Abstract
Field-theory simulation by the complex Langevin method offers an alternative to conventional sampling techniques for exploring the forces driving biomolecular liquid-liquid phase separation. Such simulations have recently been used to study several polyampholyte systems. Here, we formulate a field theory corresponding to the hydrophobic/polar (HP) lattice protein model, with finite same-site repulsion and nearest-neighbor attraction between HH bead pairs. By direct comparison with particle-based Monte Carlo simulations, we show that complex Langevin sampling of the field theory reproduces the thermodynamic properties of the HP model only if the same-site repulsion is not too strong. Unfortunately, the repulsion has to be taken weaker than what is needed to prevent condensed droplets from assuming an artificially compact shape. Analysis of a minimal and analytically solvable toy model hints that the sampling problems caused by repulsive interaction may stem from loss of ergodicity.
Highlights
Advances over the past 15 years have identified liquid–liquid phase separation (LLPS) as a driver of compartmentalization in living cells.1,2 Through LLPS, membraneless droplets are formed, with high concentrations of proteins and nucleic acids
fieldtheory simulation (FTS) offers a new tool for investigating the mechanisms of biomolecular LLPS, with potential advantages over traditional particle-based simulation (PBS)
We have studied systems where phase separation is driven by short-range hydrophobic attraction
Summary
Advances over the past 15 years have identified liquid–liquid phase separation (LLPS) as a driver of compartmentalization in living cells. Through LLPS, membraneless droplets are formed, with high concentrations of proteins and nucleic acids. Advances over the past 15 years have identified liquid–liquid phase separation (LLPS) as a driver of compartmentalization in living cells.. Through LLPS, membraneless droplets are formed, with high concentrations of proteins and nucleic acids. In this process, it has been found that intrinsically disordered proteins (IDPs) often play a key role, and several such IDPs have been shown to phase separate on their own.. To gain insight into the forces driving IDP LLPS, a broad set of theoretical and computational methods has been employed. The Flory–Huggins and Voorn–Overbeek 8 mean-field methods provide useful analytical estimates, which, are insensitive to the ordering of the amino acids along the protein chains. By using the random phase approximation, the sequence dependence of polyampholytes can be explored without resorting to extensive simulations, at the price of assuming Gaussian chains
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