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

We present a theoretical analysis of phase separated compartments as a means to facilitate chemical reactions. We find that the attractive interactions that concentrate reactants within the dense phase inhibit reactions by lowering the chemical potential and mobility of the reactants. Therefore, condensed phases are only beneficial if mobility in the condensed phase can be maintained. This can be achieved in multi-step reactions, where the proximity between enzymatic steps results in higher efficiency with less unreacted substrate, but does not increase the reaction rate. Alternatively, 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 to enhance recruitment.