Emergence of Connectivity Motifs in Networks of Model Neurons with Short- and Long-Term Plastic Synapses

Recent experimental data from the rodent cerebral cortex and olfactory bulb indicate that specific connectivity motifs are correlated with short-term dynamics of excitatory synaptic transmission. It was observed that neurons with short-term facilitating synapses form predominantly reciprocal pairwise connections, while neurons with short-term depressing synapses form predominantly unidirectional pairwise connections. The cause of these structural differences in excitatory synaptic microcircuits is unknown. We show that these connectivity motifs emerge in networks of model neurons, from the interactions between short-term synaptic dynamics (SD) and long-term spike-timing dependent plasticity (STDP). While the impact of STDP on SD was shown in simultaneous neuronal pair recordings in vitro, the mutual interactions between STDP and SD in large networks are still the subject of intense research. Our approach combines an SD phenomenological model with an STDP model that faithfully captures long-term plasticity dependence on both spike times and frequency. As a proof of concept, we first simulate and analyze recurrent networks of spiking neurons with random initial connection efficacies and where synapses are either all short-term facilitating or all depressing. For identical external inputs to the network, and as a direct consequence of internally generated activity, we find that networks with depressing synapses evolve unidirectional connectivity motifs, while networks with facilitating synapses evolve reciprocal connectivity motifs. We then show that the same results hold for heterogeneous networks, including both facilitating and depressing synapses. This does not contradict a recent theory that proposes that motifs are shaped by external inputs, but rather complements it by examining the role of both the external inputs and the internally generated network activity. Our study highlights the conditions under which SD-STDP might explain the correlation between facilitation and reciprocal connectivity motifs, as well as between depression and unidirectional motifs.

[1]  Marco Capogna,et al.  Synaptic heterogeneity between mouse paracapsular intercalated neurons of the amygdala , 2007, The Journal of physiology.

[2]  Wulfram Gerstner,et al.  A History of Spike-Timing-Dependent Plasticity , 2011, Front. Syn. Neurosci..

[3]  Xiao-Jing Wang,et al.  Mean-Field Theory of Irregularly Spiking Neuronal Populations and Working Memory in Recurrent Cortical Networks , 2003 .

[4]  Douglas L. Rosene,et al.  The Geometric Structure of the Brain Fiber Pathways , 2012, Science.

[5]  L. Abbott,et al.  Synaptic plasticity: taming the beast , 2000, Nature Neuroscience.

[6]  Matthieu Gilson,et al.  Frontiers in Computational Neuroscience Computational Neuroscience , 2022 .

[7]  Matthieu Gilson,et al.  Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks III: Partially connected neurons driven by spontaneous activity , 2009, Biological Cybernetics.

[8]  Michele Giugliano,et al.  Emergence of Connectivity Patterns from Long-Term and Short-Term Plasticities , 2012, ICANN.

[9]  L. Abbott,et al.  A Quantitative Description of Short-Term Plasticity at Excitatory Synapses in Layer 2/3 of Rat Primary Visual Cortex , 1997, The Journal of Neuroscience.

[10]  Matthieu Gilson,et al.  Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks IV , 2009, Biological Cybernetics.

[11]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[12]  Henry Markram,et al.  Synaptic pathways in neural microcircuits , 2005, Trends in Neurosciences.

[13]  Daniel A. Butts,et al.  The Applicability of Spike Time Dependent Plasticity to Development , 2010, Front. Syn. Neurosci..

[14]  Fritjof Helmchen,et al.  Chronic imaging of cortical sensory map dynamics using a genetically encoded calcium indicator , 2012, The Journal of physiology.

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

[16]  K. Deisseroth,et al.  Circuit-breakers: optical technologies for probing neural signals and systems , 2007, Nature Reviews Neuroscience.

[17]  H. Sebastian Seung,et al.  Reading the Book of Memory: Sparse Sampling versus Dense Mapping of Connectomes , 2009, Neuron.

[18]  Paolo Del Giudice,et al.  Long and short-term synaptic plasticity and the formation of working memory: A case study , 2001, Neurocomputing.

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

[20]  L. Abbott,et al.  Neural network dynamics. , 2005, Annual review of neuroscience.

[21]  Xiao-Jing Wang,et al.  Spike-Frequency Adaptation of a Generalized Leaky Integrate-and-Fire Model Neuron , 2004, Journal of Computational Neuroscience.

[22]  Henry Markram,et al.  Coding of temporal information by activity-dependent synapses. , 2002, Journal of neurophysiology.

[23]  W. Gerstner,et al.  Spike-Timing-Dependent Plasticity: A Comprehensive Overview , 2012, Front. Syn. Neurosci..

[24]  Nicholas T. Carnevale,et al.  ModelDB: A Database to Support Computational Neuroscience , 2004, Journal of Computational Neuroscience.

[25]  Michele Giugliano,et al.  The response of cortical neurons to in vivo-like input current: theory and experiment , 2008, Biological Cybernetics.

[26]  K. Martin,et al.  Excitatory synaptic inputs to spiny stellate cells in cat visual cortex , 1996, Nature.

