2009 journal article
Macroscopic modeling of slow axonal transport of rapidly diffusible soluble proteins
INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER, 36(4), 293–296.
The purpose of this paper is to develop a macroscopic model of slow axonal transport of soluble proteins which may be transported in axons by both diffusion and active molecular-motor-assisted transport mechanisms. The model relies on the “stop-and-go” hypothesis put forward by Brown et al. [A. Brown, L. Wang, P. Jung, Stochastic simulation of neurofilament transport in axons: the “stop-and-go” hypothesis, Molecular Biology of the Cell 16 (2005) 4243–4255.] according to which the motion of neurofilaments in slow axonal transport does not occur at a constant velocity; instead, neurofilaments move along microtubules alternating between short periods of rapid movement, short on-track pauses, and prolonged off-track pauses, when they temporarily disengage from microtubules. For soluble proteins, diffusion may also play an important role in overall slow axonal transport; to account for this effect governing equations of the dynamic system model developed in Craciun et al. [G. Craciun, A. Brown, A. Friedman, A dynamical system model of neurofilament in axons, Journal of Theoretical Biology 237 (2005) 316–322.] are extended to incorporate diffusivity of off track proteins (proteins unbound to a stationary matrix). The model correctly predicts that the total concentration of organelles forms the bell-shaped wave that spreads out as it propagates toward the axon tip.