Voltage sensing in ion channels: Mesoscale simulations of biological devices

Electrical signaling via voltage-gated ion channels depends upon the function of a voltage sensor (VS), identified with the S1-S4 domain in voltage-gated K+ channels. Here we investigate some energetic aspects of the sliding-helix model of the VS using simulations based on VS charges, linear dielectrics and whole-body motion. Model electrostatics in voltage-clamped boundary conditions are solved using a boundary element method. The statistical mechanical consequences of the electrostatic configurational energy are computed to gain insight into the sliding-helix mechanism and to predict experimentally measured ensemble properties such as gating charge displaced by an applied voltage. Those consequences and ensemble properties are investigated for two alternate S4 configurations, \alpha- and 3(10)-helical. Both forms of VS are found to have an inherent electrostatic stability. Maximal charge displacement is limited by geometry, specifically the range of movement where S4 charges and counter-charges overlap in the region of weak dielectric. Charge displacement responds more steeply to voltage in the \alpha-helical than the 3(10)-helical sensor. This difference is due to differences on the order of 0.1 eV in the landscapes of electrostatic energy. As a step toward integrating these VS models into a full-channel model, we include a hypothetical external load in the Hamiltonian of the system and analyze the energetic in/output relation of the VS.Comment: arXiv admin note: substantial text overlap with arXiv:1112.299

Self-organized Models of Selectivity in Ca and Na Channels

A simple pillbox model with two adjustable parameters accounts for the selectivity of both DEEA Ca channels and DEKA Na channels in many ionic solutions of different composition and concentration. Only the side chains are different in the model of the Ca and Na channels. Parameters are the same for both channels in all solutions. 'Pauling' radii are used for ions. No information from crystal structures is used in the model. Side chains are grossly approximated as spheres. The predicted properties of the Na and Ca channels are very different. How can such a simple model give such powerful results when chemical intuition says that selectivity depends on the precise relation of ions and side chains? We use Monte Carlo simulations of this model that determine the most stable-lowest free energy-structure of the ions and side chains. Structure is the computed consequence of the forces in this model. The relationship of ions and side chains vary with ionic solution and are very different in simulations of the Na and Ca channels. Selectivity is a consequence of the 'induced fit' of side chains to ions and depends on the flexibility (entropy) of the side chains as well as their location. The model captures the relation of side chains and ions well enough to account for selectivity of both Na channels and Ca channels in the wide range of conditions measured in experiments. Evidently, the structures in the real Na and Ca channels responsible for selectivity are self-organized, at their free energy minimum. Oversimplified models are enough to account for selectivity if the models calculate the 'most stable' structure as it changes from solution to solution, and mutation to mutation.Comment: Version of http://www.ima.umn.edu/2008-2009/W12.8-12.08/abstracts.html, talk given at the Institute for Mathematics and its Applications, University of Minnesota, November 19, 2008. Abstract published in Biophysical Journal, Volume 96, Issue 3, 253

Ionic selectivity in L-type calcium channels by electrostatics and hard-core repulsion

A physical model of selective “ion binding” in the L-type calcium channel is constructed, and consequences of the model are compared with experimental data. This reduced model treats only ions and the carboxylate oxygens of the EEEE locus explicitly and restricts interactions to hard-core repulsion and ion–ion and ion–dielectric electrostatic forces. The structural atoms provide a flexible environment for passing cations, thus resulting in a self-organized induced-fit model of the selectivity filter. Experimental conditions involving binary mixtures of alkali and/or alkaline earth metal ions are computed using equilibrium Monte Carlo simulations in the grand canonical ensemble. The model pore rejects alkali metal ions in the presence of biological concentrations of Ca2+ and predicts the blockade of alkali metal ion currents by micromolar Ca2+. Conductance patterns observed in varied mixtures containing Na+ and Li+, or Ba2+ and Ca2+, are predicted. Ca2+ is substantially more potent in blocking Na+ current than Ba2+. In apparent contrast to experiments using buffered Ca2+ solutions, the predicted potency of Ca2+ in blocking alkali metal ion currents depends on the species and concentration of the alkali metal ion, as is expected if these ions compete with Ca2+ for the pore. These experiments depend on the problematic estimation of Ca2+ activity in solutions buffered for Ca2+ and pH in a varying background of bulk salt. Simulations of Ca2+ distribution with the model pore bathed in solutions containing a varied amount of Li+ reveal a “barrier and well” pattern. The entry/exit barrier for Ca2+ is strongly modulated by the Li+ concentration of the bath, suggesting a physical explanation for observed kinetic phenomena. Our simulations show that the selectivity of L-type calcium channels can arise from an interplay of electrostatic and hard-core repulsion forces among ions and a few crucial channel atoms. The reduced system selects for the cation that delivers the largest charge in the smallest ion volume

