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Synaptic plasticity enables adaptive self-tuning critical networks.

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

Bottom Line: 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.

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 showing the effect of strong perturbations.A) The power law exponent λ was estimated 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 network settles into critical behavior with PABA as shown in the top left inset (t = 200 s, λ = −1.5415, R2 = 0.9998, p < 0.001). During the perturbation the network goes into a super-critical regime as shown in the second inset (t = 500 s, λ = −1.8851, R2 = 0.9967, p < 0.001) with λ for the initial part of the distribution between −1.75 and −2, but with a concentration of larger avalanches. The network returns to criticality after the perturbation as in the bottom right inset (t = 600s, λ = −1.5592, R2 = 0.9991, p < 0.001). B) Estimated deterministic dynamics for the firing rate of the network. Data for firing rates over 150 Hz come entirely from the first 500 ms of the simulation (see Fig. 2b), where the network goes through a period of stabilization. Rates between 50 and 150 Hz are due to external perturbation, with an evident fixed-point near 100Hz. Otherwise, the network settles into a fixed point near 30 Hz (inset). C) The branching ratio σ. The two insets show σ during a perturbation and after recovery. The latter inset should be compared to Fig. 2c, to see that branching ratio dynamics return to the same qualitative state. D) The distribution of scaling exponents α for 1000 neurons. All exponents lie between 0.5 and 1.0, indicating correlated fluctuations. The bulge in the tail of the distribution for 0.6 < α < 0.85 is due to the change in structural connectivity caused by STDP after the three perturbations.
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pcbi.1004043.g005: Criticality analyses showing the effect of strong perturbations.A) The power law exponent λ was estimated 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 network settles into critical behavior with PABA as shown in the top left inset (t = 200 s, λ = −1.5415, R2 = 0.9998, p < 0.001). During the perturbation the network goes into a super-critical regime as shown in the second inset (t = 500 s, λ = −1.8851, R2 = 0.9967, p < 0.001) with λ for the initial part of the distribution between −1.75 and −2, but with a concentration of larger avalanches. The network returns to criticality after the perturbation as in the bottom right inset (t = 600s, λ = −1.5592, R2 = 0.9991, p < 0.001). B) Estimated deterministic dynamics for the firing rate of the network. Data for firing rates over 150 Hz come entirely from the first 500 ms of the simulation (see Fig. 2b), where the network goes through a period of stabilization. Rates between 50 and 150 Hz are due to external perturbation, with an evident fixed-point near 100Hz. Otherwise, the network settles into a fixed point near 30 Hz (inset). C) The branching ratio σ. The two insets show σ during a perturbation and after recovery. The latter inset should be compared to Fig. 2c, to see that branching ratio dynamics return to the same qualitative state. D) The distribution of scaling exponents α for 1000 neurons. All exponents lie between 0.5 and 1.0, indicating correlated fluctuations. The bulge in the tail of the distribution for 0.6 < α < 0.85 is due to the change in structural connectivity caused by STDP after the three perturbations.

Mentions: The three criticality analyses were repeated to confirm that criticality was reattained after such perturbations. These three measures, λ, σ, and α are shown for the perturbed simulation in Fig. 5. Together, they show that the network did indeed reattain criticality. As a point of interest, the deterministic dynamics of the network firing rate were again reconstructed, this time showing the dynamics present during external perturbation. The stable point reached during a perturbation is visible as a stable fixed point near 100 Hz. Notably, the perturbations have appeared to push the low firing rate fixed point near 10 Hz through a bifurcation (see Fig. 5b inset). Care must be taken with this interpretation, however, as the data only represent an approximation of deterministic dynamics.


Synaptic plasticity enables adaptive self-tuning critical networks.

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

Criticality analyses showing the effect of strong perturbations.A) The power law exponent λ was estimated 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 network settles into critical behavior with PABA as shown in the top left inset (t = 200 s, λ = −1.5415, R2 = 0.9998, p < 0.001). During the perturbation the network goes into a super-critical regime as shown in the second inset (t = 500 s, λ = −1.8851, R2 = 0.9967, p < 0.001) with λ for the initial part of the distribution between −1.75 and −2, but with a concentration of larger avalanches. The network returns to criticality after the perturbation as in the bottom right inset (t = 600s, λ = −1.5592, R2 = 0.9991, p < 0.001). B) Estimated deterministic dynamics for the firing rate of the network. Data for firing rates over 150 Hz come entirely from the first 500 ms of the simulation (see Fig. 2b), where the network goes through a period of stabilization. Rates between 50 and 150 Hz are due to external perturbation, with an evident fixed-point near 100Hz. Otherwise, the network settles into a fixed point near 30 Hz (inset). C) The branching ratio σ. The two insets show σ during a perturbation and after recovery. The latter inset should be compared to Fig. 2c, to see that branching ratio dynamics return to the same qualitative state. D) The distribution of scaling exponents α for 1000 neurons. All exponents lie between 0.5 and 1.0, indicating correlated fluctuations. The bulge in the tail of the distribution for 0.6 < α < 0.85 is due to the change in structural connectivity caused by STDP after the three perturbations.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4295840&req=5

pcbi.1004043.g005: Criticality analyses showing the effect of strong perturbations.A) The power law exponent λ was estimated 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 network settles into critical behavior with PABA as shown in the top left inset (t = 200 s, λ = −1.5415, R2 = 0.9998, p < 0.001). During the perturbation the network goes into a super-critical regime as shown in the second inset (t = 500 s, λ = −1.8851, R2 = 0.9967, p < 0.001) with λ for the initial part of the distribution between −1.75 and −2, but with a concentration of larger avalanches. The network returns to criticality after the perturbation as in the bottom right inset (t = 600s, λ = −1.5592, R2 = 0.9991, p < 0.001). B) Estimated deterministic dynamics for the firing rate of the network. Data for firing rates over 150 Hz come entirely from the first 500 ms of the simulation (see Fig. 2b), where the network goes through a period of stabilization. Rates between 50 and 150 Hz are due to external perturbation, with an evident fixed-point near 100Hz. Otherwise, the network settles into a fixed point near 30 Hz (inset). C) The branching ratio σ. The two insets show σ during a perturbation and after recovery. The latter inset should be compared to Fig. 2c, to see that branching ratio dynamics return to the same qualitative state. D) The distribution of scaling exponents α for 1000 neurons. All exponents lie between 0.5 and 1.0, indicating correlated fluctuations. The bulge in the tail of the distribution for 0.6 < α < 0.85 is due to the change in structural connectivity caused by STDP after the three perturbations.
Mentions: The three criticality analyses were repeated to confirm that criticality was reattained after such perturbations. These three measures, λ, σ, and α are shown for the perturbed simulation in Fig. 5. Together, they show that the network did indeed reattain criticality. As a point of interest, the deterministic dynamics of the network firing rate were again reconstructed, this time showing the dynamics present during external perturbation. The stable point reached during a perturbation is visible as a stable fixed point near 100 Hz. Notably, the perturbations have appeared to push the low firing rate fixed point near 10 Hz through a bifurcation (see Fig. 5b inset). Care must be taken with this interpretation, however, as the data only represent an approximation of deterministic dynamics.

Bottom Line: 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.

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