Using stochastic thermodynamics with internal variables to capture orientational spreading in cell populations undergoing cyclic stretch

Abstract Starting from the Langevin-type dynamics proposed in Loy & Preziosi (2023 Bull. Math. Bio.85, 60. (doi:10.1007/s11538-023-01161-4)) to describe fluctuations in cell reorientation under cyclic stretch, we apply the framework of ‘stochastic thermodynamics with internal variables’ (STIV) introduced in Leadbetter et al. (2023 PNAS Nexus2, pgad417. (doi:10.1093/pnasnexus/pgad417)) to obtain a two-dimensional dynamical system that is analytically more tractable than the original stochastic dynamics and effectively captures the evolution of the orientation distribution as well as its spreading. The insight provided by the phase-portrait analysis of our reduced model reveals a novel and interesting phenomenon, which we call two-stage reorientation: When cells begin aligned with an energy maximum, their orientations spread before concentrating at the energy minimum. Our theoretical prediction suggests a new experiment to test the stochastic model.