Stochastic versus deterministic variability in simple neuronal circuits: II. Hippocampal slice

Long time series of Schaffer collateral to CA1 pyramidal cell presynaptic volleys (stratum radiatum) and population spikes (stratum pyramidale) were evoked (driven) in rat hippocampal slices. From the driven CA1 region in normal [K+] perfusate, both population spike amplitude and an input-output function consisting of population spike amplitude divided by the presynaptic volley amplitude were analyzed. Raising [K+] in the perfusion medium to 8.5 mM, slices were induced to spontaneously burst fire in CA3 and long time series of inter-burst intervals were recorded. Three tests for determinism were applied to these series: a discrete adaptation of a local flow approach, a local dispersion approach, and nonlinear prediction. Surrogate data were generated to serve as mathematical and statistical controls. All of the population spike (6/6) and input-output (6/6) time series from the normal [K+] driven circuitry were stochastic by all three methods. Although most of the time series (5/6) from the autonomously bursting high [K+] state failed to demonstrate evidence of determinism, one (1/6) of these time series did demonstrate significant determinism. This single instance of predictability could not be accounted for by the linear correlation in these data.