Kinetic models of spike-timing dependent plasticity and their functional consequences in detecting correlations

Spike-timing dependent plasticity (STDP) is a type of synaptic modification found relatively recently, but the underlying biophysical mechanisms are still unclear. Several models of STDP have been proposed, and differ by their implementation, and in particular how synaptic weights saturate to their minimal and maximal values. We analyze here kinetic models of transmitter-receptor interaction and derive a series of STDP models. In general, such kinetic models predict progressive saturation of the weights. Various forms can be obtained depending on the hypotheses made in the kinetic model, and these include a simple linear dependence on the value of the weight (“soft bounds”), mixed soft and abrupt saturation (“hard bound”), or more complex forms. We analyze in more detail simple soft-bound models of Hebbian and anti-Hebbian STDPs, in which nonlinear spike interactions (triplets) are taken into account. We show that Hebbian STDPs can be used to selectively potentiate synapses that are correlated in time, while anti-Hebbian STDPs depress correlated synapses, despite the presence of nonlinear spike interactions. This correlation detection enables neurons to develop a selectivity to correlated inputs. We also examine different versions of kinetics-based STDP models and compare their sensitivity to correlations. We conclude that kinetic models generally predict soft-bound dynamics, and that such models seem ideal for detecting correlations among large numbers of inputs.

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

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

[3]  Quan Zou,et al.  Reconstructing synaptic background activity from conductance measurements in vivo , 2005, Neurocomputing.

[4]  T. Sejnowski,et al.  Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons , 2001, Neuroscience.

[5]  Anish Arora,et al.  Phosphorylation of AMPA receptors , 2005, Molecular Neurobiology.

[6]  Richard L. Huganir,et al.  Glutamate receptor phosphorylation and synaptic plasticity , 1994, Current Opinion in Neurobiology.

[7]  Per Jesper Sjöström,et al.  Novel presynaptic mechanisms for coincidence detection in synaptic plasticity , 2006, Current Opinion in Neurobiology.

[8]  Jan Karbowski,et al.  Synchrony arising from a balanced synaptic plasticity in a network of heterogeneous neural oscillators. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[11]  Y. Dan,et al.  Spike timing-dependent plasticity: from synapse to perception. , 2006, Physiological reviews.

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

[13]  R. Christopher deCharms,et al.  Primary cortical representation of sounds by the coordination of action-potential timing , 1996, Nature.

[14]  M. Steriade,et al.  Natural waking and sleep states: a view from inside neocortical neurons. , 2001, Journal of neurophysiology.

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

[16]  R. Nicoll,et al.  Expression mechanisms underlying long-term potentiation: a postsynaptic view. , 2003, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

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

[18]  A. Aertsen,et al.  Spike synchronization and rate modulation differentially involved in motor cortical function. , 1997, Science.

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

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

[21]  Roger Anwyl,et al.  Induction and expression mechanisms of postsynaptic NMDA receptor-independent homosynaptic long-term depression , 2006, Progress in Neurobiology.

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

[23]  Ramón Huerta,et al.  Biophysical model of synaptic plasticity dynamics , 2003, Biological Cybernetics.

[24]  D. Debanne,et al.  Asynchronous pre- and postsynaptic activity induces associative long-term depression in area CA1 of the rat hippocampus in vitro. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[25]  Michael Rudolph,et al.  Do Neocortical Pyramidal Neurons Display Stochastic Resonance? , 2001, Journal of Computational Neuroscience.

[26]  P. Pavlidis,et al.  Pair Recordings Reveal All-Silent Synaptic Connections and the Postsynaptic Expression of Long-Term Potentiation , 2001, Neuron.

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

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

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

[30]  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.

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

[32]  J. Leo van Hemmen,et al.  Modeling Synaptic Plasticity in Conjunction with the Timing of Pre- and Postsynaptic Action Potentials , 2000, Neural Computation.

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

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

[35]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1990 .

[36]  Yves Frégnac,et al.  Biophysical and Phenomenological Models of Multiple Spike Interactions in Spike-timing Dependent Plasticity , 2006, Int. J. Neural Syst..

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

[38]  T. Soderling,et al.  Postsynaptic protein phosphorylation and LTP , 2000, Trends in Neurosciences.

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

[40]  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.

[41]  Ehud Zohary,et al.  Correlated neuronal discharge rate and its implications for psychophysical performance , 1994, Nature.

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

[43]  A. Aertsen,et al.  Dynamics of neuronal interactions in monkey cortex in relation to behavioural events , 1995, Nature.

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

[45]  A. Destexhe,et al.  Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo. , 1999, Journal of neurophysiology.

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

[47]  David B. Grayden,et al.  Spike-Timing-Dependent Plasticity: The Relationship to Rate-Based Learning for Models with Weight Dynamics Determined by a Stable Fixed Point , 2004, Neural Computation.

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

[49]  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.

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

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

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

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

[54]  A. Destexhe,et al.  Impact of spontaneous synaptic activity on the resting properties of cat neocortical pyramidal neurons In vivo. , 1998, Journal of neurophysiology.