Abstract
Multiple stimulation protocols using firing rate and spike-timing correlations have been found to be effective in changing synaptic efficacy by inducing long-term potentiation or depression. In many of those protocols, increases in postsynaptic calcium concentration have been shown to play a crucial role. To which extent the plasticity outcome can be explained by the dynamics of the postsynaptic calcium alone remains unclear. Here, we discuss a minimal calcium-based model of a synapse in which potentiation and depression mechanisms are triggered by calcium. We illustrate that this model gives rise to a large diversity of spike timing-dependent plasticity curves, most of which have been observed experimentally in different systems. It accounts quantitatively for plasticity outcomes evoked by protocols involving patterns with variable spike timing and firing rate in hippocampus and neocortex. Furthermore, we use the model to predict memory decay times and plasticity in the presence of uncorrelated Poisson firing. The calcium model provides a mechanistic understanding of how various stimulation protocols provoke specific synaptic changes through the dynamics of calcium concentration and thresholds implementing in simplified fashion protein signaling cascades, leading to long-term potentiation and long-term depression.
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References
Abarbanel HDI, Gibb L, Huerta R, Rabinovich M (2003) Biophysical model of synaptic plasticity dynamics. Biol Cybern 89(3):214–26
Aihara T, Abiru Y, Yamazaki Y, Watanabe H, Fukushima Y, Tsukada M (2007) The relation between spike-timing dependent plasticity and Ca2+ dynamics in the hippocampal CA1 network. Neuroscience 145(1):80–87
Artola A, Singer W (1987) Long-term potentiation and NMDA receptors in rat visual cortex. Nature 330(6149):649–652
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(2):79–97
Bagal AA, Kao JPY, Tang C-M, Thompson SM (2005) Long-term potentiation of exogenous glutamate responses at single dendritic spines. Proc Natl Acad Sci USA 102(40):14434–14439
Bear MF, Press WA, Connors BW (1992) Long-term potentiation in slices of kitten visual cortex and the effects of NMDA receptor blockade. J Neurophysiol 67(4):841–851
Bell C, Han V, Sugawara Y, Grant K (1997) Synaptic plasticity in a cerebellum-like structure depends on temporal order. Nature 387(6630):278–81
Bender VA, Bender KJ, Brasier DJ, Feldman DE (2006) Two coincidence detectors for spike timing-dependent plasticity in somatosensory cortex. J Neurosci 26(16):4166–4177
Bi G, Poo M (1998) Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. J Neurosci 18(24):10464–10472
Bi GQ, Wang HX (2002) Temporal asymmetry in spike timing-dependent synaptic plasticity. Physiol Behav 77(4–5):551–555
Bienenstock EL, Cooper LN, Munro PW (1982) Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. J Neurosci 2(1):32–48
Bliss T, Collingridge G (1993) A synaptic model of memory: long-term potentiation in the hippocampus. Nature 361(6407):31–39
Bliss T, Lømo T (1973) Long-lasting potentiation of synaptic transmission in the dentate area of the anaesthetized rabbit following stimulation of the perforant path. J Physiol 232(2):331–356
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(1):375–386
Campanac E, Debanne D (2008) Spike timing-dependent plasticity: a learning rule for dendritic integration in rat ca1 pyramidal neurons. J Physiol 586(3):779–793
Castro-Alamancos MA, Donoghue JP, Connors BW (1995) Different forms of synaptic plasticity in somatosensory and motor areas of the neocortex. J Neurosci 15(7 Pt 2):5324–5333
Clopath C, Büsing L, Vasilaki E, Gerstner W (2010) Connectivity reflects coding: a model of voltage-based STDP with homeostasis. Nat Neurosci 13(3):344–352
Collingridge GL, Kehl SJ, McLennan H (1983) Excitatory amino acids in synaptic transmission in the schaffer collateral-commissural pathway of the rat hippocampus. J Physiol 334:33–46
Cutsuridis V (2011) GABA inhibition modulates NMDA-R mediated spike timing dependent plasticity (STDP) in a biophysical model. Neural Netw 24(1):29–42
Cutsuridis V (2012) Bursts shape the NMDA-R mediated spike timing dependent plasticity curve: role of burst interspike interval and GABAergic inhibition. Cogn Neurody 6(5):421–441
