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Long-Term Plasticity, Biophysical Models

Encyclopedia of Computational Neuroscience
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Definition

Connections between neurons are called synapses. Their strength is defined as the voltage amplitude, or slope, of a postsynaptic neuron response to a presynaptic action potential. The synapses can change in strength, i.e., they are plastic, and these changes can operate on different time scales. Long-term plasticity denotes the synaptic changes that last more than 20–30 min (see Fig. 1). This is opposed to short-term plasticity that lasts hundreds of milliseconds.

Fig. 1
figure 1

Cartoon of long-term plasticity. The synaptic strength is defined as the height, or the slope, of the postsynaptic voltage response (postsynaptic potential [PSP]) to a presynaptic spike. If the weight is increased, it is called potentiation, and if it is decreased, it is called depression. Long-term plasticity denotes the changes that last more than 20 min

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References

  • Abarbanel HDI, Huerta R, Rabinovich MI (2002) Dynamical model of long-term synaptic plasticity. Proc Natl Acad Sci USA 59:10137–10143

    Google Scholar 

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

    Article  PubMed  Google Scholar 

  • Abbott LF, Varela JA, Sen K, Nelson SB (1997) Synaptic depression and cortical gain control. Science 275:220–224

    Article  CAS  PubMed  Google Scholar 

  • Ajay SM, Bhalla US (2004) A role for ERKII in synaptic pattern selectivity on the time-scale of minutes. Eur J Neurosci 20(10):2671–2680

    Article  PubMed  Google Scholar 

  • Artola A, Bröcher S, Singer W (1990) Different voltage dependent thresholds for inducing long-term depression and long-term potentiation in slices of rat visual cortex. Nature 347:69–72

    Article  CAS  PubMed  Google Scholar 

  • Badoual M, Zou Q, Davison AP, Rudolph M, Bal T, Fregnac Y, Destexhe A (2006) Biophysical and phenomenological models of multiple spike interactions in spike-timing dependent plasticity. Int J Neural Syst 16(2):79–97

    Article  PubMed  Google Scholar 

  • Barrett AB, Billings GO, Morris RGM, van Rossum MCW (2009) State based model of long-term potentiation and synaptic tagging and capture. PLoS Comp Biol 5(1):e1000259. doi:10.1371/journal.pcbi.1000259

    Article  Google Scholar 

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

    Article  CAS  PubMed  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

    CAS  PubMed  Google Scholar 

  • Bienenstock EL, Cooper LN, Munroe PW (1982) Theory of the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. J Neurosci 2:32–48. Reprinted in Anderson and Rosenfeld, 1990

    CAS  PubMed  Google Scholar 

  • Blitzer RD, Iyengar R, Landau EM (2005) Postsynaptic signaling networks: cellular cogwheels underlying long-term plasticity. Biol Psychiatry 57(2):113–119

    Article  CAS  PubMed  Google Scholar 

  • Brader JM, Senn W, Fusi S (2007) Learning real-world stimuli in a neural network with spike-driven synaptic dynamics. Neural Comput 19:2881–2912

    Article  PubMed  Google Scholar 

  • Bradshaw JM, Kubota Y, Meyer T, Schulman H (2003) An ultrasensitive Ca2+/calmodulin-dependent protein kinase II-protein phosphatase 1 switch facilitates specificity in postsynaptic calcium signaling. Proc Natl Acad Sci USA 100(18):10512–10517

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Cai Y, Gavornik JP, Cooper LN, Yeung LC, Shouval HZ (2007) Effect of stochastic synaptic and dendritic dynamics on synaptic plasticity in visual cortex and hippocampus. J Neurophysiol 97:375–386

    Article  PubMed  Google Scholar 

  • Castellani GC, Quinlan EM, Bersani F, Cooper LN, Shouval HZ (2005) A model of bidirectional synaptic plasticity: from signaling network to channel conductance. Learn Mem 12(4):423–432

