Statistical Thermodynamics for Actin-Myosin Binding: The Crucial Importance of Hydration Effects

Actomyosin is an important molecular motor, and the binding of actin and myosin is an essential research target in biophysics. Nevertheless, the physical factors driving or opposing the binding are still unclear. Here, we investigate the role of water in actin-myosin binding using the most reliable statistical-mechanical method currently available for assessing biomolecules immersed in water. This method is characterized as follows: water is treated not as a dielectric continuum but as an ensemble of molecules; the polyatomic structures of proteins are taken into consideration; and the binding free energy is decomposed into physically insightful entropic and energetic components by accounting for the hydration effect to its full extent. We find that the actin-myosin binding brings large gains of electrostatic and Lennard-Jones attractive interactions. However, these gains are accompanied by even larger losses of actin-water and myosin-water electrostatic and LJ attractive interactions. Although roughly half of the energy increase due to the losses is cancelled out by the energy decrease arising from structural reorganization of the water released upon binding, the remaining energy increase is still larger than the energy decrease brought by the gains mentioned above. Hence, the net change in system energy is positive, which opposes binding. Importantly, the binding is driven by a large gain of configurational entropy of water, which surpasses the positive change in system energy and the conformational entropy loss occurring for actin and myosin. The principal physical origin of the large water-entropy gain is as follows: the actin-myosin interface is closely packed with the achievement of high shape complementarity on the atomic level, leading to a large increase in the total volume available to the translational displacement of water molecules in the system and a resultant reduction of water crowding (i.e., entropic correlations among water molecules).