Cutsuridis V (2013) Interaction of inhibition and triplets of excitatory spikes modulates the NMDA-R-mediated synaptic plasticity in a computational model of spike timing-dependent plasticity. Hippocampus 23(1):75–86
Cutsuridis V, Hasselmo M (2012) GABAergic contributions to gating, timing, and phase precession of hippocampal neuronal activity during theta oscillations. Hippocampus 22(7):1597–1621
Delgado JY, Gómez-González JF, Desai NS (2010) Pyramidal neuron conductance state gates spike-timing-dependent plasticity. J Neurosci 30(47):15713–15725
Dudek SM, Bear MF (1993) Bidirectional long-term modification of synaptic effectiveness in the adult and immature hippocampus. J Neurosci 13(7):2910–2918
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(12):1098–1105
Feldman DE (2000) Timing-based LTP and LTD at vertical inputs to layer II/III pyramidal cells in rat barrel cortex. Neuron 27(1):45–56
Froemke RC, Dan Y (2002) Spike-timing-dependent synaptic modification induced by natural spike trains. Nature 416(6879):433–438
Froemke R, Poo MM, Dan Y (2005) Spike-timing-dependent synaptic plasticity depends on dendritic location. Nature 434(7030):221–225
Froemke RC, Tsay IA, Raad M, Long JD, Dan Y (2006) Contribution of individual spikes in burst-induced long-term synaptic modification. J Neurophysiol 95(3):1620–1629
Gerkin RC, Bi G-Q, Rubin JE (2010) Hippocampal microcircuits: a computational modeler’s resource book, vol 5. Springer series in computational neuroscience. Springer, New York
Graupner M, Brunel N (2007) STDP in a bistable synapse model based on CaMKII and associated signaling pathways. PLoS Comput Biol 3(11):2299–2323
Graupner M, Brunel N (2010) Mechanisms of induction and maintenance of spike-timing dependent plasticity in biophysical synapse models. Front Comput Neurosci 4
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 109(10):3991–3996
Gustafsson B, Wigström H, Abraham WC, Huang YY (1987) Long-term potentiation in the hippocampus using depolarizing current pulses as the conditioning stimulus to single volley synaptic potentials. J Neurosci 7(3):774–780
Hahm JO, Langdon RB, Sur M (1991) Disruption of retinogeniculate afferent segregation by antagonists to NMDA receptors. Nature 351(6327):568–570
Harnett MT, Makara JK, Spruston N, Kath WL, Magee JC (2012) Synaptic amplification by dendritic spines enhances input cooperativity. Nature 491(7425):599–602
He K, Huertas M, Hong SZ, Tie X, Hell JW, Shouval H, Kirkwood A (2015) Distinct eligibility traces for LTP and LTD in cortical synapses. Neuron 88:528–538
Hebb D (1949) The organization of behavior: a neurophsychological theory. Wiley, New York
Higgins D, Graupner M, Brunel N (2014) Memory maintenance in synapses with calcium-based plasticity in the presence of background activity. PLoS Comput Biol 10(10):e1003834
Ismailov I, Kalikulov D, Inoue T, Friedlander MJ (2004) The kinetic profile of intracellular calcium predicts long-term potentiation and long-term depression. J Neurosci 24(44):9847–9861
Jaffe DB, Johnston D, Lasser-Ross N, Lisman JE, Miyakawa H, Ross WN (1992) The spread of Na+ spikes determines the pattern of dendritic Ca2+ entry into hippocampal neurons. Nature 357(6375):244–246
Jahr C, Stevens C (1990) A quantitative description of NMDA receptor-channel kinetic behavior. J Neurosci 10(6):1830–1837
Jia H, Varga Z, Sakmann B, Konnerth A (2014) Linear integration of spine Ca2+ signals in layer 4 cortical neurons in vivo. Proc Natl Acad Sci USA 111:9277–9282
Karmarkar UR, Buonomano DV (2002) A model of spike-timing dependent plasticity: one or two coincidence detectors? J Neurophysiol 88(1):507–513
Karmarkar UR, Najarian MT, Buonomano DV (2002) Mechanisms and significance of spike-timing dependent plasticity. Biol Cybern 87(5–6):373–382
Kato HK, Watabe AM, Manabe T (2009) Non-Hebbian synaptic plasticity induced by repetitive postsynaptic action potentials. J Neurosci 29(36):11153–11160
Koester HJ, Sakmann B (1998) Calcium dynamics in single spines during coincident pre- and postsynaptic activity depend on relative timing of back-propagating action potentials and subthreshold excitatory postsynaptic potentials. Proc Natl Acad Sci USA 95(16):9596–9601
