Dense Neuron Clustering Explains Connectivity Statistics in Cortical Microcircuits

Local cortical circuits appear highly non-random, but the underlying connectivity rule remains elusive. Here, we analyze experimental data observed in layer 5 of rat neocortex and suggest a model for connectivity from which emerge essential observed non-random features of both wiring and weighting. These features include lognormal distributions of synaptic connection strength, anatomical clustering, and strong correlations between clustering and connection strength. Our model predicts that cortical microcircuits contain large groups of densely connected neurons which we call clusters. We show that such a cluster contains about one fifth of all excitatory neurons of a circuit which are very densely connected with stronger than average synapses. We demonstrate that such clustering plays an important role in the network dynamics, namely, it creates bistable neural spiking in small cortical circuits. Furthermore, introducing local clustering in large-scale networks leads to the emergence of various patterns of persistent local activity in an ongoing network activity. Thus, our results may bridge a gap between anatomical structure and persistent activity observed during working memory and other cognitive processes.

[1]  Tomoki Fukai,et al.  Recurrent Network Models for Perfect Temporal Integration of Fluctuating Correlated Inputs , 2009, PLoS Comput. Biol..

[2]  Prof. Dr. Valentino Braitenberg,et al.  Anatomy of the Cortex , 1991, Studies of Brain Function.

[3]  J. DeFelipe,et al.  Microstructure of the neocortex: Comparative aspects , 2002, Journal of neurocytology.

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

[5]  P. J. Sjöström,et al.  Functional specificity of local synaptic connections in neocortical networks , 2011, Nature.

[6]  T. Harkany,et al.  Pyramidal cell communication within local networks in layer 2/3 of rat neocortex , 2003, The Journal of physiology.

[7]  T. Kosaka,et al.  Quantitative analysis of neurons and glial cells in the rat somatosensory cortex, with special reference to GABAergic neurons and parvalbumin-containing neurons , 2004, Experimental Brain Research.

[8]  Theoden I. Netoff,et al.  Synchronization from Second Order Network Connectivity Statistics , 2011, Front. Comput. Neurosci..

[9]  Louis K. Scheffer,et al.  Semi-automated reconstruction of neural circuits using electron microscopy , 2010, Current Opinion in Neurobiology.

[10]  Arthur W. Wetzel,et al.  Network anatomy and in vivo physiology of visual cortical neurons , 2011, Nature.

[11]  Jonathan E. Rubin,et al.  The Interaction of Intrinsic Dynamics and Network Topology in Determining Network Burst Synchrony , 2011, Front. Comput. Neurosci..

[12]  Pingbo Yin,et al.  Monkeys have a limited form of short-term memory in audition , 2012, Proceedings of the National Academy of Sciences.

[13]  Katsunori Kitano,et al.  Variability v.s. synchronicity of neuronal activity in local cortical network models with different wiring topologies , 2007, Journal of Computational Neuroscience.

[14]  Matthieu Gilson,et al.  Stability versus Neuronal Specialization for STDP: Long-Tail Weight Distributions Solve the Dilemma , 2011, PloS one.

[15]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[16]  D. Chialvo.  Emergent complex neural dynamics , 2010, 1010.2530.

[17]  Xiaoqin Wang,et al.  Sustained firing in auditory cortex evoked by preferred stimuli , 2005, Nature.

[18]  Liping Wang,et al.  Persistent Neuronal Firing in Primary Somatosensory Cortex in the Absence of Working Memory of Trial-specific Features of the Sample Stimuli in a Haptic Working Memory Task , 2012, Journal of Cognitive Neuroscience.

[19]  Vladimir I. Nekorkin,et al.  Working Memory in the Network of Neuron-like Units with Noise , 2008, Int. J. Bifurc. Chaos.

[20]  Farzan Nadim,et al.  Modeling the leech heartbeat elemental oscillator II. Exploring the parameter space , 1995, Journal of Computational Neuroscience.

[21]  A. Koulakov,et al.  Correlated Connectivity and the Distribution of Firing Rates in the Neocortex , 2008, The Journal of Neuroscience.

[22]  C. Petersen,et al.  The Excitatory Neuronal Network of the C2 Barrel Column in Mouse Primary Somatosensory Cortex , 2009, Neuron.

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

[24]  A. Peters,et al.  The neuronal composition of area 17 of rat visual cortex. IV. The organization of pyramidal cells , 1987, The Journal of comparative neurology.

[25]  Andre Levchenko,et al.  Dynamic Properties of Network Motifs Contribute to Biological Network Organization , 2005, PLoS biology.

[26]  Tomoki Fukai,et al.  A Simple Neural Network Exhibiting Selective Activation of Neuronal Ensembles: From Winner-Take-All to Winners-Share-All , 1997, Neural Computation.

[27]  Olaf Sporns,et al.  The Non-Random Brain: Efficiency, Economy, and Complex Dynamics , 2010, Front. Comput. Neurosci..

