The calcium-dependent plasticity model of Cai, Gavornik, Cooper, Yeung and Shouval (Journal of Neurophysiology 97:375-386, 2007) accounts for multi-spike (triplet and burst) plasticity data from rat visual-cortex layer-4-to-layer-2/3 synapses and from hippocampal cultures by combining presynaptic stochastic vesicle release, short-term synaptic depression and facilitation, and attenuation of back-propagating action potentials (BPAPs), and it attributes the qualitative differences between the two regions to these short-term dynamics rather than to different learning rules. The source paper leaves a linked set of issues unresolved: postsynaptic (NMDA-receptor) stochasticity was not modeled; the uniqueness and robustness of the parameter fit are uncharacterized; the predicted region-specific paired-pulse BPAP depression (about 50% amplitude reduction with roughly 55 ms recovery in visual cortex versus about 30% with roughly 35 ms in hippocampus) lacks direct experimental verification; the model does not distinguish NMDA-receptor-dependent from mGluR-dependent long-term depression pathways; it was not tested on quadruplet or in-vivo-like naturalistic spike trains; and alternative frameworks (spike-suppression and triplet-based rules) account for part of the same data, so the necessity of the mechanistic ingredients is unknown. The problem remains open.

Background

Synaptic plasticity, the activity-dependent change in the strength of connections between neurons, is the leading cellular candidate for the substrate of learning and memory. Its two long-lasting forms are long-term potentiation (LTP, strengthening) and long-term depression (LTD, weakening). A well-studied induction paradigm is spike-timing-dependent plasticity (STDP): repeatedly pairing a presynaptic spike slightly before a postsynaptic action potential tends to potentiate a synapse, while the reverse order tends to weaken it. In the prevailing biophysical picture, presynaptic glutamate release together with postsynaptic depolarization relieves the magnesium block of NMDA-type (N-methyl-D-aspartate) glutamate receptors, and the resulting calcium influx into the dendritic spine drives potentiation or depression according to its amplitude and time course. Calcium-dependent plasticity models make this mapping explicit; in the Shouval-Bear-Cooper framework, postsynaptic calcium concentration is transformed into a synaptic weight change by a fixed nonlinear function whose amplitude thresholds separate depression from potentiation.

Real spike trains contain many spikes, and multi-spike induction protocols - triplets (two presynaptic spikes with one postsynaptic spike, or the converse, scanned over the two inter-spike intervals t1 and t2), quadruplets, and bursts - produce plasticity patterns that cannot be reproduced by linearly superposing spike-pair effects. In layer 2/3 pyramidal neurons of rat visual cortex (Froemke and Dan, 2002), triplet protocols show that the first spike pair in a sequence dominates the outcome and that a depression region separates two potentiation regions, whereas in hippocampal dissociated cultures (Wang et al., 2005) triplets produce almost exclusively potentiation. Deterministic calcium-based models either failed in specific regions of the visual-cortex triplet map or required an unphysiologically fast synaptic-depression component with no experimental support (Shah et al., 2006).

Cai, Gavornik, Cooper, Yeung and Shouval (2007) showed that both datasets can be reproduced within one calcium-dependent framework once presynaptic release is modeled as the stochastic, all-or-none release of a small pool of docked vesicles (two releasable vesicles per release site with short-term depression, plus short-term facilitation in hippocampus; several parameter values were taken from paired recordings in other cortical preparations, notably the barrel-cortex slice work of Feldmeyer and colleagues), combined with activity-dependent attenuation of back-propagating action potentials. A BPAP is the action-potential waveform that actively propagates from the soma back into the dendrite and supplies the depolarization that opens NMDA receptors at the synapse; in the model, the second BPAP in a pair has its amplitude reduced by roughly 50% (with recovery over roughly 55 ms) in visual cortex, versus roughly 30% (roughly 35 ms) in hippocampus. The stochastic implementation fit the visual-cortex and hippocampal triplet maps better than a deterministic implementation that replaced stochastic release by its mean effect, was more robust to changes in release probability, and reproduced the known frequency dependence of cortical plasticity (Sjostrom et al., 2001) over a broader range. The central mechanistic claim is that the qualitative differences between visual-cortex and hippocampal multi-spike plasticity reflect region-specific short-term synaptic and dendritic dynamics acting on a common learning rule, rather than fundamentally different plasticity mechanisms. Subsequent modelling has partially extended this account: a stochastic hippocampal model that adds postsynaptic receptor stochasticity reproduces several published ex vivo plasticity experiments and shows that in-vivo-like spike-timing jitter and irregular spike trains reshape the predicted plasticity (Rodrigues et al., 2023), and short-term and long-term plasticity have been combined in a model fitted to cortical data (Deperrois and Graupner, 2020).

