Cells possess non-membrane-bound bodies, many of which are now understood as
phase-separated condensates. One class of such condensates is composed of two
polymer species, where each consists of repeated binding sites that interact in
a one-to-one fashion with the binding sites of the other polymer. Previous
biologically-motivated modeling of such a two-component system surprisingly
revealed that phase separation is suppressed for certain combinations of
numbers of binding sites. This phenomenon, dubbed the "magic-number effect",
occurs if the two polymers can form fully-bonded small oligomers by virtue of
the number of binding sites in one polymer being an integer multiple of the
number of binding sites of the other. Here we use lattice-model simulations and
analytical calculations to show that this magic-number effect can be greatly
enhanced if one of the polymer species has a rigid shape that allows for
multiple distinct bonding conformations. Moreover, if one species is rigid, the
effect is robust over a much greater range of relative concentrations of the
two species. Our findings advance our understanding of the fundamental physics
of two-component polymer-based phase-separation and suggest implications for
biological and synthetic systems.Comment: 8 pages + 15 pages S
