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A dendritic mechanism for decoding traveling waves: principles and applications to motor cortex.

Heitmann S, Boonstra T, Breakspear M - PLoS Comput. Biol. (2013)

Bottom Line: We validate this proposal in the descending motor system, where we model the large receptor fields of the pyramidal tract neurons - the principle outputs of the motor cortex - decoding motor commands encoded in the direction of traveling wave patterns in motor cortex.The model replicates key findings of the descending motor system during simple motor tasks, including variable interspike intervals and weak corticospinal coherence.By additionally showing how the nature of the wave patterns can be controlled by modulating the topology of local intra-cortical connections, we hence propose a novel integrated neuronal model of encoding and decoding motor commands.

View Article: PubMed Central - PubMed

Affiliation: School of Psychiatry, The University of New South Wales, Sydney, Australia ; The Black Dog Institute, Sydney, Australia.

ABSTRACT
Traveling waves of neuronal oscillations have been observed in many cortical regions, including the motor and sensory cortex. Such waves are often modulated in a task-dependent fashion although their precise functional role remains a matter of debate. Here we conjecture that the cortex can utilize the direction and wavelength of traveling waves to encode information. We present a novel neural mechanism by which such information may be decoded by the spatial arrangement of receptors within the dendritic receptor field. In particular, we show how the density distributions of excitatory and inhibitory receptors can combine to act as a spatial filter of wave patterns. The proposed dendritic mechanism ensures that the neuron selectively responds to specific wave patterns, thus constituting a neural basis of pattern decoding. We validate this proposal in the descending motor system, where we model the large receptor fields of the pyramidal tract neurons - the principle outputs of the motor cortex - decoding motor commands encoded in the direction of traveling wave patterns in motor cortex. We use an existing model of field oscillations in motor cortex to investigate how the topology of the pyramidal cell receptor field acts to tune the cells responses to specific oscillatory wave patterns, even when those patterns are highly degraded. The model replicates key findings of the descending motor system during simple motor tasks, including variable interspike intervals and weak corticospinal coherence. By additionally showing how the nature of the wave patterns can be controlled by modulating the topology of local intra-cortical connections, we hence propose a novel integrated neuronal model of encoding and decoding motor commands.

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Gabor filtering by excitatory and inhibitory receptor densities.(A) Density profiles for excitatory (blue) and inhibitory (red) receptor populations which combine to form a Gabor filter (black). In this case, the excitatory density was nominated as Gaussian. (B) Spatial frequency response of the Gabor filter. Peaks correspond to waves of length 300 µm. (C) Excitatory (blue) and inhibitory (red) receptor samples taken from the density distributions in panel A. The combined receptor field (blue+red) represents the dendritic field of the neuron. (D) Spatial frequency response of the combined receptor field. Peaks correspond to vertically oriented waves of length 300 µm. (E) The combined receptor field superimposed on its preferred wave pattern. The wave pattern propagates from left to right at 6 mm/sec to simulate 20 Hz oscillations in the cortical field. (F) Time course of the net excitatory (blue shading) and inhibitory (red shading) conductances in response the preferred wave pattern. Faint lines show individual post-synaptic conductances for n = 40 randomly selected receptors (not to scale). Each receptor fires 20 spikes/sec on average. Heavy black line shows the dendritic current induced by the net changes in conductance. The amplitude of the dendritic current is modulated as the wave propagates across the receptor field. (G) The combined receptor field superimposed on the orthogonal wave pattern which propagates from top to bottom at 6 mm/sec. (H) Time course of the dendritic response to the orthogonal wave pattern. In this case the wave pattern does not modulate the dendritic current even though the individual receptors still fire at 20 spikes/sec on average.
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pcbi-1003260-g003: Gabor filtering by excitatory and inhibitory receptor densities.(A) Density profiles for excitatory (blue) and inhibitory (red) receptor populations which combine to form a Gabor filter (black). In this case, the excitatory density was nominated as Gaussian. (B) Spatial frequency response of the Gabor filter. Peaks correspond to waves of length 300 µm. (C) Excitatory (blue) and inhibitory (red) receptor samples taken from the density distributions in panel A. The combined receptor field (blue+red) represents the dendritic field of the neuron. (D) Spatial frequency response of the combined receptor field. Peaks correspond to vertically oriented waves of length 300 µm. (E) The combined receptor field superimposed on its preferred wave pattern. The wave pattern propagates from left to right at 6 mm/sec to simulate 20 Hz oscillations in the cortical field. (F) Time course of the net excitatory (blue shading) and inhibitory (red shading) conductances in response the preferred wave pattern. Faint lines show individual post-synaptic conductances for n = 40 randomly selected receptors (not to scale). Each receptor fires 20 spikes/sec on average. Heavy black line shows the dendritic current induced by the net changes in conductance. The amplitude of the dendritic current is modulated as the wave propagates across the receptor field. (G) The combined receptor field superimposed on the orthogonal wave pattern which propagates from top to bottom at 6 mm/sec. (H) Time course of the dendritic response to the orthogonal wave pattern. In this case the wave pattern does not modulate the dendritic current even though the individual receptors still fire at 20 spikes/sec on average.

