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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

Lifetime distributions for a network of 210 neurons with four modules (H = 2); 20% of the excitatory neurons are CH; the inhibitory neurons are LTS. Top: Histograms of lifetimes, with medians and variances, for 104 different initial conditions at sixteen pairs (gex, gin). Bottom: ordinate values on the logarithmic scale for 9 upper right (“black”) histograms from the top panel. Straight lines: fitted exponential dependencies.
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Figure 6: Lifetime distributions for a network of 210 neurons with four modules (H = 2); 20% of the excitatory neurons are CH; the inhibitory neurons are LTS. Top: Histograms of lifetimes, with medians and variances, for 104 different initial conditions at sixteen pairs (gex, gin). Bottom: ordinate values on the logarithmic scale for 9 upper right (“black”) histograms from the top panel. Straight lines: fitted exponential dependencies.

Mentions: We observed that regardless of the network architecture in the absence of inhibition (gin = 0) or at very low excitatory synaptic strength (gex = 0.05) no cases of SSA occurred and the system relaxed toward the fixed point in a non-chaotic way for all 120 tested initial conditions. Figure 6 displays extended statistics for a network with four modules (H = 2) where 20% of the excitatory neurons are CH, and the inhibitory neurons are LTS. For each of the sixteen (gex, gin) pairs, over a thousand different initial conditions were used. The top panel shows the corresponding lifetime distributions. At sufficiently high inhibition and excitation, for most of the network architectures these distributions display exponential decay. Replotting on the logarithmic scale the ordinate for the nine cases in the upper right corner of the top panel (the bottom panel of Figure 6) confirms this observation: the probability of finding a chaotic transient SSA with lifetime τ decays exponentially in τ, at a rate which depends on the network parameters. Such exponential distributions of the lifetime of chaotic transients are typical for systems with transient chaotic behavior (Lai and Tél, 2011).


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)

Lifetime distributions for a network of 210 neurons with four modules (H = 2); 20% of the excitatory neurons are CH; the inhibitory neurons are LTS. Top: Histograms of lifetimes, with medians and variances, for 104 different initial conditions at sixteen pairs (gex, gin). Bottom: ordinate values on the logarithmic scale for 9 upper right (“black”) histograms from the top panel. Straight lines: fitted exponential dependencies.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 6: Lifetime distributions for a network of 210 neurons with four modules (H = 2); 20% of the excitatory neurons are CH; the inhibitory neurons are LTS. Top: Histograms of lifetimes, with medians and variances, for 104 different initial conditions at sixteen pairs (gex, gin). Bottom: ordinate values on the logarithmic scale for 9 upper right (“black”) histograms from the top panel. Straight lines: fitted exponential dependencies.
Mentions: We observed that regardless of the network architecture in the absence of inhibition (gin = 0) or at very low excitatory synaptic strength (gex = 0.05) no cases of SSA occurred and the system relaxed toward the fixed point in a non-chaotic way for all 120 tested initial conditions. Figure 6 displays extended statistics for a network with four modules (H = 2) where 20% of the excitatory neurons are CH, and the inhibitory neurons are LTS. For each of the sixteen (gex, gin) pairs, over a thousand different initial conditions were used. The top panel shows the corresponding lifetime distributions. At sufficiently high inhibition and excitation, for most of the network architectures these distributions display exponential decay. Replotting on the logarithmic scale the ordinate for the nine cases in the upper right corner of the top panel (the bottom panel of Figure 6) confirms this observation: the probability of finding a chaotic transient SSA with lifetime τ decays exponentially in τ, at a rate which depends on the network parameters. Such exponential distributions of the lifetime of chaotic transients are typical for systems with transient chaotic behavior (Lai and Tél, 2011).

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