Converging evidence for a simplified biophysical model of synaptic plasticity

Different mechanisms that could form the molecular basis for bi-directional synaptic plasticity have been identified experimentally and corresponding biophysical models can be constructed. However, such models are complex and therefore it is hard to deduce their consequences to compare them to existing abstract models of synaptic plasticity. In this paper we examine two such models: a phenomenological one inspired by the phenomena of AMPA receptor insertion, and a more complex biophysical model based on the phenomena of AMPA receptor phosphorylation. We show that under certain approximations both these models can be mapped on to an equivalent, calcium-dependent, differential equation. Intracellular calcium concentration varies locally in each postsynaptic compartment, thus the plasticity rule we extract is a single-synapse rule. We convert this single synapse plasticity equation to a multi-synapse rule by incorporating a model of the NMDA receptor. Finally we suggest a mathematical embodiment of metaplasticity, which is consistent with observations on NMDA receptor properties and dependence on cellular activity. These results, in combination with some of our previous results, produce converging evidence for the calcium control hypothesis including a dependence of synaptic plasticity on the level of intercellular calcium as well as on the temporal pattern of calcium transients.