Theoretical predictions of gating behavior for mutants of Shaker-type Kv channels from inter-domain energetics

A multiscale physical model of Shaker-type Kv channels is used to span from atomic-scale interactions to macroscopic experimental measures such as charge/voltage (QV) and conductance/voltage (GV) relations. The model [1] comprises the experimentally well-characterized voltage sensor (VS) domains described by four replications of an independent continuum electrostatic model under voltage clamp conditions [2, 3] and a hydrophobic gate controlling the flow of ions by a vapor lock mechanism [4], connected by a simple coupling principle derived from known experimental results and trial-and-error. The total Hamiltonian of the system is calculated from the computed configurational energy for each components as a function of applied voltage, VS positions andg ate radius, allowing us to produce statistical-mechanical expectation values for macroscopic laboratory observables over the full range of physiological membrane potentials (|V| ≤ 100 mV, in 1 mV steps). The Shaker QV and GV relations seen in Seoh et al. [5] are predicted by this model. With this approach, functional energetic relations can be decomposed in terms of physical components, and thus the effects of modifications in those elements can be quantified. We find that the total work required to operate the gate is an order of magnitude larger than the work available to the VS, and that the the experimentally observed bistable gating is due to the VS slide-and-interlock behavior. The same model was systematically applied to VS charge mutants (Seoh et al. [5]). The QV and GV relations can be qualitatively predicted and the associated effects on functional domains determined. Additional features such as surface charges become significant for the pathological cases. Our engineering approach clearly elucidates that both normal function and mutant changes are electrostatic in nature.[1] Alexander Peyser, Dirk Gillespie, Roland Roth, and Wolfgang Nonner. Domain and inter-domain energetics underlying gating in Shaker-type Kv channels. Accepted: Biophys J,2014. doi:10.1016/j.bpj.2014.08.015.[2] Alexander Peyser and Wolfgang Nonner. Voltage sensing in ion channels: Mesoscale simulations of biological devices. Phys Rev E StatNonlin Soft Matter Phys, 86: 011910, Jul 2012. doi:10.1103/PhysRevE.86.011910.[3] Alexander Peyser and Wolfgang Nonner. The sliding-helix voltage sensor: mesoscale views of a robust structure-function relationship. Eur Biophys J, 41:705–721,2012. doi:10.1007/s00249-012-0847-z.[4] Roland Roth, Dirk Gillespie, Wolfgang Nonner, and Robert E. Eisenberg. Bubbles, gating, and anesthetics in ion channels. Biophys J, 94(11):4282–4298,2008. doi:10.1529/biophysj.107.120493.[5] Sang-Ah Seoh, Daniel Sigg, Diane M. Papazian, and Francisco Bezanilla. Voltage-sensing residues in the S2 and S4 segments of the Shaker K+ channel. Neuron, 16 (6):1159–1167, 1 June1996. doi:10.1016/S0896-6273(00)80142-7.[6] Stephen B. Long, Xiao Tao, Ernest B. Campbell, and Roderick MacKinnon. Atomic structure of a voltage-dependent K+ channel in a lipid membrane-like environment. Nature, 450(7168):376–382,2007. doi:10.1038/nature06265

Shockley-Ramo theorem measures conformation changes of ion channels and proteins

Theorems are rarely used in biology because they rarely help the descriptive experimentation to which biologists are devoted. A generalization of Kirchoff’s current law—the Shockley-Ramo (SR) theorem [1–6]—seems an exception. SR allows interpretation of macroscopic scale ‘gating’ currents associated with atomic scale charge movements within proteins