Active droplets controlled by enzymatic reactions.

The formation of condensates is now considered a major organizing principle of eukaryotic cells. Several studies have recently shown that the properties of these condensates are affected by enzymatic reactions. We propose here a simple generic model to study the interplay between two enzyme populations and a two-state protein. In one state, the protein forms condensed droplets through attractive interactions, while in the other state, the proteins remain dispersed. Each enzyme catalyses the production of one of these two protein states only when reactants are in its vicinity. A key feature of our model is the explicit representation of enzyme trajectories, capturing the fluctuations in their local concentrations. The spatially dependent growth rate of droplets naturally arises from the stochastic motion of these explicitly modelled enzymes. Using two complementary numerical methods-(i) Brownian dynamics simulations and (ii) a hybrid method combining Cahn-Hilliard-Cook diffusion equations with Brownian dynamics for the enzymes-we investigate how enzyme concentration and dynamics influence the evolution with time and the steady-state number and size of droplets. Our results show that the concentration and diffusion coefficient of enzymes govern the formation and size-selection of biocondensates.