Chemical reaction kinetics in phase separated systems

The theory of phase separation determines how condensates form in living cells. These condensates act as compartments that partition molecules differently in each of the phases. This partitioning leads to different physicochemical properties of both phases that can alter the kinetics of chemical reactions. The mechanisms which determine how chemical reactions are affected by coexisting phases are not clearly understood. Here, we derive the kinetic theory for chemical reactions at phase equillibrium. We show that the condition of phase equilibrium leads to a fundamental relationship that relates chemical reaction fluxes and partitioning of reacting components. A key finding is that for chemical reactions that can relax to thermodynamic equilibrium, differences in chemical flux between phases solely stem from phase dependent reaction rate coefficients. In such cases, the average compositions of reacting components are affected by phase coexistence. In comparison, phase coexistence can alter the stationary compositions of reacting components more strongly when maintaining chemical reactions away from equilibrium. As an example of such reactions we study phosphorylation processes. Our studies exemplify the enormous potential of phase separated compartments as biochemical reactors in living cells. Understanding the control of biochemical reactions via compartments is key to elucidate the functionality of stress granules for the cell and is also crucial for biochemical communication among synthetic cells and RNA catalysis in coacervate protocells.