Skip to main content
SpringerLink
Log in

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

  • Original Paper
  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abarbanel HD, Gibb L, Huerta R, Rabinovich MI (2003) Biophysical model of synaptic plasticity dynamics. Biol Cybern 89:214–226

    Article  PubMed  Google Scholar 

  • Abeles M (1991) Corticonics: neural circuits of the cerebral cortex. Cambridge University Press, Cambridge

    Google Scholar 

  • Anwyl R (2006) Induction and expression mechanisms of postsynaptic NMDA receptor-independent homosynaptic long-term depression. Prog Neurobiol 78:17–37

    Article  PubMed  CAS  Google Scholar 

  • Badoual M, Zou Q, Davison AP, Rudolph M, Bal T, Frégnac Y, Destexhe A (2006) Biophysical and phenomenological models of multiple spike interactions in spike-timing dependent plasticity. Int J Neural Syst 16:79–97

    Article  PubMed  Google Scholar 

  • Bell CC, Han VZ, Sugawara Y, Grant K (1997) Synaptic plasticity in a cerebellum-like structure depends on temporal order. Nature 387:278–281

    Article  PubMed  CAS  Google Scholar 

  • Bi GQ, Poo MM (1998) Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength and postsynaptic cell type. J Neurosci 18:10464–10472

    PubMed  CAS  Google Scholar 

  • Burkitt AN, Meffin H, Grayden DB (2004) Spike-timing-dependent plasticity: the relationship to rate-based learning for models with weight dynamics determined by a stable fixed point. Neural Comput 16:885–940

    Article  PubMed  Google Scholar 

  • Castellani GC, Quinlan EM, Cooper LN, Shouval HZ (2001) A biophysical model of bidirectional synaptic plasticity: dependence on ampa and nmda receptors. Proc Nat Acad Sci USA 98:12772–12777

    Article  PubMed  CAS  Google Scholar 

  • de Charms RC, Merzenich MM (1996) Primary cortical representation of sounds by the coordination of action-potential timing. Nature 381:610–613

    Article  Google Scholar 

  • Dan Y, Poo MM (2006) Spike timing-dependent plasticity: from synapse to perception. Physiol Rev 86:1033–1048

    Article  PubMed  Google Scholar 

  • Debanne D, Gahwiler BH, Thompson SM (1994) Asynchronous pre- and postsynaptic activity induces associative long-term depression in area CA1 of the rat hippocampus in vitro. Proc Natl Acad Sci USA 91:1148–1152

    Article  PubMed  CAS  Google Scholar 

  • Destexhe A, Paré D (1999) Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo. J Neurophysiol 81:1531–1547

    PubMed  CAS  Google Scholar 

  • Destexhe A, Mainen ZF, Sejnowski TJ (1994) An efficient method for computing synaptic conductances based on a kinetic model of receptor binding. Neural Comput 6:10–14

    Google Scholar 

  • Destexhe A, Mainen ZF, Sejnowski TJ (1998) Kinetic models of synaptic transmission. In: Methods in neuronal modeling, chapter 1, MIT Press, Cambridge, Massachusetts, pp 1–26

  • Destexhe A, Rudolph M, Fellous JM, Sejnowski TJ (2001) Fluctuating synaptic conductances recreate in-vivo-like activity in neocortical neurons. Neurosci 107:13–24

    Article  CAS  Google Scholar 

  • Destexhe A, Rudolph M, Paré D (2003) The high-conductance state of neocortical neurons in vivo. Nat Rev Neurosci 4:739–751

    Article  PubMed  CAS  Google Scholar 

  • Duguid I, Sjostrom PJ (2006) Novel presynaptic mechanisms for coincidence detection in synaptic plasticity. Curr Opin Neurobiol 16:312–322

    Article  PubMed  CAS  Google Scholar 

  • Froemke RC, Dan Y (2002) Spike timing-dependent synaptic modification induced by natural spike trains. Nature 416:433–438

