Sequence Complexity Dictates Polymer Mixing

Polymer association in confined spaces governs diverse phenomena from protein aggregation to DNA condensation. We investigate the sequence-level mechanisms underlying this behavior through exact enumeration of two confined AB-type block copolymers on a two-dimensional lattice, revealing how sequence complexity controls mixing against de-mixing. We reveal that sequence complexity (heterogeneity), quantified by Shannon entropy H2, acts as a determinant between self-folded low-mixed state and high-mixed state. High-complexity sequences (H2 = 1.86 bits) with short-length repeats achieve near-complete inter-chain overlap through cooperative chain collapse, while low-complexity blocky sequences (H2 = 1.26 bits) maintain extended conformations with less overlapping. Free energy analysis reveals a steep increase in mixing barriers for low-complexity compared to surmountable barrier for high-complexity sequences. We find that geometric confinement modulates but does not override these sequence-dependent behaviors, with asymmetric confinement enhancing heterogeneity in overlapping for both sequence type (pronounced in high-H2 sequences). Our theory could be applicable in assessing the phase behavior of repeat protein and nucleic acid sequences.