How Muscle Exploits the Steady State to Regulate Contraction

Abstract

Activation of muscle requires myosin binding. The active state of muscle is stabilized by high affinity rigor bonds at equilibrium but, the steady-state catalytic cycle of myosin ATPase decreases the lifetime of the myosin interaction by several orders of magnitude. Low myosin affinity could be a justification for including Ca2+ binding states in a model of activation. Our work supports a simple model for steady state activation, namely, the regulatory protein tropomyosin (Tm) exists in just two states, ground (C) and excited (M), separated by an energy barrier which can be overcome by interaction with myosin. The elongated shape of Tm allows for multiple potential myosin binding partners (Ui). During its strong binding phase of the catalytic cycle, any one myosin (U1) combines with C to form M by an equilibrium pathway. At time, t=0, M probability, PM=1. Although U1 most likely decays by a non-equilibrium rate (i.e., ATP binding), the lifetime of PM is constant. For t>0, before M decays to C, interaction with Ui in the strong binding phase can restore PM=1. We show that an analytical function (M function) is fully derived from the combination of equilibrium and steady state pathways and the additional opportunities (second chances) to restore PM=1 depend on the rate at which Ui transitions into the strong binding phase. When Ca2+ is introduced as a mass action regulator of the U or C supply, the M function takes the general form of the Hill equation, which is widely employed for fitting the steady state response of muscle to Ca2+. We show by simulations that stochastic events predicted by a second chance mechanism are consistent with solutions to the M function. Our results justify kinetic experiments that focus specifically on M.