using PROPKA 3.0, a validated pKa prediction tool, to test its usefulness as an enzyme design tool. The PROPKA designed variants were D182N and S185D/Q188T, G104D/A156R. Variants Y295F and G306A were designed by a consensus approach, as a complementary and validated design method. D58N was a stabilizing mutation predicted by both methods. The predictions were experimentally validated by measurements of the melting temperature (Tm ) by differential scanning calorimetry. We found that the Tm is elevated by 1.1 °C for G306A, slightly increased (in the range of 0.34 to 0.65 °C) for D182N, D58N, Y295F and unchanged or decreased for S185D/Q188T and G104D/A156R. The Tm changes were in the range predicted by PROPKA. Given the experimental errors, only the D58N and G306A show significant increase in thermodynamic stability. Given the practical importance of kinetic stability, the kinetics of the irreversible enzyme inactivation process were also investigated for the wild-type and three variants and found to be biphasic. The half-lives of thermal inactivation were approximately doubled in G306A, unchanged for D182N and, disappointingly, a lot lower for D58N. In conclusion, this study tests a new method for estimating Tm changes for mutants, adds to the available data on the effect of substitutions on protein thermostability and identifies an interesting thermostabilizing mutation, which may be beneficial also in other galactanases.

Improving the desolvation penalty in empirical protein pKa modeling.

Unlike atomistic and continuum models, empirical pk(a) predicting methods need to include desolvation contributions explicitly. This study describes a new empirical desolvation method based on the Born solvation model. The new desolvation model was evaluated by high-level Poisson-Boltzmann calculations, and discussed and compared with the current desolvation model in PROPKA-one of the most widely used empirical protein pK(a) predictors. The new desolvation model was found to remove artificial erratic behavior due to discontinuous jumps from man-made first-shell cutoffs, and thus improves the desolvation description significantly.

Protein electrostatics and pKa blind predictions; contribution from empirical predictions of internal ionizable residues.

In this study, we validate and probe the description of electrostatic interactions within proteins by predicting and comparing pK(a) values of ionizable groups in a series of mutated staphylococcal nuclease variants with experiments. This set of pK(a) values is found to be the most challenging pK(a) data to date, because ionizable residues have been introduced in hydrophobic patches in the protein interior and are therefore significantly shifted from their reference solvated values. We find that using PROPKA2 (Li et al., Proteins 2005;61:704-721) results in an rmsd value close to 2 for true blind predictions (1.6 if we reassign the tightly coupled Asp19/21 pair) and close to 1 for postpredictions with the newly developed PROPKA3 (Olsson et al., J. Chem. Theor. Comp. 2011;7:525-537). We also use the performance of the Null-model, predictions made with the reference value only, to provide a better description of the expected errors in pK(a) predictions and to compare submissions made using different subsets of the pK(a) data more consistently.

Progress in the prediction of pKa values in proteins.

The pK(a) -cooperative aims to provide a forum for experimental and theoretical researchers interested in protein pK(a) values and protein electrostatics in general. The first round of the pK(a) -cooperative, which challenged computational labs to carry out blind predictions against pK(a) s experimentally determined in the laboratory of Bertrand Garcia-Moreno, was completed and results discussed at the Telluride meeting (July 6-10, 2009). This article serves as an introduction to the reports submitted by the blind prediction participants that will be published in a special issue of PROTEINS: Structure, Function and Bioinformatics. Here, we briefly outline existing approaches for pK(a) calculations, emphasizing methods that were used by the participants in calculating the blind pK(a) values in the first round of the cooperative. We then point out some of the difficulties encountered by the participating groups in making their blind predictions, and finally try to provide some insights for future developments aimed at improving the accuracy of pK(a) calculations.

Graphical analysis of pH-dependent properties of proteins predicted using PROPKA.

BACKGROUND: Charge states of ionizable residues in proteins determine their pH-dependent properties through their pKa values. Thus, various theoretical methods to determine ionization constants of residues in biological systems have been developed. One of the more widely used approaches for predicting pKa values in proteins is the PROPKA program, which provides convenient structural rationalization of the predicted pKa values without any additional calculations. RESULTS: The PROPKA Graphical User Interface (GUI) is a new tool for studying the pH-dependent properties of proteins such as charge and stabilization energy. It facilitates a quantitative analysis of pKa values of ionizable residues together with their structural determinants by providing a direct link between the pKa data, predicted by the PROPKA calculations, and the structure via the Visual Molecular Dynamics (VMD) program. The GUI also calculates contributions to the pH-dependent unfolding free energy at a given pH for each ionizable group in the protein. Moreover, the PROPKA-computed pKa values or energy contributions of the ionizable residues in question can be displayed interactively. The PROPKA GUI can also be used for comparing pH-dependent properties of more than one structure at the same time. CONCLUSIONS: The GUI considerably extends the analysis and validation possibilities of the PROPKA approach. The PROPKA GUI can conveniently be used to investigate ionizable groups, and their interactions, of residues with significantly perturbed pKa values or residues that contribute to the stabilization energy the most. Charge-dependent properties can be studied either for a single protein or simultaneously with other homologous structures, which makes it a helpful tool, for instance, in protein design studies or structure-based function predictions. The GUI is implemented as a Tcl/Tk plug-in for VMD, and can be obtained online at http://propka.ki.ku.dk/~luca/wiki/index.php/GUI_Web.

