Effective Motion of a Virus Trafficking Inside a Biological Cell

Virus trafficking is fundamental for infection success and plasmid cytosolic trafficking is a key step of gene delivery. Based on the main physical properties of the cellular transport machinery such as microtubules, motor proteins, our goal here is to derive a mathematical model to study cytoplasmic trafficking. Because experimental results reveal that both active and passive movement are necessary for a virus to reach the cell nucleus, by taking into account the complex interactions of the virus with the microtubules, we derive here an estimate of the mean time a virus reaches the nucleus. In particular, we present a mathematical procedure in which the complex viral movement, oscillating between pure diffusion and a deterministic movement along microtubules, can be approximated by a steady state stochastic equation with a constant effective drift. An explicit expression for the drift amplitude is given as a function of the real drift, the density of microtubules and other physical parameters. The present approach can be used to model viral trafficking inside the cytoplasm, which is a fundamental step of viral infection, leading to viral replication and in some cases to cell damage.