Firing rate-dependent phase responses of Purkinje cells support transient oscillations

Abstract

Both spike rate and timing can transmit information in the brain. Phase response curves (PRCs) quantify how a neuron transforms input to output by spike timing. PRCs exhibit strong firing-rate adaptation, but its mechanism and relevance for network output are poorly understood. Using our Purkinje cell (PC) model, we demonstrate that the rate adaptation is caused by rate-dependent subthreshold membrane potentials efficiently regulating the activation of Na+ channels. Then, we use a realistic PC network model to examine how rate-dependent responses synchronize spikes in the scenario of reciprocal inhibition-caused high-frequency oscillations. The changes in PRC cause oscillations and spike correlations only at high firing rates. The causal role of the PRC is confirmed using a simpler coupled oscillator network model. This mechanism enables transient oscillations between fast-spiking neurons that thereby form PC assemblies. Our work demonstrates that rate adaptation of PRCs can spatio-temporally organize the PC input to cerebellar nuclei.

The Cellular Electrophysiological Properties Underlying Multiplexed Coding in Purkinje Cells

“…The predicted spiking thresholds should be close to real numbers given the well-validated spiking properties of our model ( Fig. 1 in this work; Zang et al, 2018 , 2020 ) and consequently PF dendritic spikes should not be a rare signal in vivo . According to our simulation results ( Figs.…”

“…The PC was separated into four parts, axon initial segment, soma, main dendrites and spiny dendrites. The model used here was the same as the original model ( Zang et al, 2018 , 2020 ) except some minor changes to current conductances in spiny dendrites. In spiny dendrites, the Kv3 current was decreased by 33%.…”

“…Using a well-validated computational model ( Zang et al, 2018 , 2020 ), we are able to replicate linear computation and localized PF dendritic spikes in a single neuron for the first time. We validate dendritic spike properties with experimental data, make predictions of their thresholds, and explore their computational units.…”

Reciprocally inhibitory circuits operating with distinct mechanisms are differently robust to perturbation and modulation

“…Reciprocal inhibition is ubiquitous in nervous systems, where it has many functions in sensory, motor, and cortical systems. Reciprocal inhibition between individual neurons or groups of neurons is the ‘building block’ of most half-center oscillators that generate antiphase and multiphase activity patterns ( Arbas and Calabrese, 1987a ; Arbas and Calabrese, 1987b ; Brown, 1997 ; Calabrese, 1998 ; Getting, 1989 ; Marder and Calabrese, 1996 ; Perkel and Mulloney, 1974 ; Sakurai and Katz, 2016 ; Satterlie, 1985 ; Soffe et al, 2001 ; Zang et al, 2020 ). Due to their well-defined output, small reciprocally inhibitory circuits provide an excellent platform for investigating the resilience of circuits to internal and environmental challenges.…”

Reciprocally Inhibitory Circuits Operating With Distinct Mechanisms Are Differently Robust to Perturbation and Modulation

“…Reciprocal inhibition is ubiquitous in nervous systems, where it has many functions. Lateral inhibition is important in many sensory systems, and reciprocal inhibition between individual neurons or groups of neurons is the "building block" of many half-center oscillators that generate antiphase and multiphase activity patterns (Arbas and Calabrese, 1987a, b;Brown, 1911;Calabrese, 1998;Getting, 1989;Marder and Calabrese, 1996;Perkel and Mulloney, 1974;Sakurai and Katz, 2016;Satterlie, 1985;Soffe et al, 2001;Zang et al, 2020). Due to their well-defined output, small reciprocally inhibitory circuits provide an excellent platform for investigating the resilience of circuits to internal and environmental challenges.…”