We have assumed a model of neuronal dynamics in which ISIs are independent. This assumption simplifies the estimation of the information rate, since it reduces the estimation of the multidimensional distribution of spike times to the estimation of the one dimensional ISI distributions (p(T) and ), from which the mutual information can be calculated exactly. Under what conditions will ISIs be independent? Since correlated ISIs can arise either from the spike generating mechanism itself or the input signal, we consider the validity of our assumptions about each in turn.
The first assumption is that the spike generating mechanism does not induce correlations between ISIs. We have used a standard ``memoryless'' integrate-and-fire model in which the length of one ISI has no influence on subsequent ISIs. At least in cortical neurons, this assumption is not strictly valid for at least two reasons. First, on long time scales, adaptation (i.e. a change in the firing rate that depends on the firing rate itself) becomes important. Second, low-pass filtering by dendrites may induce temporal correlations in the effective synaptic current reaching the spike generator, even if they did not exist in the input ensemble. Correlations between ISIs may either increase or decrease the information rate.
The second assumption is that the correlations do not arise from the synaptic drive. This assumption may be inadequate for at least three reasons. First, it requires that EPSCs be much shorter than typical ISIs. Correlations in the synaptic drive are unlikely to arise from the fast AMPA component, but might well arise from the NMDA component, which decays much more slowly. A second potential source of correlations in the synaptic drive is correlations in the spike trains of each of the input neurons. To the extent that each input spike train is not a homogenous Poisson spike train, the model must be reevaluated. Finally, correlations might arise through the history-dependence of efficacy at individual synapses [Dobrunz and Stevens, 1997, Markram and Tsodyks, 1996, Abbott et al., 1997, Varela et al., 1997, Zador and Dobrunz, 1997]. We have made no attempt to explore the potentially important consequences of such use-dependent effects.