Mechanism of Functional Expression of the Molecular Machines

A variety of self-assembly and ordering processes are sustaining life. They are microscopic, mesoscopic, or macroscopic. In this book, we are concerned with the microscopic processes. We raise the following two questions: (1) It appears that the processes occur at a great expense of entropy, but is this true?; and (2) how is water imperative in life phenomena? Upon the processes, the entropy is considerably lowered if one looks at only the biomolecules. When the effect of water is taken into account to its full extent, matters become substantially different.

We argue that a self-assembly process occurs primarily to increase the system entropy. The water entropy increases whereas the conformational entropy of biomolecules decreases, and the increase is larger than the decrease. In many cases, the ordering processes can successfully be described by the potential of mean force induced between biomolecules or a solute and a biomolecule, in particular, its entropic component. The entropic effect or potential originates from the translational displacement of water molecules coexisting with biomolecules in the entire system: The conventional view looking at only the water near the biomolecular surface is inadequate. The hydration entropy of a biomolecule, the loss of water entropy upon biomolecule insertion, plays crucially important roles. The calculation of this quantity with sufficient accuracy is a central issue.

The ATP hydrolysis cycle is utilized in such processes as the unidirectional movement of myosin along F-actin, assistance in protein folding performed by a chaperonin, transport of diverse substrates across the membrane by an ABC transporter, and rotation of the central subunit within F₁-ATPase. On the other hand, the proton motive force is utilized in the functional rotation of the multidrug efflux transporter AcrB. In this chapter, we elucidate the mechanism of these ordering processes. We also argue how the processes are coupled with the ATP hydrolysis cycle or the proton motive force. Like in the self-assembly processes, the key factor is the entropic effect originating from the translational displacement of water molecules in the system.

Let us take protein folding as an example. The initial and final states of the folding process are visually different: Protein is in unfolded and folded states, respectively. Therefore, it can readily be understood that protein folding spontaneously occurs as an irreversible process accompanying a decrease in the system free energy. On the other hand, the conformations of F₁-ATPase before and after a 120° rotation of the central subunit, for example, are the same. Nevertheless, the directed rotation occurs. Hence, in the prevailing view, this rotation process is differently treated: It is made possible by converting the free energy of ATP hydrolysis to a work, and F₁-ATPase is referred to as “molecular rotatory machine.” The work is necessary for the central subunit (i.e., γ subunit) to rotate against the viscous resistance force by water. Similarly, the unidirectional movement of S1 is realized by converting the free energy of ATP hydrolysis to a work that is necessary for S1 to move against the viscous resistance force by water. We disagree with this view (also see Sect. 3.​2.​5) In this chapter, we argue that protein folding and the directed rotation, for example, can be treated within the same theoretical framework.