The 2006 study by Shah, Yeung, Cooper, Cai and Shouval proposed that the nonlinear interaction between successive spike pairs in spike-timing-dependent plasticity (STDP) - demonstrated by visual-cortex triplet experiments - arises from two short-term biophysical processes embedded in a calcium-dependent plasticity (CaDP) model: use-dependent presynaptic depression of NMDA-receptor-mediated transmission and use-dependent attenuation of back-propagating action potentials (BPAPs). The fitted parameters were not independently measured; one region of triplet-parameter space resisted explanation without an ad hoc fast presynaptic suppression that conflicts with measured NMDA paired-pulse depression; the model's predicted pre-before-post (pre-post) LTD window lacked experimental support; and the biophysical model had not been experimentally distinguished from phenomenological suppression or triplet rules. The subsequent literature shows that the same group's stochastic-release implementation (Cai et al. 2007) fits the triplet data without the ad hoc mechanism and yields explicit, still-unverified predictions for paired BPAP depression and its recovery in visual cortex, that independent biophysical models (Urakubo et al. 2008; Graupner and Brunel 2012) reproduce triplet data through different mechanisms, and that as late as 2020-2026 authors still state that no experiments have directly explored how short-term plasticity shapes long-term plasticity induction or measured BPAP attenuation in the cortical triplet regime. The surviving open core is precise and experimental: measure the BPAP attenuation parameters at sub-100 ms interspike intervals in the cortical preparation used for triplet induction, identify the mechanism operating in the triplet region where measured presynaptic depression is insufficient, and design experiments that discriminate the competing accounts in untested regions of parameter space and under naturalistic spike trains.

Background

Spike-timing-dependent plasticity (STDP) is the family of long-lasting synaptic changes - long-term potentiation (LTP, strengthening) and long-term depression (LTD, weakening) - whose sign and magnitude depend on the millisecond-scale timing of presynaptic spikes relative to postsynaptic spikes: in cortical and hippocampal preparations, repeated pre-before-post pairings typically induce LTP and post-before-pre pairings induce LTD. Most learning rules therefore express the weight change as a function of the pair timing difference Δt=tpost−tpre\Delta t=t_{\mathrm{post}}-t_{\mathrm{pre}} repeated at a fixed frequency. Experiments showed, however, that this pairwise description fails for more realistic spike patterns. When induction uses spike triplets (two presynaptic spikes with one postsynaptic spike, or one presynaptic spike with two postsynaptic spikes), the contribution of the first spike pair dominates over the second and pair contributions do not add linearly; pair-based rules also cannot reproduce the observed dependence of plasticity on repetition frequency (Sjöström et al. 2001; Froemke and Dan 2002; Wang et al. 2005).

A leading biophysical framework for such rules is calcium-dependent plasticity (CaDP). The N-methyl-D-aspartate (NMDA) receptor - a glutamate-gated channel that is blocked by Mg2+ at rest and passes Ca2+ only when glutamate binding coincides with depolarization - is treated as the coincidence detector, and the time course of postsynaptic Ca2+ determines the sign and magnitude of plasticity through a U-shaped function Ω(Ca)\Omega(\mathrm{Ca}) (no change at low Ca2+, depression at intermediate levels, potentiation at high levels) together with a Ca2+-dependent learning rate η\eta (Shouval et al. 2002). The postsynaptic depolarization during pairing is supplied by the back-propagating action potential (BPAP), a somatic spike that actively propagates into the dendrite; BPAPs attenuate in an activity-dependent way, chiefly through slow recovery of dendritic Na+ channels from inactivation (Colbert et al. 1997). Presynaptically, repeated spikes cause short-term depression (STD), the reversible, use-dependent decline of neurotransmitter release produced by depletion of a finite releasable vesicle pool, which is measurable as paired-pulse depression of the NMDA component of the excitatory postsynaptic potential (EPSP); Philpot et al. (2001) quantified this depression in visual cortex at 10 and 40 Hz and showed it is modified by visual experience.

