Energetics of molecular motor proteins: could it pay to take a free ride?

Molecular motor proteins are used in biological systems to generate directed motion. They consist of one end that can bind to and then move along a filament. The other end can then bind to a cargo that needs transporting and the motor then pulls it along. Here, we consider the energetics of this process allowing for the friction force exerted by the surrounding fluid, given that the process takes place in a confined geometry. In nature, not all motor/cargo complexes are bound to the filament, many are in solution. Here, we address the question of whether this can be energetically favourable given that the unbound complexes will be transported by the flow generated by those that are bound. A simple theory suggests that this is the case and that there exists an optimal coverage of bound complexes. Simulations of a model of this system that includes all the relevant hydrodynamic effects confirm that the assumptions in the theory are valid so long as the coverage of bound complexes is not too low. Using realistic values for the parameters involved yields an optimal coverage that is plausible for the biological systems involved.