Model cerebellar granule cells can faithfully transmit modulated firing rate signals.

Christian Rã¶Ssert,John Porrill,Sergio Solinas,Paul Dean,Egidio D'Angelo

doi:10.3389/fncel.2014.00304

Abstract

A crucial assumption of many high-level system models of the cerebellum is that information in the granular layer is encoded in a linear manner. However, granule cells are known for their non-linear and resonant synaptic and intrinsic properties that could potentially impede linear signal transmission. In this modeling study we analyse how electrophysiological granule cell properties and spike sampling influence information coded by firing rate modulation, assuming no signal-related, i.e., uncorrelated inhibitory feedback (open-loop mode). A detailed one-compartment granule cell model was excited in simulation by either direct current or mossy-fiber synaptic inputs. Vestibular signals were represented as tonic inputs to the flocculus modulated at frequencies up to 20 Hz (approximate upper frequency limit of vestibular-ocular reflex, VOR). Model outputs were assessed using estimates of both the transfer function, and the fidelity of input-signal reconstruction measured as variance-accounted-for. The detailed granule cell model with realistic mossy-fiber synaptic inputs could transmit information faithfully and linearly in the frequency range of the vestibular-ocular reflex. This was achieved most simply if the model neurons had a firing rate at least twice the highest required frequency of modulation, but lower rates were also adequate provided a population of neurons was utilized, especially in combination with push-pull coding. The exact number of neurons required for faithful transmission depended on the precise values of firing rate and noise. The model neurons were also able to combine excitatory and inhibitory signals linearly, and could be replaced by a simpler (modified) integrate-and-fire neuron in the case of high tonic firing rates. These findings suggest that granule cells can in principle code modulated firing-rate inputs in a linear manner, and are thus consistent with the high-level adaptive-filter model of the cerebellar microcircuit.

Highlights

Understanding the function of the cerebellar microcircuit means relating the properties of its neural constituents to its overall computational capacity
Noise-free stimulation We looked first at granule-cell firing rate produced by sinusoidal modulation of a steady current
The spike delay had to be added to explain the phase lag [Figures 3A2,B2; compare phase of granule cell (GrC) model to passive IF model], that cannot be produced by the resonant current and reflects the delay induced by ion-channel spike generation

Summary

Introduction

Understanding the function of the cerebellar microcircuit means relating the properties of its neural constituents to its overall computational capacity. Detailed models of spiking neurons and networks are powerful tools for making contact with experiment, but the focus on low-level features such as channel properties can preclude computational analysis. The granule cells process the very extensive mossy-fiber input to the cerebellum, and are the most numerous type of neuron in the cerebellum itself, and in the entire mammalian brain (e.g., Herculano-Houzel, 2010). They function as part of a recurrent network in the granular layer, which involves inhibitory feedback from Golgi cells, and our long-term goal is to characterize how this network as a whole can transform mossy fiber inputs

Methods

Results

Discussion

Conclusion