A unified model of NMDA receptor-dependent bidirectional synaptic plasticity

Abstract

Synapses in the brain are bidirectionally modifiable, but the routes of induction are diverse. In various experimental paradigms, N-methyl-D-aspartate receptor-dependent long-term depression and long-term potentiation have been induced selectively by varying the membrane potential of the postsynaptic neurons during presynaptic stimulation of a constant frequency, the rate of presynaptic stimulation, and the timing of pre-and postsynaptic action potentials. In this paper, we present a mathematical embodiment of bidirectional synaptic plasticity that is able to explain diverse induction protocols with a fixed set of parameters. The key assumptions and consequences of the model can be tested experimentally; further, the model provides the foundation for a unified theory of N-methyl-D-aspartate receptordependent synaptic plasticity.S ynapses throughout the brain are bidirectionally modifiable.This property, postulated in almost every theoretical description of synaptic plasticity, has been most clearly demonstrated at the Schaffer collateral-CA1 synapse in the hippocampus. Here, it was shown that a low-frequency tetanus induces long-term depression (LTD), whereas high-frequency stimulation produces long-term potentiation (LTP) of the stimulated synapses, and that LTD and LTP are inversely related (1-4). Similar results have been obtained at excitatory synapses throughout the brain.A considerable body of evidence indicates that the important variable is actually the amount of integrated postsynaptic N-methyl-D-aspartate (NMDA) receptor (NMDAR) activation during conditioning (1, 2, 4-6). Modest NMDAR activation induces LTD, whereas strong activation produces LTP. Because of their voltage dependence, the contribution of NMDARs to synaptic transmission during conditioning stimulation varies with the level of postsynaptic depolarization. Thus, it is possible to induce LTD or LTP with a constant stimulation frequency by clamping the postsynaptic membrane potential at different values (approximately Ϫ50 mV for LTD and Ϫ20 mV for LTP).Recently, it has been demonstrated that synaptic modification also can depend on the precise timing of pre-and postsynaptic action potentials (7-11). If a presynaptic action potential occurs in a window of several tens of milliseconds before a back-propagating postsynaptic action potential, LTP is induced. In contrast, if a presynaptic action potential occurs after the postsynaptic spike, LTD is induced.Ideally, one would like to develop a unified description of bidirectional synaptic plasticity that can account for all routes of induction. One approach is to look beyond the various induction protocols to the critical role of calcium influx through NMDARs. One attractive idea is that modest increases in postsynaptic calcium trigger LTD, whereas large increases trigger . This hypothesis is consistent with the classical rate-based induction protocols if it is assumed that high-frequency stimulation triggers a larger rise in postsynaptic calcium than does low-frequency stimulation. Indeed, recent...

Time scales of memory, learning, and plasticity

“…Experiments show that the temporal order is only important in a small regime of presynaptic activation (Sjöström et al 2001) and, furthermore, that synaptic modifications seem to be independent of the spiking of the postsynaptic cell (Golding et al 2002). Thus, alternative models have been developed, for instance, calcium-based plasticity (Lisman 1989;Shouval et al 2002;Yeung et al 2004;Graupner and Brunel 2012).…”

Calcium control of triphasic hippocampal STDP

“…Firstly, we aim to ascertain whether the Calcium control hypothesis -which has been demonstrated to successfully reproduce earlier STDP data obtained in culture (Figure 1a), as well as that induced by other activity patterns -can be revised to account for this joint dependency [18,[41][42][43][44][45][46][47][48]. The experimental data we aim to replicate can be characterised by considering the effects of two different stimulation protocols -pairing 100 single preand post-synaptic spikes (hereafter referred to as 'spike pairing') at low frequencies (0.1-5Hz), which generates a depression-only learning rule ( Figure 1b); or pairing a single pre-synaptic spike with two post-synaptic spikes (hereafter referred to as 'triplet pairing'), which generates a triphasic bidirectional learning rule after 100 pairings at a frequency of 5Hz (Figure 1c), an unsaturated potentiation-only rule after 30 pairings at 5Hz (Figure 1d), or mild depression after 100 pairings at a frequency of 0.5Hz (data not shown).…”

“…The temporal extent of spike pair interactions at low frequencies is primarily determined by the slow time constant of the bAP, which dictates the duration of residual depolarisation and therefore partial relief of NMDA blockade in the spine following a post-synaptic action potential; and that of the NMDA receptor, which dictates the duration of glutamate binding following pre-synaptic input [18]. In the simulations described above, the slow time constant of the NMDA receptor (τ NMDA,s =152ms) is much larger than that of the bAP (τ bAP,s =25ms), and hence pre-post interactions extend over a larger temporal window than post-pre interactions.…”

“…The kinetics of kinase and phosphotase activation also differ significantly, as LTP can be rapidly induced by appropriate patterns of activity while LTD requires prolonged stimulation [15,17,29]. Computational modelling of synaptic plasticity has demonstrated that the dynamics of Calcium influx through the NMDA receptor (NMDAr) is sufficient to account for empirical data obtained using multiple stimulation protocols, integrating an array of experimental results within a single theoretical framework [18,[41][42][43][44][45][46][47][48]. However, these models as yet fail to assimilate or replicate various aspects of more recently obtained synaptic plasticity data such as those described above.…”

“…In spite of the heterogeneity of plasticity mechanisms observed throughout the brain, changes in the strength of excitatory synapses afferent on CA1 pyramidal neurons in the hippocampus represent the best studied form in the mammalian cortex [9][10][11][12]. At these synapses, Calcium influx into dendritic spines represents the critical signal for synaptic plasticity induction [13][14][15][16][17][18][19][20]. Large, transient elevations in intracellular [Ca 2+ ] generate LTP via the preferential activation of kinase pathways while modest, sustained elevations in intracellular [Ca 2+ ] generate LTD via the preferential activation of phosphotase pathways [21][22][23][24][25].…”