Numerical analysis of the voltage-clamp technique applied to frog neuromuscular junctions

The nonlinear cable equation was solved numerically by means of an implicit procedure. The correlation between end-plate length and fiber diameter was determined in frog (Rana pipiens) sartorius muscles stained with gold chloride (Löwit, 1875). The diameter of the fibers stained by the Löwit method was 80 (74-85) micron (median and its 95% confidence interval for 52 fibers), the length of the end plates in the same fibers was 382 (353-417) micron. The fibers simulated were 80 micron in diameter. To solve the equation the muscle fibers were represented by 500 segments 20 micron long, and the equation was solved in steps of 10 microseconds; a double exponential function was incorporated to the first seven segments to represent the neuromuscular junction. The potential of the first segment of the cable was set to the clamping level and the membrane potential of the remaining segments calculated. The current needed to hold the first segment was estimated by adding the current flowing through the first segment to the current flowing from it to the second segment. Our results indicate that the lack of space clamp in the point voltage-clamp studies of the frog neuromuscular junction introduces serious errors in the estimates of the end-plate conductance value, the kinetics of the conductance changes, and the reversal potential of the end-plate currents. The possibility of an efficient voltage-clamp technique is also explored. Our calculations suggest that the study of end-plate current and conductance is possible with little error if the end-plate potential is controlled at both ends of the synaptic area simultaneously.