Shah, Yeung, Cooper, Cai and Shouval (2006) asked whether these two short-term processes, embedded in the CaDP model, could account for the triplet nonlinearities. Presynaptic STD was modeled as depletion of a release-ready resource RR,

dRdt=1−Rτr−P0 R∑iδ(t−ti),\frac{\mathrm{d}R}{\mathrm{d}t}=\frac{1-R}{\tau_r}-P_0\,R\sum_i\delta(t-t_i),

where P0P_0 is the released fraction per spike, τr\tau_r the recovery time constant, and tit_i the presynaptic spike times, with parameters extracted from the NMDA-EPSP depression data of Philpot et al. (2001) (P0=0.304P_0=0.304, τr=141 ms\tau_r=141\ \mathrm{ms}); BPAP attenuation was modeled as an analogous use-dependent postsynaptic resource, with a per-spike reduction and recovery time constant that were fitted to the triplet data rather than measured (roughly a 70% reduction with roughly 30 ms recovery). The extended model improved the match to the visual-cortex triplet maps of Froemke and Dan (2002) but left specific discrepancies and unverified assumptions that the authors themselves flagged. In parallel, phenomenological accounts reproduced much of the same data without explicit biophysics: the suppression model of Froemke and Dan, in which each spike transiently reduces the plasticity efficacy of following spikes of the same neuron, and the triplet rule of Pfister and Gerstner (2006), a learning rule in which the synaptic weight change depends on combinations of three pre- and postsynaptic spikes rather than only on spike pairs. The unresolved target is the experimental and mechanistic completion of this program.

Problem Statement

Determine, by direct experiment together with quantitative modeling, the biophysical mechanisms and parameter values by which successive spikes interact in cortical synaptic plasticity, so that the nonlinear behavior of multi-spike (triplet and larger) induction protocols is explained by identified processes rather than fitted assumptions. The general question was posed by the source work and still stands after the subsequent literature; this statement decomposes it into the following jointly linked parts, which share this single objective:

(1) Measure the short-term, activity-dependent attenuation of dendritic BPAPs, and the paired-pulse depression of presynaptic NMDA-EPSPs, on the sub-100 ms timescale in the visual-cortical preparation in which triplet plasticity is induced (layer 2/3 pyramidal neurons in rat visual-cortex slices), establishing their magnitudes and recovery time constants - to confirm or refute the attenuation parameters that were fitted rather than measured in the deterministic biophysical model and the values predicted by the subsequent stochastic model of the same group, including the predicted difference between visual cortex and hippocampus.

(2) Identify the mechanism, and its parameter regime, that accounts for the region of the triplet-parameter map in which a postsynaptic spike is followed by two presynaptic spikes (the post-pre-pre region of the two-presynaptic-one-postsynaptic triplet map), where presynaptic NMDA-mediated paired-pulse depression of the measured magnitude is insufficient: either an additional, faster and larger presynaptic suppression - which conflicts with existing paired-pulse NMDA data - or another biochemical or stochastic process whose identity and parameters remain to be determined.

(3) Establish experimentally whether the deterministic CaDP prediction of a pre-post LTD window (depression for certain pre-before-post time lags) exists in cortical plasticity, and quantify how stochastic synaptic transmission reshapes this prediction in the triplet context.

(4) Design and perform systematic experiments in the currently untested regions of triplet-parameter space, and under naturalistic spike trains (higher-order spike patterns and other frequencies), that discriminate between the extended CaDP model with short-term dynamics and the competing phenomenological suppression/triplet and alternative biophysical models, thereby identifying the physiological mechanisms actually operating.

Because the measurements called for here cannot be satisfied from the existing literature, the discriminating experiments and their protocols and quantitative predicted outcomes are to be specified precisely enough that each of parts (1)-(4) can be independently confirmed or refuted.

References

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