Continuum model of voltage-dependent gating. Macroscopic conductance, gating current, and single-channel behavior. 1989

D G Levitt
Department of Physiology, University of Minnesota, Minneapolis 55455.

It is assumed that the conformational change of the voltage-gated channel is continuous, characterized by movement along a generalized one-dimensional reaction coordinate, x, varying from 0 to 1. This large conformational change is coupled to the movement of most of the gating charge. Superimposed on this large movement is a smaller, very fast conformational change that opens or closes the channel. The large conformational change perturbs the channel so that opening is favored near x = 1 and closing is favored near x = 0. The movement along the x axis is described by a generalized Nernst-Planck equation, whereas the open-close transition is modeled as a discrete reaction-rate process. The macroscopic conductance, gating current, and single-channel behavior of a simple, linearized version of the model is described. Although the model has only seven adjustable constants (about the same as would be required for a conventional three-state model), it can mimic the behavior of the delayed rectified K+ channel with 12 or more closed states. The single-channel behavior of the model can have bursts of rapid openings and closings, separated by long closed times. If the conformational change is assumed to correspond to the rotation and translation of charged helices, then this model can be used to estimate the effective rotational diffusion coefficient of the helix. Such calculations for the delayed rectifier K+ channel indicate that the motion must be very restricted.

UI MeSH Term Description Entries
D007473 Ion Channels Gated, ion-selective glycoproteins that traverse membranes. The stimulus for ION CHANNEL GATING can be due to a variety of stimuli such as LIGANDS, a TRANSMEMBRANE POTENTIAL DIFFERENCE, mechanical deformation or through INTRACELLULAR SIGNALING PEPTIDES AND PROTEINS. Membrane Channels,Ion Channel,Ionic Channel,Ionic Channels,Membrane Channel,Channel, Ion,Channel, Ionic,Channel, Membrane,Channels, Ion,Channels, Ionic,Channels, Membrane
D007700 Kinetics The rate dynamics in chemical or physical systems.
D008433 Mathematics The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed) Mathematic
D008962 Models, Theoretical Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment. Experimental Model,Experimental Models,Mathematical Model,Model, Experimental,Models (Theoretical),Models, Experimental,Models, Theoretic,Theoretical Study,Mathematical Models,Model (Theoretical),Model, Mathematical,Model, Theoretical,Models, Mathematical,Studies, Theoretical,Study, Theoretical,Theoretical Model,Theoretical Models,Theoretical Studies
D004553 Electric Conductivity The ability of a substrate to allow the passage of ELECTRONS. Electrical Conductivity,Conductivity, Electric,Conductivity, Electrical
D013816 Thermodynamics A rigorously mathematical analysis of energy relationships (heat, work, temperature, and equilibrium). It describes systems whose states are determined by thermal parameters, such as temperature, in addition to mechanical and electromagnetic parameters. (From Hawley's Condensed Chemical Dictionary, 12th ed) Thermodynamic

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