Numerical Techniques for Applications of Analytical Theories to Sequence-Dependent Phase Separations of Intrinsically Disordered Proteins

TL;DR

This paper provides computational techniques for analyzing sequence-dependent liquid-liquid phase separation in intrinsically disordered proteins, bridging analytical theories with numerical methods and simulations.

Contribution

It introduces practical numerical procedures for extracting phase behavior from analytical models and compares them with explicit-chain simulations for sequence-specific LLPS.

Findings

Determination of spinodal and binodal phase boundaries from free energy functions.

Construction of tie lines for multi-component LLPS systems.

Field-theoretic simulation of heteropolymeric systems using complex Langevin dynamics.

Abstract

Biomolecular condensates, physically underpinned to a significant extent by liquid-liquid phase separation (LLPS), are now widely recognized by numerous experimental studies to be of fundamental biological, biomedical, and biophysical importance. In the face of experimental discoveries, analytical formulations emerged as a powerful yet tractable tool in recent theoretical investigations of the role of LLPS in the assembly and dissociation of these condensates. The pertinent LLPS often involves, though not exclusively, intrinsically disordered proteins engaging in multivalent interactions that are governed by their amino acid sequences. For researchers interested in applying these theoretical methods, here we provide a practical guide to a set of computational techniques devised for extracting sequence-dependent LLPS properties from analytical formulations. The numerical procedures covered include those for the determinination of spinodal and binodal phase boundaries from a general free energy function with examples based on the random phase approximation in polymer theory, construction of tie lines for multiple-component LLPS, and field-theoretic simulation of multiple-chain heteropolymeric systems using complex Langevin dynamics. Since a more accurate physical picture often requires comparing analytical theory against explicit-chain model predictions, a commonly utilized methodology for coarse-grained molecular dynamics simulations of sequence-specific LLPS is also briefly outlined.