Equilibrium fluctuation relations for voltage coupling in membrane proteins.
Equilibrium fluctuation relations for voltage coupling in membrane proteins.
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DOI：
10.1016/j.bbamem.2015.08.008
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发表时间：
2015-11
期刊：
影响因子：
--
通讯作者：
Warshel A
中科院分区：
文献类型：
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作者：
Kim I;Warshel A
建立了一个通用理论框架，用于解释外部电势对膜蛋白能量学的影响。该框架基于两个（正向/反向）概率密度之间的自由能关系，这种关系最近已推广到非平衡过程，并在功 - 涨落定理中达到顶峰。从沿着“电压耦合”反应坐标的构象态概率密度出发，考虑离子通道的电压激活，我们研究了这两个构象态之间的几种相互关联的自由能关系。在零膜电位下（即两个“非平衡”构象态之间）的自由能差被证明等同于沿着电压耦合的一维反应坐标的两个“平衡”构象态之间的自由能差。此外，对电压耦合的自由能函数（自由能）应用线性响应近似应满足一般自由能关系的要求，根据其他可实验测量的量得出了门控电荷的一种新表达式。这种联系在统计力学中是常见的，被称为平衡涨落 - 响应关系。通过使用膜蛋白的粗粒化（CG）模型（包括膜、电解质和电极）考虑单位电荷在外部电势影响下在膜内的运动来说明该理论。CG模型为两个构象态产生了马库斯型电压依赖的自由能抛物线，这允许对单位电荷运动的平衡自由能差、势垒自由能以及通道激活的电压依赖性（Q - V曲线）进行定量估计。此外，我们的分析为定点突变或药物结合时自由能景观（抛物线）与Q - V曲线之间的相关性提供了定量依据。综上所述，通过将电压耦合作为能量间隙的反应坐标引入，本理论从统计力学的平衡理论为电压敏感膜蛋白中电压激活的热力学模型提供了坚实的物理基础。这种表述也在CG模型和传统的宏观处理之间提供了一座强有力的桥梁，为更好地理解离子通道中电压门控的结构 - 功能相关性以及离子泵和转运蛋白中的生电现象提供了一个直观且定量的框架。
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 reaction coordinate of “voltage coupling”, we investigate several interconnected free energy relations between these two conformational states, considering voltage activation of ion channels. The free energy difference at zero membrane potential (i.e., between the two “non-equilibrium” conformational states) is shown to be equivalent to the free energy difference between the two “equilibrium” conformational states along the one-dimensional reaction coordinate of voltage coupling. Furthermore, the requirement that the application of linear response approximation to the free energy functions (free energies) of voltage coupling should satisfy the general free energy relations, yields a novel expression for the gating charge in terms of other experimentally measurable quantities. This connection is familiar in statistical mechanics, known as the equilibrium fluctuation-response relation. The theory is illustrated by considering the movement of a unit charge within the membrane under the influence of an external potential, 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 two conformational states, which allow for quantitative estimations of an equilibrium free energy difference, a free energy of barrier, and the voltage dependency of channel activation (Q-V curve) for the unit charge movement. In addition, our analysis offers a quantitative rationale for the correlation between the free energy landscapes (parabolas) and the Q-V curve, upon site-directed mutagenesis or drug binding. Taken together, by introducing the voltage coupling as a reaction coordinate of energy gab, the present theory offers a firm physical foundation from the equilibrium theory of statistical mechanics for the thermodynamic models of voltage activation in voltage-sensitive membrane proteins. This formulation also provides a powerful bridge between the CG model and the conventional macroscopic treatments, offering an intuitive and quantitative 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.