Kinetic inversion of repressors and activators in gene expression regulation.

In gene expression regulation, repressors and activators compete to bind with the gene’s regulatory element, and the chance of activators binding with the regulatory element dictates the activation level of the gene. In a thermal equilibrium regime, this chance of binding is well determined by the concentrations of activators and repressors as well as their binding free energies to the regulatory element -- a high level of repressor will result in a low chance of activator binding. However, inspired by the experimental observations of cooperativity between activators and repressors, we propose a non-equilibrium dynamics model to describe the gene regulatory dynamics when the concentration of the repressor changes rapidly over time. We demonstrate a minimal Markov model where a rapidly changing level of repressor significantly increases the level of activation beyond predicted by equilibrium theory and effectively enhance the activator. Our model introduced an internal degree of freedom of the regulatory element, and its kinetic barrier allows the system to harnesses the chemical work done by the rapidly changing concentration of the repressor and use it to boost the level of gene activation beyond the equilibrium prediction.