Two pharmacologically distinct forms of LTD are known in the systems in question: one dependent on NMDA receptors and one dependent on metabotropic glutamate receptors (mGluRs, G-protein-coupled glutamate receptors that signal through intracellular biochemical cascades). The stochastic model's depression components capture only short-term dynamics and do not represent these distinct molecular pathways.

The paper itself leaves a connected set of issues unresolved, and these define the problem this task addresses. They jointly bear on one scientific objective - establishing whether the stochastic short-term-dynamics account of multi-spike plasticity is correct, experimentally verified, parameter-identifiable, and uniquely required - because each issue fixes a different load-bearing element of the same account: the postsynaptic noise model, the provenance and identifiability of the parameters, the experimental status of the dendritic mechanism, the biochemical interpretation of the depression components, the range of protocols over which the account holds, and its necessity relative to simpler alternatives.

Problem Statement

The problem, as left open by Cai et al. (2007) and still standing after the intervening literature, is to establish whether the stochastic short-term synaptic and dendritic dynamics account of multi-spike plasticity in visual cortex and hippocampus is correct, experimentally verified, parameter-identifiable, and uniquely required. The six linked components below are facets of this objective, each fixing a different load-bearing element of the same account:

  1. Postsynaptic stochasticity: incorporate stochastic NMDA-receptor binding and channel opening (the original model treats postsynaptic receptor binding deterministically, assuming a single vesicle release saturates the postsynaptic binding sites) and determine how postsynaptic stochasticity changes the multi-spike plasticity maps, especially the visual-cortex maps and the regions where experimental data are sparse.

  2. Parameter identifiability and robustness: characterize how the model's predictions depend on the parameter choices (number of releasable vesicles, release probability, depression and facilitation time constants, BPAP attenuation magnitude and recovery time constant), determine whether the existing sparse triplet data admit many equally good parameter sets, and establish whether the fits transfer across synapses, preparations, and experimental conditions.

  3. Experimental verification of the dendritic prediction: specify and justify a paired-pulse measurement of BPAP amplitude depression in visual-cortex layer 2/3 pyramidal dendrites and in hippocampal dendrites, and state the measured outcomes that would confirm or refute the prediction that attenuation in visual cortex (about 50% with roughly 55 ms recovery) is substantially stronger than in hippocampus (about 30% with roughly 35 ms).

  4. LTD-pathway resolution: determine whether the observed differences between visual-cortex and hippocampal multi-spike plasticity are fully explained by short-term synaptic and dendritic dynamics, or whether distinct molecular pathways for depression (NMDA-receptor-dependent versus mGluR-dependent LTD, with their associated biochemical cascades) contribute to the differences and must be modeled separately.

  5. Generalization in protocol space: test the account on more complex and naturalistic spike patterns - quadruplets, bursts, and in-vivo-like irregular spike trains - and on forms of plasticity beyond the triplet and burst protocols used in the original fit, in both regions.

  6. Uniqueness versus simpler alternatives: establish whether the model's mechanistic ingredients (stochastic vesicle release, short-term depression and facilitation, and BPAP attenuation) are uniquely required to reproduce the multi-spike plasticity data of visual cortex and hippocampus, or whether simpler frameworks - spike-suppression rules, triplet-based phenomenological rules, voltage-based or calcium-threshold rules - account for the same data, and which mechanistic claims the data actually support.

The components are stated as a set because the source presents them as one connected set of unresolved issues about the same account.

References

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