PROPKA3: Consistent Treatment of Internal and Surface Residues in Empirical pKa Predictions.

In this study, we have revised the rules and parameters for one of the most commonly used empirical pKa predictors, PROPKA, based on better physical description of the desolvation and dielectric response for the protein. We have introduced a new and consistent approach to interpolate the description between the previously distinct classifications into internal and surface residues, which otherwise is found to give rise to an erratic and discontinuous behavior. Since the goal of this study is to lay out the framework and validate the concept, it focuses on Asp and Glu residues where the protein pKa values and structures are assumed to be more reliable. The new and improved implementation is evaluated and discussed; it is found to agree better with experiment than the previous implementation (in parentheses): rmsd = 0.79 (0.91) for Asp and Glu, 0.75 (0.97) for Tyr, 0.65 (0.72) for Lys, and 1.00 (1.37) for His residues. The most significant advance, however, is in reducing the number of outliers and removing unreasonable sensitivity to small structural changes that arise from classifying residues as either internal or surface.

Improved Treatment of Ligands and Coupling Effects in Empirical Calculation and Rationalization of pKa Values.

The new empirical rules for protein pKa predictions implemented in the PROPKA3.0 software package (Olsson et al. J. Chem. Theory Comput.2010, 7, 525-537) have been extended to the prediction of pKa shifts of active site residues and ionizable ligand groups in protein-ligand complexes. We present new algorithms that allow pKa shifts due to inductive (i.e., covalently coupled) intraligand interactions, as well as noncovalently coupled interligand interactions in multiligand complexes, to be included in the prediction. The number of different ligand chemical groups that are automatically recognized has been increased to 18, and the general implementation has been changed so that new functional groups can be added easily by the user, aided by a new and more general protonation scheme. Except for a few cases, the new algorithms in PROPKA3.1 are found to yield results similar to or better than those obtained with PROPKA2.0 (Bas et al. Proteins: Struct., Funct., Bioinf.2008, 73, 765-783). Finally, we present a novel algorithm that identifies noncovalently coupled ionizable groups, where pKa prediction may be especially difficult. This is a general improvement to PROPKA and is applied to proteins with and without ligands.

Simulation of tunneling in enzyme catalysis by combining a biased propagation approach and the quantum classical path method: application to lipoxygenase.

The ability of using wave function propagation approaches to simulate isotope effects in enzymes is explored, focusing on the large H/D kinetic isotope effect of soybean lipoxygenase-1 (SLO-1). The H/D kinetic isotope effect (KIE) is calculated as the ratio of the rate constants for hydrogen and deuterium transfer. The rate constants are calculated from the time course of the H and D nuclear wave functions. The propagations are done using one-dimensional proton potentials generated as sections from the full multidimensional surface of the reacting system in the protein. The sections are obtained during a classical empirical valence bond (EVB) molecular dynamics simulation of SLO-1. Since the propagations require an extremely long time for treating realistic activation barriers, it is essential to use an effective biasing approach. Thus, we develop here an approach that uses the classical quantum path (QCP) method to evaluate the quantum free energy change associated with the biasing potential. This approach provides an interesting alternative to full QCP simulations and to other current approaches for simulating isotope effects in proteins. In particular, this approach can be used to evaluate the quantum mechanical transmission factor or other dynamical effects, while still obtaining reliable quantized activation free energies due to the QCP correction.

A new paradigm for electrostatic catalysis of radical reactions in vitamin B12 enzymes.

The catalytic power of enzymes containing coenzyme B(12) cofactor has been, in some respects, the "last bastion" for the strain hypothesis. The present work explores the origin of this effect by using simulation methods that overcome the sampling difficulties of previous energy minimization studies. It is found that the major part of the catalytic effect is due to the electrostatic interaction between the ribose and the protein, and that the strain contribution is very small. Remarkably, enzymes can use electrostatic effects even in a radical process, when the charge distribution of the reacting fragments does not change significantly during the reaction. Electrostatic catalysis can, in such cases, be obtained by attaching a polar group to the leaving fragment and designing an active site that interacts more strongly with this group in the product state than in the reactant state. The finding that evolution had to use this trick provides further evidence to the observation that it is extremely hard to catalyze enzymatic reactions by nonelectrostatic factors. The trick used by B(12) enzymes may, in fact, be a very powerful new strategy in enzyme design.

