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

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

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