    Article  PubMed Central  PubMed  Google Scholar 

  • Clopath C (2009) Synaptic plasticity across different time scales and its functional implications. PhD thesis, EPFL, no 4498. doi:10.5075/epfl-thesis-4498

    Google Scholar 

  • Clopath C (2012) Synaptic consolidation: an approach to long-term learning. Cogn Neurodyn 6(3):251–257

    Google Scholar 

  • Clopath C, Gerstner W (2010) Voltage and spike timing interact in STDP – a unified model. Front Synaptic Neurosci 2:25. doi:10.3389/fn-syn.2010.00025

    PubMed Central  PubMed  Google Scholar 

  • Clopath C, Ziegler L, Vasilaki E, Buesing L, Gerstner W (2008) Tag-trigger-consolidation: a model of early and late long-term-potentiation and depression. PLoS Comput Biol 4(12):e1000248

    Article  PubMed Central  PubMed  Google Scholar 

  • Clopath C, Vasilaki E, Buesing L, Gerstner W (2010) Connectivity reflects coding: a model of voltage-based spike-timing-dependent-plasticity with homeostasis. Nat Neurosci 13:344–352

    Article  CAS  PubMed  Google Scholar 

  • Dudek SM, Bear MF (1992) Homosynaptic long-term depression in area CA1 of hippocampus and effects of N-methyl-d-aspartate receptor blockade. Proc Natl Acad Sci USA 89:4363–4367

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Dudek SM, Bear MF (1993) Bidirectional long-term modification of synaptic effectiveness in the adult and immature hippocampus. J Neurosci 13:2910–2918

    CAS  PubMed  Google Scholar 

  • Egger V, Feldmeyer D, Sakmann B (1999) Coincidence detection and changes of synaptic efficacy in spiny stellate neurons in rat barrel cortex. Nat Neurosci 2:1098–1105

    Article  CAS  PubMed  Google Scholar 

  • Feldman DE (2012) The spike-timing dependence of plasticity. Neuron 75(4):556–571

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Frey U, Morris RGM (1997) Synaptic tagging and long-term potentiation. Nature 385:533–536

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • Froemke RC, Poo M-M, Dan Y (2005) Spike-timing-dependent synaptic plasticity depends on dendritic location. Nature 434:221–225

    Article  CAS  PubMed  Google Scholar 

  • Fusi S, Drew PJ, Abbott LF (2005) Cascade models of synaptically stored memories. Neuron 45:599–611

    Article  CAS  PubMed  Google Scholar 

  • Gamble E, Koch C (1987) The dynamics of free calcium in dendritic spines in response to repetitive synaptic input. Science 236:1311–1315

    Article  CAS  PubMed  Google Scholar 

  • Gerstner W, Kempter R, van Hemmen JL, Wagner H (1996) A neuronal learning rule for sub-millisecond temporal coding. Nature 383(6595):76–78

    Article  CAS  PubMed  Google Scholar 

  • Graupner M (2008) Induction and maintenance of synaptic plasticity. PhD thesis, Université Pierre et Marie Curie Paris V and TU Dresden

    Google Scholar 

  • Graupner M, Brunel N (2007) STDP in a bistable synapse model based on CaMKII and associate signaling pathways. PLoS Comput Biol 3:e221. doi:10.1371/journal.pcbi.0030221

    Article  PubMed Central  PubMed  Google Scholar 

  • Graupner M, Brunel N (2010) Mechanisms of induction and maintenance of spike-timing dependent plasticity in biophysical synapse models. Front Comput Neurosci 4:136

    Article  PubMed Central  PubMed  Google Scholar 

  • Graupner M, Brunel N (2012) Calcium-based plasticity model explains sensitivity of synaptic changes to spike pattern, rate, and dendritic location. Proc Natl Acad Sci USA 10(109):3991–3996

