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Synaptic plasticity enables adaptive self-tuning critical networks.

Stepp N, Plenz D, Srinivasa N - PLoS Comput. Biol. (2015)

Bottom Line: Here, we simulate a 10,000 neuron, deterministic, plastic network of spiking neurons.Brief external perturbations lead to adaptive, long-term modification of intrinsic network connectivity through long-term excitatory plasticity, whereas long-term inhibitory plasticity enables rapid self-tuning of the network back to a critical state.The critical state is characterized by a branching parameter oscillating around unity, a critical exponent close to -3/2 and a long tail distribution of a self-similarity parameter between 0.5 and 1.

View Article: PubMed Central - PubMed

Affiliation: Center for Neural and Emergent Systems, Information and System Sciences Lab, HRL Laboratories LLC, Malibu, California, United States of America.

ABSTRACT
During rest, the mammalian cortex displays spontaneous neural activity. Spiking of single neurons during rest has been described as irregular and asynchronous. In contrast, recent in vivo and in vitro population measures of spontaneous activity, using the LFP, EEG, MEG or fMRI suggest that the default state of the cortex is critical, manifested by spontaneous, scale-invariant, cascades of activity known as neuronal avalanches. Criticality keeps a network poised for optimal information processing, but this view seems to be difficult to reconcile with apparently irregular single neuron spiking. Here, we simulate a 10,000 neuron, deterministic, plastic network of spiking neurons. We show that a combination of short- and long-term synaptic plasticity enables these networks to exhibit criticality in the face of intrinsic, i.e. self-sustained, asynchronous spiking. Brief external perturbations lead to adaptive, long-term modification of intrinsic network connectivity through long-term excitatory plasticity, whereas long-term inhibitory plasticity enables rapid self-tuning of the network back to a critical state. The critical state is characterized by a branching parameter oscillating around unity, a critical exponent close to -3/2 and a long tail distribution of a self-similarity parameter between 0.5 and 1.

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Criticality analyses.A) The exponent λ was measured during network evolution for a sliding time-window, then further grouped into a sliding window of λ estimates in order to show histograms changing over time. The top right inset shows sub-critical behavior (t = 20 s, λ = −2.49, R2 = 0.9855, p < 0.001). Once the network reaches a steady state exhibiting PABA, the network becomes critical with λ ≈ −1.5. For example, the late stage inset (top left) shows critical behavior (t = 500 s, λ = −1.481, R2 = 0.9984, p < 0.001). B) Estimated deterministic dynamics for the firing rate of the network. Data for firing rates over 50 Hz come entirely from the first 500 ms of the simulation, where the network goes through a period of stabilization. Firing rates during that period visit a sequence of multi- and meta-stable states until settling into a stable fixed point near 30 Hz (inset). C) The branching ratio σ. The two insets show σ at different stages. The early stage shows a very high firing rate regime, and a steep drop to a relatively low firing rate during which σ fluctuates widely. Eventually the network settles down, at about 0.7 s, and oscillates around σ = 1 for the remainder of the simulation. D) The distribution of scaling exponents α measured from 1 s to 900 s for 1000 randomly chosen neurons. All exponents lie between 0.5 and 1.0, indicating correlated fluctuations.
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pcbi.1004043.g002: Criticality analyses.A) The exponent λ was measured during network evolution for a sliding time-window, then further grouped into a sliding window of λ estimates in order to show histograms changing over time. The top right inset shows sub-critical behavior (t = 20 s, λ = −2.49, R2 = 0.9855, p < 0.001). Once the network reaches a steady state exhibiting PABA, the network becomes critical with λ ≈ −1.5. For example, the late stage inset (top left) shows critical behavior (t = 500 s, λ = −1.481, R2 = 0.9984, p < 0.001). B) Estimated deterministic dynamics for the firing rate of the network. Data for firing rates over 50 Hz come entirely from the first 500 ms of the simulation, where the network goes through a period of stabilization. Firing rates during that period visit a sequence of multi- and meta-stable states until settling into a stable fixed point near 30 Hz (inset). C) The branching ratio σ. The two insets show σ at different stages. The early stage shows a very high firing rate regime, and a steep drop to a relatively low firing rate during which σ fluctuates widely. Eventually the network settles down, at about 0.7 s, and oscillates around σ = 1 for the remainder of the simulation. D) The distribution of scaling exponents α measured from 1 s to 900 s for 1000 randomly chosen neurons. All exponents lie between 0.5 and 1.0, indicating correlated fluctuations.

Mentions: Treating the firing rate of the network as a dynamical system in its own right, it is possible to estimate fixed points in order to identify stable (and unstable) firing rates. Assuming a Langevin model for the firing rate, Fig. 2b shows a reconstruction of the deterministic dynamics [30, 31]. Firing rates greater than 50 Hz exist entirely in the first 500 ms of the simulation, when the network goes through a stabilization period. During this period, firing rates visit a sequence of multi- and meta-stable states until settling into a stable fixed point near 30 Hz. More study is required to know whether the fixed points at greater firing rates still exist or have been annihilated due to bifurcations, a bifurcation being a change in the number or type of fixed points. It is worth noting that a stable and unstable fixed point pair near 10 Hz (see Fig. 2b inset) is very near a bifurcation.


