Physical limits to acceleration of enzymatic reactions inside phase-separated compartments

We present a theoretical analysis of phase-separated compartments to facilitate enzymatic chemical reactions. While phase separation can facilitate reactions by increasing local concentration, it can also hinder the mobility of reactants. In particular, we find that the attractive interactions that concentrate reactants within the dense phase can inhibit reactions by lowering the mobility of the reactants. This mobility loss severely limits the potential to enhance reaction rates. Phase separation provides greater benefit in situations where multiple sequential reactions occur and/or high order reactions, provided the enzymes are unsaturated, transport to the condensate is not limiting, and the reactants are mobile. We show that mobility can be maintained if recruitment to the condensed phase is driven by multiple attractive moieties that can bind and release independently. However, the spacers necessary to ensure independence between stickers are prone to entangle with the dense phase scaffold. We find an optimal sticker affinity that balances the need for rapid binding/unbinding kinetics and minimal entanglement. Reaction rates can be accelerated by shrinking the size of the dense phase with a corresponding increase in the number of stickers. Our results showcase the potential capabilities of phase-separated compartments to act as biochemical reaction crucibles within living cells.