Abstract
The mechanism that regulates the number and
the type of receptors at a synapse control
the synaptic weight. Any fluctuations of their number
results in a variation of the synaptic weight and affects
the reliability of the synaptic transmission. Moreover,
certain experimental protocols have lead to a Long Term
Potentiation of a synapse, a mechanism which is associated
with a change of the number and the type of certain
receptors . The regulation of synaptic plasticity
is a fundamental process underlying learning and memory. Recently, single molecule tracking has revealed
that the number of postsynaptic receptors, which participate to the synaptic transmission, is not fixed but
it changes due to constant traffick of receptors on the surface
of neurons. Receptors move in and out from synaptic
regions and following these observations, many
questions have been raised: in particular, what determines
the time spent by a receptor inside a synapse? How
receptors can be stabilized inside a synapse? How long
they stay inside synaptic microdomains? Such questions
are partially answered in the present paper. In particular,
our computation of the Dwell time of a receptor inside
a specific microdomain,called post synaptic domain (PSD).
In the present
article, we propose to estimate the mean time spent by a Brownian molecule inside a microdomain which contains a small hole on the boundary and agonist molecules located inside. We found that
the mean time depends on several parameters such as the backward binding rate (with the agonist
molecules), the mean escape time from the microdomain and the mean time a molecule reaches the
binding sites (forward binding rate). In addition, we estimate the mean and the variance of the
number of bounds made by a molecule before it exits. In particular, we apply the present results to obtain an estimate of the mean time spent (Dwell
time) by a Brownian receptor inside a synaptic domain, when it moves freely by lateral diffusion on
the surface of a neuron and interacts locally with scaffolding molecules.
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