Synaptic plasticity enables adaptive self-tuning critical networks.

Stepp N, Plenz D, Srinivasa N - PLoS Comput. Biol. (2015)

Criticality analyses.A) The exponent λ was measured during network evolution for a sliding time-window, then further grouped into a sliding window of λ estimates in order to show histograms changing over time. The top right inset shows sub-critical behavior (t = 20 s, λ = −2.49, R2 = 0.9855, p < 0.001). Once the network reaches a steady state exhibiting PABA, the network becomes critical with λ ≈ −1.5. For example, the late stage inset (top left) shows critical behavior (t = 500 s, λ = −1.481, R2 = 0.9984, p < 0.001). B) Estimated deterministic dynamics for the firing rate of the network. Data for firing rates over 50 Hz come entirely from the first 500 ms of the simulation, where the network goes through a period of stabilization. Firing rates during that period visit a sequence of multi- and meta-stable states until settling into a stable fixed point near 30 Hz (inset). C) The branching ratio σ. The two insets show σ at different stages. The early stage shows a very high firing rate regime, and a steep drop to a relatively low firing rate during which σ fluctuates widely. Eventually the network settles down, at about 0.7 s, and oscillates around σ = 1 for the remainder of the simulation. D) The distribution of scaling exponents α measured from 1 s to 900 s for 1000 randomly chosen neurons. All exponents lie between 0.5 and 1.0, indicating correlated fluctuations.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4295840&req=5

pcbi.1004043.g002: Criticality analyses.A) The exponent λ was measured during network evolution for a sliding time-window, then further grouped into a sliding window of λ estimates in order to show histograms changing over time. The top right inset shows sub-critical behavior (t = 20 s, λ = −2.49, R2 = 0.9855, p < 0.001). Once the network reaches a steady state exhibiting PABA, the network becomes critical with λ ≈ −1.5. For example, the late stage inset (top left) shows critical behavior (t = 500 s, λ = −1.481, R2 = 0.9984, p < 0.001). B) Estimated deterministic dynamics for the firing rate of the network. Data for firing rates over 50 Hz come entirely from the first 500 ms of the simulation, where the network goes through a period of stabilization. Firing rates during that period visit a sequence of multi- and meta-stable states until settling into a stable fixed point near 30 Hz (inset). C) The branching ratio σ. The two insets show σ at different stages. The early stage shows a very high firing rate regime, and a steep drop to a relatively low firing rate during which σ fluctuates widely. Eventually the network settles down, at about 0.7 s, and oscillates around σ = 1 for the remainder of the simulation. D) The distribution of scaling exponents α measured from 1 s to 900 s for 1000 randomly chosen neurons. All exponents lie between 0.5 and 1.0, indicating correlated fluctuations.
Mentions: Treating the firing rate of the network as a dynamical system in its own right, it is possible to estimate fixed points in order to identify stable (and unstable) firing rates. Assuming a Langevin model for the firing rate, Fig. 2b shows a reconstruction of the deterministic dynamics [30, 31]. Firing rates greater than 50 Hz exist entirely in the first 500 ms of the simulation, when the network goes through a stabilization period. During this period, firing rates visit a sequence of multi- and meta-stable states until settling into a stable fixed point near 30 Hz. More study is required to know whether the fixed points at greater firing rates still exist or have been annihilated due to bifurcations, a bifurcation being a change in the number or type of fixed points. It is worth noting that a stable and unstable fixed point pair near 10 Hz (see Fig. 2b inset) is very near a bifurcation.

Bottom Line: Here, we simulate a 10,000 neuron, deterministic, plastic network of spiking neurons.Brief external perturbations lead to adaptive, long-term modification of intrinsic network connectivity through long-term excitatory plasticity, whereas long-term inhibitory plasticity enables rapid self-tuning of the network back to a critical state.The critical state is characterized by a branching parameter oscillating around unity, a critical exponent close to -3/2 and a long tail distribution of a self-similarity parameter between 0.5 and 1.

View Article: PubMed Central - PubMed

Affiliation: Center for Neural and Emergent Systems, Information and System Sciences Lab, HRL Laboratories LLC, Malibu, California, United States of America.

ABSTRACT
During rest, the mammalian cortex displays spontaneous neural activity. Spiking of single neurons during rest has been described as irregular and asynchronous. In contrast, recent in vivo and in vitro population measures of spontaneous activity, using the LFP, EEG, MEG or fMRI suggest that the default state of the cortex is critical, manifested by spontaneous, scale-invariant, cascades of activity known as neuronal avalanches. Criticality keeps a network poised for optimal information processing, but this view seems to be difficult to reconcile with apparently irregular single neuron spiking. Here, we simulate a 10,000 neuron, deterministic, plastic network of spiking neurons. We show that a combination of short- and long-term synaptic plasticity enables these networks to exhibit criticality in the face of intrinsic, i.e. self-sustained, asynchronous spiking. Brief external perturbations lead to adaptive, long-term modification of intrinsic network connectivity through long-term excitatory plasticity, whereas long-term inhibitory plasticity enables rapid self-tuning of the network back to a critical state. The critical state is characterized by a branching parameter oscillating around unity, a critical exponent close to -3/2 and a long tail distribution of a self-similarity parameter between 0.5 and 1.

Show MeSH
Related in: MedlinePlus