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Sustained oscillations, irregular firing, and chaotic dynamics in hierarchical modular networks with mixtures of electrophysiological cell types.

Tomov P, Pena RF, Zaks MA, Roque AC - Front Comput Neurosci (2014)

Bottom Line: The duration of self-sustained activity strongly depends on the initial conditions, suggesting a transient chaotic regime.Extensive analysis of the self-sustained activity states showed that their lifetime expectancy increases with the number of network modules and is favored when the network is composed of excitatory neurons of the RS and CH classes combined with inhibitory neurons of the LTS class.These results indicate that the existence and properties of the self-sustained cortical activity states depend on both the topology of the network and the neuronal mixture that comprises the network.

View Article: PubMed Central - PubMed

Affiliation: Institute of Mathematics, Humboldt University of Berlin Berlin, Germany.

ABSTRACT
The cerebral cortex exhibits neural activity even in the absence of external stimuli. This self-sustained activity is characterized by irregular firing of individual neurons and population oscillations with a broad frequency range. Questions that arise in this context, are: What are the mechanisms responsible for the existence of neuronal spiking activity in the cortex without external input? Do these mechanisms depend on the structural organization of the cortical connections? Do they depend on intrinsic characteristics of the cortical neurons? To approach the answers to these questions, we have used computer simulations of cortical network models. Our networks have hierarchical modular architecture and are composed of combinations of neuron models that reproduce the firing behavior of the five main cortical electrophysiological cell classes: regular spiking (RS), chattering (CH), intrinsically bursting (IB), low threshold spiking (LTS), and fast spiking (FS). The population of excitatory neurons is built of RS cells (always present) and either CH or IB cells. Inhibitory neurons belong to the same class, either LTS or FS. Long-lived self-sustained activity states in our network simulations display irregular single neuron firing and oscillatory activity similar to experimentally measured ones. The duration of self-sustained activity strongly depends on the initial conditions, suggesting a transient chaotic regime. Extensive analysis of the self-sustained activity states showed that their lifetime expectancy increases with the number of network modules and is favored when the network is composed of excitatory neurons of the RS and CH classes combined with inhibitory neurons of the LTS class. These results indicate that the existence and properties of the self-sustained cortical activity states depend on both the topology of the network and the neuronal mixture that comprises the network.

No MeSH data available.


Related in: MedlinePlus

Example of dependence of the spiking properties on the initial conditions. The figure shows the network measures for a fixed network architecture: H = 2, RS excitatory neurons, LTS inhibitory neurons, gex = 0.15, gin = 0.7, and five different initial conditions, one for each column. The first row: network activity A(t) over the active period, from the end of the external stimulation (time 0 in the horizontal axis) until last spike of a network (indicated by the number under the right end of the time axis, in ms). The second row: global frequency spectrum of the activity (horizontal axis: frequency in Hz, vertical axis: amplitude). The third row: distribution of the firing rates over the ensemble of neurons in the active period (the mean of each distribution is shown inside the corresponding plot and the maximal rate is shown at the extreme right of the horizontal axis). The fourth row: distribution of the ISIs (in ms) over the ensemble of neurons for the active period (with CV and the peak value of the distribution indicated inside each plot). The fifth row: distribution of the CVs of the ISIs of the network neurons; the peak of each distribution is shown inside the plot.
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Figure 7: Example of dependence of the spiking properties on the initial conditions. The figure shows the network measures for a fixed network architecture: H = 2, RS excitatory neurons, LTS inhibitory neurons, gex = 0.15, gin = 0.7, and five different initial conditions, one for each column. The first row: network activity A(t) over the active period, from the end of the external stimulation (time 0 in the horizontal axis) until last spike of a network (indicated by the number under the right end of the time axis, in ms). The second row: global frequency spectrum of the activity (horizontal axis: frequency in Hz, vertical axis: amplitude). The third row: distribution of the firing rates over the ensemble of neurons in the active period (the mean of each distribution is shown inside the corresponding plot and the maximal rate is shown at the extreme right of the horizontal axis). The fourth row: distribution of the ISIs (in ms) over the ensemble of neurons for the active period (with CV and the peak value of the distribution indicated inside each plot). The fifth row: distribution of the CVs of the ISIs of the network neurons; the peak of each distribution is shown inside the plot.

Mentions: Figure 7 presents characteristics for an example network of four modules (H = 2), with RS excitatory neurons and LTS inhibitory neurons at gex = 0.15, gin = 0.7, computed between the end of the external input and the last network spike. For all runs the duration of SSA exceeded 500 ms. Each column of the figure stands for a different set of initial conditions, whose SSA lifetime is shown in the activity plots on the first row. In all cases the type of activity pattern is oscillatory SSA (the only observed SSA type at low synaptic strengths). Further rows in the figure show the global frequency distribution of the network activity calculated via the Fourier transform, distributions of the neuronal firing rates fi, of the interspike intervals (ISI) with their coefficients of variation (CV) and, in the last row, of the CVs for the ISIs of individual neurons.