[27]  Thomas K. Berger,et al.  Heterogeneity in the pyramidal network of the medial prefrontal cortex , 2006, Nature Neuroscience.

[28]  G. Bi,et al.  Timing in synaptic plasticity: from detection to integration , 2005, Trends in Neurosciences.

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

[30]  A. Barabasi,et al.  Taming complexity , 2005 .

[31]  H. Markram,et al.  Disynaptic Inhibition between Neocortical Pyramidal Cells Mediated by Martinotti Cells , 2007, Neuron.

[32]  B. Sakmann,et al.  Developmental Switch in the Short-Term Modification of Unitary EPSPs Evoked in Layer 2/3 and Layer 5 Pyramidal Neurons of Rat Neocortex , 1999, The Journal of Neuroscience.

[33]  Bartlett W. Mel,et al.  Cortical rewiring and information storage , 2004, Nature.

[34]  T. Margrie,et al.  Glutamatergic transmission and plasticity between olfactory bulb mitral cells , 2008, The Journal of physiology.

[35]  P. D. Giudice,et al.  Modelling the formation of working memory with networks of integrate-and-fire neurons connected by plastic synapses , 2003, Journal of Physiology-Paris.

[36]  W. Senn,et al.  Neocortical pyramidal cells respond as integrate-and-fire neurons to in vivo-like input currents. , 2003, Journal of neurophysiology.

[37]  H. Markram,et al.  Differential signaling via the same axon of neocortical pyramidal neurons. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[38]  M. Alexander,et al.  Principles of Neural Science , 1981 .

[39]  J. Pfister,et al.  A triplet spike-timing–dependent plasticity model generalizes the Bienenstock–Cooper–Munro rule to higher-order spatiotemporal correlations , 2011, Proceedings of the National Academy of Sciences.

[40]  Sadri Hassani,et al.  Nonlinear Dynamics and Chaos , 2000 .

[41]  W. Gerstner,et al.  Triplets of Spikes in a Model of Spike Timing-Dependent Plasticity , 2006, The Journal of Neuroscience.

[42]  L. Abbott,et al.  Competitive Hebbian learning through spike-timing-dependent synaptic plasticity , 2000, Nature Neuroscience.

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

[44]  Carson C. Chow,et al.  Calcium time course as a signal for spike-timing-dependent plasticity. , 2005, Journal of neurophysiology.

[45]  N. Brunel,et al.  Calcium-based plasticity model explains sensitivity of synaptic changes to spike pattern, rate, and dendritic location , 2012, Proceedings of the National Academy of Sciences.

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

[47]  Mounir Boukadoum,et al.  Mechanisms Gating the Flow of Information in the Cortex: What They Might Look Like and What Their Uses may be , 2010, Front. Comput. Neurosci..

[48]  B. Strowbridge,et al.  Long-term plasticity of excitatory inputs to granule cells in the rat olfactory bulb , 2009, Nature Neuroscience.

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

[50]  R. Douglas,et al.  Mapping the Matrix: The Ways of Neocortex , 2007, Neuron.

[51]  Ian R. Wickersham,et al.  Monosynaptic Restriction of Transsynaptic Tracing from Single, Genetically Targeted Neurons , 2007, Neuron.

[52]  Henry Markram,et al.  Neural Networks with Dynamic Synapses , 1998, Neural Computation.

[53]  Paul Miller,et al.  Excitatory, Inhibitory, and Structural Plasticity Produce Correlated Connectivity in Random Networks Trained to Solve Paired-Stimulus Tasks , 2011, Front. Comput. Neurosci..

[54]  Misha Tsodyks,et al.  Persistent Activity in Neural Networks with Dynamic Synapses , 2007, PLoS Comput. Biol..

[55]  Henry C. Tuckwell,et al.  Stochastic processes in the neurosciences , 1989 .

[56]  Peter Dayan,et al.  Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems , 2001 .

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

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

[59]  The Accounting Review , 1972 .

[60]  Wulfram Gerstner,et al.  Frontiers in Synaptic Neuroscience Synaptic Neuroscience , 2022 .

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

[62]  G. Laurent,et al.  Corrigendum: Conditional modulation of spike-timing-dependent plasticity for olfactory learning , 2012, Nature.

[63]  J. Livet,et al.  A technicolour approach to the connectome , 2008, Nature Reviews Neuroscience.

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

[65]  Nathan Intrator,et al.  Theory of Cortical Plasticity , 2004 .

[66]  Piet Van Mieghem,et al.  Emergence of Modular Structure in a Large-Scale Brain Network with Interactions between Dynamics and Connectivity , 2010, Front. Comput. Neurosci..

[67]  Thomas A. Cleland,et al.  Decorrelation of Odor Representations via Spike Timing-Dependent Plasticity , 2010, Front. Comput. Neurosci..

[68]  Maurizio Mattia,et al.  Frequency-dependent response properties of adapting spiking neurons. , 2007, Mathematical biosciences.

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

[70]  Henry Markram,et al.  Multiquantal release underlies the distribution of synaptic effi cacies in the neocortex , 2022 .

