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Reconstructing the three-dimensional GABAergic microcircuit of the striatum.

Humphries MD, Wood R, Gurney K - PLoS Comput. Biol. (2010)

Bottom Line: From these, we found the probabilities of intersection between the neurites of two neurons given their inter-somatic distance, and used these to construct three-dimensional striatal networks.We show that both properties influence striatal dynamics: the most potent inhibition of a MSN arises from a region of striatum at the edge of its dendritic field; and the combination of local gap junction and distal synaptic networks between FSIs sets a robust input-output regime for the MSN population.Our models thus intimately link striatal micro-anatomy to its dynamics, providing a biologically grounded platform for further study.

View Article: PubMed Central - PubMed

Affiliation: Adaptive Behaviour Research Group, Department of Psychology, University of Sheffield, Sheffield, United Kingdom. m.d.humphries@shef.ac.uk

ABSTRACT
A system's wiring constrains its dynamics, yet modelling of neural structures often overlooks the specific networks formed by their neurons. We developed an approach for constructing anatomically realistic networks and reconstructed the GABAergic microcircuit formed by the medium spiny neurons (MSNs) and fast-spiking interneurons (FSIs) of the adult rat striatum. We grew dendrite and axon models for these neurons and extracted probabilities for the presence of these neurites as a function of distance from the soma. From these, we found the probabilities of intersection between the neurites of two neurons given their inter-somatic distance, and used these to construct three-dimensional striatal networks. The MSN dendrite models predicted that half of all dendritic spines are within 100µm of the soma. The constructed networks predict distributions of gap junctions between FSI dendrites, synaptic contacts between MSNs, and synaptic inputs from FSIs to MSNs that are consistent with current estimates. The models predict that to achieve this, FSIs should be at most 1% of the striatal population. They also show that the striatum is sparsely connected: FSI-MSN and MSN-MSN contacts respectively form 7% and 1.7% of all possible connections. The models predict two striking network properties: the dominant GABAergic input to a MSN arises from neurons with somas at the edge of its dendritic field; and FSIs are inter-connected on two different spatial scales: locally by gap junctions and distally by synapses. We show that both properties influence striatal dynamics: the most potent inhibition of a MSN arises from a region of striatum at the edge of its dendritic field; and the combination of local gap junction and distal synaptic networks between FSIs sets a robust input-output regime for the MSN population. Our models thus intimately link striatal micro-anatomy to its dynamics, providing a biologically grounded platform for further study.

Show MeSH
Effects on simulated striatal activity of changing the spatial scales of the inter-FSI synaptic and gap junction networks.We ran simulations of a -on-the-side cube of striatum (giving 10613 MSNs) for each FSI density (giving 106, 318, and 531 FSIs respectively); each neuron was driven for 10 simulated seconds by background cortical input of around 475 spikes/s – just above the threshold for causing a MSN to spike [80]. To investigate the effects of the spatial scales of inter-FSI connections, we ran two sets of simulations: one set (panels A–C) using networks built with the expected intersection functions reported here (equation 20 and Table 4); the other set (panels D–F) using networks built the same way except that the FSI-FSI gap junction and synaptic functions were swapped – thus inverting the spatial relationships between the inter-FSI gap junction and synaptic networks. A The resulting empirical cumulative distribution functions (ECDFs) of MSN firing rates for each density of FSIs when using the normal anatomical model. The distribution of MSN firing rates remained largely the same with increasing FSI density, and the model MSNs had very low firing rates, characteristic of MSN activity in vivo. B The resulting ECDFs of FSI firing rates from the same simulations, showing that increasing the density of FSIs increased the proportion of silent FSIs, but also broadened the distribution of firing rates. C Raster plots of 1 s of activity of all FSIs in each simulation, illustrating these changes in firing rate distribution: the figures given below each raster show how the median firing rate of the active FSIs remained relatively consistent, even though firing rate distributions broadened, and the proportion of active FSIs fell. D The ECDFs of MSN firing rates after swapping the FSI connection functions shows that the MSN firing rate distribution was no longer constant; indeed for 3% FSIs the distribution was that of an MSN-only model, as all FSIs were silent. E The corresponding ECDFs of FSI firing rates show a dramatic effect on FSI activity. For 1% FSIs, swapping the connection functions caused an increased proportion of silent FSIs, but with a broadened spread of rates compared to the normal model; the 3% FSI network was completely silent. The 5% FSI network entered a pathological state where only two FSIs fired at extreme rates (indicated by the two crosses). F These changes in FSI firing rate distribution are clear in the corresponding 1 s raster plots.
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pcbi-1001011-g009: Effects on simulated striatal activity of changing the spatial scales of the inter-FSI synaptic and gap junction networks.We ran simulations of a -on-the-side cube of striatum (giving 10613 MSNs) for each FSI density (giving 106, 318, and 531 FSIs respectively); each neuron was driven for 10 simulated seconds by background cortical input of around 475 spikes/s – just above the threshold for causing a MSN to spike [80]. To investigate the effects of the spatial scales of inter-FSI connections, we ran two sets of simulations: one set (panels A–C) using networks built with the expected intersection functions reported here (equation 20 and Table 4); the other set (panels D–F) using networks built the same way except that the FSI-FSI gap junction and synaptic functions were swapped – thus inverting the spatial relationships between the inter-FSI gap junction and synaptic networks. A The resulting empirical cumulative distribution functions (ECDFs) of MSN firing rates for each density of FSIs when using the normal anatomical model. The distribution of MSN firing rates remained largely the same with increasing FSI density, and the model MSNs had very low firing rates, characteristic of MSN activity in vivo. B The resulting ECDFs of FSI firing rates from the same simulations, showing that increasing the density of FSIs increased the proportion of silent FSIs, but also broadened the distribution of firing rates. C Raster plots of 1 s of activity of all FSIs in each simulation, illustrating these changes in firing rate distribution: the figures given below each raster show how the median firing rate of the active FSIs remained relatively consistent, even though firing rate distributions broadened, and the proportion of active FSIs fell. D The ECDFs of MSN firing rates after swapping the FSI connection functions shows that the MSN firing rate distribution was no longer constant; indeed for 3% FSIs the distribution was that of an MSN-only model, as all FSIs were silent. E The corresponding ECDFs of FSI firing rates show a dramatic effect on FSI activity. For 1% FSIs, swapping the connection functions caused an increased proportion of silent FSIs, but with a broadened spread of rates compared to the normal model; the 3% FSI network was completely silent. The 5% FSI network entered a pathological state where only two FSIs fired at extreme rates (indicated by the two crosses). F These changes in FSI firing rate distribution are clear in the corresponding 1 s raster plots.

