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Degree Correlations Optimize Neuronal Network Sensitivity to Sub-Threshold Stimuli.

Schmeltzer C, Kihara AH, Sokolov IM, Rüdiger S - PLoS ONE (2015)

Bottom Line: We devise a method to calculate firing rates from a self-consistent system of equations taking into account the degree distribution and degree correlations in the network.We show that assortative degree correlations strongly improve the sensitivity for weak stimuli and propose that such networks possess an advantage in signal processing.We moreover find that there exists an optimum in assortativity at an intermediate level leading to a maximum in input/output mutual information.

View Article: PubMed Central - PubMed

Affiliation: Institut für Physik, Humboldt-Universität zu Berlin, Germany.

ABSTRACT
Information processing in the brain crucially depends on the topology of the neuronal connections. We investigate how the topology influences the response of a population of leaky integrate-and-fire neurons to a stimulus. We devise a method to calculate firing rates from a self-consistent system of equations taking into account the degree distribution and degree correlations in the network. We show that assortative degree correlations strongly improve the sensitivity for weak stimuli and propose that such networks possess an advantage in signal processing. We moreover find that there exists an optimum in assortativity at an intermediate level leading to a maximum in input/output mutual information.

No MeSH data available.


Schematic of the heterogeneous neuronal networks.(A) In the uncorrelated network, highly connected neurons and poorly connected neurons are joined randomly. Here, red nodes represent an exemplary well connected subpopulation, while blue nodes represent all remaining populations with smaller in-degree k. (B) In the assortative network, neurons with similar connectivity are joined preferably. The network is stimulated by Poissonian external input spike trains with mean rate s, which are injected to each neuron. The network response r to the stimulus is quantified by the average firing rate of a randomly chosen fraction of the network (n neurons).
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pone.0121794.g001: Schematic of the heterogeneous neuronal networks.(A) In the uncorrelated network, highly connected neurons and poorly connected neurons are joined randomly. Here, red nodes represent an exemplary well connected subpopulation, while blue nodes represent all remaining populations with smaller in-degree k. (B) In the assortative network, neurons with similar connectivity are joined preferably. The network is stimulated by Poissonian external input spike trains with mean rate s, which are injected to each neuron. The network response r to the stimulus is quantified by the average firing rate of a randomly chosen fraction of the network (n neurons).

Mentions: To describe collective neuronal activity one often uses the population-density approach, which was successfully applied to cortical circuits of identical neurons [9, 30–32] and to networks of heterogeneous neurons [21]. In the population density approach, the spiking and interplay of many neurons, for instance in the network of a single cortical column, is captured by a probability density function for the states of statistically similar neurons [24, 31]. Here we extend this theory to include the heterogeneity of the network in terms of the degree of a given neuron, i.e., the number of synaptic connections the neuron possesses. We find that the network’s heterogeneity leads to substantial deviations from simple mean-field calculations, where one ignores the network properties. Our method is to divide the whole neuronal population in subpopulations according to the number of incoming synaptic links, or the in-degreek, of neurons. This allows us to consider networks with different levels of assortativity with respect to k (Fig 1), which is a measure of the correlations in the degree of nodes [33]. Degree correlations in neural networks may result from a number of processes including plasticity and they are interesting for a number of reasons. First, degree correlations can be considered the most basic statistical property of a complex network except for the degree distribution itself. Second, there have been large efforts devoted to understand correlations in neuronal spiking [34], but the effects of correlations in structural connectivity have been much less studied so far. Finally, statistical network properties have been considered in the context of synchronization [35], but the characterization of spiking in the unsynchronized regime has not received similar attention in the context of complex networks.


Degree Correlations Optimize Neuronal Network Sensitivity to Sub-Threshold Stimuli.

Schmeltzer C, Kihara AH, Sokolov IM, Rüdiger S - PLoS ONE (2015)

Schematic of the heterogeneous neuronal networks.(A) In the uncorrelated network, highly connected neurons and poorly connected neurons are joined randomly. Here, red nodes represent an exemplary well connected subpopulation, while blue nodes represent all remaining populations with smaller in-degree k. (B) In the assortative network, neurons with similar connectivity are joined preferably. The network is stimulated by Poissonian external input spike trains with mean rate s, which are injected to each neuron. The network response r to the stimulus is quantified by the average firing rate of a randomly chosen fraction of the network (n neurons).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4482728&req=5

pone.0121794.g001: Schematic of the heterogeneous neuronal networks.(A) In the uncorrelated network, highly connected neurons and poorly connected neurons are joined randomly. Here, red nodes represent an exemplary well connected subpopulation, while blue nodes represent all remaining populations with smaller in-degree k. (B) In the assortative network, neurons with similar connectivity are joined preferably. The network is stimulated by Poissonian external input spike trains with mean rate s, which are injected to each neuron. The network response r to the stimulus is quantified by the average firing rate of a randomly chosen fraction of the network (n neurons).
Mentions: To describe collective neuronal activity one often uses the population-density approach, which was successfully applied to cortical circuits of identical neurons [9, 30–32] and to networks of heterogeneous neurons [21]. In the population density approach, the spiking and interplay of many neurons, for instance in the network of a single cortical column, is captured by a probability density function for the states of statistically similar neurons [24, 31]. Here we extend this theory to include the heterogeneity of the network in terms of the degree of a given neuron, i.e., the number of synaptic connections the neuron possesses. We find that the network’s heterogeneity leads to substantial deviations from simple mean-field calculations, where one ignores the network properties. Our method is to divide the whole neuronal population in subpopulations according to the number of incoming synaptic links, or the in-degreek, of neurons. This allows us to consider networks with different levels of assortativity with respect to k (Fig 1), which is a measure of the correlations in the degree of nodes [33]. Degree correlations in neural networks may result from a number of processes including plasticity and they are interesting for a number of reasons. First, degree correlations can be considered the most basic statistical property of a complex network except for the degree distribution itself. Second, there have been large efforts devoted to understand correlations in neuronal spiking [34], but the effects of correlations in structural connectivity have been much less studied so far. Finally, statistical network properties have been considered in the context of synchronization [35], but the characterization of spiking in the unsynchronized regime has not received similar attention in the context of complex networks.

Bottom Line: We devise a method to calculate firing rates from a self-consistent system of equations taking into account the degree distribution and degree correlations in the network.We show that assortative degree correlations strongly improve the sensitivity for weak stimuli and propose that such networks possess an advantage in signal processing.We moreover find that there exists an optimum in assortativity at an intermediate level leading to a maximum in input/output mutual information.

View Article: PubMed Central - PubMed

Affiliation: Institut für Physik, Humboldt-Universität zu Berlin, Germany.

ABSTRACT
Information processing in the brain crucially depends on the topology of the neuronal connections. We investigate how the topology influences the response of a population of leaky integrate-and-fire neurons to a stimulus. We devise a method to calculate firing rates from a self-consistent system of equations taking into account the degree distribution and degree correlations in the network. We show that assortative degree correlations strongly improve the sensitivity for weak stimuli and propose that such networks possess an advantage in signal processing. We moreover find that there exists an optimum in assortativity at an intermediate level leading to a maximum in input/output mutual information.

No MeSH data available.