Sodium conductance kinetics

Methods are described for extracting the rate constants, governing the transitions between states, for a generalized, linear three discrete state model for the Na conductance,g _Na. It is shown that the problem cannot be solved given only the time course ofg _Na during some test potential step with fixed initial conditions. However, if the effects of any two durations of some conditioning potential step on the peakg _Na during the test step are taken into account, and the physically required assumption that the steady state is an equilibrium state is made, then the rate constants for both conditioning and test potentials can be solved for simultaneously. These methods were applied to thev ⁵ model of Goldman (5) in which theg _Na(t) was described in terms of a generalized linear second order variable. After extensive computations involving some 20,000 combinations of experimentally determined input values, it was not found possible to extract a set of rate constants that were all real and positive as is required. It was concluded that if the transitions between states are first order and there are no subunit interactions, then the Na gating unit displays more than three states.