A new algorithm for voltage clamp by iteration: a learning control of a nonlinear neuronal system

Abstract

Voltage-clamp of excitable membrane allows the measurement of membrane currents associated with electrical potential changes across the membrane. However, it has been impossible in practice to apply the conventional analog feedback voltage-clamp circuits to single electrode voltage clamping in central neurons. The reason for this is that the feedback system becomes unstable because of the positive feedback required for compensation of capacitative loss through the wall of the microelectrode. Park et al. (1981) proposed a new iterative technique to solve this problem. It requires that the potential to be clamped repeats itself with little or no change. The amount of current needed to clamp the membrane potential is not determined at once, but in a step-wise, trial and error fashion in the course of a set of repetitions. Since the feedback loop is open in real time, the system has great stability, and this advantage can be exploited in single electrode preparations. The computation algorithm which calculates the current waveform based on the voltage deviation during the last trial is the central part of the iterative voltage-clamp system. In this paper, we propose a new algorithm, which has several theoretical and practical advantages over the original one proposed by Park et al. First, two parameters used in the new algorithm are predetermined by a current-clamp experiment. Second, the speed of convergence of the new algorithm is faster than that of the Park's original algorithm. This was shown by computer simulation of iterative voltage clamp of artificial membrane following Hodgkin-Huxley equations for squid axon membrane and Rall's compartment model for a neuron with dendrites. Finally, we offer proof that the new algorithm is certain to converge for the general cases of voltage-clamp experiments with active membrane properties, synaptic membranes, etc. Consequently, the new algorithm for iterative voltage clamp is very suitable for single electrode voltage clamp in the central neurons. The new algorithm has been successfully applied to voltage-clamp experiments on rubrospinal neurons of cats (Tsukahara, Murakami, Kawato, Oda, and Etoh, in preparation).