Modeling the effect of degradative pathway associated with Nodes of Ranvier on axonal transport drug delivery

The goal of this paper is to develop a mechanistic model of axonal transport drug delivery. The model accounts for the dynamics of transport of pharmaceutical agent complexes (\PACs) by dynein motors along microtubules (MTs) from the axon periphery toward the neuron soma, PAC accumulation in the axon, and PAC transport out of the axon via a degradative pathway that is associated with Nodes of Ranvier. The model assumes two populations of PACs: (1) PACs that are in retrograde transit propelled by dynein motors and (2) PACs accumulated at Nodes of Ranvier. The obtained governing equations describing the dynamics of these two PAC populations are transformed into dimensionless form and solved analytically utilizing Laplace transform. The obtained results reveal that for certain values of kinetic constants involved in the model the concentration of accumulated PACs can be independent of the position in the axon. To explain the obtained result this case is analyzed separately. Physical significance of computational results is discussed.