Effect of pharmaceutical agent degradation on axonal transport drug delivery: An analytical solution for a transient situation

This paper is motivated by recent experimental research that demonstrated pharmacological efficiency of axonal transport drug delivery. The purpose is to develop a model of this process and to study how the rate of destruction of pharmaceutical agent complexes (PACs) affects their transport in the axon. The model includes two populations of PACs: PACs in the state when they are driven retrogradely (from the axon terminal toward the neuron soma) by dynein motors and PACs residing in the accumulated state (but can still be re-released to the dynein-driven state). The coupling between the kinetic states is accounted for by first-order reactions. Utilizing Laplace transform, analytical solutions for concentrations of these two populations of PACs are obtained. The effect of PAC destruction is investigated for different values of other parameters. It is shown that the shapes of the waves describing the PAC concentrations can be significantly affected by transport parameters.