    Article  Google Scholar 

  • Gupta A, Wang Y, Markram H (2000) Organizing principles for a diversity of gabaergic interneurons and synapses in the neocortex. Science 287:273–278

    Article  CAS  PubMed  Google Scholar 

  • Gustafsson B, Wigstrom H, Abraham WC, Huang Y-Y (1987) Long-term potentiation in the hippocampus using depolarizing current pulses as the conditioning stimulus. J Neurosci 7:774–780

    CAS  PubMed  Google Scholar 

  • Gütig R, Aharonov R, Rotter S, Sompolinsky H (2003) Learning input correlations through non-linear temporally asymmetric Hebbian plasticity. J Neurosci 23(9):3697–3714

    PubMed  Google Scholar 

  • Hayer A, Bhalla US (2005) Molecular switches at the synapse emerge from receptor and kinase traffic. PLoS Comput Biol 1(2):e20

    Article  PubMed Central  Google Scholar 

  • Hebb DO (1949) The organization of behavior. Wiley, New York

    Google Scholar 

  • Holmes WR, Levy WB (1990) Insights into associative long-term potentiation from computational models of NMDA receptor-mediated calcium influx and intracellular calcium concentration changes. J Neurophysiol 63:1148–1168

    CAS  PubMed  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 

  • Karmarkar UR, Najarian MT, Buonomano DV (2002) Mechanisms and significance of spike-timing dependent plasticity. Biol Cybern 87:373–382

    Article  PubMed  Google Scholar 

  • Kelso SR, Ganong AH, Brown TH (1986) Hebbian synapses in hippocampus. Proc Natl Acad Sci USA 83:5326–5330

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Kempter R, Gerstner W, van Hemmen JL (1999) Hebbian learning and spiking neurons. Phys Rev E 59:4498–4514

    Article  CAS  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • Kubota Y, Bower JM (2001) Transient versus asymptotic dynamics of CaM kinase II: possible roles of phosphatase. J Comput Neurosci 11(3):263–279

    Article  CAS  PubMed  Google Scholar 

  • Ling DSF, Benardo LS, Serrano PA, Blace N, Kelly MT, Crary JF, Sacktor TC (2002) Protein kinase Mζ is necessary and sufficient for LTP maintenance. Nat Neurosci 5:295–296

    Article  CAS  PubMed  Google Scholar 

  • Lisman J (1985) A mechanism for memory storage insensitive to molecular turnover: a bistable autophosphorylating kinase. Proc Natl Acad Sci USA 82:3055–3057

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Lisman J (1989) A mechanism for Hebb and anti-Hebb processes underlying learning and memory. Proc Natl Acad Sci USA 86:9574–9578

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Lisman JE, Zhabotinsky AM (2001) A model of synaptic memory: a CaMKII/PP1 switch that potentiates transmission by organizing an AMPA receptor anchoring assembly. Neuron 31:191–201

    Article  CAS  PubMed  Google Scholar 

  • Lisman J, Schulman H, Cline H (2002) The molecular basis of CaMKII function in synaptic and behavioural memory. Nat Rev Neurosci 3:175–190

    Article  CAS  PubMed  Google Scholar 

  • Lu J, Li C, Zhao J-P, Poo MM, Zhang X (2007) Spike-timing-dependent plasticity of neocortical excitatory synapses on inhibitory interneurons depends on target cell type. J Neurosci 27:9711–9720

    Article  CAS  PubMed  Google Scholar 

  • Malinow R, Schulman H, Tsien RW (1989) Inhibition of postsynaptic PKC or CaMKII blocks induction but not expression of ltp. Science 245:862–866

    Article  CAS  PubMed  Google Scholar 

  • Markram H, Tsodyks M (1996) Redistribution of synaptic efficacy between neocortical pyramidal neurons. Nature 382:807–810

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • Markram H, Wu Y, Tosdyks M (1998) Differential signaling via the same axon of neocortical pyramidal neurons. Proc Natl Acad Sci USA 95:5323–5328