Sustained oscillations, irregular firing, and chaotic dynamics in hierarchical modular networks with mixtures of electrophysiological cell types.

Tomov P, Pena RF, Zaks MA, Roque AC - Front Comput Neurosci (2014)

Example of dependence of the spiking properties on the initial conditions. The figure shows the network measures for a fixed network architecture: H = 2, RS excitatory neurons, LTS inhibitory neurons, gex = 0.15, gin = 0.7, and five different initial conditions, one for each column. The first row: network activity A(t) over the active period, from the end of the external stimulation (time 0 in the horizontal axis) until last spike of a network (indicated by the number under the right end of the time axis, in ms). The second row: global frequency spectrum of the activity (horizontal axis: frequency in Hz, vertical axis: amplitude). The third row: distribution of the firing rates over the ensemble of neurons in the active period (the mean of each distribution is shown inside the corresponding plot and the maximal rate is shown at the extreme right of the horizontal axis). The fourth row: distribution of the ISIs (in ms) over the ensemble of neurons for the active period (with CV and the peak value of the distribution indicated inside each plot). The fifth row: distribution of the CVs of the ISIs of the network neurons; the peak of each distribution is shown inside the plot.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4151042&req=5

Figure 7: Example of dependence of the spiking properties on the initial conditions. The figure shows the network measures for a fixed network architecture: H = 2, RS excitatory neurons, LTS inhibitory neurons, gex = 0.15, gin = 0.7, and five different initial conditions, one for each column. The first row: network activity A(t) over the active period, from the end of the external stimulation (time 0 in the horizontal axis) until last spike of a network (indicated by the number under the right end of the time axis, in ms). The second row: global frequency spectrum of the activity (horizontal axis: frequency in Hz, vertical axis: amplitude). The third row: distribution of the firing rates over the ensemble of neurons in the active period (the mean of each distribution is shown inside the corresponding plot and the maximal rate is shown at the extreme right of the horizontal axis). The fourth row: distribution of the ISIs (in ms) over the ensemble of neurons for the active period (with CV and the peak value of the distribution indicated inside each plot). The fifth row: distribution of the CVs of the ISIs of the network neurons; the peak of each distribution is shown inside the plot.
Mentions: Figure 7 presents characteristics for an example network of four modules (H = 2), with RS excitatory neurons and LTS inhibitory neurons at gex = 0.15, gin = 0.7, computed between the end of the external input and the last network spike. For all runs the duration of SSA exceeded 500 ms. Each column of the figure stands for a different set of initial conditions, whose SSA lifetime is shown in the activity plots on the first row. In all cases the type of activity pattern is oscillatory SSA (the only observed SSA type at low synaptic strengths). Further rows in the figure show the global frequency distribution of the network activity calculated via the Fourier transform, distributions of the neuronal firing rates fi, of the interspike intervals (ISI) with their coefficients of variation (CV) and, in the last row, of the CVs for the ISIs of individual neurons.

Bottom Line: The duration of self-sustained activity strongly depends on the initial conditions, suggesting a transient chaotic regime.Extensive analysis of the self-sustained activity states showed that their lifetime expectancy increases with the number of network modules and is favored when the network is composed of excitatory neurons of the RS and CH classes combined with inhibitory neurons of the LTS class.These results indicate that the existence and properties of the self-sustained cortical activity states depend on both the topology of the network and the neuronal mixture that comprises the network.

View Article: PubMed Central - PubMed

Affiliation: Institute of Mathematics, Humboldt University of Berlin Berlin, Germany.

ABSTRACT
The cerebral cortex exhibits neural activity even in the absence of external stimuli. This self-sustained activity is characterized by irregular firing of individual neurons and population oscillations with a broad frequency range. Questions that arise in this context, are: What are the mechanisms responsible for the existence of neuronal spiking activity in the cortex without external input? Do these mechanisms depend on the structural organization of the cortical connections? Do they depend on intrinsic characteristics of the cortical neurons? To approach the answers to these questions, we have used computer simulations of cortical network models. Our networks have hierarchical modular architecture and are composed of combinations of neuron models that reproduce the firing behavior of the five main cortical electrophysiological cell classes: regular spiking (RS), chattering (CH), intrinsically bursting (IB), low threshold spiking (LTS), and fast spiking (FS). The population of excitatory neurons is built of RS cells (always present) and either CH or IB cells. Inhibitory neurons belong to the same class, either LTS or FS. Long-lived self-sustained activity states in our network simulations display irregular single neuron firing and oscillatory activity similar to experimentally measured ones. The duration of self-sustained activity strongly depends on the initial conditions, suggesting a transient chaotic regime. Extensive analysis of the self-sustained activity states showed that their lifetime expectancy increases with the number of network modules and is favored when the network is composed of excitatory neurons of the RS and CH classes combined with inhibitory neurons of the LTS class. These results indicate that the existence and properties of the self-sustained cortical activity states depend on both the topology of the network and the neuronal mixture that comprises the network.

No MeSH data available.


Related in: MedlinePlus