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

Abstract

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).

How Does the Recently Discovered Peptide MIP Exhibit Much Higher Binding Affinity than an Anticancer Protein p53 for an Oncoprotein MDM2?

“…When all of the biomolecule structures in the six simulations are simultaneously treated, the result is − T ΔΔ S C ∼ 2 kcal/mol. On the other hand, − T ΔΔ S C estimated by our simplified method, which was shown to be reliable in our earlier works − on the binding of biomolecules, is ∼1 kcal/mol. Hence, it is reasonable to assume that − T ΔΔ S C can be approximated by zero: We obtain ΔΔ F ∼ −4.80 ± 0.69 kcal/mol.…”

“…The water-entropy gain is a principal contributor to large, negative BFE. As argued in our earlier publications, − most of the gain is ascribed to an increase in translational, configurational entropy of water, which originates primarily from the mitigation of water crowing (i.e., entropic correlation among water molecules) in the system. The mitigation is brought by a decrease in the total EV.…”

“…In the previous hybrid method used in our earlier works on the binding of two biomolecules, − ε VH,1 was neglected. This was justifiable because the change in ε VH,1 upon binding, Δε VH,1 , was much smaller than Δε VH,2 , which was attributed to the sufficiently high hydrophilicity of the portions of biomolecules within the binding interface.…”

“…More details of the calculation procedure are described in Section S3.1 of the SI. Δ S C can also be estimated by our simplified method which has been quite successful in studies on the binding of two biomolecules − (Section S3.2, SI).…”

Polymer‐Carrying Ability of Actin Filaments Interacting with Myosin Motors in a Biological Motility System In Vitro

“…In addition, depletion forces with respect to the entropic effect may lead to the stable burial of myosin heads among the PEGs. [ 36–38 ] In conclusion, the attachment of PEGs up to 2 kDa maintains the sliding movement of actin filaments interacting with myosin heads. Application of a greater size induces a substantial failure in motility even when the filaments contain 20% of PEG‐attached actin.…”