The Gated Narrow Escape Time for molecular signaling

TL;DR

This paper develops new mathematical models to analyze how switching between states affects the time it takes for a diffusing ligand to activate a target, revealing insights into cellular signaling modulation.

Contribution

It introduces exact and asymptotic solutions for the mean activation time with state switching, including a new formula for narrow escape time under switching conditions.

Findings

Activation time is highly sensitive to switching rates.

Fast activation is possible despite the ligand spending most time in non-activating states.

New formulas for narrow escape time with switching are derived.

Abstract

The mean time for a diffusing ligand to activate a target protein located on the surface of a microdomain can regulate cellular signaling. When the ligand switches between various states induced by chemical interactions or conformational changes, while target activation occurs in only one state, this activation time is affected. We investigate this dynamics using new equations for the sojourn times spent in each state. For two states, we obtain exact solutions in dimension one, and asymptotic ones confirmed by Brownian simulations in dimension 3. We find that the activation time is quite sensitive to changes of the switching rates, which can be used to modulate signaling. Interestingly, our analysis reveals that activation can be fast although the ligand spends most of the time 'hidden' in the non-activating state. Finally, we obtain a new formula for the narrow escape time in the presence of switching.