Non-equilibrium Statistical Mechanics in Biological Systems

Unlike equilibrium systems, which are characterized by a time-independent distribution of particles and energy, non-equilibrium systems experience constant fluxes of matter or energy, often due to external driving forces. These systems can exhibit a wide range of dynamic behaviors some of which can appear as self-organizing. Building on the framework of non-equilibrium statistical mechanics, Jeremy England in his paper "Statistical Physics of Adaptation" derives an equation which relates the relative forwards probability of transitioning between two possible macrostates with their respective reverse probability, entropy, and average energy dissipation across all possible micro trajectories. He showed that structures which are better at absorbing and dissipating energy into their surroundings during their formation have a higher likelihood of occurring, which can possibly explain how life-like behaviors emerge in non-equilibrium systems. In this project, we test England's equation on a toy model of self replicating populations, as well as attempt to apply it to a biological dataset. In the toy model under certain constraints we do find that our intuition of the systems dynamics does track with England's equation, that is we observe that the population with the greatest replication rate tends to have the highest energy dissipation when it's population makes up the greater fraction of the total population of particles. In the biological dataset we analyze protein-protein interactions and how the relative bonding energy and binding rates compare for different mutations. We explore the limitations of his equation when trying to make predictions about highly complex biological systems.