  Biomolecules composed of a limited set of chemical building blocks can
co-localize into distinct, spatially segregated compartments known as
biomolecular condensates. While many condensates are known to form
spontaneously via phase separation, it has been unclear how immiscible
condensates with precisely controlled molecular compositions assemble from a
small number of chemical building blocks. We address this question by
establishing a connection between the specificity of biomolecular interactions
and the thermodynamic stability of coexisting condensates. By computing the
minimum interaction specificity required to assemble condensates with target
molecular compositions, we show how to design heteropolymer mixtures that
produce compositionally complex condensates using only a small number of
monomer types. Our results provide insight into how compositional specificity
arises in naturally occurring multicomponent condensates and demonstrate a
rational algorithm for engineering complex artificial condensates from simple
chemical building blocks.
