Apamin-induced irregular firing in vitro and irregular single-spike firing observed in vivo in dopamine neurons is chaotic

Dopamine neurons of the substantia nigra often fire action potentials irregularly in vivo, but in vitro fire in a regular, pacemaker-like firing pattern. Bath application of apamin, a blocker of calcium-activated potassium channels, can shift a dopamine neuron from pacemaker-like to irregular firing. To determine whether the irregular firing was caused by intrinsic cellular mechanisms rather than random synaptic input or some other form of noise, spike density functions of interspike interval records were analyzed using non-linear forecasting methods to quantify any non-linear (non-periodic) structure. Intrinsic cellular mechanisms are capable of producing chaotic firing, which is deterministic, non-linear, and loses predictability exponentially with increasing forecast time. To determine whether forecasting spike density functions could reliably measure predictability, forecasting was first applied to spike density functions produced by computer simulations of pacemaker-like, chaotic, and random firing, as well as pacemaker-like and chaotic firing that were randomly synaptically driven. Exponential loss of predictability was successfully detected in both chaotic and randomly driven chaotic firing. Predictability scaled faster than exponentially for random spiking, and linearly (slower than exponentially) for randomly driven pacemaker firing. The method was then applied to experimental records of apamin-induced irregular firing of rat dopaminergic neurons of the substantia nigra in vitro and in vivo. Exponential loss of predictability was detected in both cases, consistent with chaotic firing. Experimental records of pacemaker-like firing in vitro showed linear scaling, consistent with a randomly driven pacemaker. Several schemes for neural encoding of synaptic inputs have been suggested, such as rate codes or temporal codes. However, our results suggest that under some conditions, the irregular firing of dopamine neurons does not reflect the random temporal dynamics of its inputs, but rather the intrinsic, deterministic dynamics of dopamine cells themselves, under the tonic neuromodulatory influence of apamin in vitro and possibly that of an unidentified endogenous modulatory substance in vivo.