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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

Synaptic signal combination and signal trough inhibitory synapse. Reconstruction quality (VAF) (A–C) of N = 100 synaptically activated (AMPA + NMDA) granule cells with m(FI) = 6 spikes/s but different input configurations as depicted by clipart above. Mean, standard deviation of effective firing-rate in spikes/s and mean of VAF in % given as triplet [m(Feff)/std(Feff)/m(VAF)] in the following. Baseline condition for all following simulations: modulation amplitude a = 1. (A) Two different input signals to two excitatory synapses respectively (dark red line) (37/8.2/95.0) or to one and three excitatory synapses (light red line) (37/8.0/95.9). (B) Two different input signals to 4 excitatory and 4 inhibitory synapses respectively, best reconstruction x(t) = xA(t) −0.23xB(t) (solid orange line) (38/7.7/91.9). Additional simulations for reduced synaptic conductance (45%) and increased inhibition rate m(FI) = 40 spikes/s (dotted orange line) (38/6.3/96.1). (C) One input signal to the 4 inhibitory synapses only (solid blue line) (38/8.6/90.2). Additional simulations for reduced synaptic conductance (45%) and increased inhibition rate m(FI) = 40 spikes/s, (dotted blue line) (38/7.2/86.6).
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Figure 8: Synaptic signal combination and signal trough inhibitory synapse. Reconstruction quality (VAF) (A–C) of N = 100 synaptically activated (AMPA + NMDA) granule cells with m(FI) = 6 spikes/s but different input configurations as depicted by clipart above. Mean, standard deviation of effective firing-rate in spikes/s and mean of VAF in % given as triplet [m(Feff)/std(Feff)/m(VAF)] in the following. Baseline condition for all following simulations: modulation amplitude a = 1. (A) Two different input signals to two excitatory synapses respectively (dark red line) (37/8.2/95.0) or to one and three excitatory synapses (light red line) (37/8.0/95.9). (B) Two different input signals to 4 excitatory and 4 inhibitory synapses respectively, best reconstruction x(t) = xA(t) −0.23xB(t) (solid orange line) (38/7.7/91.9). Additional simulations for reduced synaptic conductance (45%) and increased inhibition rate m(FI) = 40 spikes/s (dotted orange line) (38/6.3/96.1). (C) One input signal to the 4 inhibitory synapses only (solid blue line) (38/8.6/90.2). Additional simulations for reduced synaptic conductance (45%) and increased inhibition rate m(FI) = 40 spikes/s, (dotted blue line) (38/7.2/86.6).

Mentions: In previous simulations the same signal has been conveyed by excitatory synapses only. We thus continued our analysis by testing signal combination at excitatory synapses (Figure 8A), at excitatory and inhibitory synapses (Figure 8B) and signal transmission through inhibitory synapses alone (Figure 8C). In the following the rate of inhibition was normally distributed, all spike trains were created by iIF coding, N = 100, a = 1 and all other parameters are chosen to always produce a mean effective firing-rate of Feff = ~40 spikes/s.


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)

Synaptic signal combination and signal trough inhibitory synapse. Reconstruction quality (VAF) (A–C) of N = 100 synaptically activated (AMPA + NMDA) granule cells with m(FI) = 6 spikes/s but different input configurations as depicted by clipart above. Mean, standard deviation of effective firing-rate in spikes/s and mean of VAF in % given as triplet [m(Feff)/std(Feff)/m(VAF)] in the following. Baseline condition for all following simulations: modulation amplitude a = 1. (A) Two different input signals to two excitatory synapses respectively (dark red line) (37/8.2/95.0) or to one and three excitatory synapses (light red line) (37/8.0/95.9). (B) Two different input signals to 4 excitatory and 4 inhibitory synapses respectively, best reconstruction x(t) = xA(t) −0.23xB(t) (solid orange line) (38/7.7/91.9). Additional simulations for reduced synaptic conductance (45%) and increased inhibition rate m(FI) = 40 spikes/s (dotted orange line) (38/6.3/96.1). (C) One input signal to the 4 inhibitory synapses only (solid blue line) (38/8.6/90.2). Additional simulations for reduced synaptic conductance (45%) and increased inhibition rate m(FI) = 40 spikes/s, (dotted blue line) (38/7.2/86.6).
© Copyright Policy - open-access
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4195316&req=5

Figure 8: Synaptic signal combination and signal trough inhibitory synapse. Reconstruction quality (VAF) (A–C) of N = 100 synaptically activated (AMPA + NMDA) granule cells with m(FI) = 6 spikes/s but different input configurations as depicted by clipart above. Mean, standard deviation of effective firing-rate in spikes/s and mean of VAF in % given as triplet [m(Feff)/std(Feff)/m(VAF)] in the following. Baseline condition for all following simulations: modulation amplitude a = 1. (A) Two different input signals to two excitatory synapses respectively (dark red line) (37/8.2/95.0) or to one and three excitatory synapses (light red line) (37/8.0/95.9). (B) Two different input signals to 4 excitatory and 4 inhibitory synapses respectively, best reconstruction x(t) = xA(t) −0.23xB(t) (solid orange line) (38/7.7/91.9). Additional simulations for reduced synaptic conductance (45%) and increased inhibition rate m(FI) = 40 spikes/s (dotted orange line) (38/6.3/96.1). (C) One input signal to the 4 inhibitory synapses only (solid blue line) (38/8.6/90.2). Additional simulations for reduced synaptic conductance (45%) and increased inhibition rate m(FI) = 40 spikes/s, (dotted blue line) (38/7.2/86.6).
Mentions: In previous simulations the same signal has been conveyed by excitatory synapses only. We thus continued our analysis by testing signal combination at excitatory synapses (Figure 8A), at excitatory and inhibitory synapses (Figure 8B) and signal transmission through inhibitory synapses alone (Figure 8C). In the following the rate of inhibition was normally distributed, all spike trains were created by iIF coding, N = 100, a = 1 and all other parameters are chosen to always produce a mean effective firing-rate of Feff = ~40 spikes/s.

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