Model and simulation setup.

a) Top: the three particles that make up the model. Bottom left: schematics of the interactions. Bottom right: a schematic representation of the implemented reaction cycle. b) Concentration profiles along the z coordinate of a typical slab simulation at steady state, along with a snapshot of the simulated system. Scaffold proteins are depicted in blue, phosphorylated scaffold in red, and protein kinases in green.

Phase separation depends on reaction imbalance and enzyme concentration.

a) Phase diagram as a function of λp at fixed kinase concentration. For each value of λp, the two points represent the total protein concentration in the dilute and condensed phases, respectively. Each point is shaded to show the ratio of P particles (NP) over the total (NT) at steady state, following the scale on the left. The dashed bars represent the dilute and condensed phase concentrations at equilibrium. The snapshots illustrate different product concentrations P at different λp points and how they correlate with phase separation. b) Saturation concentration as a function of kinase concentration, for three fixed values of λp .

Phase behavior depends on the intensity of interaction modifications induced by phosphorylation.

a) Snapshots from the simulations showing the phase coexistence. a) Partition coefficient of all proteins as a function of Δε, normalized with respect to its value at Δε = 0. Lower Cp means that proteins prefer the dilute phase, which increases the critical concentration. The grey line represents the critical Δε over which P proteins are no longer able to phase separate on their own. c) Protein concentration of the dilute phase (full squares) and dilute phase (empty squares), normalized with respect to their value at Δε = 0. d) Free energy of transfer of P proteins compared to their fraction as a function of Δε. Higher transfer free energies mean that proteins prefer to partition in the dilute phase (see Methods). The point at Δε = 0 is taken from the simulations with no reactions and only scaffold proteins. All data presented in this figure was obtained from simulations at λp = 0.05.

Phosphorylation accumulation at the condensate’s interface.

In this figure, we represent different quantities as a function of the distance from the center of the condensed phase. Data from the simulations at λp = 0.05 τ−1, ϵP = 0.3. a) Rate flux of the two reactions. Fluxes were quantified by direct reaction counting (dots), and reaction activity recomputation (line, see Methods). The bottom plot shows the net particle flux at the interface (positive means more P proteins produced). The shaded area indicates the extension of the condensed phase. b) Comparison between protein concentration and microscopic reaction rates of phosphorylation (top panel) and dephosphorylation (bottom panel). Protein concentrations are plotted on the left y-axis, while the microscopic rate is plotted on the right y-axis.

The interface effect is relevant for real-world condensates.

a) Intermolecular energy as a function of the distance from the slab center, obtained from the CALVADOS simulations of NDDX4 and FUS-LC protein domains. The dashed red lines represent the fitted data, through which we extracted the interfacial width shown in the inset (see Methods section). On top, snapshots of the phase coexistence simulations of the two systems. b) Estimate of the relative weight of the interfacial activity in a spherical condensate, as a function of the diameter. In the sketch, we illustrate the involved quantities: the total amount of reactions per time ΦS and Φbulk are obtained by multiplying the average rates RS and Rbulk by the respective volumes. The ratio ΦS/Φtot is plotted at fixed interfacial width l = 14 nm and at different values of ω. These values have the same order of magnitude as the ratio RS/Rbulk measured in our simulations (see Methods).