Shaping Neural Circuits by High Order Synaptic Interactions

Spike timing dependent plasticity (STDP) is believed to play an important role in shaping the structure of neural circuits. Here we show that STDP generates effective interactions between synapses of different neurons, which were neglected in previous theoretical treatments, and can be described as a sum over contributions from structural motifs. These interactions can have a pivotal influence on the connectivity patterns that emerge under the influence of STDP. In particular, we consider two highly ordered forms of structure: wide synfire chains, in which groups of neurons project to each other sequentially, and self connected assemblies. We show that high order synaptic interactions can enable the formation of both structures, depending on the form of the STDP function and the time course of synaptic currents. Furthermore, within a certain regime of biophysical parameters, emergence of the ordered connectivity occurs robustly and autonomously in a stochastic network of spiking neurons, without a need to expose the neural network to structured inputs during learning.

[1]  H Sompolinsky,et al.  Dynamics of random neural networks with bistable units. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Dean V Buonomano,et al.  A learning rule for the emergence of stable dynamics and timing in recurrent networks. , 2005, Journal of neurophysiology.

[3]  Baktash Babadi,et al.  Pairwise Analysis Can Account for Network Structures Arising from Spike-Timing Dependent Plasticity , 2013, PLoS Comput. Biol..

[4]  Y. Loewenstein,et al.  Multiplicative Dynamics Underlie the Emergence of the Log-Normal Distribution of Spine Sizes in the Neocortex In Vivo , 2011, The Journal of Neuroscience.

[5]  Sen Song,et al.  Highly Nonrandom Features of Synaptic Connectivity in Local Cortical Circuits , 2005, PLoS biology.

[6]  Stefan Rotter,et al.  Recurrent interactions in spiking networks with arbitrary topology. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  R Linsker,et al.  From basic network principles to neural architecture: emergence of orientation columns. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Wolfgang Maass,et al.  Emergence of Dynamic Memory Traces in Cortical Microcircuit Models through STDP , 2013, The Journal of Neuroscience.

[9]  D. Amit,et al.  Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. , 1997, Cerebral cortex.

[10]  Ad Aertsen,et al.  Stable propagation of synchronous spiking in cortical neural networks , 1999, Nature.

[11]  A. Litwin-Kumar,et al.  Slow dynamics and high variability in balanced cortical networks with clustered connections , 2012, Nature Neuroscience.

[12]  Henning Sprekeler,et al.  Inhibitory Plasticity Balances Excitation and Inhibition in Sensory Pathways and Memory Networks , 2011, Science.

[13]  K. D. Punta,et al.  An ultra-sparse code underlies the generation of neural sequences in a songbird , 2002 .

[14]  J. Knott.  The organization of behavior: A neuropsychological theory , 1951 .

[15]  Yotam Luz,et al.  Balancing Feed-Forward Excitation and Inhibition via Hebbian Inhibitory Synaptic Plasticity , 2012, PLoS Comput. Biol..

[16]  H. Markram,et al.  Regulation of Synaptic Efficacy by Coincidence of Postsynaptic APs and EPSPs , 1997, Science.

[17]  Daniel D. Lee,et al.  Equilibrium properties of temporally asymmetric Hebbian plasticity. , 2000, Physical review letters.

[18]  Terrence J. Sejnowski,et al.  Spike propagation synchronized by temporally asymmetric Hebbian learning , 2002, Biological Cybernetics.

[19]  Richard Kempter,et al.  State-dependencies of learning across brain scales , 2015, Front. Comput. Neurosci..

[20]  R. Kempter,et al.  Hebbian learning and spiking neurons , 1999 .

[21]  E. Kandel,et al.  Proceedings of the National Academy of Sciences of the United States of America. Annual subject and author indexes. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[22]  Stefan Rotter,et al.  How Structure Determines Correlations in Neuronal Networks , 2011, PLoS Comput. Biol..

[23]  Mark C. W. van Rossum,et al.  Stable Hebbian Learning from Spike Timing-Dependent Plasticity , 2000, The Journal of Neuroscience.

[24]  J. Altman,et al.  JOURNAL OF COMPARATIVE AND PHYSIOLOGICAL PSYCHOLOGY , 2005 .

[25]  W. Gerstner,et al.  Connectivity reflects coding: a model of voltage-based STDP with homeostasis , 2010, Nature Neuroscience.

[26]  Michael S. Brainard,et al.  What songbirds teach us about learning , 2002, Nature.

[27]  A. Reyes.  Synchrony-dependent propagation of firing rate in iteratively constructed networks in vitro , 2003, Nature Neuroscience.

[28]  Wulfram Gerstner,et al.  Phenomenological models of synaptic plasticity based on spike timing , 2008, Biological Cybernetics.

[29]  Thomas K. Berger,et al.  A synaptic organizing principle for cortical neuronal groups , 2011, Proceedings of the National Academy of Sciences.

