Coupling reactive and diffusive fluxes to predict catalysis-driven chemotaxis at the nanoscale

Chemotaxis is a phenomenon in which particles move up or down chemical concentration gradients. While the initial studies of chemotaxis focused on bacterial movement towards food and away from toxins, several recent experiments have suggested that enzymes can convert the chemical energy from reactions into directed motion along substrate gradients. Here, we have developed a theory for nanoscale chemotaxis that is based upon the free energy released during enzyme catalysis. We adopt Mielke’s framework, which models the conventional reaction-diffusion equation as a gradient descent of the Helmholtz free energy with respect to an Onsager-type dissipation potential. We introduce a new term into this potential that couples the diffusive flux of an enzyme to a simple chemical reaction. This coupling term breaks the spatial symmetry of the system and generates an advective flow for the catalyst, which depends on the rate at which free energy is released during the chemical reaction. We derive a modified reaction-diffusion equation and numerically solve this equation for a simple three-component system. Our simulation results suggest that coupling the diffusive and reactive fluxes can promote the directed motion of the catalyst. The extent of chemotaxis depends on the thermodynamic driving force, the reaction kinetics, and the strength of the coupling. Furthermore, our simulations demonstrate that the modified reaction-diffusion equation delays the relaxation of the system towards its equilibrium state.