Finite-size scaling analysis of protein droplet formation.

Daniel Nilsson,Anders Irbäck

doi:10.1103/physreve.101.022413

Abstract

The formation of biomolecular condensates inside cells often involve intrinsically disordered proteins (IDPs), and several of these IDPs are also capable of forming dropletlike dense assemblies on their own, through liquid-liquid phase separation. When modeling thermodynamic phase changes, it is well known that finite-size scaling analysis can be a valuable tool. However, to our knowledge, this approach has not been applied before to the computationally challenging problem of modeling sequence-dependent biomolecular phase separation. Here we implement finite-size scaling methods to investigate the phase behavior of two 10-bead sequences in a continuous hydrophobic-polar protein model. Combined with reversible explicit-chain Monte Carlo simulations of these sequences, finite-size scaling analysis turns out to be both feasible and rewarding, despite relying on theoretical results for asymptotically large systems. While both sequences form dense clusters at low temperature, this analysis shows that only one of them undergoes liquid-liquid phase separation. Furthermore, the transition temperature at which droplet formation sets in is observed to converge slowly with system size, so that even for our largest systems the transition is shifted by about 8%. Using finite-size scaling analysis, this shift can be estimated and corrected for.

Highlights

Advances over the past decade have shown that, in addition to classical membrane-bound organelles, various membraneless liquidlike droplets of proteins and nucleic acids can be found within living cells [1,2]
We investigate the thermodynamics of droplet formation in this model by using Monte Carlo (MC) methods to generate samples from the canonical (NV T ) ensemble
Using the model and MC methods described in Sec

Summary

Introduction

Advances over the past decade have shown that, in addition to classical membrane-bound organelles, various membraneless liquidlike droplets of proteins and nucleic acids can be found within living cells [1,2]. It has been demonstrated in vitro that several of these IDPs are able to phase separate on their own [3,4,5], depending on the solution conditions. To rationalize the phase behavior of IDPs and its dependence on solution conditions, a variety of theoretical and computational methods have been employed. A widely used method is Flory-Huggins mean-field theory [6,7] and its extension to polyelectrolytes by Voorn and Overbeek [8]. This approach is sensitive only to the overall composition of amino acids but not to their ordering along the chains. One way to overcome this shortcoming without resorting to explicit-chain simulation is offered by the randomphase approximation [9], which has been applied to model the phase-separating ability of IDPs with different charge patterns [10]

Methods

Results

Conclusion