Heterogeneity induced Block Copolymer Segregation in Confinement

Motivated by the work on block copolymer models that provide insights into epigenetics driven chromosome organization, we investigate the segregation behavior of five distinct 2-block co-polymers (BCPs) system with varying block sizes, confined within both symmetric and lateral geometries. Using exact enumeration method and Langevin dynamics simulation, our simple self-avoiding polymer model reveals robust behaviors (across statics and dynamic studies) despite strong finite-size effects. We observe that as block length increases, polymer compaction intensifies relying on non-specific interaction, leading to longer segregation times. The dynamic study clearly demonstrates the formation of globular lamellar phases and condensed, stable complex structures in long-range block copolymer (BCP) systems, providing a simplified analogy to lamellar-mediated chromatin compaction, which involves structures that are difficult to segregate under physiological conditions. Dominance of specific interaction over non-specific interaction in long range BCP systems leads to phase separation driven self assemblies which provides a simplified analogy to heterochromatin--inactive or stable domains. In contrast, short-range block sequences remain in a coiled state, exhibiting minimal overlap or interaction due to strong short range attraction, which may corresponds to euchromatin regions where diverse epigenetic states coexist, resulting in active, non-condensed structures. We also observe that asymmetric or lateral confinement favors more segregation between the BCPs irrespective of their underlying sequence.