Threshold measurement: applications to excitable membranes of nerve and muscle

Tracking the firing threshold of membranes is best accomplished with threshold hunters, automatic devices that adjust stimulus strength so as to hold constant the probability of an all-or-none response. We present a formalism for analyzing the performance of threshold hunters. An index for error is defined between the threshold of the membrane and the output of the threshold hunter. Errors are separated into tracking error, quantization error, and a fluctuation error that reflects the probabilistic nature of responses to liminal stimuli. The engineering trade-offs between these errors are quantified for conditions where the threshold undergoes rapid transients (e.g. after conditioning impulses) and where it changes more gradually (e.g. during exposure to anesthetics or recovery from tetanus). Several methods for decreasing the total error of the threshold hunter by using the outcomes from previous test stimuli are analyzed quantitatively to provide criteria for the design of hunters to extract a maximum of information concerning threshold with a minimum of interference with the preparation. In nerve axon the distribution of the firing threshold depends on impulse activity patterns, and a strategy for measuring this effect is presented.