Mathematical modeling and parameter estimation of axonal cargo transport.

A systems approach was developed and implemented to simulate and analyze motor-assisted axonal transport in nervous system. The methodology employs a Galerkin based linear finite element solver of a system of three coupled partial differential equations governing axonal diffusion-reaction-advection with an efficient optimization algorithm and an experimental time-space series to extract physio-chemical and biological information from experiments and to analyze the dynamics of molecular motor protein-assisted axonal transport. Our simulations were successfully applied and compared to a synthetic dataset based on measured motility parameters as well as experimental data of microtubule-associated protein MAP1A transport in mouse retinal ganglion cells (Nixon et al. 1990) and light neurofilament subunit transport within the optic nerve (Jung and Shea 1999). Parameter sensitivity analysis was performed to quantify the dependence of the dynamics of axonal transport on model parameters. Based on sensitivity analysis, we recommend a sampling strategy for future experiments that would produce the most sensitive and informative data. Our synergistic approach has excellent potential for efficiently probing our understanding of mechanisms of motor-mediated axonal transport in the nervous system.