Spike output jitter, mean firing time and coefficient of variation

To understand how a single neurone processes information, it is critical to examine the relationship between input and output. Marsalek, Koch and Maunsell's study focused on output jitter (standard deviation of output interpike interval) found that for the integrate-and-fire (I&F) model this response measure converges towards zero as the number of inputs increases indefinitely when interarrival times of excitatory inputs (EPSPs) are normally or uniformly distributed. In this work we present a complete, theoretical investigation, corroborated by numerical simulation, of output jitter in the I&F model with a variety of input distributions and a range of values of number of inputs, N. Our main results are: the exponential distribution input is a critical case and its output jitter is independent of N. For input distributions with tails which decrease faster than the exponential distribution, output jitter converges to zero as discovered by Marsalek, Koch and Maunsell; whereas an input distribution with a more slowly decreasing tail induces divergence of output jitter. Exact formulae for mean firing time are also obtained which enable us to estimate the coefficient of variation. The I&F model with leakage is also briefly considered.