Modelling spatial constraints and scaling effects of catalyst phase separation on linear pathway kinetics

Chemical reactions are usually studied under the assumption that both substrates and catalysts are well mixed (WM) throughout the system. Although this is often applicable to test-tube experimental conditions, it is not realistic in cellular environments, where biomolecules can undergo liquid-liquid phase separation (LLPS) and form condensates, leading to important functional outcomes, including the modulation of catalytic action. Similar processes may also play a role in protocellular systems, like primitive coacervates, or in membrane-assisted prebiotic pathways. Here we explore whether the de-mixing of catalysts could lead to the formation of micro-environments that influence the kinetics of a linear (multi-step) reaction pathway, as compared to a WM system. We implemented a general lattice model to simulate LLPS of an ensemble of different catalysts and extended it to include diffusion and a sequence of reactions of small substrates. We carried out a quantitative analysis of how the phase separation of the catalysts affects reaction times depending on the affinity between substrates and catalysts, the length of the reaction pathway, the system size, and the degree of homogeneity of the condensate. A key aspect underlying the differences reported between the two scenarios is that the scale invariance observed in the WM system is broken by condensation processes. The main theoretical implications of our results for mean-field chemistry are drawn, extending the mass action kinetics scheme to include substrate initial hitting times to reach the catalysts condensate. We finally test this approach by considering open non-linear conditions, where we successfully predict, through microscopic simulations, that phase separation inhibits chemical oscillatory behaviour, providing a possible explanation for the marginal role that this complex dynamic behaviour plays in real metabolisms.