An analytical solution describing retrograde viral transport in an axon

An analytical solution representing a wave of viral concentration as it propagates from the axon synapse toward the neuron soma is obtained. The obtained solution is based on a model of molecular motor-assisted retrograde transport of a neurotropic virus in an axon of a peripheral nervous system. It is established that the velocity of the viral concentration wave is almost independent of the rate of viral destruction in the axon, but depends on viral diffusivity, especially right after viral uptake at the synapse, when viral concentration gradient is large. As time progresses, the velocity of the viral concentration wave approaches that of a dynein motor, which indicates that for a large time viral transport in an axon is almost exclusively motor-driven.