A THREE-KINETIC-STATE MODEL OF AXONAL TRANSPORT DRUG DELIVERY

Abstract

This paper develops a model of axonal transport drug delivery that includes three populations (kinetic states) of pharmaceutical agent complexes (PACs), namely PACs transported by dynein motors, PACs freely suspended in the cytosol, and PACs accumulated at the Nodes of Ranvier. The number of model parameters is minimized by recasting governing equations into the dimensionless form. The obtained equations are solved numerically. The dependencies of the three PAC concentrations as well as the diffusion-driven, motor-driven, and total PAC fluxes on the PAC diffusivity and the length of the axon are investigated. Two situations are analyzed: when all kinetic constantans are the same (in this case the dynein-driven PAC flux exceeds the diffusion flux by a large amount) and when kinetic constants describing PAC transition from the freely suspended state are small (in the this case the diffusion-driven flux is the major component of the total flux, but since the diffusion transport mechanism is highly inefficient compared to the motor-driven one for large particles, the total PAC flux is much smaller in this case).