Steady-state kinetics of solitary batrachotoxin-treated sodium channels. Kinetics on a bounded continuum of polymer conformations.

The underlying principles of the kinetics and equilibrium of a solitary sodium channel in the steady state are examined. Both the open and closed kinetics are postulated to result from round-trip excursions from a transition region that separates the openable and closed forms. Exponential behavior of the kinetics can have origins different from small-molecule systems. These differences suggest that the probability density functions (PDFs) that describe the time dependences of the open and closed forms arise from a distribution of rate constants. The distribution is likely to arise from a thermal modulation of the channel structure, and this provides a physical basis for the following three-variable equation: [formula; see text] Here, A0 is a scaling term, k is the mean rate constant, and sigma quantifies the Gaussian spread for the contributions of a range of effective rate constants. The maximum contribution is made by k, with rates faster and slower contributing less. (When sigma, the standard deviation of the spread, goes to zero, then p(f) = A0 e-kt.) The equation is applied to the single-channel steady-state probability density functions for batrachotoxin-treated sodium channels (1986. Keller et al. J. Gen. Physiol. 88: 1-23). The following characteristics are found: (a) The data for both open and closed forms of the channel are fit well with the above equation, which represents a Gaussian distribution of first-order rate processes. (b) The simple relationship [formula; see text] holds for the mean effective rat constants. Or, equivalently stated, the values of P open calculated from the k values closely agree with the P open values found directly from the PDF data. (c) In agreement with the known behavior of voltage-dependent rate constants, the voltage dependences of the mean effective rate constants for the opening and closing of the channel are equal and opposite over the voltage range studied. That is, [formula; see text] "Bursts" are related to the well-known cage effect of solution chemistry.