Mentions: We first established the impact of the different FSI densities on the dynamics of the model. Figure 9 shows that increasing the FSI density did not alter the distribution of MSN firing rates or their variability (the median MSN inter-spike interval coefficient of variation was 0.8 for all FSI densities); nonetheless, the model MSNs had the very low firing rates characteristic of MSN activity in vivo. Increasing the FSI density increased the proportion of FSIs that did not fire, but also resulted in a broader and more heterogenous firing rate distribution. Despite this, the median firing rate of active FSIs was consistent across the changes in FSI density. The FSIs' firing rates of up to 80 spikes/s were also consistent with those observed in vivo [69]. Figure 9C shows that the active FSIs fired in a variety of desynchronised states, with no evidence of strong, network-wide synchrony for any tested FSI density.


Reconstructing the three-dimensional GABAergic microcircuit of the striatum.

Humphries MD, Wood R, Gurney K - PLoS Comput. Biol. (2010)

Effects on simulated striatal activity of changing the spatial scales of the inter-FSI synaptic and gap junction networks.We ran simulations of a -on-the-side cube of striatum (giving 10613 MSNs) for each FSI density (giving 106, 318, and 531 FSIs respectively); each neuron was driven for 10 simulated seconds by background cortical input of around 475 spikes/s – just above the threshold for causing a MSN to spike [80]. To investigate the effects of the spatial scales of inter-FSI connections, we ran two sets of simulations: one set (panels A–C) using networks built with the expected intersection functions reported here (equation 20 and Table 4); the other set (panels D–F) using networks built the same way except that the FSI-FSI gap junction and synaptic functions were swapped – thus inverting the spatial relationships between the inter-FSI gap junction and synaptic networks. A The resulting empirical cumulative distribution functions (ECDFs) of MSN firing rates for each density of FSIs when using the normal anatomical model. The distribution of MSN firing rates remained largely the same with increasing FSI density, and the model MSNs had very low firing rates, characteristic of MSN activity in vivo. B The resulting ECDFs of FSI firing rates from the same simulations, showing that increasing the density of FSIs increased the proportion of silent FSIs, but also broadened the distribution of firing rates. C Raster plots of 1 s of activity of all FSIs in each simulation, illustrating these changes in firing rate distribution: the figures given below each raster show how the median firing rate of the active FSIs remained relatively consistent, even though firing rate distributions broadened, and the proportion of active FSIs fell. D The ECDFs of MSN firing rates after swapping the FSI connection functions shows that the MSN firing rate distribution was no longer constant; indeed for 3% FSIs the distribution was that of an MSN-only model, as all FSIs were silent. E The corresponding ECDFs of FSI firing rates show a dramatic effect on FSI activity. For 1% FSIs, swapping the connection functions caused an increased proportion of silent FSIs, but with a broadened spread of rates compared to the normal model; the 3% FSI network was completely silent. The 5% FSI network entered a pathological state where only two FSIs fired at extreme rates (indicated by the two crosses). F These changes in FSI firing rate distribution are clear in the corresponding 1 s raster plots.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2991252&req=5

