Open Access

Zakarya Benayad, Sören von Bülow, Lukas S. Stelzl, Gerhard Hummer

• Disordered proteins and nucleic acids can condense into droplets that resemble the membraneless organelles observed in living cells. MD simulations offer a unique tool to characterize the molecular interactions governing the formation of these biomolecular condensates, their physico-chemical properties, and the factors controlling their composition and size. However, biopolymer condensation depends sensitively on the balance between different energetic and entropic contributions. Here, we develop a general strategy to fine-tune the potential energy function for molecular dynamics simulations of biopolymer phase separation. We rebalance protein-protein interactions against solvation and entropic contributions to match the excess free energy of transferring proteins between dilute solution and condensate. We illustrate this formalism by simulating liquid droplet formation of the FUS low complexity domain (LCD) with a rebalanced MARTINI model. By scaling the strength of the nonbonded interactions in the coarse-grained MARTINI potential energy function, we map out a phase diagram in the plane of protein concentration and interaction strength. Above a critical scaling factor of αc ≈ 0.6, FUS LCD condensation is observed, where α = 1 and 0 correspond to full and repulsive interactions in the MARTINI model, respectively. For a scaling factor α = 0.65, we recover the experimental densities of the dilute and dense phases, and thus the excess protein transfer free energy into the droplet and the saturation concentration where FUS LCD condenses. In the region of phase separation, we simulate FUS LCD droplets of four different sizes in stable equilibrium with the dilute phase and slabs of condensed FUS LCD for tens of microseconds, and over one millisecond in aggregate. We determine surface tensions in the range of 0.01 to 0.4mN/m from the fluctuations of the droplet shape and from the capillary-wave-like broadening of the interface between the two phases. From the dynamics of the protein end-to-end distance, we estimate shear viscosities from 0.001 to 0.02Pas for the FUS LCD droplets with scaling factors α in the range of 0.625 to 0.75, where we observe liquid droplets. Significant hydration of the interior of the droplets keeps the proteins mobile and the droplets fluid.