Scaling of prediction error does not confirm chaotic dynamics underlying irregular firing using interspike intervals...

Dopamine neurons in the substantia nigra pars compacta often fire in an irregular, single spike mode in vivo, and a similar firing pattern can be observed in vitro when small conductance calcium-activated potassium channel blockers are applied to the bath. It is not clear whether the irregular firing is due to stochastic processes or nonlinear deterministic processes. A previous study [Neuroscience 104 (2001) 829] used nonlinear forecasting methods applied to a continuous function derived from the interspike interval (ISI) data from irregularly firing dopamine neurons to show that the predictability scaled exponentially with forecast horizon and was consistent with nonlinear deterministic chaos. However, we show here that the observed exponential scaling is also consistent with a stochastic process, because it did not differ significantly from that of shuffled surrogate data. On the other hand, nonlinear forecasting directly from the ISI data using the package TISEAN provided some evidence for nonlinear deterministic structure in four of five records obtained in vitro and in two of nine records obtained in vivo. Although we cannot rule out a role for nonlinear chaotic dynamics in structuring the firing pattern, we suggest an alternate hypothesis that includes a mechanism by which the firing pattern can become more variable in the presence of a constant level of background noise.