Narrow escape to small windows on a small ball modeling the viral entry into the cell nucleus

TL;DR

This paper models viral entry into the cell nucleus through small nuclear pores using stochastic processes, deriving formulas for the probability and timing of successful nuclear entry based on cell geometry.

Contribution

It introduces a switching stochastic process model and asymptotic formulas for viral entry probability and timing, validated by simulations.

Findings

Formulas accurately predict viral entry probability and timing.

Geometrical parameters critically influence infection efficiency.

Asymptotic results match stochastic simulation outcomes.

Abstract

A certain class of viruses replicates inside a cell if they can enter the nucleus through one of many small target pores, before being permanently trapped or degraded. We adopt for viral motion a switching stochastic process model and we estimate here the probability and the conditional mean first passage time for a viral particle to attain alive the nucleus. The cell nucleus is covered with thousands of small absorbing nuclear pores and the minimum distance between them defines the smallest spatial scale that limits the efficiency of stochastic simulations. Using the Neuman-Green's function method to solve the steady-state Fokker-Planck equation, we derive asymptotic formula for the probability and mean arrival time to a small window for various pores' distributions, that agree with stochastic simulations. These formulas reveal how key geometrical parameters defines the cytoplasmic stage of viral infection.