Introducing physics students to biophysical reactions

The understanding of many biophysical processes, such as the activity of molecular motors combines physical modeling with biochemical rate equations. Physics students with no chemistry background who have been exposed to the usual undergraduate physics curriculum up to graduate-level statistical mechanics, would be well-served by learning biophysically important biochemical dynamics in a manner that is consistent with their physics-based epistemology. We motivate this in the context of myosin molecular motors and ATP hydrolysis which is minimally a three-state, linear system of rate equations and derive how breaking detailed balance leads to damped oscillations in deterministic relaxation and to oscillatory, cyclic correlations in a stochastic steady state. Instead of simply declaring the system to be non-equilibrium, we first problematize and then explain why ATP abundance in the cell is intrinsically a non-equilibrium steady state. We next clarify the distinction between detailed balance in statistical mechanics and in chemical rate equations, and show why general two-state systems necessarily satisfy detailed balance (in a dynamical sense) while three-state systems may not. Finally, in contrast to simply invalidating the fluctuation-dissipation (FD) theorem (familiar to physics students from statistical mechanics) in non-equilibrium systems, we demonstrate an analogy to FD in the relationship between three-component rate equations and their stochastic representations.