IMPACT OF TEMPORAL VARIATION AND THE BALANCE BETWEEN EXCITATION AND INHIBITION ON THE OUTPUT OF THE PERFECT INTEGRATE-AND-FIRE MODEL

We consider how the output of the perfect integrate-and-fire (I&F).mod el of a single neuron is affected by the properties of the input, firs t of all by the distribution of afferent excitatory and inhibitory pos tsynaptic potential (EPSP, IPSP) inter-arrival times, discriminating p articularly between short- and long-tailed forms, and by the degree of balance between excitation and inhibition (as measured by the ratio, r, between the numbers of inhibitory and excitatory inputs). We find t hat the coefficient of variation (CV; standard deviation divided by me an) of efferent interspike interval (ISI) is an increasing function of the length of the tail of the distribution of EPSP inter-arrival time s and the ratio r. There is a range of values of r in which the CV of output ISIs is between 0.5 and 1. Too tight a balance between EPSPs an d IPSPs will cause the model to produce a CV outside the interval cons idered to correspond to the physiological range. Going to the extreme, an exact balance between EPSPs and IPSPs as considered in [24] ensure s a long-tailed ISI output distribution for which the moments such as mean and variance cannot be defined. In this case it is meaningless to consider quantities like output jitter, CV, etc. of the efferent ISIs . The longer the tail of the input inter-arrival time distribution, th e less is the requirement for balance between EPSPs and IPSPs in order to evoke output spike trains with a CV between 0.5 and 1. For a given short-tailed input distribution, the range of values of r in which th e CV of efferent ISIs is between 0.5 and 1 is almost completely inside the range in which output jitter (standard deviation of efferent ISI) is greater than input jitter. Only when the CV is smaller than 0.5 or the input distribution is a long-tailed one is output less than input jitter [21]. The I&F model tends to enlarge low input jitter and redu ce high input jitter. We also provide a novel theoretical framework, b ased upon extreme value theory in statistics, for estimating output ji tter, CV and mean firing time.