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

Abstract

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.bacterial reaction center | membrane potential | electrogenicity | proton/electron transfer T he use of electrometric techniques to study time-dependent membrane potentials has been exploited in elucidating charge motions in membrane proteins, thereby offering mechanistic insights into the function of membrane-bound channels and pumps (1). For example, data from time-resolved measurements of voltage changes across the redox-driven proton pump cytochrome c oxidase have been used to propose a sequence of electron and proton-transfer events within the enzyme (2). These studies enabled observation of proton-transfer reactions that are typically "invisible" when using spectroscopic techniques and to link these events to electron-transfer reactions. Unfortunately, a correlation of the observed voltage changes with the number and displacements of transferred charges is challenging because the nature of the dielectric response in a protein-membrane system is complex. Thus, it is not straightforward to use macroscopic models to obtain a unique relationship between internal charge motions and the generated potential. The problem is particularly serious if the dielectric or electrostatic response changes significantly in the time range of the experiment. For example, in the case of cytochrome c oxidase a voltage change may be generated by the relaxation of water molecules in an intraprotein proton pathway approximately perpendicular to the membrane surface in response to an int...

Analyzing the electrogenicity of cytochrome c oxidase

“…Each system was then fed into a next step to determine the electrolyte charge distributions and the electrode potentials under an external voltage of 0.1 V. The changes in electrode potentials after the ETs/PTs were used to estimate the voltage generation (the difference in electrode potentials before and after the charge separation). The validity of our approach has been established recently in systematic works (34,37,38).…”

“…In presenting the results, we note that the reported observed values must be normalized because they depend on factors such as the quantum yield, the number of proteins in the membrane (e.g., see ref. 34), and also whether or not the measurements can resolve individual chargetransfer (for example, the very large difference in the electrogenicity of the WT reported in refs. 33 and 43 indicates that we have very different analysis).…”

“…Our method is based on using the CG treatment, which is described in detail elsewhere (34)(35)(36)(37)(38), where we model the protein/membrane system (39) and its interaction with the external potential (Fig. 2).…”

“…To address this challenge, we designed an approach, which is described in detail in ref. 34. In this approach, we determine the relevant potential by applying external potentials of different values, evaluate the resulting changes in the electrolyte distribution, and evaluate the total free energy of the complete protein/membrane/electrolyte/electrode system (an example of the free energy trend is given in Fig.…”

“…The challenge of quantifying the relationship between voltage measurements and charge transport processes has been addressed in our recent work (34), where we developed a specialized coarsegrained (CG) approach (see below) and validated the method using data from measurements of charge-transfer processes…”