On the Firing Rate Dependency of the Phase Response Curve of Rat Purkinje Neurons In Vitro

Synchronous spiking during cerebellar tasks has been observed across Purkinje cells: however, little is known about the intrinsic cellular mechanisms responsible for its initiation, cessation and stability. The Phase Response Curve (PRC), a simple input-output characterization of single cells, can provide insights into individual and collective properties of neurons and networks, by quantifying the impact of an infinitesimal depolarizing current pulse on the time of occurrence of subsequent action potentials, while a neuron is firing tonically. Recently, the PRC theory applied to cerebellar Purkinje cells revealed that these behave as phase-independent integrators at low firing rates, and switch to a phase-dependent mode at high rates. Given the implications for computation and information processing in the cerebellum and the possible role of synchrony in the communication with its post-synaptic targets, we further explored the firing rate dependency of the PRC in Purkinje cells. We isolated key factors for the experimental estimation of the PRC and developed a closed-loop approach to reliably compute the PRC across diverse firing rates in the same cell. Our results show unambiguously that the PRC of individual Purkinje cells is firing rate dependent and that it smoothly transitions from phase independent integrator to a phase dependent mode. Using computational models we show that neither channel noise nor a realistic cell morphology are responsible for the rate dependent shift in the phase response curve.Author Summary: The phase response curve (PRC) quantifies the effect of an infinitesimal perturbation on the phase of an oscillator, be it mechanical, electronic or biological. In the particular case of neurons, PRCs can be employed to infer several network properties that are influenced by intrinsic membrane mechanisms. It has been shown that the PRC of tonically firing Purkinje Cells is flat at low firing rates, which has profound implications for information processing in the cerebellum. Here, we propose a novel method to estimate the PRC of single Purkinje cells at various firing rates and use it to unveil the smooth transition between flat and phasic PRC. Furthermore, we address potential explanations for the observed transition using computational modeling.