A model of axonal transport drug delivery: effects of diffusivity

This paper investigates the effects of diffusivity on retrograde dynein-driven transport of pharmaceutical agent complexes (PACs) in axons. The model is designed with two goals in mind: (1) to capture results on axonal transport drug delivery reported in recent experimental research by Filler et al. (Filler AG, Whiteside GT, Bacon M, Frederickson M, Howe FA, Rabinowitz MD, Sokoloff AJ, Deacon TW, Abell C, Munglani R, Griffiths JR, Bell BA, Lever AML. Tri-partite complex for axonal transport drug delivery achieves pharmacological effect. BMC Neuroscience 2010; 11: 8) and (2) to produce analytically tractable equations. It is shown that the inclusion of a diffusion process in the model produces equations that can still be solved by Laplace transform, although the last step of the solution, finding the inverse Laplace transform, has to be accomplished numerically, thus leading to a hybrid analytical and numerical solution technique. The effects of diffusivity and the kinetic rates describing PAC transition between the dynein-driven and accumulated states on transport of PACs toward the neuron soma are investigated.