[28]  Wei Chen,et al.  A few strong connections: optimizing information retention in neuronal avalanches , 2010, BMC Neuroscience.

[29]  Kevin L. Briggman,et al.  Wiring specificity in the direction-selectivity circuit of the retina , 2011, Nature.

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

[31]  Yun Wang,et al.  Synaptic connections and small circuits involving excitatory and inhibitory neurons in layers 2-5 of adult rat and cat neocortex: triple intracellular recordings and biocytin labelling in vitro. , 2002, Cerebral cortex.

[32]  H. Markram.  A network of tufted layer 5 pyramidal neurons. , 1997, Cerebral cortex.

[33]  V. Mountcastle.  The columnar organization of the neocortex. , 1997, Brain : a journal of neurology.

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

[35]  T. M. Mayhew,et al.  Anatomy of the Cortex: Statistics and Geometry. , 1991 .

[36]  J. Szentágothai.  "Specificity versus (quasi-) randomness" revisited. , 1990, Acta morphologica Hungarica.

[37]  R. Morgan,et al.  Nonrandom connectivity of the epileptic dentate gyrus predicts a major role for neuronal hubs in seizures , 2008, Proceedings of the National Academy of Sciences.

[38]  Dietmar Plenz,et al.  The organization of strong links in complex networks , 2011, Nature Physics.

[39]  X. Wang,et al.  Synaptic Basis of Cortical Persistent Activity: the Importance of NMDA Receptors to Working Memory , 1999, The Journal of Neuroscience.

[40]  P. J. Sjöström,et al.  Rate, Timing, and Cooperativity Jointly Determine Cortical Synaptic Plasticity , 2001, Neuron.

[41]  A. Peters,et al.  The neuronal composition of area 17 of rat visual cortex. III. Numerical considerations , 1985, The Journal of comparative neurology.

[42]  T. Pasternak,et al.  Working memory in primate sensory systems , 2005, Nature Reviews Neuroscience.

[43]  Vernon B Mountcastle,et al.  Introduction. Computation in cortical columns. , 2003, Cerebral cortex.

[44]  R. Douglas,et al.  A Quantitative Map of the Circuit of Cat Primary Visual Cortex , 2004, The Journal of Neuroscience.

[45]  A. Koulakov,et al.  Model for a robust neural integrator , 2002, Nature Neuroscience.

[46]  Ifije E. Ohiorhenuan,et al.  Sparse coding and high-order correlations in fine-scale cortical networks , 2010, Nature.

[47]  Pak-Ming Lau,et al.  Synaptic mechanisms of persistent reverberatory activity in neuronal networks. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[48]  H. Markram,et al.  The neocortical microcircuit as a tabula rasa. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[49]  Paul Leonard Gabbott,et al.  Local‐circuit neurones in the medial prefrontal cortex (areas 25, 32 and 24b) in the rat: Morphology and quantitative distribution , 1997, The Journal of comparative neurology.

[50]  Tomoki Fukai,et al.  Associative memory model with long-tail-distributed Hebbian synaptic connections , 2013, Front. Comput. Neurosci..

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

[52]  Henry Markram,et al.  Innate Neural Assemblies for Lego Memory , 2011, Front. Neural Circuits.

[53]  V. Nekorkin,et al.  Activity clusters in dynamical model of the working memory system , 2008, Network.

[54]  H. Markram,et al.  Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex. , 1997, The Journal of physiology.

[55]  R. Yuste,et al.  The Brain Activity Map Project and the Challenge of Functional Connectomics , 2012, Neuron.

[56]  C. Beaulieu,et al.  Numerical data on neocortical neurons in adult rat, with special reference to the GABA population , 1993, Brain Research.

[57]  Alison L. Barth,et al.  An Embedded Subnetwork of Highly Active Neurons in the Neocortex , 2010, Neuron.

[58]  V. Mountcastle.  Modality and topographic properties of single neurons of cat's somatic sensory cortex. , 1957, Journal of neurophysiology.

[59]  D. Plenz,et al.  The organizing principles of neuronal avalanches: cell assemblies in the cortex? , 2007, Trends in Neurosciences.

[60]  A. Thomson,et al.  Interlaminar connections in the neocortex. , 2003, Cerebral cortex.

[61]  A. Reyes,et al.  Layer and frequency dependencies of phase response properties of pyramidal neurons in rat motor cortex , 2007, The European journal of neuroscience.

[62]  K. Rockland,et al.  Some thoughts on cortical minicolumns , 2004, Experimental Brain Research.

[63]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

[64]  M. Tsodyks,et al.  Synaptic Theory of Working Memory , 2008, Science.

[65]  Tomoki Fukai,et al.  Optimal spike-based communication in excitable networks with strong-sparse and weak-dense links , 2012, Scientific Reports.

[66]  M. Stewart,et al.  Distribution of neurons and glia in the visual cortex (area 17) of the adult albino rat: A quantitative description , 1987, Neuroscience.