Kovalchuk Y, Eilers J, Lisman J, Konnerth A (2000) NMDA receptor-mediated subthreshold Ca(2+) signals in spines of hippocampal neurons. J Neurosci 20(5):1791–1799
Kumar A, Mehta MR (2011) Frequency-dependent changes in NMDAR-dependent synaptic plasticity. Front Comput Neurosci 5:38
Letzkus JJ, Kampa BM, Stuart GJ (2006) Learning rules for spike timing-dependent plasticity depend on dendritic synapse location. J Neurosci 26(41):10420–10429
Levy WB, Steward O (1983) Temporal contiguity requirements for long-term associative potentiation/depression in the hippocampus. Neuroscience 8(4):791–797
Lynch G, Larson J, Kelso S, Barrionuevo G, Schottler F (1983) Intracellular injections of EGTA block induction of hippocampal long-term potentiation. Nature 305(5936):719–721
Magee J, Johnston D (1997) A synaptically controlled, associative signal for Hebbian plasticity in hippocampal neurons. Science 275(5297):209–213
Majewska A, Brown E, Ross J, Yuste R (2000) Mechanisms of calcium decay kinetics in hippocampal spines: role of spine calcium pumps and calcium diffusion through the spine neck in biochemical compartmentalization. J Neurosci 20(5):1722–1734
Malenka RC, Kauer JA, Zucker RS, Nicoll RA (1988) Postsynaptic calcium is sufficient for potentiation of hippocampal synaptic transmission. Science 242(4875):81–84
Markram H, J. Lübke, Frotscher M, Sakmann B (1997) Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science 275(5297):213–215
Mishra RK, Kim S, Guzman SJ, Jonas P (2016) Symmetric spike timing-dependent plasticity at CA3–CA3 synapses optimizes storage and recall in autoassociative networks. Nat Commun 7:11552
Mizuno T, Kanazawa I, Sakurai M (2001) Differential induction of LTP and LTD is not determined solely by instantaneous calcium concentration: an essential involvement of a temporal factor. Eur J Neurosci 14(4):701–708
Mooney R, Madison DV, Shatz CJ (1993) Enhancement of transmission at the developing retinogeniculate synapse. Neuron 10(5):815–825
Morris RG, Anderson E, Lynch GS, Baudry M (1986) Selective impairment of learning and blockade of long-term potentiation by an N-methyl-D-aspartate receptor antagonist, AP5. Nature 319(6056):774–776
Müllner FE, Wierenga CJ, Bonhoeffer T (2015) Precision of inhibition: dendritic inhibition by individual GABAergic synapses on hippocampal pyramidal cells is confined in space and time. Neuron 87(3):576–589
Nabavi S, Kessels HW, Alfonso S, Aow J, Fox R, Malinow R (2013) Metabotropic NMDA receptor function is required for NMDA receptor-dependent long-term depression. Proc Natl Acad Sci USA 110(10):4027–4032
Neveu D, Zucker RS (1996) Long-lasting potentiation and depression without presynaptic activity. J Neurophysiol 75(5):2157–2160
Nevian T, Sakmann B (2004) Single spine Ca2+ signals evoked by coincident EPSPs and backpropagating action potentials in spiny stellate cells of layer 4 in the juvenile rat somatosensory barrel cortex. J Neurosci 24(7):1689–1699
Nevian T, Sakmann B (2006) Spine Ca2+ signaling in spike-timing-dependent plasticity. J Neurosci 26(43):11001–11013
Nishiyama M, Hong K, Mikoshiba K, Poo MM, Kato K (2000) Calcium stores regulate the polarity and input specificity of synaptic modification. Nature 408(6812):584–588
Nowak L, Bregestovski P, Ascher P, Herbet A, Prochiantz A (1984) Magnesium gates glutamate-activated channels in mouse central neurones. Nature 307(5950):462–465
O’Connor DH, Wittenberg GM, Wang SS-H (2005) Dissection of bidirectional synaptic plasticity into saturable unidirectional processes. J Neurophysiol 94(2):1565–1573
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(27):9679–9684
Paille V, Fino E, Du K, Morera-Herreras T, Perez S, Kotaleski JH, Venance L (2013) GABAergic circuits control spike-timing-dependent plasticity. J Neurosci 33(22):9353–9363
Pawlak V, Kerr JND (2008) Dopamine receptor activation is required for corticostriatal spike-timing-dependent plasticity. J Neurosci 28(10):2435–2446
Petersen C, Malenka R, Nicoll R, Hopfield J (1998) All-or-none potentiation at CA3-CA1 synapses. Proc Natl Acad Sci USA 95(8):4732–4737
Pfister J-P, Gerstner W (2006) Triplets of spikes in a model of spike timing-dependent plasticity. J Neurosci 26(38):9673–9682
Risken H (1996) The Fokker-Planck equation. Springer.
