Self-consistent Sharp Interface Theory of Active Condensate Dynamics

Biomolecular condensates help organize the cell cytoplasm and nucleoplasminto spatial compartments with different chemical compositions. A key featureof such compositional patterning is the local enrichment of enzymaticallyactive biomolecules which, after transient binding via molecular interactions,catalyze reactions among their substrates. Thereby, biomolecular condensatesprovide a spatial template for non-uniform concentration profiles ofsubstrates. In turn, the concentration profiles of substrates, and theirmolecular interactions with enzymes, drive enzyme fluxes which can enable novelnon-equilibrium dynamics. To analyze this generic class of systems, with acurrent focus on self-propelled droplet motion, we here develop aself-consistent sharp interface theory. In our theory, we diverge from theusual bottom-up approach, which involves calculating the dynamics ofconcentration profiles based on a given chemical potential gradient. Instead,reminiscent of control theory, we take the reverse approach by deriving thechemical potential profile and enzyme fluxes required to maintain a desiredcondensate form and dynamics. The chemical potential profile and currents ofenzymes come with a corresponding power dissipation rate, which allows us toderive a thermodynamic consistency criterion for the passive part of the system(here, reciprocal enzyme-enzyme interactions). As a first use case of ourtheory, we study the role of reciprocal interactions, where the transport ofsubstrates due to reactions and diffusion is, in part, compensated byredistribution due to molecular interactions. More generally, our theoryapplies to mass-conserved active matter systems with moving phase boundaries.