    Article  PubMed  CAS  Google Scholar 

  • Gerstner W, Kistler W (2002) Spiking neuron models. Cambridge University Press, Cambridge

    Google Scholar 

  • Gerstner W, Kempter R, van Hemmen JL, Wagner H (1996) A neuronal learning rule for sub-millisecond temporal coding. Nature 383:76–81

    Article  PubMed  CAS  Google Scholar 

  • Gütig R, Aharonov R, Rotter S, Sompolinsky H (2003) Learning input correlations through nonlinear temporally asymmetric Hebbian plasticity. J Neurosci 23:3697–3714

    PubMed  Google Scholar 

  • Hebb DO (1949) The organization of behavior. John Wesley & Sons, New York

    Google Scholar 

  • Hines ML, Carnevale NT (1997) The neuron simulation environment. Neural Comput 9:1179–1209

    Article  PubMed  CAS  Google Scholar 

  • Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol (Lond) 117:500–544

    CAS  Google Scholar 

  • Izhikevich EM, Desai NS (2003) Relating STDP to BCM. Neural Comput 15:1511–1523

    Article  PubMed  Google Scholar 

  • Karbowski J, Ermentrout GB (2002) Synchrony arising from a balanced synaptic plasticity in a network of heterogeneous neural oscillators. Phys Rev E 65:031902

    Article  Google Scholar 

  • Karmarkar UR, Buonomano DV (2002) A model of spike-timing dependent plasticity: one or two coincidence detectors? J Neurophysiol 88:507–513

    PubMed  Google Scholar 

  • Kistler WM, van Hemmen JL (2000) Modeling synaptic plasticity in conjuction with the timing of pre- and postsynaptic action potentials. Neural Comput 12:385–405

    Article  PubMed  CAS  Google Scholar 

  • Levy WB, Steward O (1983) Temporal contiguity requirements for long-term associative potentiation/depression in hippocampus. Neurosci 8:791–797

    Article  CAS  Google Scholar 

  • Magee JC, Johnston DA (1997) A synaptically controlled, associative signal for hebbian plasticity in hippocampal neurons. Science 275:209–213

    Article  PubMed  CAS  Google Scholar 

  • Markram H, Lübke J, Frotscher M, Sakmann B (1997) Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science 275:213–215

    Article  PubMed  CAS  Google Scholar 

  • Montgomery JM, Pavlidis P, Madison DV (2001) Pair recordings reveal all-silent synaptic connections and the postsynaptic expression of long-term potentiation. Neuron 29:691–701

    Article  PubMed  CAS  Google Scholar 

  • Morrison A, Aertsen A and Diesmann M (2007) Spike-timing dependent plasticity in balanced random networks. Neural Comput (in press)

  • Nicoll RA (2003) Expression mechanisms underlying long-term potentiation: a postsynaptic view. Philos Trans R Soc Lond B 358: 721–726

    Article  CAS  Google Scholar 

  • Paré D, Shink E, Gaudreau H, Destexhe A, Lang E (1998) Impact of spontaneous synaptic activity on the resting properties of cat neocortical neurons in vivo. J Neurophysiol 79:1450–1460

    PubMed  Google Scholar 

  • Pfister JP, Gerstner W (2006) Triplets of spikes in a model of spike timing-dependent plasticity. J Neurosci 26:9673–9682

    Article  PubMed  CAS  Google Scholar 

  • Riehle A, Grun S, Diesmann M, Aertsen A (1997) Spike synchronization and rate modulation differentially involved in motor cortical function. Science 278:1950–1953

    Article  PubMed  CAS  Google Scholar 

  • Roche KW, Tingley WG, Huganir RL (1994) Glutamate receptor phosphorylation and synaptic plasticity. Curr Opin Neurobiol 4:383–388

    Article  PubMed  CAS  Google Scholar 

  • van Rossum MC, Bi GQ, Turrigiano GG (2000) Stable Hebbian learning from spike timing-dependent plasticity. J Neurosci 20:2211–2221

