A small neurotransmitter molecule diffuses in a synaptic cleft of width

PHYSICS · Subjective · Fermi University Physics · Thermal, Statistical & Complex Systems · Non-equilibrium statistical mechanics and stochastic thermodynamics · Non-equilibrium statistical mechanics and stochastic thermodynamics

Error, Chance and the Machine, Ch Random processes in continuous time

Problem

A small neurotransmitter molecule diffuses in a synaptic cleft of width L=20 nmL = 20\,\mathrm{nm}, with diffusion coefficient D=8.0×10−10 m2 s−1D = 8.0\times10^{-10}\,\mathrm{m^2\,s^{-1}}. Model the cleft as a one-dimensional interval with absorbing boundaries (the two membranes) at x=0x=0 and x=Lx=L, and suppose the molecule starts at the mid-point x=L/2x = L/2. Compute the mean first-passage time to reach either membrane.

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