Nucleation of Biomolecular Condensates from Finite-Sized Simulations

The nucleation of protein condensates is a concentration-driven process of assembly. When condensation is modelled in the canonical ensemble - where the total number of peptides is constant - its dynamics and thermodynamics are influenced by finite-size effects, resulting in the formation of a single, stable condensate droplet. Here, we take advantage of a general theoretical description of the thermodynamics of condensate droplet formation in the canonical ensemble to obtain information on the thermodynamics and kinetics of nucleation in the macroscopic limit. We apply our approach to two phase-separating systems with different physicochemical characteristics: NDDX4 and FUS-LC. From the properties of the steady-state condensate droplet obtained in finite-size, coarse-grained molecular simulations of these two peptides, we estimate the macroscopic equilibrium density of the dilute protein solution and the surface tension of the condensates. Analyses of nucleation free energy barriers reveal that NDDX4 dilute phases are kinetically unstable over a wide range of concentrations. FUS-LC condensation, on the other hand, is consistently associated with activated nucleation events. Differences in the behaviour of the two systems can be explained by different contributions to bulk and surface free energies of the emerging phases, which correlate with single-chain hydrophilicity and the dynamics of monomer exchange between the condensate and lean solution. The approach presented here is general and provides a straightforward and efficient route to obtain emergent, ensemble properties of protein condensates from finite-sized nucleation simulations.