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GATING CURRENT MODELS COMPUTED WITH CONSISTENT INTERACTIONS

Banff International Research Station for Mathematical Innovation and Discovery

Gating currents of the voltage sensor involve back-and forth movements of positively charged arginines through the hydrophobic plug of the gating pore. Transient movements of the permanent charge of the arginines induce structural changes and polarization charge nearby. The moving permanent charge induces current flow everywhere. Everything interacts with everything else in this structural model so everything must interact with everything else in the mathematics, as everything does in the structure. Energy variational methods EnVarA are used to compute gating currents in which all movements of charge and mass satisfy conservation laws of current and mass. Conservation laws are partial differential equations in space and time. Ordinary differential equations cannot capture such interactions with one set of parameters. Indeed, they may inadvertently violate conservation of current. Conservation of current is particularly important since small violations (<0.01%) quickly (microseconds) produce forces that destroy molecules. Our model reproduces signature properties of gating current: (1) equality of ON and OFF charge (2) saturating voltage dependence and (3) many (but not all) details of the shape of charge movement as a function of voltage, time, and solution composition. The model computes gating current flowing in the baths produced by arginines moving in the voltage sensor. The movement of arginines induces current flow everywhere producing ‘capacitive’ pile ups at the ends of the channel. Such pile-ups at charged interfaces are well studied in measurements and theories of physical chemistry but they are not typically included in models of gating current or ion channels. The pile-ups of charge change local electric fields, and they store charge in series with the charge storage of the arginines of the voltage sensor. Implications are being investigated. Joint with Robert S. Eisenberg, Chun Liu, Francisco Bezanilla

Mathematics; Partial differential equations; Biology and other natural sciences; Applied analysis / inverse problems

video/mp4

Author affiliation: Feng Chia University

2017-01-26

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59840

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/