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Miller KD, MacKay DJC (1994) The role of constraints in Hebbian learning. Neural Comput 6:100–126

    Article  Google Scholar 

  • Miller P, Zhabotinsky AM, Lisman JE, Wang XJ (2005) The stability of s stochastic CaMKII switch: dependence on the number of enzyme molecules and protein turnover. PLoS Biol 3:e107

    Article  PubMed Central  PubMed  Google Scholar 

  • Morrison A, Diesmann M, Gerstner W (2008) Phenomenological models of synaptic plasticity based on spike timing. Biol Cybern 98(6):459–478

    Article  PubMed Central  PubMed  Google Scholar 

  • Nevian T, Sakmann B (2006) Spine Ca2+ signaling in spike-timing-dependent plasticity. J Neurosci 26(43):11001–11013

    Article  CAS  PubMed  Google Scholar 

  • Ngezahayo A, Schachner M, Artola A (2000) Synaptic activation modulates the induction of bidirectional synaptic changes in adult mouse hippocampus. J Neurosci 20:2451–2458

    CAS  PubMed  Google Scholar 

  • O’Connor DH, Wittenberg GM, Wang SS–H (2005) Graded bidirectional synaptic plasticity is composed of switch-like unitary events. Proc Natl Acad Sci USA 102:9679–9684

    Article  PubMed Central  PubMed  Google Scholar 

  • Oja E (1982) A simplified neuron model as a principal component analyzer. J Math Biol 15:267–273

    Article  CAS  PubMed  Google Scholar 

  • Okamoto H, Ichikawa K (2000) Switching characteristics of a model for biochemical-reaction networks describing autophosphorylation versus dephosphorylation of Ca2+/calmodulin-dependent protein kinase ii. Biol Cybern 82:35–47

    Article  CAS  PubMed  Google Scholar 

  • Othmakhov N, Griffith LC, Lisman JE (1997) Postsynaptic inhibitors of calcium/calmodulin-dependent protein kinase type ii block induction but not maintenance of pairing induced long-term potentiation. J Neurosci 17:5357–5365

    Google Scholar 

  • Pawlak V, Wickens JR, Kirkwood A, Kerr JN (2010) Timing is not everything: neuromodulation opens the STDP gate. Front Synaptic Neurosci 2:146

    Article  PubMed Central  PubMed  Google Scholar 

  • Petersen CC, Malenka RC, Nicoll RA, Hopfield JJ (1998) All-or-none potentiation of CA3-CA1 synapses. Proc Natl Acad Sci USA 95:4732–4737

    Article  CAS  PubMed Central  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • Piomelli D (2003) The molecular logic of endocannabinoid signalling. Nat Rev Neurosci 4:873–884

    Article  CAS  PubMed  Google Scholar 

  • Reymann KG, Frey JU (2007) The late maintenance of hippocampal LTP: requirements, phases, synaptic tagging, late associativity and implications. Neuropharmacology 52:24–40

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  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 

  • Sajikumar S, Frey JU (2004a) Late-associativity, synaptic tagging, and the role of dopamine during ltp and ltd. Neurobiol Learn Mem 82:12–25

    Article  CAS  PubMed  Google Scholar 

  • Sajikumar S, Frey JU (2004b) Resetting of synaptic tags is time- and activity dependent in rat hippocampal CA1 in vitro. Neuroscience 129:503–507

    Article  CAS  PubMed  Google Scholar 

  • Saudargiene A, Porr B, Wörgötter F (2003) How the shape of pre- and postsynaptic signals can influence STDP: a biophysical model. Neural Comput 16:595–626

    Article  Google Scholar 

  • Sejnowski TJ, Tesauro G (1989) The Hebb rule for synaptic plasticity: algorithms and implementations. In: Byrne JH, Berry WO (eds) Neural models of plasticity. Academic, pp 94–103

    Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • Shouval HZ (2005) Clusters of interacting receptors can stabilize synaptic efficacies. Proc Natl Acad Sci USA 102(40):14440–14445

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Shouval HZ (2007) Models of synaptic plasticity. Scholarpedia 2(7):1605

    Google Scholar 

  • Shouval HZ (2009) Maintenance of synaptic plasticity. Scholarpedia 4(1):1606

    Google Scholar 

  • Shouval HZ, Kalantzis G (2005) Stochastic properties of synaptic transmission affect the shape of spike time-dependent plasticity curves. J Neurophysiol Scholarpedia 93(2):1069–1073

    Article  PubMed  Google Scholar 

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

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Sjoestroem J, Gerstner W (2010) Spike-timing dependent plasticity. Scholarpedia 5(2):1362

    Google Scholar 

  • Sjöström PJ, Häusser M (2006) A cooperative switch determines the sign of synaptic plasticity in distal dendrites of neocortical pyramidal neurons. Neuron 51(2):227–238

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • Sjöström PJ, Turrigiano GG, Nelson SB (2003) Neocortical ltd via coincident activation of presynaptic NMDA and cannabinoid receptors. Neuron 39:641–654

    Article  PubMed  Google Scholar 

  • Sjöström PJ, Turrigiano GG, Nelson SB (2004) Endocannabinoid-dependent neocortical layer-5 LTD in the absence of postsynaptic spiking. J Neurophysiol 92:3338–3343

    Article  PubMed  Google Scholar 

  • Smolen P (2007) A model of late long-term potentiation simulates aspects of memory maintenance. PLoS One 2:e445

    Article  PubMed Central  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • Turrigiano GG, Nelson SB (2004) Homeostatic plasticity in the developing nervous system. Nat Rev Neurosci 5:97–107

    Article  CAS  PubMed  Google Scholar 

  • Tzounopoulos T, Kim Y, Oertel D, Trussell LO (2004) Cell-specific, spike timing dependent plasticities in the dorsal cochlear nucleus. Nat Neurosci 7:719–725

    Article  CAS  PubMed  Google Scholar 

  • Urakubo H, Honda M, Froemke RC, Kuroda S (2008) Requirement of an allosteric kinetics of NMDA receptors for spike timing-dependent plasticity. J Neurosci 28(13):3310–3323

    Article  CAS  PubMed  Google Scholar 

  • van Rossum MCW, Bi GQ, Turrigiano GG (2000) Stable Hebbian learning from spike timing-dependent plasticity. J Neurosci 20:8812–8821

    PubMed  Google Scholar 

  • Wang HX, Gerkin RC, Nauen DW, Bi GQ (2005) Coactivation and timing-dependent integration of synaptic potentiation and depression. Nat Neurosci 8:187–193

    Article  CAS  PubMed  Google Scholar 

  • Wittenberg GM, Sullivan MR, Tsien JZ (2002) Synaptic reentry reinforcement based network model for long-term memory consolidation. Hippocampus 12(5):637–647

    Article  PubMed  Google Scholar 

  • Zador A, Koch C, Brown TH (1990) Biophysical model of a hebbian synapse. Proc Natl Acad Sci 87:6718–6722

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Zhabotinsky AM (2000) Bistability in the Ca2+/calmodulin-dependent protein kinase-phosphatase system. Biophys J 79(5):2211–2221

    Article  CAS  PubMed Central  PubMed  Google Scholar 

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Acknowledgments

This work has been supported by the Swiss National Science Foundation, grant PA00P3_139703.

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Clopath, C. (2014). Long-Term Plasticity, Biophysical Models. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_351-1

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  1. Latest

    Long-Term Plasticity, Biophysical Models
    Published:
    18 September 2019

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_351-2

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    Long-Term Plasticity, Biophysical Models
    Published:
    21 March 2014

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_351-1