Influence of intercellular clefts on potential and current distribution in a multifiber preparation

A theoretical model is presented for current and voltage clamp of multifiber bundles in a double sucrose gap. Attention is focused on methodological errors introduced by the intercellular cleft resistance. The bundle is approximated by a continuous geometry. Voltage distribution, as a function of radial distance and time, is defined by a parabolic partial differential equation which is specified for different membrane characteristics. Assuming a linear membrane, analytical solutions are given for current step and voltage step conditions. The theoretical relations (based on Bessel functions) may be used to calculate membrane conductance and capacity from experimental clamp data. The case of a nonlinear membrane with standard Hodgkin-Huxley kinetics for excitatory Na current is treated assuming maximum Na conductances (gNa) of 120, 10, and 1 mmho/cm2. Numerical simulations are presented for potential and current distribution in a bundle of 60 microns diameter during depolarizing voltage steps. Adequate voltage control is restricted to the peripheral fibers of the bundle whereas the membrane potential of the inner fibers deviates from the command level during early inward current, tending to the Na equilibrium potential. In the peak current-voltage diagram the loss of voltage control is reflected by an increased steepness of the negative region and a decreased slope conductance of the positive region. With gNa = 120 mmho/cm2, the positive slope conductance is approximately 25% of the slope expected from ideal space clamping. With the lower values of gNa, the slope conductance ratio is in the order of 50%. Implications of the results for an experimental voltage clamp analysis of early inward current on multifiber preparations are discussed.