pcbi-1001011-g009: Effects on simulated striatal activity of changing the spatial scales of the inter-FSI synaptic and gap junction networks.We ran simulations of a -on-the-side cube of striatum (giving 10613 MSNs) for each FSI density (giving 106, 318, and 531 FSIs respectively); each neuron was driven for 10 simulated seconds by background cortical input of around 475 spikes/s – just above the threshold for causing a MSN to spike [80]. To investigate the effects of the spatial scales of inter-FSI connections, we ran two sets of simulations: one set (panels A–C) using networks built with the expected intersection functions reported here (equation 20 and Table 4); the other set (panels D–F) using networks built the same way except that the FSI-FSI gap junction and synaptic functions were swapped – thus inverting the spatial relationships between the inter-FSI gap junction and synaptic networks. A The resulting empirical cumulative distribution functions (ECDFs) of MSN firing rates for each density of FSIs when using the normal anatomical model. The distribution of MSN firing rates remained largely the same with increasing FSI density, and the model MSNs had very low firing rates, characteristic of MSN activity in vivo. B The resulting ECDFs of FSI firing rates from the same simulations, showing that increasing the density of FSIs increased the proportion of silent FSIs, but also broadened the distribution of firing rates. C Raster plots of 1 s of activity of all FSIs in each simulation, illustrating these changes in firing rate distribution: the figures given below each raster show how the median firing rate of the active FSIs remained relatively consistent, even though firing rate distributions broadened, and the proportion of active FSIs fell. D The ECDFs of MSN firing rates after swapping the FSI connection functions shows that the MSN firing rate distribution was no longer constant; indeed for 3% FSIs the distribution was that of an MSN-only model, as all FSIs were silent. E The corresponding ECDFs of FSI firing rates show a dramatic effect on FSI activity. For 1% FSIs, swapping the connection functions caused an increased proportion of silent FSIs, but with a broadened spread of rates compared to the normal model; the 3% FSI network was completely silent. The 5% FSI network entered a pathological state where only two FSIs fired at extreme rates (indicated by the two crosses). F These changes in FSI firing rate distribution are clear in the corresponding 1 s raster plots.
Mentions: We first established the impact of the different FSI densities on the dynamics of the model. Figure 9 shows that increasing the FSI density did not alter the distribution of MSN firing rates or their variability (the median MSN inter-spike interval coefficient of variation was 0.8 for all FSI densities); nonetheless, the model MSNs had the very low firing rates characteristic of MSN activity in vivo. Increasing the FSI density increased the proportion of FSIs that did not fire, but also resulted in a broader and more heterogenous firing rate distribution. Despite this, the median firing rate of active FSIs was consistent across the changes in FSI density. The FSIs' firing rates of up to 80 spikes/s were also consistent with those observed in vivo [69]. Figure 9C shows that the active FSIs fired in a variety of desynchronised states, with no evidence of strong, network-wide synchrony for any tested FSI density.

Bottom Line: From these, we found the probabilities of intersection between the neurites of two neurons given their inter-somatic distance, and used these to construct three-dimensional striatal networks.We show that both properties influence striatal dynamics: the most potent inhibition of a MSN arises from a region of striatum at the edge of its dendritic field; and the combination of local gap junction and distal synaptic networks between FSIs sets a robust input-output regime for the MSN population.Our models thus intimately link striatal micro-anatomy to its dynamics, providing a biologically grounded platform for further study.

View Article: PubMed Central - PubMed

Affiliation: Adaptive Behaviour Research Group, Department of Psychology, University of Sheffield, Sheffield, United Kingdom. m.d.humphries@shef.ac.uk

ABSTRACT
A system's wiring constrains its dynamics, yet modelling of neural structures often overlooks the specific networks formed by their neurons. We developed an approach for constructing anatomically realistic networks and reconstructed the GABAergic microcircuit formed by the medium spiny neurons (MSNs) and fast-spiking interneurons (FSIs) of the adult rat striatum. We grew dendrite and axon models for these neurons and extracted probabilities for the presence of these neurites as a function of distance from the soma. From these, we found the probabilities of intersection between the neurites of two neurons given their inter-somatic distance, and used these to construct three-dimensional striatal networks. The MSN dendrite models predicted that half of all dendritic spines are within 100µm of the soma. The constructed networks predict distributions of gap junctions between FSI dendrites, synaptic contacts between MSNs, and synaptic inputs from FSIs to MSNs that are consistent with current estimates. The models predict that to achieve this, FSIs should be at most 1% of the striatal population. They also show that the striatum is sparsely connected: FSI-MSN and MSN-MSN contacts respectively form 7% and 1.7% of all possible connections. The models predict two striking network properties: the dominant GABAergic input to a MSN arises from neurons with somas at the edge of its dendritic field; and FSIs are inter-connected on two different spatial scales: locally by gap junctions and distally by synapses. We show that both properties influence striatal dynamics: the most potent inhibition of a MSN arises from a region of striatum at the edge of its dendritic field; and the combination of local gap junction and distal synaptic networks between FSIs sets a robust input-output regime for the MSN population. Our models thus intimately link striatal micro-anatomy to its dynamics, providing a biologically grounded platform for further study.

Show MeSH