Analytical solution of the steady-state molecular-motor-assisted transport equations governing distribution of intracellular particles within a cell dendrite

A steady-state analytical solution is obtained for a one-dimensional problem describing transport of intracellular organelles in a cell arm (a dendrite or axon). The model of intracellular trafficking of organelles (intracellular particles) is based on molecular-motor-assisted transport equations suggested by Smith and Simmons [D.A. Smith, R.M. Simmons, Models of motor-assisted transport of intracellular particles, Biophysical Journal 80 (2001) 45–68.]. According to this model, a fraction of intracellular space is occupied by filaments (microtubules); the remaining space allows for diffusion of unbound particles. Depending on the direction of particle transport provided by molecular motors running along these microtubules, the microtubules are divided into inward and outward microtubules. Unbound (free) organelles may bind to microtubules; organelles attached to microtubules may detach from them; the binding/detachment kinetic processes are specified by the first rate constants.