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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

Transmission with low firing-rate. Transfer function gain (A1,B1), phase (A2,B2), VAF (A3,B3) and reconstruction sample (A4,B4) for 100 cell populations of passive IF (dashed lines), resonant IF (rIF) (dotted lines) and GrC model (solid lines) without (A) and with (B) additive filtered slow noise (τn = 100 ms). In addition to the normal case where population is encoding the whole signal (blue lines) push-pull coding (red lines) is shown. In this case, half of the cells encode only the positive and the negative part of the signal respectively. Input current adjusted for all recordings to result in m(Feff) = 4 spikes/s and std(Feff) = 2 spikes/s. [m(VAF) in % for IF/rIF/GrC: 50.9/50.8/46.4; 82.5/80.1/68.3 (push-pull); 72.0/73.1/72.4 (slow noise); 93.8/93.1/87.6 (push-pull + slow noise)].
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Figure 5: Transmission with low firing-rate. Transfer function gain (A1,B1), phase (A2,B2), VAF (A3,B3) and reconstruction sample (A4,B4) for 100 cell populations of passive IF (dashed lines), resonant IF (rIF) (dotted lines) and GrC model (solid lines) without (A) and with (B) additive filtered slow noise (τn = 100 ms). In addition to the normal case where population is encoding the whole signal (blue lines) push-pull coding (red lines) is shown. In this case, half of the cells encode only the positive and the negative part of the signal respectively. Input current adjusted for all recordings to result in m(Feff) = 4 spikes/s and std(Feff) = 2 spikes/s. [m(VAF) in % for IF/rIF/GrC: 50.9/50.8/46.4; 82.5/80.1/68.3 (push-pull); 72.0/73.1/72.4 (slow noise); 93.8/93.1/87.6 (push-pull + slow noise)].

Mentions: While the intrinsic properties of the GrC model have only a slight influence on transmission properties for sufficiently high firing-rates, this ceases to be the case when the firing-rates are smaller than the maximum input signal frequency. When analysing all three models (GrC, resonant IF and passive IF) in a population of 100 cells with m(Feff) = 4 spikes/s (Figure 5A, blue lines) it can be observed that the gain and phase for the passive IF population is flat over the whole frequency range and the resonant IF population just shows a small phase lag at higher frequencies due to the induced spike delay (Figures 5A1,A2). In contrast, the response of the GrC model population shows a large gain decay and phase lag at higher frequencies. Similarly, the VAF (Figure 5A3) of the IF populations is rather flat between 40 and 60% over the whole frequency range, whereas for the GrC population, VAF falls off to lower values for 20 Hz which was already seen for the case F0 = 20 spikes/s (Figure 3C2). This relation can be explained by the effect that since the higher frequency content is highly damped, as seen from the strong gain decay, and therefore any reconstruction potential erroneous, the Wiener filter tries instead to optimize the low frequency content of the signal.


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)

Transmission with low firing-rate. Transfer function gain (A1,B1), phase (A2,B2), VAF (A3,B3) and reconstruction sample (A4,B4) for 100 cell populations of passive IF (dashed lines), resonant IF (rIF) (dotted lines) and GrC model (solid lines) without (A) and with (B) additive filtered slow noise (τn = 100 ms). In addition to the normal case where population is encoding the whole signal (blue lines) push-pull coding (red lines) is shown. In this case, half of the cells encode only the positive and the negative part of the signal respectively. Input current adjusted for all recordings to result in m(Feff) = 4 spikes/s and std(Feff) = 2 spikes/s. [m(VAF) in % for IF/rIF/GrC: 50.9/50.8/46.4; 82.5/80.1/68.3 (push-pull); 72.0/73.1/72.4 (slow noise); 93.8/93.1/87.6 (push-pull + slow noise)].
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Figure 5: Transmission with low firing-rate. Transfer function gain (A1,B1), phase (A2,B2), VAF (A3,B3) and reconstruction sample (A4,B4) for 100 cell populations of passive IF (dashed lines), resonant IF (rIF) (dotted lines) and GrC model (solid lines) without (A) and with (B) additive filtered slow noise (τn = 100 ms). In addition to the normal case where population is encoding the whole signal (blue lines) push-pull coding (red lines) is shown. In this case, half of the cells encode only the positive and the negative part of the signal respectively. Input current adjusted for all recordings to result in m(Feff) = 4 spikes/s and std(Feff) = 2 spikes/s. [m(VAF) in % for IF/rIF/GrC: 50.9/50.8/46.4; 82.5/80.1/68.3 (push-pull); 72.0/73.1/72.4 (slow noise); 93.8/93.1/87.6 (push-pull + slow noise)].
Mentions: While the intrinsic properties of the GrC model have only a slight influence on transmission properties for sufficiently high firing-rates, this ceases to be the case when the firing-rates are smaller than the maximum input signal frequency. When analysing all three models (GrC, resonant IF and passive IF) in a population of 100 cells with m(Feff) = 4 spikes/s (Figure 5A, blue lines) it can be observed that the gain and phase for the passive IF population is flat over the whole frequency range and the resonant IF population just shows a small phase lag at higher frequencies due to the induced spike delay (Figures 5A1,A2). In contrast, the response of the GrC model population shows a large gain decay and phase lag at higher frequencies. Similarly, the VAF (Figure 5A3) of the IF populations is rather flat between 40 and 60% over the whole frequency range, whereas for the GrC population, VAF falls off to lower values for 20 Hz which was already seen for the case F0 = 20 spikes/s (Figure 3C2). This relation can be explained by the effect that since the higher frequency content is highly damped, as seen from the strong gain decay, and therefore any reconstruction potential erroneous, the Wiener filter tries instead to optimize the low frequency content of the signal.

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