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

Rössert C, Solinas S, D'Angelo E, Dean P, Porrill J - Front Cell Neurosci (2014)

Bottom Line: 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 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychology, University of Sheffield Sheffield, UK.

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.

No MeSH data available.


Related in: MedlinePlus

Information transmission by model GrC in response to modulated current injection, with additive noise. Baseline condition for all following simulations: population size N = 100, mean carrier-rate m(F0) ≈ 40 spikes/s, std(F0) ≈ 0 spikes/s and modulation amplitude a = 1. (A) Effects of noise on transfer function of GrC model (A1 gain, A2 phase) measured using the sampling-rate filter method, with 20 Hz low-pass filtered white noise as the input signal (black lines) and fast (τn = 1 ms, an = 4, dark green lines) or slow (τn = 100 ms, an = 2, light green lines) additive correlated white noise. (B) Reconstruction, from stimulation with additive fast (green line) or slow (light green line) noise, of input signal (black line) from GrC response. Total input current to one exemplary cell shown in gray. (C) Reconstruction quality (VAF) for GrC model under varying conditions. (C1) Effects of population size N and fast noise (N = 1: red, N = 10: blue, and N = 100: green line), slow noise (N = 1: light red, N = 10: light blue, and N = 100: light green line) or without noise (N = 100: black line). Mean % VAF for N = 1 32.1 fast noise; 33.6 slow noise. For N = 10 81.6 and 76.7 respectively. For N = 100 97.1 and 95.1 respectively. For N = 100 without noise 89.2. (C2) Effects of carrier-rate F0 and fast noise (20 spikes/s, blue: 40 spikes/s, red: 80 spikes/s green) or slow noise (20 spikes/s, light blue: 40 spikes/s, light red: 80 spikes/s light green). Mean % VAF for 20 spikes/s 95.0 fast noise; 93.4 slow noise. For 40 spikes/s 97.1 and 95.1 respectively. For 80 spikes/s 97.6 and 95.2 respectively. (C3) Effects of modulation amplitude a and fast noise (a = 0.05: blue, a = 0.1: red, and a = 1: green line) or slow noise (a = 0.05: light blue, a = 0.1: light red, and a = 1: light green lines) Mean % VAF for a = 0.05 10.0 fast noise; 13.6 slow noise. For a = 0.1 31.0 and 35.6 respectively. For a = 1 97.1 and 95.1 respectively.
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Figure 4: Information transmission by model GrC in response to modulated current injection, with additive noise. Baseline condition for all following simulations: population size N = 100, mean carrier-rate m(F0) ≈ 40 spikes/s, std(F0) ≈ 0 spikes/s and modulation amplitude a = 1. (A) Effects of noise on transfer function of GrC model (A1 gain, A2 phase) measured using the sampling-rate filter method, with 20 Hz low-pass filtered white noise as the input signal (black lines) and fast (τn = 1 ms, an = 4, dark green lines) or slow (τn = 100 ms, an = 2, light green lines) additive correlated white noise. (B) Reconstruction, from stimulation with additive fast (green line) or slow (light green line) noise, of input signal (black line) from GrC response. Total input current to one exemplary cell shown in gray. (C) Reconstruction quality (VAF) for GrC model under varying conditions. (C1) Effects of population size N and fast noise (N = 1: red, N = 10: blue, and N = 100: green line), slow noise (N = 1: light red, N = 10: light blue, and N = 100: light green line) or without noise (N = 100: black line). Mean % VAF for N = 1 32.1 fast noise; 33.6 slow noise. For N = 10 81.6 and 76.7 respectively. For N = 100 97.1 and 95.1 respectively. For N = 100 without noise 89.2. (C2) Effects of carrier-rate F0 and fast noise (20 spikes/s, blue: 40 spikes/s, red: 80 spikes/s green) or slow noise (20 spikes/s, light blue: 40 spikes/s, light red: 80 spikes/s light green). Mean % VAF for 20 spikes/s 95.0 fast noise; 93.4 slow noise. For 40 spikes/s 97.1 and 95.1 respectively. For 80 spikes/s 97.6 and 95.2 respectively. (C3) Effects of modulation amplitude a and fast noise (a = 0.05: blue, a = 0.1: red, and a = 1: green line) or slow noise (a = 0.05: light blue, a = 0.1: light red, and a = 1: light green lines) Mean % VAF for a = 0.05 10.0 fast noise; 13.6 slow noise. For a = 0.1 31.0 and 35.6 respectively. For a = 1 97.1 and 95.1 respectively.

Mentions: The effects of noise on the transfer function of the model GrC cell are shown in panels 4A1,A2. Comparison of the transfer functions in the noise–free case (black lines) with those previously shown (Figures 3B1,B2; red lines) indicate that increasing amplitude modulation leads to a gain decrease in the absence of noise, and is accompanied by a drop in VAF for high frequencies (Figure 4C1; black lines) as shown before (Figure 3C3). Panels 4A1,A2 also show that the addition of filtered white noise (green lines) irrespective of slow or fast, exposes the spike resonance (Figure 3A1) which otherwise is hidden under the much larger carrier-rate resonance.


