Modeling gating charge and voltage changes in response to charge separation in membrane proteins

Exploring the Phospholipid Transport Mechanism of ATP8A1-CDC50

P4-ATPase translocates lipids from the exoplasmic to the cytosolic plasma membrane leaflet to maintain lipid asymmetry distribution in eukaryotic cells. P4-ATPase is associated with severe neurodegenerative and metabolic diseases such as neurological and motor disorders. Thus, it is important to understand its transport mechanism. However, even with progress in X-ray diffraction and cryo-electron microscopy techniques, it is difficult to obtain the dynamic information of the phospholipid transport process in detail. There are still some problems required to be resolved: (1) when does the lipid transport happen? (2) How do the key residues on the transmembrane helices contribute to the free energy of important states? In this work, we explore the phospholipid transport mechanism using a coarse-grained model and binding free energy calculations. We obtained the free energy landscape by coupling the protein conformational changes and the phospholipid transport event, taking ATP8A1-CDC50 (the typical subtype of P4-ATPase) as the research object. According to the results, we found that the phospholipid would bind to the ATP8A1-CDC50 at the early stage when ATP8A1-CDC50 changes from E2P to E2Pi-PL state. We also found that the electrostatic effects play crucial roles in the phospholipid transport process. The information obtained from this work could help us in designing novel drugs for P-type flippase disorders.

Generation of Photoelectric Responses by Photosystem II Core Complexes in the Presence of Externally Added Cytochrome c

The effect of exogenous cytochrome c (cyt c) on kinetics of photoelectric responses (Δψ) of two types of photosystem II (PSII) core complexes (intact - PSII with active water-oxidizing complex and Mn-depleted complex) reconstituted into liposomes has been investigated by direct electrometric technique. PSII complexes were localized in the proteoliposome membranes with their donor side outward. An additional electrogenic phase was observed in the kinetics of Δψ generation in response to a laser flash besides the main fast (<0.3 µs) electrogenic component due to electron transfer from the redox-active tyrosine Y_Z to the primary quinone acceptor Q_A in the presence of oxidized cyt c (cyt c³⁺) entrapped in the internal space of proteoliposomes with intact PSII complexes. This component with characteristic time τ ≈ 40 µs and relative amplitude of ~10% of the total Δψ was attributed to the vectorial electron transfer from Q_A^- to cyt c³⁺ serving as an external acceptor. An additional electrogenic component with τ ~ 70 µs and a relative amplitude of ~20% of the total Δψ also appeared in the kinetics of Δψ formation, when cyt c²⁺ was added to the suspension of proteoliposomes containing Mn-depleted PSII core complexes. This component was attributed to the electrogenic transfer of an electron from cyt c²⁺ to photooxidized tyrosine Y_Z. These data imply that cyt c³⁺ serves as a very effective exogenous electron acceptor for Q_A^- in the case of intact PSII core complexes, and cyt c²⁺ is an extremely efficient artificial electron donor for Y_Z in the Mn-depleted PSII. The obtained data on the roles of cyt c²⁺ and cyt c³⁺ as an electron donor and acceptor for PSII, respectively, can be used to develop hybrid photoelectrochemical solar energy-converting systems based on photosynthetic pigment-protein complexes.

Validating a Coarse-Grained Voltage Activation Model by Comparing Its Performance to the Results of Monte Carlo Simulations

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.

Analyzing the electrogenicity of cytochrome c oxidase

Measurements of voltage changes in response to charge separation within membrane proteins can offer fundamental information on spectroscopically "invisible" steps. For example, results from studies of voltage changes associated with electron and proton transfer in cytochrome c oxidase could, in principle, be used to discriminate between different theoretical models describing the molecular mechanism of proton pumping. Earlier analyses of data from these measurements have been based on macroscopic considerations that may not allow for exploring the actual molecular mechanisms. Here, we have used a coarse-grained model describing the relation between observed voltage changes and specific charge-transfer reactions, which includes an explicit description of the membrane, the electrolytes, and the electrodes. The results from these calculations offer mechanistic insights at the molecular level. Our main conclusion is that previously assumed mechanistic evidence that was based on electrogenic measurements is not unique. However, the ability of our calculations to obtain reliable voltage changes means that we have a tool that can be used to describe a wide range of electrogenic charge transfers in channels and transporters, by combining voltage measurements with other experiments and simulations to analyze new mechanistic proposals.