[71]  G. Laurent,et al.  Conditional modulation of spike-timing-dependent plasticity for olfactory learning , 2012, Nature.

[72]  Jesper Tegnér,et al.  Spike-timing-dependent plasticity: common themes and divergent vistas , 2002, Biological Cybernetics.

[73]  Wulfram Gerstner,et al.  Tag-Trigger-Consolidation: A Model of Early and Late Long-Term-Potentiation and Depression , 2008, PLoS Comput. Biol..

[74]  J. E. Glynn,et al.  Numerical Recipes: The Art of Scientific Computing , 1989 .

[75]  H. Markram,et al.  Matched Pre- and Post-Synaptic Changes Underlie Synaptic Plasticity over Long Time Scales , 2013, The Journal of Neuroscience.

[76]  H. Markram,et al.  Redistribution of synaptic efficacy between neocortical pyramidal neurons , 1996, Nature.

[77]  H. Markram,et al.  Potential for multiple mechanisms, phenomena and algorithms for synaptic plasticity at single synapses , 1998, Neuropharmacology.

[78]  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.

[79]  D. Buonomano,et al.  Cortical plasticity: from synapses to maps. , 1998, Annual review of neuroscience.

[80]  D. Buonomano,et al.  Distinct Functional Types of Associative Long-Term Potentiation in Neocortical and Hippocampal Pyramidal Neurons , 1999, The Journal of Neuroscience.

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

[82]  J. Bower,et al.  Facilitating and nonfacilitating synapses on pyramidal cells: a correlation between physiology and morphology. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[83]  Markus Diesmann,et al.  Limits to the Development of Feed-Forward Structures in Large Recurrent Neuronal Networks , 2011, Front. Comput. Neurosci..

[84]  Markus Diesmann,et al.  Random wiring limits the development of functional structure in large recurrent neuronal networks , 2010, BMC Neuroscience.

[85]  Lars Buesing,et al.  Democratic Population Decisions Result in Robust Policy-Gradient Learning: A Parametric Study with GPU Simulations , 2011, PloS one.

[86]  Wolfgang Maass,et al.  Motif distribution, dynamical properties, and computational performance of two data-based cortical microcircuit templates , 2009, Journal of Physiology-Paris.

[87]  Jean-Pascal Pfister,et al.  Beyond Pair-Based STDP: a Phenomenological Rule for Spike Triplet and Frequency Effects , 2005, NIPS.

[88]  Idan Segev,et al.  Multiple mechanisms govern the dynamics of depression at neocortical synapses of young rats , 2004, The Journal of physiology.

[89]  Lawrence Hubert,et al.  Evaluating the symmetry of a proximity matrix , 1979 .

[90]  R. Zucker,et al.  A General Model of Synaptic Transmission and Short-Term Plasticity , 2009, Neuron.

[91]  Karl J. Friston Functional and Effective Connectivity: A Review , 2011, Brain Connect..

[92]  R. Douglas,et al.  Recurrent neuronal circuits in the neocortex , 2007, Current Biology.

[93]  Wulfram Gerstner,et al.  A neuronal learning rule for sub-millisecond temporal coding , 1996, Nature.

[94]  H. Markram,et al.  The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[95]  Markus Diesmann,et al.  Spike-Timing-Dependent Plasticity in Balanced Random Networks , 2007, Neural Computation.

[96]  Michele Giugliano,et al.  The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs , 2008, Biological Cybernetics.

[97]  Wulfram Gerstner,et al.  Temporal coding in the sub-millisecond range: Model of barn owl auditory pathway , 1995, NIPS.

[98]  Misha Tsodyks,et al.  The Emergence of Up and Down States in Cortical Networks , 2006, PLoS Comput. Biol..

[99]  Maurizio Mattia,et al.  Finite-size dynamics of inhibitory and excitatory interacting spiking neurons. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[100]  W. Denk,et al.  Serial Block-Face Scanning Electron Microscopy to Reconstruct Three-Dimensional Tissue Nanostructure , 2004, PLoS biology.

[101]  A. Destexhe,et al.  The high-conductance state of neocortical neurons in vivo , 2003, Nature Reviews Neuroscience.

[102]  Michele Pignatelli Structure and function of the olfactory bulb microcircuit , 2009 .

[103]  D. Hansel,et al.  On the Distribution of Firing Rates in Networks of Cortical Neurons , 2011, The Journal of Neuroscience.

[104]  Wulfram Gerstner,et al.  Spike-Based Reinforcement Learning in Continuous State and Action Space: When Policy Gradient Methods Fail , 2009, PLoS Comput. Biol..

[105]  Fiona E. N. LeBeau,et al.  Microcircuits in action – from CPGs to neocortex , 2005, Trends in Neurosciences.

[106]  J. Shappir,et al.  In-cell recordings by extracellular microelectrodes , 2010, Nature Methods.

[107]  H. Markram,et al.  Spontaneous and evoked synaptic rewiring in the neonatal neocortex , 2006, Proceedings of the National Academy of Sciences.

[108]  Wulfram Gerstner,et al.  Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. , 2005, Journal of neurophysiology.