Chapter 14 - Modeling Intracellular Transport in Neurons

Abstract

The chapter addresses several problems related to intracellular transport in axons, long processes of neurons that serve to transmit electrical signals. Since defects in axonal transport are related to various neurodegenerative diseases, its mechanistic understanding is of extreme importance. The focus is on problems which allow elegant analytical treatments and modeling approaches. The following are considered: 1) Axonal transport drug delivery; 2) Effect of dynein velocity distribution on propagation of positive injury signals in axons (with application to the problem of how injured neurons can measure the distance between the lesion site and the neuron soma); 3) Merging of viral concentration waves in retrograde viral transport in axons. We demonstrate that in minimal models of the above processes, time-dependent analytical solutions can be obtained utilizing the Laplace transform, while for more complicated models that include several populations of transported particles, a numerical approach is required. The chapter thus shows how far the analytical approach can be pushed and how much physics can be incorporated into minimal models that allow analytical treatments. It is shown that depending on the values of kinetic and transport parameters different transport regimes are possible.