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The voltage sensitivity of membrane proteins is reflected in the response of the voltage sensing domains (VSDs) to the changes in membrane potential. This response is implicated in the displacement of positively charged residues, associated with the conformational changes of VSDs. The displaced charges generate nonlinear (i.e., voltage-dependent) capacitance current called the gating current (and its corresponding gating charge), which is a key experimental quantity that characterizes voltage activation in VSMP. However, the relevant theoretical/computational approaches, aimed to correlate the structural information on VSMP to electrophysiological measurements, have been rather limited, posing a broad challenge in computer simulations of VSMP. Concomitant with the development of our coarse-graining (CG) model of voltage coupling, we apply our theoretical framework for the treatments of voltage effects in membrane proteins to modeling the VSMP activation, taking the VSDs (Ci-VSD) derived from the Ciona intestinalis voltage sensitive phosphatase (Ci-VSP) as a model system. Our CG model reproduces the observed gating charge of Ci-VSD activation in several different perspectives. In particular, a new closed-form expression of the gating charge is evaluated in both nonequilibrium and equilibrium ways, while considering the fluctuation-dissipation relation that connects a nonequilibrium measurement of the gating charge to an equilibrium measurement of charge fluctuations (i.e., the voltage-independent linear component of membrane capacitance). In turn, the expression uncovers a novel link that connects an equilibrium measurement of the voltage-independent linear capacitance to a nonequilibrium measurement of the voltage-dependent nonlinear capacitance (whose integral over voltage is equal to the gating charge). In addition, our CG model yields capacitor-like voltage dependent free energy parabolas, resulting in the free energy difference and the free energy barrier for the Ci-VSD activation at "zero" (depolarization) membrane potential. Significantly, the resultant voltage dependent energetics enables a direct evaluation of capacitance-voltage relationship (C-V curve) as well as charge-voltage relationship (Q-V curve) that is in a good agreement with the observed measurement of Ci-VSD voltage activation. Importantly, an extension of our kinetic/thermodynamic model of voltage dependent activation in VSMP allows for novel derivations of voltage-dependent rate constants, whose parameters are expressed by the intrinsic properties of VSMP. These novel closed-form expressions offer a physicochemical foundation for the semiempirical Eyring-type voltage dependent rate equations that have been the cornerstone for the phenomenological (kinetic) descriptions of gating and membrane currents in the mechanistic study of ion channels and transporters. Our extended theoretical framework developed in the present study has potential implications on the roles played by gating charge fluctuations for the spike generations in nerve cells within the framework of the Hodgkin-Huxley-type model.

A 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., (Copyright © 2015 Elsevier B.V. All rights reserved.)

Measurements of voltage changes in response to charge separation within membrane proteins can offer fundamental information on mechanisms of charge transport and displacement processes. A recent example is provided by studies of cytochrome c oxidase. However, the interpretation of the observed voltage changes in terms of the number of charge equivalents and transfer distances is far from being trivial or unique. Using continuum approaches to describe the voltage generation may involve significant uncertainties and reliable microscopic simulations are not yet available. Here, we attempt to solve this problem by using a coarse-grained model of membrane proteins, which includes an explicit description of the membrane, the electrolytes, and the electrodes. The model evaluates the gating charges and the electrode potentials (c.f. measured voltage) upon charge transfer within the protein. The accuracy of the model is evaluated by a comparison of measured voltage changes associated with electron and proton transfer in bacterial photosynthetic reaction centers to those calculated using our coarse-grained model. The calculations reproduce the experimental observations and thus indicate that the method is of general use. Interestingly, it is found that charge-separation processes with different spatial directions (but the same distance perpendicular to the membrane) can give similar observed voltage changes, which indicates that caution should be exercised when using simplified interpretation of the relationship between charge displacement and voltage changes.

Quantitative structure-based modeling of voltage activation of ion channels is very challenging. For example, it is very hard to reach converging results, by microscopic simulations while macroscopic treatments involve major uncertainties regarding key features. The current work overcomes some of the above challenges by using our recently developed coarse-grained (CG) model in simulating the activation of the Kv1.2 channel. The CG model has allowed us to explore problems that cannot be fully addressed at present by microscopic simulations, while providing insights on some features that are not usually considered in continuum models, including the distribution of the electrolytes between the membrane and the electrodes during the activation process and thus the physical nature of the gating current. Here, we demonstrate that the CG model yields realistic gating charges and free energy landscapes that allow us to simulate the fluctuating gating current in the activation processes. Our ability to simulate the time dependence of the fast gating current allows us to reproduce the observed trend and provides a clear description of its relationship to the landscape involved in the activation process.