Understanding the thermodynamic driving forces for directed motion at the nanoscale

Chemotaxis refers to directed motion in response to concentration gradients. The possibility of designing active materials with myriad applications has generated significant interest in directed motion at the nanoscale. In particular, considerable controversy surrounds the experiments and proposed mechanisms concerning enzymatic chemotaxis. We have utilized theory and simulation to understand the influence of specific binding interactions and catalysis in driving molecular chemotaxis. Starting from McMilllan-Mayer theory and Schellman's treatment of macromolecular binding, we have derived a thermodynamic force that drives two interacting co-solutes to move towards each other. To simulate chemotaxis, we have numerically solved the appropriate one-dimensional Fokker-Planck equations, and our results show qualitative agreement with several prior experimental studies. We have also derived a modified reaction-diffusion equation that couples the translational motion of an enzyme to the chemical reaction it catalyzes. We investigate the role of this coupling in allowing the chemotaxis of the enzyme to be driven by the energy dissipated during the reaction. Our results may potentially challenge the traditional view that reactions are solely the result of random molecular collisions.