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Modeling Synaptic Dynamics Driven by Receptor Lateral Diffusion

David Holcman ^*  and Antoine Triller 

^* Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel; and Institut National de la Santé et de la Recherche Médicale, UR497, Département de Biologie, Ecole Normale Supérieure, Paris, France

Correspondence: Address reprint requests to David Holcman, E-mail: david.holcman{at}weizmann.ac.il.

The synaptic weight between a pre- and a postsynaptic neuron depends in part on the number of postsynaptic receptors. On the surface of neurons, receptors traffic by random motion in and out from a microstructure called the postsynaptic density (PSD). In the PSD, receptors can be stabilized at the membrane when they bind to scaffolding proteins. We propose a mathematical model to compute the postsynaptic counterpart of the synaptic weight based on receptor trafficking. We take into account the receptor fluxes at the PSD, which can be regulated by neuronal activity, and the interactions of receptors with the scaffolding molecules. Using a Markovian approach, we estimate the mean and the fluctuations of the number of bound receptors. When the number of receptors is large, a deterministic system is also derived. Moreover, these equations can be used, for example, to fit fluorescence-recovery-after-photobleaching experiments to determine, in living neurons, the chemical binding constants for the receptors/scaffolding molecules interaction at synapses.