Biophysical and Phenomenological Models of Multiple Spike Interactions in Spike-timing Dependent Plasticity

Spike-timing dependent plasticity (STDP) is a form of associative synaptic modification which depends on the respective timing of pre- and post-synaptic spikes. The biophysical mechanisms underlying this form of plasticity are currently not known. We present here a biophysical model which captures the characteristics of STDP, such as its frequency dependency, and the effects of spike pair or spike triplet interactions. We also make links with other well-known plasticity rules. A simplified phenomenological model is also derived, which should be useful for fast numerical simulation and analytical investigation of the impact of STDP at the network level.

[1]  D. E. Goldman.  POTENTIAL, IMPEDANCE, AND RECTIFICATION IN MEMBRANES , 1943, The Journal of general physiology.

[2]  C. Stevens,et al.  Voltage dependence of NMDA-activated macroscopic conductances predicted by single-channel kinetics , 1990, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[3]  R. Zucker,et al.  Selective induction of LTP and LTD by postsynaptic [Ca2+]i elevation. , 1999, Journal of neurophysiology.

[4]  W. Levy,et al.  Temporal contiguity requirements for long-term associative potentiation/depression in the hippocampus , 1983, Neuroscience.

[5]  R. Silver,et al.  Synaptic connections between layer 4 spiny neurone‐ layer 2/3 pyramidal cell pairs in juvenile rat barrel cortex: physiology and anatomy of interlaminar signalling within a cortical column , 2002, The Journal of physiology.

[6]  G. Collingridge,et al.  Differential Roles of NR2A and NR2B-Containing NMDA Receptors in Cortical Long-Term Potentiation and Long-Term Depression , 2004, The Journal of Neuroscience.

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

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

[9]  Bernardo L. Sabatini,et al.  Analysis of calcium channels in single spines using optical fluctuation analysis , 2000, Nature.

[10]  W. Singer,et al.  Long-term depression of excitatory synaptic transmission and its relationship to long-term potentiation , 1993, Trends in Neurosciences.

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

[12]  R. Malenka,et al.  Mechanisms underlying induction of homosynaptic long-term depression in area CA1 of the hippocampus , 1992, Neuron.

[13]  Robert S. Zucker,et al.  Postsynaptic Levels of [Ca2+]i Needed to Trigger LTD and LTP , 1996, Neuron.

[14]  H. Markram,et al.  Dendritic calcium transients evoked by single back‐propagating action potentials in rat neocortical pyramidal neurons. , 1995, The Journal of physiology.

[15]  Rafael Yuste,et al.  Calcium Dynamics of Spines Depend on Their Dendritic Location , 2002, Neuron.

[16]  M. Kennedy,et al.  Regulation of brain Type II Ca 2+ calmodulin -dependent protein kinase by autophosphorylation: A Ca2+-triggered molecular switch , 1986, Cell.

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

[18]  A. C. Greenwood,et al.  Bidirectional synaptic plasticity correlated with the magnitude of dendritic calcium transients above a threshold. , 2001, Journal of neurophysiology.

[19]  D. Feldman,et al.  Timing-Based LTP and LTD at Vertical Inputs to Layer II/III Pyramidal Cells in Rat Barrel Cortex , 2000, Neuron.

[20]  S. B. Kater,et al.  Dendritic spines: cellular specializations imparting both stability and flexibility to synaptic function. , 1994, Annual review of neuroscience.

[21]  K. Svoboda,et al.  The Life Cycle of Ca2+ Ions in Dendritic Spines , 2002, Neuron.

[22]  L. Stryer,et al.  Range of messenger action of calcium ion and inositol 1,4,5-trisphosphate. , 1992, Science.

[23]  G. Carmignoto,et al.  Activity-dependent decrease in NMDA receptor responses during development of the visual cortex. , 1992, Science.

[24]  R. Zucker.  Calcium- and activity-dependent synaptic plasticity , 1999, Current Opinion in Neurobiology.

[25]  T. Sejnowski,et al.  [Letters to nature] , 1996, Nature.

[26]  M. Häusser,et al.  Dendritic coincidence detection of EPSPs and action potentials , 2001, Nature Neuroscience.

[27]  H. Schulman,et al.  Neuronal Ca2+/calmodulin-dependent protein kinases. , 1992, Annual review of biochemistry.

[28]  S. Nelson,et al.  Orientation selectivity of cortical neurons during intracellular blockade of inhibition. , 1994, Science.

[29]  P. d'Alcantara,et al.  Bidirectional synaptic plasticity as a consequence of interdependent Ca2+‐controlled phosphorylation and dephosphorylation pathways , 2003, The European journal of neuroscience.

[30]  H. Shouval,et al.  Stochastic properties of synaptic transmission affect the shape of spike time-dependent plasticity curves. , 2005, Journal of neurophysiology.

