A triplet spike-timing–dependent plasticity model generalizes the Bienenstock–Cooper–Munro rule to higher-order spatiotemporal correlations

Synaptic strength depresses for low and potentiates for high activation of the postsynaptic neuron. This feature is a key property of the Bienenstock–Cooper–Munro (BCM) synaptic learning rule, which has been shown to maximize the selectivity of the postsynaptic neuron, and thereby offers a possible explanation for experience-dependent cortical plasticity such as orientation selectivity. However, the BCM framework is rate-based and a significant amount of recent work has shown that synaptic plasticity also depends on the precise timing of presynaptic and postsynaptic spikes. Here we consider a triplet model of spike-timing–dependent plasticity (STDP) that depends on the interactions of three precisely timed spikes. Triplet STDP has been shown to describe plasticity experiments that the classical STDP rule, based on pairs of spikes, has failed to capture. In the case of rate-based patterns, we show a tight correspondence between the triplet STDP rule and the BCM rule. We analytically demonstrate the selectivity property of the triplet STDP rule for orthogonal inputs and perform numerical simulations for nonorthogonal inputs. Moreover, in contrast to BCM, we show that triplet STDP can also induce selectivity for input patterns consisting of higher-order spatiotemporal correlations, which exist in natural stimuli and have been measured in the brain. We show that this sensitivity to higher-order correlations can be used to develop direction and speed selectivity.

[1]  D. Hubel,et al.  Receptive fields, binocular interaction and functional architecture in the cat's visual cortex , 1962, The Journal of physiology.

[2]  T. Bliss,et al.  Long‐lasting potentiation of synaptic transmission in the dentate area of the anaesthetized rabbit following stimulation of the perforant path , 1973, The Journal of physiology.

[3]  E. Bienenstock,et al.  Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex , 1982, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[4]  R. L. Valois,et al.  The orientation and direction selectivity of cells in macaque visual cortex , 1982, Vision Research.

[5]  W. Singer,et al.  Different voltage-dependent thresholds for inducing long-term depression and long-term potentiation in slices of rat visual cortex , 1990, Nature.

[6]  M. Bear,et al.  Homosynaptic long-term depression in area CA1 of hippocampus and effects of N-methyl-D-aspartate receptor blockade. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Nathan Intrator,et al.  Objective function formulation of the BCM theory of visual cortical plasticity: Statistical connections, stability conditions , 1992, Neural Networks.

[8]  T. Bliss,et al.  A synaptic model of memory: long-term potentiation in the hippocampus , 1993, Nature.

[9]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

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

[11]  David J. Field,et al.  Emergence of simple-cell receptive field properties by learning a sparse code for natural images , 1996, Nature.

[12]  M. Bear,et al.  Experience-dependent modification of synaptic plasticity in visual cortex , 1996, Nature.

[13]  Leon N. Cooper,et al.  BCM network develops orientation selectivity and ocular dominance in natural scene environment , 1997, Vision Research.

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

[15]  D. Johnston,et al.  Regulation of Synaptic Efficacy by Coincidence of Postsynaptic APs and EPSPs , 1997 .

[16]  Nathan Intrator,et al.  Receptive Field Formation in Natural Scene Environments: Comparison of Single-Cell Learning Rules , 1997, Neural Computation.

[17]  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.

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

[19]  R. Nicoll,et al.  Long-term potentiation--a decade of progress? , 1999, Science.

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

[21]  Leon N. Cooper,et al.  Formation of Direction Selectivity in Natural Scene Environments , 2000, Neural Computation.

[22]  Henry Markram,et al.  An Algorithm for Modifying Neurotransmitter Release Probability Based on Pre- and Postsynaptic Spike Timing , 2001, Neural Computation.

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

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

[25]  Eero P. Simoncelli,et al.  Natural image statistics and neural representation. , 2001, Annual review of neuroscience.

[26]  L. Cooper,et al.  A biophysical model of bidirectional synaptic plasticity: Dependence on AMPA and NMDA receptors , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[27]  Wulfram Gerstner,et al.  Spiking Neuron Models , 2002 .

[28]  L. Cooper,et al.  A unified model of NMDA receptor-dependent bidirectional synaptic plasticity , 2002, Proceedings of the National Academy of Sciences of the United States of America.

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

[30]  Rajesh P. N. Rao,et al.  Self–organizing neural systems based on predictive learning , 2003, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[31]  Eugene M. Izhikevich,et al.  Relating STDP to BCM , 2003, Neural Computation.

[32]  Rajesh P. N. Rao,et al.  Motion detection and prediction through spike-timing dependent plasticity. , 2004, Network.

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

[34]  W. Gerstner,et al.  Generalized Bienenstock-Cooper-Munro rule for spiking neurons that maximizes information transmission. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[35]  David W. Nauen,et al.  Coactivation and timing-dependent integration of synaptic potentiation and depression , 2005, Nature Neuroscience.

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

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

[38]  Y. Dan,et al.  Contribution of individual spikes in burst-induced long-term synaptic modification. , 2006, Journal of neurophysiology.

[39]  Leonard E. White,et al.  Vision and Cortical Map Development , 2007, Neuron.

[40]  G. Buzsáki,et al.  Sequential structure of neocortical spontaneous activity in vivo , 2007, Proceedings of the National Academy of Sciences.

[41]  Stephen D. Van Hooser,et al.  Experience with moving visual stimuli drives the early development of cortical direction selectivity , 2008, Nature.

[42]  Eero P. Simoncelli,et al.  Spatio-temporal correlations and visual signalling in a complete neuronal population , 2008, Nature.

[43]  Wulfram Gerstner,et al.  An online Hebbian learning rule that performs independent component analysis , 2008, BMC Neuroscience.

[44]  Romain Brette,et al.  Generation of Correlated Spike Trains , 2009, Neural Computation.

[45]  Stefano Panzeri,et al.  The impact of high-order interactions on the rate of synchronous discharge and information transmission in somatosensory cortex , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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

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

[48]  Jean-Pascal Pfister,et al.  STDP in Adaptive Neurons Gives Close-To-Optimal Information Transmission , 2010, Front. Comput. Neurosci..

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