A spherical vesicle of radius diffuses in cytoplasm of viscosity at body temperature

PHYSICS · Multi-part · 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 spherical vesicle of radius a=100 nma = 100\,\mathrm{nm} diffuses in cytoplasm of viscosity η=2.0×10−3 Pa s\eta = 2.0\times10^{-3}\,\mathrm{Pa\,s} at body temperature T=310 KT = 310\,\mathrm{K}. Model its motion by the Langevin equation with drag coefficient γ=6πηa\gamma = 6\pi\eta a. ((a)) Compute the diffusion coefficient D=kBT/γD = k_{\rm B}T/\gamma. ((b)) The vesicle starts at the centre of a cell of diameter 10 μm10\,\mu\mathrm{m}, modelled as a one-dimensional interval with absorbing boundaries at the cell membrane on either side. Compute the mean first-passage time to reach a membrane.

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