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.