Stochastic Modeling of RNA Hairpin Dynamics: Equilibrium and Out-of-Equilibrium Kinetics

Abstract

The project aims to investigate the equilibrium and out-of-equilibrium aspects of the RNA forced unfolding/refolding processes using a theoretical stochastic model. Our study is motivated by a series of experiments whereby an RNA hairpin P5ab was manipulated by an optical tweezers apparatus in an attempt to extract the equilibrium parameters controlling the RNA folding or unfolding kinetics which involves a discontinuous transition. Forced unfolding of the RNA hairpin was used later to test the Crooks fluctuation theorem relating the direct and reverse out-of-equilibrium processes. The theoretical model revolves around the Gibbs free energy as a function of two connected dynamic variables that describe the hairpin microstates i.e. the number of bound complementary base pairs, n, and the coordinate x, which describes the distance between the hairpin's ends. The evolution of the dynamic variables is described by a combination of a continuous Langevin equation for the x coordinate and a discrete Markov process for the n variable. The external force applied is part of the Gibbs free energy and enters both the Langevin equation and in the transition probabilities of the Markov process.Out-of-equilibrium aspects of the forced unfolding/refolding are controlled by the force rate growth and the study of its effects in connection to the Crooks theorem is one of the goals of the project.