Potential of mean force between a large solute and a biomolecular complex: a model analysis on protein flux through chaperonin system

Insertion of a large solute into an even larger vessel comprising biopolymers followed by release of the same solute from it is one of the important functions sustaining life. As a typical example, an unfolded protein is inserted into a chaperonin from bulk aqueous solution, a cochaperonin acting as a lid is attached to the chaperonin rim and the protein folds into its native structure within the closed cavity, the cochaperonin is detached after the folding is finished, and the folded protein is released back to the bulk solution. On the basis of the experimental observations manifesting that the basic aspects of the protein flux through the chaperonin system is independent of the chaperonin, cochaperonin, and protein species, we adopt a simple model system with which we can cover the whole cycle of the protein flux. We calculate the spatial distribution of the solvent-mediated potential of mean force (PMF) between a spherical solute and a cylindrical vessel or vessel/lid complex. The calculation is performed using the three-dimensional integral equation theory, and the PMF is decomposed into energetic and entropic components. We argue that an unfolded protein with a larger excluded volume (EV) and weak hydrophobicity is entropically inserted into the chaperonin cavity and constrained within a small space almost in its center. The switch from insertion to release is achieved by decreasing the EV and turning the protein surface hydrophilic in the folding process. For this release, in which the energetic component is a requisite, the feature that the chaperonin inner surface in the absence of the cochaperonin is not hydrophilic plays essential roles. On the other hand, the inner surface of the chaperonin/cochaperonin complex is hydrophilic, and the protein is energetically repelled from it: The protein remains constrained within the small space mentioned above without contacting the inner surface for correct folding. The structural and inner-surface properties of the chaperonin or complex are controlled by the adenosine triphosphate (ATP) binding to the chaperonin, hydrolysis of ATP into adenosine diphosphate (ADP) and Pi, and dissociation of ADP and Pi. The function of the chaperonin system is exhibited by synchronizing the chemical cycle of ATP hydrolysis with hydration properties of a protein in the water confined on the scale of a nanometer which are substantially different from those in the bulk water.