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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 receptor-dependent synaptic plasticity.

SUBMITTER: Shouval HZ

PROVIDER: S-EPMC125058 | biostudies-literature | 2002 Aug

REPOSITORIES: biostudies-literature

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A unified model of NMDA receptor-dependent bidirectional synaptic plasticity.

Shouval Harel Z HZ Bear Mark F MF Cooper Leon N LN

Proceedings of the National Academy of Sciences of the United States of America 20020722 16

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 mathematic ...[more]

PMID: 12136127

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Project description:Neuronal activity regulates brain development and synaptic plasticity through N-methyl-D-aspartate receptors (NMDARs) and calcium-dependent signaling pathways. Intracellular sodium ([Na(+)](i)) also exerts a regulatory influence on NMDAR channel activity, and [Na(+)](i) may, therefore, function as a signaling molecule. In an attempt to mimic the influence of neuronal activity on synaptic plasticity, we used brevetoxin-2 (PbTx-2), a voltage-gated sodium channel (VGSC) gating modifier, to manipulate [Na(+)](i) in cerebrocortical neurons. The acute application of PbTx-2 produced concentration-dependent increments in both intracellular [Na(+)] and [Ca(2+)]. Pharmacological evaluation showed that PbTx-2-induced Ca(2+) influx primarily involved VGSC activation and NMDAR-mediated entry. Additionally, PbTx-2 robustly potentiated NMDA-induced Ca(2+) influx. PbTx-2-exposed neurons showed enhanced neurite outgrowth, increased dendritic arbor complexity, and increased dendritic filopodia density. The appearance of spontaneous calcium oscillations, reflecting synchronous neuronal activity, was accelerated by PbTx-2 treatment. Parallel to this response, PbTx-2 increased cerebrocortical neuron synaptic density. PbTx-2 stimulation of neurite outgrowth, dendritic arborization, and synaptogenesis all exhibited bidirectional concentration-response profiles. This profile paralleled that of NMDA, which also produced bidirectional concentration-response profiles for neurite outgrowth and synaptogenesis. These data are consistent with the hypothesis that PbTx-2-enhanced neuronal plasticity involves NMDAR-dependent signaling. Our results demonstrate that PbTx-2 mimics activity-dependent neuronal structural plasticity in cerebrocortical neurons through an increase in [Na(+)](i), up-regulation of NMDAR function, and engagement of downstream Ca(2+)-dependent signaling pathways. These data suggest that VGSC gating modifiers may represent a pharmacologic strategy to regulate neuronal plasticity through NMDAR-dependent mechanisms.

Project description:We show that a 2-step phospho/dephosphorylation cycle for the alpha-amino-3-hydroxy-5-methyl-4-isoxazole proprionic acid receptor (AMPAR), as used in in vivo learning experiments to assess long-term potentiation (LTP) induction and establishment, exhibits bistability for a wide range of parameters, consistent with values derived from biological literature. The AMPAR model we propose, hence, is a candidate for memory storage and switching behavior at a molecular-microscopic level. Furthermore, the stochastic formulation of the deterministic model leads to a mesoscopic interpretation by considering the effect of enzymatic fluctuations on the Michelis-Menten average dynamics. Under suitable hypotheses, this leads to a stochastic dynamical system with multiplicative noise whose probability density evolves according to a Fokker-Planck equation in the Stratonovich sense. In this approach, the probability density associated with each AMPAR phosphorylation state allows one to compute the probability of any concentration value, whereas the Michaelis-Menten equations consider the average concentration dynamics. We show that bistable dynamics are robust for multiplicative stochastic perturbations and that the presence of both noise and bistability simulates LTP and long-term depression (LTD) behavior. Interestingly, the LTP part of this model has been experimentally verified as a result of in vivo, one-trial inhibitory avoidance learning protocol in rats, that produced the same changes in hippocampal AMPARs phosphorylation state as observed with in vitro induction of LTP with high-frequency stimulation (HFS). A consequence of this model is the possibility of characterizing a molecular switch with a defined biochemical set of reactions showing bistability and bidirectionality. Thus, this 3-enzymes-based biophysical model can predict LTP as well as LTD and their transition rates. The theoretical results can be, in principle, validated by in vitro and in vivo experiments, such as fluorescence measurements and electrophysiological recordings at multiple scales, from molecules to neurons. A further consequence is that the bistable regime occurs only within certain parametric windows, which may simulate a "history-dependent threshold". This effect might be related to the Bienenstock-Cooper-Munro theory of synaptic plasticity.

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A unified model of NMDA receptor-dependent bidirectional synaptic plasticity.

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A unified model of NMDA receptor-dependent bidirectional synaptic plasticity.

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