......................................................................

NJIT Mathematical Biology Seminar

Tuesday, December 6, 2005, 4:00 pm
Cullimore Hall 611
New Jersey Institute of Technology

......................................................................

A method for decoding neurophysiological responses to arbitrary spike trains

Esther Stern

Department of Physiology and Biophysics
Mount Sinai School of Medicine

Many physiological responses elicited by neuronal spikes - intracellular calcium transients, synaptic potentials, muscle contractions - are built up of discrete, elementary responses to each spike. However, the spikes are fired in trains of arbitrary temporal complexity, and each elementary response not only sums with previous ones, but can itself be modified by the previous history of the activity. To completely characterize the spike-response transfer function, we wish to derive a small number of functions - the elementary response kernel and additional functions that describe the dependence on previous history - that will predict the response to any arbitrary spike train. We have developed a method to do this. Given the spike times in a train and the observed overall response, we use least-squares minimization to construct an estimated response that best approximates the observed response. In the process we derive three functions that completely define the response. We avoid the need for any initial assumptions about these functions by using techniques of mathematical analysis such as the calculus of variations. Furthermore, although the nonlinear problem is broken into several linear ones that must still be solved iteratively, few iterations are required. Each iteration itself finds the solution in one step, without search.