On the physics of multidrug efflux through a biomolecular complex

Insertion and release of a solute into and from a vessel comprising biopolymers is a fundamental function in a biological system. A typical example is found in a multidrug efflux transporter. "Multidrug efflux" signifies that solutes such as drug molecules with diverse properties can be handled. In our view, the mechanism of the multidrug efflux is not chemically specific but rather has to be based on a physical factor. In earlier works, we showed that the spatial distribution of the solute-vessel potential of mean force (PMF) induced by the solvent plays imperative roles in the insertion∕release process. The PMF can be decomposed into the energetic and entropic components. The entropic component, which originates from the translational displacement of solvent molecules, is rather insensitive to the solute-solvent and vessel inner surface-solvent affinities. This feature is not shared with the energetic component. When the vessel inner surface is neither solvophobic nor solvophilic, the solvents within the vessel cavity and in the bulk offer almost the same environment to any solute with solvophobicity or solvophilicity, and the energetic component becomes much smaller than the entropic component (i.e., the latter predominates over the former). Our idea is that the multidrug efflux can be realized if the insertion/release process is accomplished by the entropic component exhibiting the insensitivity to the solute properties. However, we have recently argued that the entropic release of the solute is not feasible as long as the vessel geometry is fixed. Here we consider a model of TolC, a cylindrical vessel possessing an entrance at one end and an exit at the other end for the solute. The spatial distribution of the PMF is calculated by employing the three-dimensional integral equation theory with rigid-body models in which the constituents interact only through hard-body potentials. Since the behavior of these models is purely entropic in origin, our analysis is focused on the entropic component. We show that the entropically inserted solute can be released by a continuous variation of the vessel geometry which forms a time-dependent entropic force continuing to accelerate the solute motion to the exit. Solutes with a wide range of sizes are entropically released using the same vessel-geometry variation. The results obtained are fairly general and also applicable to the efflux pump protein AcrB and ATP-binding cassette transporter.