Firing Dynamics of Cerebellar Purkinje Cells

Abstract

Knowledge of intrinsic neuronal firing dynamics is a critical first step to establishing an accurate biophysical model of any neuron. In this study we examined cerebellar Purkinje cells to determine the bifurcations likely to underlie firing dynamics within a biophysically realistic and experimentally supported model. We show that Purkinje cell dynamics are consistent with a system undergoing a saddle-node bifurcation of fixed points in the transition from rest to firing and a saddle homoclinic bifurcation from firing to rest. Our analyses account for numerous observed Purkinje cell firing properties that include bistability, plateau potentials, specific aspects of the frequency-current (F-I) relationship, first spike latency, and the ability for climbing fiber input to induce state transitions in the bistable regime. We also experimentally confirm new properties predicted from our model and analysis that include the presence of a depolarizing afterpotential (DAP), the ability to fire at low frequencies (<50 Hz) and with a high gain in the F-I relationship, and a bistable region limited to low-frequency firing. Purkinje cell dynamics, including bistability, prove to arise from numerous biophysical factors that include the DAP, fast refractory dynamics, and a long membrane time constant. A hyperpolarizing activated cation current (I(H)) is shown not to be directly involved in establishing bistable dynamics but rather reduces the range for bistability. A combined electrophysiological and modeling approach thus accounts for several properties of Purkinje cells, providing a firm basis from which to assess Purkinje cell output patterns.

Dendritic Calcium Signaling Triggered by Spontaneous and Sensory-Evoked Climbing Fiber Input to Cerebellar Purkinje Cells In Vivo

“…CF input can itself trigger the transitions between up and down states in Purkinje cells (Loewenstein et al, 2005;Fernandez et al, 2007;McKay et al, 2007). Our observation that the [Ca 2ϩ ] transients associated with the CF inputs that triggered the transition from the firing up state to the silent down state were larger than those associated with CF inputs that did not trigger transitions suggests that the larger Ca 2ϩ influx may play a role in regulating transitions from the up state to the down state.…”

“…These findings indicate that the global dendritic Ca 2ϩ signal triggered by the CF event is not a unitary all-or-none event but rather is modulatable depending on the membrane potential of the cell and the synaptic inputs it receives in vivo. The source of this modulation can be the intrinsic bistability of the Purkinje cell (Williams et al, 2002;Loewenstein et al, 2005;Fernandez et al, 2007;McKay et al, 2007) (cf. Schonewille et al, 2006), which we demonstrate can determine distinct levels of dendritic Ca 2ϩ signal.…”

CaV2.1 P/Q-type calcium channel alternative splicing affects the functional impact of familial hemiplegic migraine mutations: Implications for calcium channelopathies

“…In addition to tonic depolarizations, neurons experience various frequencies of burst firing in which brief periods of tonic firing are interspersed with silent periods as the membrane potential drops below threshold. [47][48][49][50][51] During the tonic firing periods P/Q-type channels will inactivate and during silent periods they will have the opportunity to recover from inactivation. Based upon the above noted splice-variant changes in accumulation of inactivation and recovery from inactivation, we predicted that bursts of depolarization would also differentially affect WT and FHM-1 mutated Ca V 2.1 (+47) and Ca V 2.1 (Δ47) variant channels.…”

Computer simulations of neuron-glia interactions mediated by ion flux

“…Firing pattern transitions of cerebellar Purkinje cells that do not depend on ion concentration changes have been analyzed theoretically by Fernandez et al (2007).…”