Limits...
Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses.

Ocker GK, Litwin-Kumar A, Doiron B - PLoS Comput. Biol. (2015)

Bottom Line: The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models.For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure.Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.

View Article: PubMed Central - PubMed

Affiliation: Department of Neuroscience, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America; Center for the Neural Basis of Cognition, University of Pittsburgh and Carnegie Melon University, Pittsburgh, Pennsylvania, United States of America.

ABSTRACT
The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.

No MeSH data available.


Related in: MedlinePlus

Reduced theory for the plasticity of two-synapse motifs.In each panel, the strength of a different motif or mixed motif is plotted as it evolves. Red: theoretical prediction (Eqs (42)–(50)). Shaded lines: individual trials of the same initial network. (A) Mean synaptic weight. (B) Divergent motifs. (C) Convergent motifs. (D) Mixed recurrent motifs (strength of connections conditioned on their being part of a two-synapse loop). (E) Mixed divergent motifs (strength of individual synapses conditioned on their being part of a divergent motif). (F) Mixed convergent motifs. (G) Chain motifs. (H) Mixed chains type A (strength of individual synapses conditioned on their being the first in a chain). (I) Mixed chains type B (strength of individual synapses conditioned on their being the second in a chain). The STDP rule was in the depression-dominated balanced regime, as in Fig 6B.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4546203&req=5

pcbi.1004458.g007: Reduced theory for the plasticity of two-synapse motifs.In each panel, the strength of a different motif or mixed motif is plotted as it evolves. Red: theoretical prediction (Eqs (42)–(50)). Shaded lines: individual trials of the same initial network. (A) Mean synaptic weight. (B) Divergent motifs. (C) Convergent motifs. (D) Mixed recurrent motifs (strength of connections conditioned on their being part of a two-synapse loop). (E) Mixed divergent motifs (strength of individual synapses conditioned on their being part of a divergent motif). (F) Mixed convergent motifs. (G) Chain motifs. (H) Mixed chains type A (strength of individual synapses conditioned on their being the first in a chain). (I) Mixed chains type B (strength of individual synapses conditioned on their being the second in a chain). The STDP rule was in the depression-dominated balanced regime, as in Fig 6B.

Mentions: We refer to the mean field theory of Eqs (42)–(50) as the motif dynamics for a recurrent network with STDP. This theory accurately predicts the transient dynamics of the one- and two-synapse motifs of the full stochastic spiking network (Fig 7, compare red versus thin black curves), owing to significant drift compared to diffusion in the weight dynamics and these network-averaged motif strengths. The derivation and successful application of this reduced theory to a large spiking network is a central result of our study. However, recall that our theory requires the overall synaptic weights to be small so that our linear response ansatz remains valid. Thus, as expected, our theoretical predictions for the evolution of motif structure fail for sufficiently large initial mean synaptic weight p(0) (S2 Text). This is because for large recurrent weights the firing rate dynamics become unstable, and linearization about a background state is not possible.


Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses.

Ocker GK, Litwin-Kumar A, Doiron B - PLoS Comput. Biol. (2015)

Reduced theory for the plasticity of two-synapse motifs.In each panel, the strength of a different motif or mixed motif is plotted as it evolves. Red: theoretical prediction (Eqs (42)–(50)). Shaded lines: individual trials of the same initial network. (A) Mean synaptic weight. (B) Divergent motifs. (C) Convergent motifs. (D) Mixed recurrent motifs (strength of connections conditioned on their being part of a two-synapse loop). (E) Mixed divergent motifs (strength of individual synapses conditioned on their being part of a divergent motif). (F) Mixed convergent motifs. (G) Chain motifs. (H) Mixed chains type A (strength of individual synapses conditioned on their being the first in a chain). (I) Mixed chains type B (strength of individual synapses conditioned on their being the second in a chain). The STDP rule was in the depression-dominated balanced regime, as in Fig 6B.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4546203&req=5

pcbi.1004458.g007: Reduced theory for the plasticity of two-synapse motifs.In each panel, the strength of a different motif or mixed motif is plotted as it evolves. Red: theoretical prediction (Eqs (42)–(50)). Shaded lines: individual trials of the same initial network. (A) Mean synaptic weight. (B) Divergent motifs. (C) Convergent motifs. (D) Mixed recurrent motifs (strength of connections conditioned on their being part of a two-synapse loop). (E) Mixed divergent motifs (strength of individual synapses conditioned on their being part of a divergent motif). (F) Mixed convergent motifs. (G) Chain motifs. (H) Mixed chains type A (strength of individual synapses conditioned on their being the first in a chain). (I) Mixed chains type B (strength of individual synapses conditioned on their being the second in a chain). The STDP rule was in the depression-dominated balanced regime, as in Fig 6B.
Mentions: We refer to the mean field theory of Eqs (42)–(50) as the motif dynamics for a recurrent network with STDP. This theory accurately predicts the transient dynamics of the one- and two-synapse motifs of the full stochastic spiking network (Fig 7, compare red versus thin black curves), owing to significant drift compared to diffusion in the weight dynamics and these network-averaged motif strengths. The derivation and successful application of this reduced theory to a large spiking network is a central result of our study. However, recall that our theory requires the overall synaptic weights to be small so that our linear response ansatz remains valid. Thus, as expected, our theoretical predictions for the evolution of motif structure fail for sufficiently large initial mean synaptic weight p(0) (S2 Text). This is because for large recurrent weights the firing rate dynamics become unstable, and linearization about a background state is not possible.

Bottom Line: The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models.For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure.Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.

View Article: PubMed Central - PubMed

Affiliation: Department of Neuroscience, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America; Center for the Neural Basis of Cognition, University of Pittsburgh and Carnegie Melon University, Pittsburgh, Pennsylvania, United States of America.

ABSTRACT
The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.

No MeSH data available.


Related in: MedlinePlus