  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.