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

Rössert C, Solinas S, D'Angelo E, Dean P, Porrill J - Front Cell Neurosci (2014)

Information transmission by model GrC in response to modulated current injection, with additive noise. Baseline condition for all following simulations: population size N = 100, mean carrier-rate m(F0) ≈ 40 spikes/s, std(F0) ≈ 0 spikes/s and modulation amplitude a = 1. (A) Effects of noise on transfer function of GrC model (A1 gain, A2 phase) measured using the sampling-rate filter method, with 20 Hz low-pass filtered white noise as the input signal (black lines) and fast (τn = 1 ms, an = 4, dark green lines) or slow (τn = 100 ms, an = 2, light green lines) additive correlated white noise. (B) Reconstruction, from stimulation with additive fast (green line) or slow (light green line) noise, of input signal (black line) from GrC response. Total input current to one exemplary cell shown in gray. (C) Reconstruction quality (VAF) for GrC model under varying conditions. (C1) Effects of population size N and fast noise (N = 1: red, N = 10: blue, and N = 100: green line), slow noise (N = 1: light red, N = 10: light blue, and N = 100: light green line) or without noise (N = 100: black line). Mean % VAF for N = 1 32.1 fast noise; 33.6 slow noise. For N = 10 81.6 and 76.7 respectively. For N = 100 97.1 and 95.1 respectively. For N = 100 without noise 89.2. (C2) Effects of carrier-rate F0 and fast noise (20 spikes/s, blue: 40 spikes/s, red: 80 spikes/s green) or slow noise (20 spikes/s, light blue: 40 spikes/s, light red: 80 spikes/s light green). Mean % VAF for 20 spikes/s 95.0 fast noise; 93.4 slow noise. For 40 spikes/s 97.1 and 95.1 respectively. For 80 spikes/s 97.6 and 95.2 respectively. (C3) Effects of modulation amplitude a and fast noise (a = 0.05: blue, a = 0.1: red, and a = 1: green line) or slow noise (a = 0.05: light blue, a = 0.1: light red, and a = 1: light green lines) Mean % VAF for a = 0.05 10.0 fast noise; 13.6 slow noise. For a = 0.1 31.0 and 35.6 respectively. For a = 1 97.1 and 95.1 respectively.
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Figure 4: Information transmission by model GrC in response to modulated current injection, with additive noise. Baseline condition for all following simulations: population size N = 100, mean carrier-rate m(F0) ≈ 40 spikes/s, std(F0) ≈ 0 spikes/s and modulation amplitude a = 1. (A) Effects of noise on transfer function of GrC model (A1 gain, A2 phase) measured using the sampling-rate filter method, with 20 Hz low-pass filtered white noise as the input signal (black lines) and fast (τn = 1 ms, an = 4, dark green lines) or slow (τn = 100 ms, an = 2, light green lines) additive correlated white noise. (B) Reconstruction, from stimulation with additive fast (green line) or slow (light green line) noise, of input signal (black line) from GrC response. Total input current to one exemplary cell shown in gray. (C) Reconstruction quality (VAF) for GrC model under varying conditions. (C1) Effects of population size N and fast noise (N = 1: red, N = 10: blue, and N = 100: green line), slow noise (N = 1: light red, N = 10: light blue, and N = 100: light green line) or without noise (N = 100: black line). Mean % VAF for N = 1 32.1 fast noise; 33.6 slow noise. For N = 10 81.6 and 76.7 respectively. For N = 100 97.1 and 95.1 respectively. For N = 100 without noise 89.2. (C2) Effects of carrier-rate F0 and fast noise (20 spikes/s, blue: 40 spikes/s, red: 80 spikes/s green) or slow noise (20 spikes/s, light blue: 40 spikes/s, light red: 80 spikes/s light green). Mean % VAF for 20 spikes/s 95.0 fast noise; 93.4 slow noise. For 40 spikes/s 97.1 and 95.1 respectively. For 80 spikes/s 97.6 and 95.2 respectively. (C3) Effects of modulation amplitude a and fast noise (a = 0.05: blue, a = 0.1: red, and a = 1: green line) or slow noise (a = 0.05: light blue, a = 0.1: light red, and a = 1: light green lines) Mean % VAF for a = 0.05 10.0 fast noise; 13.6 slow noise. For a = 0.1 31.0 and 35.6 respectively. For a = 1 97.1 and 95.1 respectively.
Mentions: The effects of noise on the transfer function of the model GrC cell are shown in panels 4A1,A2. Comparison of the transfer functions in the noise–free case (black lines) with those previously shown (Figures 3B1,B2; red lines) indicate that increasing amplitude modulation leads to a gain decrease in the absence of noise, and is accompanied by a drop in VAF for high frequencies (Figure 4C1; black lines) as shown before (Figure 3C3). Panels 4A1,A2 also show that the addition of filtered white noise (green lines) irrespective of slow or fast, exposes the spike resonance (Figure 3A1) which otherwise is hidden under the much larger carrier-rate resonance.

Bottom Line: 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 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychology, University of Sheffield Sheffield, UK.

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.

No MeSH data available.


Related in: MedlinePlus