[31]  R S Zucker,et al.  Postsynaptic calcium is sufficient for potentiation of hippocampal synaptic transmission. , 1988, Science.

[32]  Y. Frégnac,et al.  Activity-dependent regulation of receptive field properties of cat area 17 by supervised Hebbian learning. , 1999, Journal of neurobiology.

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

[34]  R. Colbran,et al.  Protein Phosphatases and Calcium/Calmodulin-Dependent Protein Kinase II-Dependent Synaptic Plasticity , 2004, The Journal of Neuroscience.

[35]  J I Gold,et al.  A model of dendritic spine Ca2+ concentration exploring possible bases for a sliding synaptic modification threshold. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[36]  Hiroki Yasuda,et al.  Long-term depression in rat visual cortex is associated with a lower rise of postsynaptic calcium than long-term potentiation , 1996, Neuroscience Research.

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

[38]  Daniel J. Brasier,et al.  Spike-time dependent plasticity investigated using whole cell recording in rat somatosensory cortex (S1) in vivo. , 2004 .

[39]  Nicholas T. Carnevale,et al.  The NEURON Simulation Environment , 1997, Neural Computation.

[40]  W Singer,et al.  Intracellular injection of Ca2+ chelators blocks induction of long-term depression in rat visual cortex. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[41]  D. Johnston,et al.  A Synaptically Controlled, Associative Signal for Hebbian Plasticity in Hippocampal Neurons , 1997, Science.

[42]  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.

[43]  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.

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

[45]  J. Lisman,et al.  A mechanism for the Hebb and the anti-Hebb processes underlying learning and memory. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[46]  L. Cooper,et al.  A physiological basis for a theory of synapse modification. , 1987, Science.

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

[48]  J J Eggermont,et al.  Neuronal pair and triplet interactions in the auditory midbrain of the leopard frog. , 1991, Journal of neurophysiology.

[49]  W. Denk,et al.  Dendritic spines as basic functional units of neuronal integration , 1995, Nature.

[50]  R. Nicoll,et al.  Ca2+ Signaling Requirements for Long-Term Depression in the Hippocampus , 1996, Neuron.

[51]  U. Karmarkar,et al.  A model of spike-timing dependent plasticity: one or two coincidence detectors? , 2002, Journal of neurophysiology.

[52]  M. Sheng,et al.  Role of NMDA Receptor Subtypes in Governing the Direction of Hippocampal Synaptic Plasticity , 2004, Science.

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

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

[55]  A. Destexhe.  Kinetic Models of Synaptic Transmission , 1997 .

[56]  Thomas H. Brown,et al.  Hebbian synaptic plasticity , 1998 .

[57]  W Singer,et al.  Genetic and epigenetic regulation of NMDA receptor expression in the rat visual cortex , 1999, The European journal of neuroscience.

[58]  M. V. Rossum,et al.  In Neural Computation , 2022 .

[59]  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.

[60]  M. Bear,et al.  Homosynaptic long-term depression in the visual cortex , 1994, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[61]  M. Bear,et al.  Mechanism for a sliding synaptic modification threshold , 1995, Neuron.

[62]  A. Hodgkin,et al.  The effect of sodium ions on the electrical activity of the giant axon of the squid , 1949, The Journal of physiology.

[63]  M. Poo,et al.  Calcium stores regulate the polarity and input specificity of synaptic modification , 2000, Nature.

[64]  R. Nicoll,et al.  Two Distinct Forms of Long-Term Depression Coexist in CA1 Hippocampal Pyramidal Cells , 1997, Neuron.

[65]  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.

[66]  Charlotte A. Boettiger,et al.  Developmentally Restricted Synaptic Plasticity in a Songbird Nucleus Required for Song Learning , 2001, Neuron.

[67]  T J Sejnowski,et al.  Ionic mechanisms for intrinsic slow oscillations in thalamic relay neurons. , 1993, Biophysical journal.

[68]  V. Han,et al.  Synaptic plasticity in a cerebellum-like structure depends on temporal order , 1997, Nature.

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

[70]  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.

[71]  M. Bear,et al.  Bidirectional, experience-dependent regulation of N-methyl-D-aspartate receptor subunit composition in the rat visual cortex during postnatal development. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[72]  A. Zhabotinsky.  Bistability in the Ca(2+)/calmodulin-dependent protein kinase-phosphatase system. , 2000, Biophysical journal.

[73]  Terrence J. Sejnowski,et al.  An Efficient Method for Computing Synaptic Conductances Based on a Kinetic Model of Receptor Binding , 1994, Neural Computation.

[74]  G. Lynch,et al.  Intracellular injections of EGTA block induction of hippocampal long-term potentiation , 1983, Nature.

[75]  J. Lisman.  A mechanism for memory storage insensitive to molecular turnover: a bistable autophosphorylating kinase. , 1985, Proceedings of the National Academy of Sciences of the United States of America.

[76]  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.