Mentions: To study the effect of the spatial arrangement of dendritic receptors on soma current, we simulated the synaptic currents flowing into the dendrite using the conductance-based model,(1)where is the membrane capacitance, is the membrane potential, is the membrane leak current, and are the net synaptic currents of the excitatory and inhibitory receptor populations respectively. The spatial densities of the receptor populations were chosen so they combined to form a Gabor filter (Figure 3A). The Gabor filter was tuned to respond maximally to waves of length 300 µm (Figure 3B). Many combinations of excitatory and inhibitory densities can satisfy this requirement. Here, we nominated the excitatory density as a Gaussian distribution ( µm; peak density 0.4 synapse/µm2) and solved for the inhibitory distribution given a Gabor function with µm and a peak density of 0.2 synapse/µm2 (see Methods). The resulting distributions have a width of approximately 600 µm which corresponds to the width of PTN receptor fields [36], [37], [55]. The total number of synapses circumscribed by these distributions also fell within physiological estimates of 60,000 to 100,000 synapses per neuron [56]–[58]. Supplementary Figure S1 gives an alternative example where the inhibitory distribution is nominated as Gaussian and we solve the excitatory density. In both cases, the density distributions were randomly sampled to simulate the placement of excitatory and inhibitory receptors within the dendritic field (panel C). In both cases, the estimated frequency response of the combined receptor field (panel D) matched that of the target Gabor filter (panel B), as expected.


A dendritic mechanism for decoding traveling waves: principles and applications to motor cortex.

Heitmann S, Boonstra T, Breakspear M - PLoS Comput. Biol. (2013)

Gabor filtering by excitatory and inhibitory receptor densities.(A) Density profiles for excitatory (blue) and inhibitory (red) receptor populations which combine to form a Gabor filter (black). In this case, the excitatory density was nominated as Gaussian. (B) Spatial frequency response of the Gabor filter. Peaks correspond to waves of length 300 µm. (C) Excitatory (blue) and inhibitory (red) receptor samples taken from the density distributions in panel A. The combined receptor field (blue+red) represents the dendritic field of the neuron. (D) Spatial frequency response of the combined receptor field. Peaks correspond to vertically oriented waves of length 300 µm. (E) The combined receptor field superimposed on its preferred wave pattern. The wave pattern propagates from left to right at 6 mm/sec to simulate 20 Hz oscillations in the cortical field. (F) Time course of the net excitatory (blue shading) and inhibitory (red shading) conductances in response the preferred wave pattern. Faint lines show individual post-synaptic conductances for n = 40 randomly selected receptors (not to scale). Each receptor fires 20 spikes/sec on average. Heavy black line shows the dendritic current induced by the net changes in conductance. The amplitude of the dendritic current is modulated as the wave propagates across the receptor field. (G) The combined receptor field superimposed on the orthogonal wave pattern which propagates from top to bottom at 6 mm/sec. (H) Time course of the dendritic response to the orthogonal wave pattern. In this case the wave pattern does not modulate the dendritic current even though the individual receptors still fire at 20 spikes/sec on average.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3814333&req=5