Exploring pathways and barriers for coupled ET/PT in cytochrome c oxidase: a general framework for examining energetics and mechanistic alternatives.

Gaining a detailed understanding of the energetics of the proton pumping process in cytochrome c oxidase (CcO) is one of the challenges of modern biophysics. Although there are several current mechanistic proposals, most of these ideas have not been subjected to consistent structure-function considerations. In particular most works have not related the activation barriers for different mechanistic proposals to the protein structure. The present work describes a general approach for exploring the energetics of different feasible models of the action of CcO, using the observed protein structure, established simulation methods and a modified Marcus' formulation. We start by reviewing our methods for evaluation of the energy diagrams for different proton translocation paths and then present a systematic analysis of various constraints that should be imposed on any energy diagram for the pumping process. After the general analysis we turn to the actual computational study, where we construct energy diagrams for forward and backward paths, using the estimated calculated reduction potentials and pK(a) values of all the relevant sites (including internal water molecules). We then explore the relationship between the calculated energy diagrams and key experimental constraints. This comparison allows us to identify some barriers that are not fully consistent with the overall requirement for an efficient pumping. In particular we identify back leakage channels, which are hard to block without stopping the forward channels. This helps to identify open problems that will require further experimental and theoretical studies. We also consider reasonable adjustments of the calculated barriers that may lead to a working pump. Although the present analysis does not establish a unique and workable model for the mechanism of CcO, it presents what is probably the most consistent current analysis of the barriers for different feasible pathways. Perhaps more importantly, the framework developed here should provide a general way for examining any proposal for the action of CcO as well as for the analysis of further experimental findings about the action of this fascinating system.

Transition state theory can be used in studies of enzyme catalysis: lessons from simulations of tunnelling and dynamical effects in lipoxygenase and other systems.

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.

Monte Carlo simulations of proton pumps: on the working principles of the biological valve that controls proton pumping in cytochrome c oxidase.

Gaining a detailed understanding of the proton-pumping process in cytochrome c oxidase (COX) is one of the challenges of modern biophysics. Recent mutation experiments have highlighted this challenge by showing that a single mutation (the N139D mutation) blocks the overall pumping while continuing to channel protons to the binuclear center without inhibiting the oxidase activity. Rationalizing this result has been a major problem because the mutation is quite far from E286, which is believed to serve as the branching point for the proton transport in the pumping process. In the absence of a reasonable explanation for this important observation, we have developed a Monte Carlo simulation method that can convert mutation and structural information to pathways for proton translocation and simulate the pumping process in COX on a millisecond and even subsecond time scale. This tool allows us to reproduce and propose a possible explanation to the effect of the N139D mutation and to offer a consistent model for the origin of the "valve effect" in COX, which is crucial for maintaining uphill proton pumping. Furthermore, obtaining the first structure-based simulation of proton pumping in COX, or in any other protein, indicates that our approach should provide a powerful tool for verification of mechanistic hypotheses about the action of proton transport proteins.

Simulating redox coupled proton transfer in cytochrome c oxidase: looking for the proton bottleneck.

Gaining a detailed understanding of the molecular nature of the redox coupled proton transfer in cytochrome c oxidase (COX) is one of the challenges of modern biophysics. The present work addresses this by integrating approaches for simulations of proton transport (PTR) and electron transfer (ET). The resulting method converts the electrostatic energies of different charge configurations and reorganization energies to free-energy profiles for different PTR and ET pathways. This approach provides for the first time a tool to study the actual activation barriers and kinetics of different feasible PTR processes in the cycle of COX. Using this tool, we explore the PTR through the bottleneck water molecules. It is found that a stepwise PTR along this commonly assumed path leads to far too high barriers and is, thus, inconsistent with the observed kinetics. Furthermore, the simulated free-energy profile does not provide a simple gating mechanism. Fortunately, we obtain reasonable kinetics when we consider a PTR that involves a concerted transfer of protons to and from E286. Finally, semi-qualitative considerations of the forward and backward barriers point toward open questions about the actual gating process and offer a feasible pumping mechanism. Although further studies are clearly needed, we believe that our approach offers a general and effective tool for correlating the structure of COX with its function.

Solute solvent dynamics and energetics in enzyme catalysis: the S(N)2 reaction of dehalogenase as a general benchmark.