    Google Scholar 

  • Rubin J, Lee DD, Sompolinsky H (2001) Equilibrium properties of temporally asymmetric Hebbian plasticity. Phys Rev Lett 86:364–367

    Article  PubMed  CAS  Google Scholar 

  • Rubin JE, Gerkin RC, Bi G-Q, Chow CC (2005) Calcium time course as a signal for spike-timing-dependent plasticity. J Neurophysiol 93:2600–2613

    Article  PubMed  Google Scholar 

  • Rudolph M, Destexhe A (2001) Do neocortical pyramidal neurons display stochastic resonance? J Comput Neurosci 11:19–42

    Article  PubMed  CAS  Google Scholar 

  • Senn W, Markram H, Tsodyks M (2001) An algorithm for modifying neurotransmitter release probability based on pre- and postsynaptic spike timing. Neural Comput 13:35–67

    Article  PubMed  CAS  Google Scholar 

  • Shouval HZ, Kalantzis G (2005) Stochastic properties of synaptic transmission affect the shape of spike time-dependent plasticity curves. J Neurophysiol 93:1069–1073

    Article  PubMed  Google Scholar 

  • Shouval HZ, Bear MF, Cooper LN (2002) A unified model of nmda receptor-dependent bidirectional synaptic plasticity. Proc Nat Acad Sci USA 99:10831–10836

    Article  PubMed  CAS  Google Scholar 

  • Sjöström J, Turrigiano GG, Nelson SB (2001) Rate, timing, and cooperativity jointly determine cortical synaptic plasticity. Neuron 32:1149–1164

    Article  PubMed  Google Scholar 

  • Soderling TR, Derkach VA (2000) Postsynaptic protein phosphorylation and LTP. Trends Neurosci 23:75–80

    Article  PubMed  CAS  Google Scholar 

  • Song S, Abbott LF (2001) Cortical development and remapping through spike timing-dependent plasticity. Neuron 32:339–350

    Article  PubMed  CAS  Google Scholar 

  • Song S, Miller KD, Abbott LF (2000) Competitive Hebbian learning through spike-timing dependent synaptic plasticity. Nat Neurosci 3:919–926

    Article  PubMed  CAS  Google Scholar 

  • Steriade M, Timofeev I, Grenier F (2001) Natural waking and sleep states: a view from inside neocortical neurons. J Neurophysiol 85:1969–1985

    PubMed  CAS  Google Scholar 

  • Vaadia E, Haalman I, Abeles M, Bergman H, Prut Y, Slovin H, Aertsen A (1995) Dynamics of neuronal interactions in monkey cortex in relation to behavioural events. Nature 373:515–518

    Article  PubMed  CAS  Google Scholar 

  • Wang JQ, Arora A, Yang L, Parelkar NK, Zhang G, Liu X, Choe ES, Mao L (2005) Phosphorylation of AMPA receptors: mechanisms and synaptic plasticity. Mol Neurobiol 32:237–249

    Article  PubMed  CAS  Google Scholar 

  • Zohary E, Shadlen MN, Newsome WT (1994) Correlated neuronal discharge rate and its implications for psychophysical performance. Nature 370:140–143

    Article  PubMed  CAS  Google Scholar 

  • Zou Q, Rudolph M, Roy N, Sanchez-Vives M, Contreras D, Destexhe A. Reconstructing synaptic background activity from conductance measurements in vivo. Neurocomputing 65:673–678

Download references

Author information

Authors and Affiliations

  1. Integrative and Computational Neuroscience Unit (UNIC), CNRS, 1 Avenue de la Terrasse, 91198, Gif-sur-Yvette, France

    Quan Zou & Alain Destexhe

Authors
  1. Quan Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alain Destexhe
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alain Destexhe.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zou, Q., Destexhe, A. Kinetic models of spike-timing dependent plasticity and their functional consequences in detecting correlations. Biol Cybern 97, 81–97 (2007). https://doi.org/10.1007/s00422-007-0155-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00422-007-0155-3

Keywords

Search

Navigation