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Biomolecular condensates, physically underpinned to a significant extent byliquid-liquid phase separation (LLPS), are now widely recognized by numerousexperimental studies to be of fundamental biological, biomedical, andbiophysical importance. In the face of experimental discoveries, analyticalformulations emerged as a powerful yet tractable tool in recent theoreticalinvestigations of the role of LLPS in the assembly and dissociation of thesecondensates. The pertinent LLPS often involves, though not exclusively,intrinsically disordered proteins engaging in multivalent interactions that aregoverned by their amino acid sequences. For researchers interested in applyingthese theoretical methods, here we provide a practical guide to a set ofcomputational techniques devised for extracting sequence-dependent LLPSproperties from analytical formulations. The numerical procedures coveredinclude those for the determinination of spinodal and binodal phase boundariesfrom a general free energy function with examples based on the random phaseapproximation in polymer theory, construction of tie lines formultiple-component LLPS, and field-theoretic simulation of multiple-chainheteropolymeric systems using complex Langevin dynamics. Since a more accuratephysical picture often requires comparing analytical theory againstexplicit-chain model predictions, a commonly utilized methodology forcoarse-grained molecular dynamics simulations of sequence-specific LLPS is alsobriefly outlined.

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