[30]  L. Abbott,et al.  Cortical Development and Remapping through Spike Timing-Dependent Plasticity , 2001, Neuron.

[31]  P. J. Sjöström,et al.  Correction: Highly Nonrandom Features of Synaptic Connectivity in Local Cortical Circuits , 2005, PLoS Biology.

[32]  Moshe Abeles,et al.  Corticonics: Neural Circuits of Cerebral Cortex , 1991 .

[33]  N. Matsuki,et al.  Interpyramid spike transmission stabilizes the sparseness of recurrent network activity. , 2013, Cerebral cortex.

[34]  Jürgen Jost,et al.  Self-organization in Balanced State Networks by STDP and Homeostatic Plasticity , 2015, PLoS Comput. Biol..

[35]  Brent Doiron,et al.  Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses , 2015, PLoS Comput. Biol..

[36]  Matthieu Gilson,et al.  Spike-timing-dependent plasticity for neurons with recurrent connections , 2007, Biological Cybernetics.

[37]  G. Bi,et al.  Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type , 1998, The Journal of Neuroscience.

[38]  Jochen Triesch,et al.  Robust development of synfire chains from multiple plasticity mechanisms , 2014, Front. Comput. Neurosci..

[39]  M. Poo,et al.  Coincident Pre- and Postsynaptic Activity Modifies GABAergic Synapses by Postsynaptic Changes in Cl− Transporter Activity , 2003, Neuron.

[40]  E. Callaway,et al.  Excitatory cortical neurons form fine-scale functional networks , 2005, Nature.

[41]  Xiao-Jing Wang,et al.  Mean-Driven and Fluctuation-Driven Persistent Activity in Recurrent Networks , 2007, Neural Computation.

[42]  W Rall,et al.  Dendritic location of synapses and possible mechanisms for the monosynaptic EPSP in motoneurons. , 1967, Journal of neurophysiology.

[43]  Eric Shea-Brown,et al.  Motif statistics and spike correlations in neuronal networks , 2012, BMC Neuroscience.

[44]  Baktash Babadi,et al.  Intrinsic Stability of Temporally Shifted Spike-Timing Dependent Plasticity , 2010, PLoS Comput. Biol..

[45]  Haim Sompolinsky,et al.  Learning Input Correlations through Nonlinear Temporally Asymmetric Hebbian Plasticity , 2003, The Journal of Neuroscience.

[46]  Alireza Valizadeh,et al.  Self-organization of synchronous activity propagation in neuronal networks driven by local excitation , 2015, Front. Comput. Neurosci..

[47]  A. Hawkes.  Point Spectra of Some Mutually Exciting Point Processes , 1971 .

[48]  Dezhe Z. Jin,et al.  Support for a synaptic chain model of neuronal sequence generation , 2010, Nature.

[49]  Richard Hans Robert Hahnloser,et al.  Spike-Time-Dependent Plasticity and Heterosynaptic Competition Organize Networks to Produce Long Scale-Free Sequences of Neural Activity , 2010, Neuron.

[50]  K. Svoboda,et al.  Experience-dependent structural synaptic plasticity in the mammalian brain , 2009, Nature Reviews Neuroscience.

[51]  Y. Dan,et al.  Spike-timing-dependent synaptic modification induced by natural spike trains , 2002, Nature.

[52]  D. O. Hebb,et al.  The organization of behavior , 1988 .

[53]  A. Litwin-Kumar,et al.  Formation and maintenance of neuronal assemblies through synaptic plasticity , 2014, Nature Communications.

[54]  Eric Shea-Brown,et al.  Impact of Network Structure and Cellular Response on Spike Time Correlations , 2011, PLoS Comput. Biol..

[55]  Tomoki Fukai,et al.  A Stochastic Method to Predict the Consequence of Arbitrary Forms of Spike-Timing-Dependent Plasticity , 2003, Neural Computation.

[56]  Xiao-Jing Wang,et al.  Probabilistic Decision Making by Slow Reverberation in Cortical Circuits , 2002, Neuron.

[57]  Richard Hans Robert Hahnloser,et al.  An ultra-sparse code underliesthe generation of neural sequences in a songbird , 2002, Nature.

[58]  Johannes J. Letzkus,et al.  Cortical feed-forward networks for binding different streams of sensory information , 2006, Nature Neuroscience.

[59]  Simonis Priscilla,et al.  アフリカのカミキリムシ科Prosopocera lactator(Cerambycidae)の緑がかった白スケール内の光子多結晶 , 2012 .

[60]  W G Regehr,et al.  Timing of synaptic transmission. , 1999, Annual review of physiology.

[61]  Yotam Luz,et al.  The Effect of STDP Temporal Kernel Structure on the Learning Dynamics of Single Excitatory and Inhibitory Synapses , 2014, PloS one.