Theoretical models of emergent structure and organization in (bio-) polymeric systems.

Abstract

In the first part of the study, I discuss how free-standing, helices may occur in semi-flexible polymeric systems without using torsional potentials. The helical motif is ubiquitous in macro-molecular systems and understanding the emergence of these structures is of interest to a broad community of researchers. Experiments have shown how a polymeric chain made of micron-sized colloidal monomers spontaneously forms a helical structure when the chain is heated above a threshold temperature. I outline how a minimal coarse-grained polymer model provides mechanistic insights into the formation of these structures [1]. Furthermore, in a separate study, I establish that switching on generic interactions e.g. the bare Coulomb potential or other long-ranged spherically symmetric repulsive interactions between monomers of the bead-spring model of a uniformly-charged, semi-flexible polymer, induce instabilities which results in the formation of transient helical structures [2]. The key factors which control the emergence of these structures is the persistence length and the charge density. The transient helices may also be induced by switching on screened Coulomb interactions, such that monomers have charges of differing polarities. and magnitudes. Moreover, the transient helices can be made long-lived when the polymer is confined to a cuboid of appropriate dimensions. In the second part of the study, I elucidate key aspects of the organization of bacterial chromosomes at micron-length scales. The mechanism of chromosome organization of E.coli is one of the least understood aspects of its life cycle. In this thesis we rely on the principles of entropic repulsion to shed light on the organization of E.coli chromosome. The E.coli chromosome is often modeled as a bead spring ring polymer. We introduce cross-links in the DNA ring polymer, resulting in the formation of loops within each bacterial chromosome. I use simulations to show that the chosen polymer topology leads to an emergent organization of the chromosome-polymer along the cell long-axis, such that various segments get spatially localized as seen in-vivo, through FISH experiments. This organization relies on the mechanism of entropic repulsion between the constituent loops. Additionally, the contact map generated from our simulations reproduces the macro-domain-like organization, as seen in Hi-C maps of previous experiments. Thus, observations from complementary experimental techniques probing bacterial chromosome organization were reconciled [3]. In a different study, I outline the principles by which certain ring polymer architectures lead to higher entropic forces of segregation, in confinement. Furthermore, I show how the polymer organizes itself in different ways in cylindrical confinement depending on the polymer topology it adopts. The results were validated using an analytical blob-theory approach. Lastly, it was established that the same mechanism can also be invoked to explain the organization of C.crescentus chromosomes [4].