One of the most useful ways of describing and analyzing enzyme catalysis is the description of the enzyme as an effective solvent for the reacting substrate. Here, we illustrate this concept by considering the S(N)2 reaction of haloalkan dehalogenase (DhlA), analyze the energetics and dynamics of the solvent coordinate, and evaluate their relative catalytic effect. It is demonstrated that almost the entire catalytic effect is associated with the preorganization of the protein-solvent coordinate. It is clarified that this effect is associated with the fact that the transition state is "solvated" by the protein more than in the reference solution reaction. This effect is fundamentally different than the frequently proposed desolvation mechanism. The possible catalytic role of dynamical effects is analyzed by considering several reasonable ways of defining "dynamical contributions to catalysis". It is found that these contributions are small regardless of the definition used. It is also shown that the effect of the difference in the relaxation time of the solvent coordinate in the enzyme and solution reaction is rather trivial relative to the effect of the corresponding changes in reorganization free energy.

Simulations of the large kinetic isotope effect and the temperature dependence of the hydrogen atom transfer in lipoxygenase.

Elucidating the role of nuclear quantum mechanical (NQM) effects in enzyme catalysis is a topic of significant current interest. Despite the great experimental progress in this field it is important to have theoretical approaches capable of evaluating and analyzing nuclear quantum mechanical contributions to catalysis. In this study, we use the catalytic reaction of lipoxygenase, which is characterized by an extremely large kinetic isotope effect, as a challenging test case for our simulation approach. This is done by applying the quantum classical path (QCP) method with an empirical valence bond potential energy surface. Our computational strategy evaluates the relevant NQM corrections and reproduces the large observed kinetic isotope effect and the temperature dependence of the H atom transfer reaction while being less successful with the D atom transfer reaction. However, the main point of our study is not so much to explore the temperature dependence of the isotope effect but rather to develop and validate an approach for calculations of nuclear quantum mechanical contributions to activation free energies. Here, we find that the deviation between the calculated and observed activation free energies is small for both H and D at all investigated temperatures. The present study also explores the nature of the reorganization energy in the enzyme and solution reactions. It is found that the outer-sphere reorganization energy is extremely small. This reflects the fact that the considered reaction involves a very small charge transfer. The implication of this finding is discussed in the framework of the qualitative vibronic model. The main point of the present study is, however, that the rigorous QCP approach provides a reliable computational tool for evaluating NQM contributions to catalysis even when the given reaction includes large tunneling contributions. Interestingly, our results indicate that the NQM effects in the lipoxygenase reaction are similar in the enzyme and in the reference solution reactions, and thus do not contribute to catalysis. We also reached similar conclusions in studies of other enzymes.

Simulating large nuclear quantum mechanical corrections in hydrogen atom transfer reactions in metalloenzymes.

The role of nuclear quantum mechanical effects in enzyme catalysis has recently attracted significant interest both from theoretical and experimental points of view. From a theoretical point of view, it is undoubtedly a challenge to try to account for the observed tunneling in the protein by microscopic simulations without adjustable parameters. One of the most spectacular examples of nuclear quantum mechanical effects is the reaction of lipoxygenase, which is characterized by a very large kinetic isotope effect and, thus, provides an excellent benchmark for simulation approaches. In the present study, we report a microscopic simulation of the large kinetic isotope effect in soybean lipoxygenase and its temperature dependence. This is, to the best of our knowledge, the first time that a very large nuclear quantum mechanical contribution to the activation free energy of a hydrogen atom transfer reaction and its temperature dependence have been evaluated by microscopic simulation. The simulation reproduces quite well the experimental kinetic information and the corresponding difference between the classical and quantum mechanical activation free energies for the H and D transfer reactions.

Frozen density functional free energy simulations of redox proteins: computational studies of the reduction potential of plastocyanin and rusticyanin.

The evaluation of reduction potentials of proteins by ab initio approaches presents a major challenge for computational chemistry. This is addressed in the present investigation by reporting detailed calculations of the reduction potentials of the blue copper proteins plastocyanin and rusticyanin using the QM/MM all-atom frozen density functional theory, FDFT, method. The relevant ab initio free energies are evaluated by using a classical reference potential. This approach appears to provide a general consistent and effective way for reproducing the configurational ensemble needed for consistent ab initio free energy calculations. The FDFT formulation allows us to treat a large part of the protein quantum mechanically by a consistently coupled QM/QM/MM embedding method while still retaining a proper configurational sampling. To establish the importance of proper configurational sampling and the need for a complete representation of the protein+solvent environment, we also consider several classical approaches. These include the semi-macroscopic PDLD/S-LRA method and classical all-atom simulations with and without a polarizable force field. The difference between the reduction potentials of the two blue copper proteins is reproduced in a reasonable way, and its origin is deduced from the different calculations. It is found that the protein permanent dipole tunes down the reduction potential for plastocyanin compared to the active site in regular water solvent, whereas in rusticyanin it is instead tuned up. This electrostatic environment, which is the major effect determining the reduction potential, is a property of the entire protein and solvent system and cannot be ascribed to any particular single interaction.