Rubin JE, Gerkin RC, Bi G-Q, Chow CC (2005) Calcium time course as a signal for spike-timing-dependent plasticity. J Neurophysiol 93(5):2600–2613
Rudolph M, Pelletier JG, Paré D, Destexhe A (2005) Characterization of synaptic conductances and integrative properties during electrically induced EEG-activated states in neocortical neurons in vivo. J Neurophysiol 94(4):2805–2821
Sabatini B, Svoboda K (2000) Analysis of calcium channels in single spines using optical fluctuation analysis. Nature 408(6812):589–593
Sabatini BL, Oertner TG, Svoboda K (2002) The life cycle of Ca(2+) ions in dendritic spines. Neuron 33(3):439–452
Schiller J, Schiller Y, Clapham DE (1998) NMDA receptors amplify calcium influx into dendritic spines during associative pre- and postsynaptic activation. Nat Neurosci 1(2):114–118
Seol GH, Ziburkus J, Huang S, Song L, Kim IT, Takamiya K, Huganir RL, Lee H-K, Kirkwood A (2007) Neuromodulators control the polarity of spike-timing-dependent synaptic plasticity. Neuron 55(6):919–929
Shouval HZ, Kalantzis G (2005) Stochastic properties of synaptic transmission affect the shape of spike time-dependent plasticity curves. J Neurophysiol 93(2):1069–1073
Shouval HZ, Bear MF, Cooper LN (2002) A unified model of NMDA receptor-dependent bidirectional synaptic plasticity. Proc Natl Acad Sci USA 99(16):10831–10836
Shouval HZ, Wang SS-H, Wittenberg GM (2010) Spike timing dependent plasticity: a consequence of more fundamental learning rules. Front Comput Neurosci 4(19)
Silver IA, Erecińska M (1990) Intracellular and extracellular changes of [Ca2+] in hypoxia and ischemia in rat brain in vivo. J Gen Physiol 95(5):837–866
Sjöström P, Turrigiano G, Nelson S (2001) Rate, timing, and cooperativity jointly determine cortical synaptic plasticity. Neuron 32(6):1149–1164
Sjöström PJ, Turrigiano GG, Nelson SB (2003) Neocortical LTD via coincident activation of presynaptic NMDA and cannabinoid receptors. Neuron 39(4):641–654
Tigaret CM, Olivo V, Sadowski JHLP, Ashby MC, Mellor JR (2016) Coordinated activation of distinct Ca(2+) sources and metabotropic glutamate receptors encodes Hebbian synaptic plasticity. Nat Commun 7:10289
Tsukada M, Aihara T, Kobayashi Y, Shimazaki H (2005) Spatial analysis of spike-timing-dependent LTP and LTD in the CA1 area of hippocampal slices using optical imaging. Hippocampus 15(1):104–109
Wang H-X, Gerkin RC, Nauen DW, Bi G-Q (2005) Coactivation and timing-dependent integration of synaptic potentiation and depression. Nat Neurosci 8(2):187–193
Wang SS, Denk W, Häusser M (2000) Coincidence detection in single dendritic spines mediated by calcium release. Nat Neurosci 3(12):1266–1273
Wittenberg GM, Wang SS-H (2006) Malleability of spike-timing-dependent plasticity at the CA3-CA1 synapse. J Neurosci 26(24):6610–6617
Yang S, Tang Y, Zucker R (1999) Selective induction of LTP and LTD by postsynaptic [Ca2+]i elevation. J Neurophysiol 81(2):781–787
Yuste R, Denk W (1995) Dendritic spines as basic functional units of neuronal integration. Nature 375(6533):682–684
Yuste R, Majewska A, Cash SS, Denk W (1999) Mechanisms of calcium influx into hippocampal spines: heterogeneity among spines, coincidence detection by NMDA receptors, and optical quantal analysis. J Neurosci 19(6):1976–1987
Zhabotinsky AM (2000) Bistability in the Ca(2+)/calmodulin-dependent protein kinase-phosphatase system. Biophys J 79(5):2211–2221
Zhang J-C, Lau P-M, Bi G-Q (2009) Gain in sensitivity and loss in temporal contrast of STDP by dopaminergic modulation at hippocampal synapses. Proc Natl Acad Sci USA 106(31):13028–13033
Zhou Q, Tao HW, Ming Poo M (2003) Reversal and stabilization of synaptic modifications in a developing visual system. Science 300(5627):1953–1957
Zucker RS (1999) Calcium- and activity-dependent synaptic plasticity. Curr Opin Neurobiol 9(3):305–313
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Graupner, M., Brunel, N. (2018). Modeling Synaptic Plasticity in Hippocampus: A Calcium-Based Approach. In: Cutsuridis, V., Graham, B., Cobb, S., Vida, I. (eds) Hippocampal Microcircuits. Springer Series in Computational Neuroscience. Springer, Cham. https://doi.org/10.1007/978-3-319-99103-0_17
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