A Quantitative Description of the Voltage-Dependent Capacitance in Frog Skeletal Muscle in Terms of Equilibrium Statistical Mechanics

We present an analysis of experimental steady-state properties of charge movements in voltage-clamped frog skeletal muscle; by adopting an approach based on equilibrium statistical mechanics, detailed assumptions about the dynamics of the charge movement were avoided. Different components of the charge movements, as characterized by their sensitivities to local anaesthetics, were taken to correspond to different types of independent subsystem (integral membrane proteins). Quantitative agreement with the data for the q_β and q_γ components was obtained for the simplest subsystems, having two energy levels; however, q_α required three (or more) energy levels. Each of the subsystems can be interpreted as having a charged group, minimum valency z, able to occupy two or more positions within the membrane. The tetracaine-sensitive q_γ charge can be described in terms of an ensemble of subsystems having z = 4.5, each occupying one of two levels whose free energies at zero applied voltage differ by 1.7 × 10^-1 eV. Likewise, the lidocaine-sensitive q_β has z = 1.0, free energy difference 1.9 × 10^-2 eV. However, the simplest model for the lidocaine-resistant q_α involves a charge of valency 1.7 moving between three levels having relative free energies at zero applied voltage -9.7 × 10^-2, 0, and 2.1 × 10^-2 eV respectively, where the intermediate level `sees' about 50% of the applied voltage.