  Cells contain multiple condensates which spontaneously form due to the
heterotypic interactions between their components. Although the proteins and
disordered region sequences that are responsible for condensate formation have
been extensively studied, the rule of interactions between the components that
allow demixing, i.e., the coexistence of multiple condensates, is yet to be
elucidated. Here we construct an effective theory of the interaction between
heteropolymers by fitting it to the molecular dynamics simulation results
obtained for more than 200 sequences sampled from the disordered regions of
human proteins. We find that the sum of amino acid pair interactions across two
heteropolymers predicts the Boyle temperature qualitatively well, which can be
quantitatively improved by the dimer pair approximation, where we incorporate
the effect of neighboring amino acids in the sequences. The improved theory,
combined with the finding of a metric that captures the effective interaction
strength between distinct sequences, allowed the selection of up to three
disordered region sequences that demix with each other in multicomponent
simulations, as well as the generation of artificial sequences that demix with
a given sequence.The theory points to a generic sequence design strategy to
demix or hypermix thanks to the low dimensional nature of the space of the
interactions that we identify. As a consequence of the geometric arguments in
the space of interactions, we find that the number of distinct sequences that
can demix with each other is strongly constrained, irrespective of the choice
of the coarse-grained model. Altogether, we construct a theoretical basis for
methods to estimate the effective interaction between heteropolymers, which can
be utilized in predicting phase separation properties as well as rules of
assignment in the localization and functions of disordered proteins.
