Information flow, Gating, and Energetics in dimeric molecular motors

Abstract: Molecular motors belonging to the kinesin and myosin super family hydrolyze ATP by cycling through a sequence of chemical states. These cytoplasmic motors are dimers made up of two linked identical monomeric globular proteins. Fueled by the free energy generated by ATP hydrolysis, the motors walk on polar tracks (microtubule or filamentous actin) processively, which means that only one head detaches and executes a mechanical step while the other stays bound to the track. Thus, the one motor head must regulate chemical state of the other, referred to as "gating", a concept that is not fully understood. Inspired by experiments, showing that only a fraction of the energy from ATP hydrolysis is used to advance the kinesin motors against load, we demonstrate that additional energy is used for coordinating the chemical cycles of the two heads in the dimer - a feature that characterizes gating. To this end, we develop a general framework based on information theory and stochastic thermodynamics, and establish that gating could be quantified in terms of information flow between the motor heads. Applications of the theory to kinesin-1 and Myosin V show that information flow occurs, with positive cooperativity, at external resistive loads that are less than a critical value, $F_c$. When force exceeds $F_c$, effective information flow ceases. Interestingly, $F_c$, which is independent of the input energy generated through ATP hydrolysis, coincides with force at which the probability of backward steps starts to increase. Our findings suggest that transport efficiency is optimal only at forces less than $F_c$, which implies that these motors must operate at low loads under $\textit{in vivo}$ conditions.