A model for ultra-fast charge transport in membrane proteins

Isolated proteins have recently been observed to transport charge and reactivity over very long distances with extraordinary rates and near perfect efficiencies in spite of their site. This is not the case if the peptide is in water, where the efficiency of charge hopping to the next site is reduced to approximately 2%. Here, water is not an ideal solvent for charge transport. The issue at hand is how to explain such enormous charge transfer quenching in water compared to another typical medium, namely lipid. We performed molecular dynamics simulations to computationally substantiate the novel long-distance charge transfer yield of the polypeptides in lipids. This is characterized by the charge transfer persistent-distance decay constant and not by the rate, which is seldom, if ever, measured and hence not directly addressed here. This model can encompass an extremely wide range of yields over very long distances in peptides in various media. The calculations here demonstrate the good charge transport efficiency in lipids in contrast to the poor efficiency in water. The protein charge transport also exhibits a very strong anisotropic effect in lipids. The peptide secondary structure effect of charge transfer in membranes is analyzed in contrast to that in water. These results suggest that this model can be useful for the prediction of charge transfer efficiency in various environments of interest and indicate that the charge transfer is highly efficient in membrane proteins.

A Microscopic Capacitor Model of Voltage Coupling in Membrane Proteins: Gating Charge Fluctuations in Ci-VSD

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.

Refining the treatment of membrane proteins by coarse-grained models

Obtaining a quantitative description of the membrane proteins stability is crucial for understanding many biological processes. However the advance in this direction has remained a major challenge for both experimental studies and molecular modeling. One of the possible directions is the use of coarse-grained models but such models must be carefully calibrated and validated. Here we use a recent progress in benchmark studies on the energetics of amino acid residue and peptide membrane insertion and membrane protein stability in refining our previously developed coarse-grained model (Vicatos et al., Proteins 2014;82:1168). Our refined model parameters were fitted and/or tested to reproduce water/membrane partitioning energetics of amino acid side chains and a couple of model peptides. This new model provides a reasonable agreement with experiment for absolute folding free energies of several β-barrel membrane proteins as well as effects of point mutations on a relative stability for one of those proteins, OmpLA. The consideration and ranking of different rotameric states for a mutated residue was found to be essential to achieve satisfactory agreement with the reference data.

Multi-scaled normal mode analysis method for dynamics simulation of protein-membrane complexes: A case study of potassium channel gating motion correlations

Membrane proteins play critically important roles in many cellular activities such as ions and small molecule transportation, signal recognition, and transduction. In order to fulfill their functions, these proteins must be placed in different membrane environments and a variety of protein-lipid interactions may affect the behavior of these proteins. One of the key effects of protein-lipid interactions is their ability to change the dynamics status of membrane proteins, thus adjusting their functions. Here, we present a multi-scaled normal mode analysis (mNMA) method to study the dynamics perturbation to the membrane proteins imposed by lipid bi-layer membrane fluctuations. In mNMA, channel proteins are simulated at all-atom level while the membrane is described with a coarse-grained model. mNMA calculations clearly show that channel gating motion can tightly couple with a variety of membrane deformations, including bending and twisting. We then examined bi-channel systems where two channels were separated with different distances. From mNMA calculations, we observed both positive and negative gating correlations between two neighboring channels, and the correlation has a maximum as the channel center-to-center distance is close to 2.5 times of their diameter. This distance is larger than recently found maximum attraction distance between two proteins embedded in membrane which is 1.5 times of the protein size, indicating that membrane fluctuation might impose collective motions among proteins within a larger area. The hybrid resolution feature in mNMA provides atomic dynamics information for key components in the system without costing much computer resource. We expect it to be a conventional simulation tool for ordinary laboratories to study the dynamics of very complicated biological assemblies. The source code is available upon request to the authors.

Equilibrium fluctuation relations for voltage coupling in membrane proteins

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.