Activation kinetics of T-type calcium channel by a path probability approximation

We previously formulated dynamics of ion channel gates by the path probability method. In this study, we apply that theoretical approach to derive the activation rate kinetics of T-type calcium channel in thalamic relay neurons. We derive explicit expressions of the forward and backward rate constants and show that the proposed rate constants accurately capture form of the empirical time constant, and that they also provide its saturation to a constant value at depolarized membrane potentials. We also compare our derivations with linear and nonlinear thermodynamic models of rate kinetics obtained from the same calcium channel, and show that it is possible to capture saturation of the time constant for the depolarized membrane potentials by the only proposed rate constants.