Equilibrium fluctuation relations for voltage coupling in membrane proteins

AbstractA general theoretical framework is developed to account for the effects of an external potential on the energetics of membrane proteins. The framework is based on the free energy relation between two (forward/backward) probability densities, which was recently generalized to non-equilibrium processes, culminating in the work-fluctuation theorem. Starting from the probability densities of the conformational states along the "voltage coupling" reaction coordinate, we investigate several interconnected free energy relations between these two conformational states, considering voltage activation of ion channels. The free energy difference between the two conformational states at zero (depolarization) membrane potential (i.e., known as the chemical component of free energy change in ion channels) is shown to be equivalent to the free energy difference between the two “equilibrium” (resting and activated) conformational states along the one-dimensional voltage couplin reaction coordinate. Furthermore, the requirement that the application of linear response approximation to the free energy functionals of voltage coupling should satisfy the general free energy relations, yields a novel closed-form expression for the gating charge in terms of other basic properties of ion channels. This connection is familiar in statistical mechanics, known as the equilibrium fluctuation-response relation. The theory is illustrated by considering the coupling of a unit charge to the external voltage in the two sites near the surface of membrane, representing the activated and resting states. This is done using a coarse-graining (CG) model of membrane proteins, which includes the membrane, the electrolytes and the electrodes. The CG model yields Marcus-type voltage dependent free energy parabolas for the response of the electrostatic environment (electrolytes etc.) to the transition from the initial to the final configuratinal states, leading to equilibrium free energy difference and free energy barrier that follow the trend of the equilibrium fluctuation relation and the Marcus theory of electron transfer. These energetics also allow for a direct estimation of the voltage dependence of channel activation (Q-V curve), offering a quantitative rationale for a correlation between the voltage dependence parabolas and the Q-V curve, upon site-directed mutagenesis or drug binding. Taken together, by introducing the voltage coupling as the energy gap reaction coordinate, our framework brings new perspectives to the thermodynamic models of voltage activation in voltage-sensitive membrane proteins, offering an a framework for a better understating of the structure-function correlations of voltage gating in ion channels as well as electrogenic phenomena in ion pumps and transporters. Significantly, this formulation also provides a powerful bridge between the CG model of voltage coupling and the conventional macroscopic treatments

Powering computational enzyme design with natural evolutionary information

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Electrostatic Contributions to Protein Stability and Folding Energy

The ability to predict the thermal stability of proteins based on their corresponding sequence is a problem of great fundamental and practical importance. Here we report an approach for calculating the electrostatic contribution to protein stability based on the use of the semimacroscopic protein dipole Langevin dipole (PDLD/S) in its linear response approximation version for self-energy with a dielectric constant, (εpεp) and an effective dielectric for charge–charge interactions (εeffεeff). The method is applied to the test cases of ubiquitin, lipase, dihydrofolate reductase and cold shock proteins with series of εpεp and εeffεeff. It is found that the optimal values of these dielectric constants lead to very promising results, both for the relative stability and the absolute folding energy. Consideration of the specific values of the optimal dielectric constants leads to an exciting conceptual description of the reorganization effect during the folding process. Although this description should be examined by further microscopic studies, the practical use of the current approach seems to offer a powerful tool for protein design and for studies of the energetics of protein folding.This work was supported by NIH Grant GM2449

Coarse grained model for exploring voltage dependent ion channels

AbstractThe relationship between the membrane voltage and the gating of voltage activated ion channels and other systems have been a problem of great current interest. Unfortunately, reliable molecular simulations of external voltage effects present a major challenge, since meaningful converging microscopic simulations are not yet available and macroscopic treatments involve major uncertainties in terms of the dielectric used and other key features. This work extends our coarse grained (CG) model to simulations of membrane/protein systems under external potential. Special attention is devoted to a consistent modeling of the effect of external potential due to the electrodes, emphasizing semimacroscopic description of the electrolytes in the solution regions between the membranes and the electrodes, as well as the coupling between the combined potential from the electrodes plus the electrolytes and the protein ionized groups. We also provide a clear connection to microscopic treatment of the electrolytes and thus can explore possible conceptual problems that are hard to resolve by other current approaches. For example, we obtain a clear description of the charge distribution in the entire electrolyte system, including near the electrodes in membrane/electrodes systems (where continuum models do not seem to provide the relevant results). Furthermore, the present treatment provides an insight on the distribution of the electrolyte charges before and after equilibration across the membrane, and thus on the nature of the gating charge. The different aspects of the model have been carefully validated by considering problems ranging for the simple Debye–Huckel, and the Gouy–Chapman models to the evaluation of the electrolyte distribution between two electrodes, as well as the effect of extending the simulation system by periodic replicas. Overall the clear connection to microscopic descriptions combined with the power of the CG modeling seems to offer a powerful tool for exploring the balance between the protein conformational energy and the interaction with the external potential in voltage activated channels. To illustrate these features we present a preliminary study of the gating charge in the voltage activated Kv1.2 channel, using the actual change in the electrolyte charge distribution rather than the conventional macroscopic estimate. We also discuss other special features of the model, which include the ability to capture the effect of changes in the protonation states of the protein residues during the close to open voltage induced transition. This article is part of a Special Issue entitled: Membrane protein structure and function

On the relationship between thermal stability and catalytic power of enzymes

The  possible  relationship  between  the  thermal  stability  and  the  catalytic  power  of  enzymes  is  of   great  current  interest.  In  particular,  it  has  been  suggested  that  thermophilic  or  hyperthermophilic   (Tm)   enzymes   have   lower   catalytic   power   at   a   given   temperature   than   the   corresponding   mesophilic   (Ms)   enzymes,   because   the   thermophilic   enzymes   are   less   flexible   (assuming   that   flexibility   and   catalysis   are   directly   correlated).   These   suggestions   presume   that   the   reduced   dynamics   of   the   thermophilic   enzymes   is   the   reason   for   their   reduced   catalytic   power.   The   present  paper  takes  the  specific  case  of  dihydrofolate  reductase  (DHFR) and explores the validity of the above argument by simulation approaches. It is found that the Tm enzymes have restricted motions in the direction of the folding coordinate, but this is not relevant to the chemical process, since the motions along the reaction coordinate are perpendicular to the folding motions. Moreover, it is shown that the rate of the chemical reaction is determined by the activation barrier and the corresponding reorganization energy, rather than by dynamics or flexibility in the ground state. In fact, as far as flexibility is concerned, we conclude that the displacement along the reaction coordinate is larger in the Tm enzyme than in the Ms enzyme and that the general trend in enzyme catalysis is that the best catalyst involves less motion during the reaction than the less optimal catalyst. The relationship between thermal stability and catalysis appears to reflect the fact that in order to obtain small electrostatic reorganization energy it is necessary to invest some folding energy in the overall preorganization process. Thus, the optimized catalysts are less stable. This trend is clearly observed in the DHFR case

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

AbstractGaining 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

MEDIATE - Molecular DockIng at homE: Turning collaborative simulations into therapeutic solutions

IntroductionCollaborative computing has attracted great interest in the possibility of joining the efforts of researchers worldwide. Its relevance has further increased during the pandemic crisis since it allows for the strengthening of scientific collaborations while avoiding physical interactions. Thus, the E4C consortium presents the MEDIATE initiative which invited researchers to contribute via their virtual screening simulations that will be combined with AI-based consensus approaches to provide robust and method-independent predictions. The best compounds will be tested, and the biological results will be 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

Advances in Molecular Quantum Chemistry Contained in the Q-Chem 4 Program Package

A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Møller–Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube