Modeling DNA and Virus Trafficking in the Cell Cytoplasm1

Cytosol trafficking is a limiting step of viral infection or DNA delivery. Starting from the cell surface, most viruses have to travel through a crowded and risky environment in order to reach a small nuclear pore. This work is dedicated to estimating the probability pN of a viral arrival success and, in that case, the mean time τN it takes. Viral movement is described by a stochastic equation, containing both a drift and a Brownian component. The drift part represents the movement along microtubules, while the Brownian component corresponds to the free diffusion. The success of a viral infection is limited by a killing activity occurring inside the cytoplasm. We model the killing activity by a steady state killing rate k. Because nuclear pores occupy a small fraction of the nuclear area, we use this property to obtain asymptotic estimates of pN and τN as a function of the diffusion constant D, the amplitude of the drift B and the killing rate k.