pcbi-1003260-g003: Gabor filtering by excitatory and inhibitory receptor densities.(A) Density profiles for excitatory (blue) and inhibitory (red) receptor populations which combine to form a Gabor filter (black). In this case, the excitatory density was nominated as Gaussian. (B) Spatial frequency response of the Gabor filter. Peaks correspond to waves of length 300 µm. (C) Excitatory (blue) and inhibitory (red) receptor samples taken from the density distributions in panel A. The combined receptor field (blue+red) represents the dendritic field of the neuron. (D) Spatial frequency response of the combined receptor field. Peaks correspond to vertically oriented waves of length 300 µm. (E) The combined receptor field superimposed on its preferred wave pattern. The wave pattern propagates from left to right at 6 mm/sec to simulate 20 Hz oscillations in the cortical field. (F) Time course of the net excitatory (blue shading) and inhibitory (red shading) conductances in response the preferred wave pattern. Faint lines show individual post-synaptic conductances for n = 40 randomly selected receptors (not to scale). Each receptor fires 20 spikes/sec on average. Heavy black line shows the dendritic current induced by the net changes in conductance. The amplitude of the dendritic current is modulated as the wave propagates across the receptor field. (G) The combined receptor field superimposed on the orthogonal wave pattern which propagates from top to bottom at 6 mm/sec. (H) Time course of the dendritic response to the orthogonal wave pattern. In this case the wave pattern does not modulate the dendritic current even though the individual receptors still fire at 20 spikes/sec on average.
Mentions: To study the effect of the spatial arrangement of dendritic receptors on soma current, we simulated the synaptic currents flowing into the dendrite using the conductance-based model,(1)where is the membrane capacitance, is the membrane potential, is the membrane leak current, and are the net synaptic currents of the excitatory and inhibitory receptor populations respectively. The spatial densities of the receptor populations were chosen so they combined to form a Gabor filter (Figure 3A). The Gabor filter was tuned to respond maximally to waves of length 300 µm (Figure 3B). Many combinations of excitatory and inhibitory densities can satisfy this requirement. Here, we nominated the excitatory density as a Gaussian distribution ( µm; peak density 0.4 synapse/µm2) and solved for the inhibitory distribution given a Gabor function with µm and a peak density of 0.2 synapse/µm2 (see Methods). The resulting distributions have a width of approximately 600 µm which corresponds to the width of PTN receptor fields [36], [37], [55]. The total number of synapses circumscribed by these distributions also fell within physiological estimates of 60,000 to 100,000 synapses per neuron [56]–[58]. Supplementary Figure S1 gives an alternative example where the inhibitory distribution is nominated as Gaussian and we solve the excitatory density. In both cases, the density distributions were randomly sampled to simulate the placement of excitatory and inhibitory receptors within the dendritic field (panel C). In both cases, the estimated frequency response of the combined receptor field (panel D) matched that of the target Gabor filter (panel B), as expected.

Bottom Line: We validate this proposal in the descending motor system, where we model the large receptor fields of the pyramidal tract neurons - the principle outputs of the motor cortex - decoding motor commands encoded in the direction of traveling wave patterns in motor cortex.The model replicates key findings of the descending motor system during simple motor tasks, including variable interspike intervals and weak corticospinal coherence.By additionally showing how the nature of the wave patterns can be controlled by modulating the topology of local intra-cortical connections, we hence propose a novel integrated neuronal model of encoding and decoding motor commands.

View Article: PubMed Central - PubMed

Affiliation: School of Psychiatry, The University of New South Wales, Sydney, Australia ; The Black Dog Institute, Sydney, Australia.

ABSTRACT
Traveling waves of neuronal oscillations have been observed in many cortical regions, including the motor and sensory cortex. Such waves are often modulated in a task-dependent fashion although their precise functional role remains a matter of debate. Here we conjecture that the cortex can utilize the direction and wavelength of traveling waves to encode information. We present a novel neural mechanism by which such information may be decoded by the spatial arrangement of receptors within the dendritic receptor field. In particular, we show how the density distributions of excitatory and inhibitory receptors can combine to act as a spatial filter of wave patterns. The proposed dendritic mechanism ensures that the neuron selectively responds to specific wave patterns, thus constituting a neural basis of pattern decoding. We validate this proposal in the descending motor system, where we model the large receptor fields of the pyramidal tract neurons - the principle outputs of the motor cortex - decoding motor commands encoded in the direction of traveling wave patterns in motor cortex. We use an existing model of field oscillations in motor cortex to investigate how the topology of the pyramidal cell receptor field acts to tune the cells responses to specific oscillatory wave patterns, even when those patterns are highly degraded. The model replicates key findings of the descending motor system during simple motor tasks, including variable interspike intervals and weak corticospinal coherence. By additionally showing how the nature of the wave patterns can be controlled by modulating the topology of local intra-cortical connections, we hence propose a novel integrated neuronal model of encoding and decoding motor commands.

Show MeSH
Related in: MedlinePlus