Abstract
The conformational states of a semiflexible polymer enclosed in a volume V:=ℓ3 are studied as stochastic realizations of paths using the stochastic curvature approach developed in [Rev. E 100, 012503 (2019)], in the regime whenever 3ℓ/ℓp>1, where ℓp is the persistence length. The cases of a semiflexible polymer enclosed in a cube and sphere are considered. In these cases, we explore the Spakowitz–Wang–type polymer shape transition, where the critical persistence length distinguishes between an oscillating and a monotonic phase at the level of the mean-square end-to-end distance. This shape transition provides evidence of a universal signature of the behavior of a semiflexible polymer confined in a compact domain.
Highlights
Semiflexible polymers is a term coined to understand a variety of physical systems that involve linear molecules
We carry out an extension of the stochastic curvature formalism introduced in [17] to analyze the conformational states of a semiflexible polymer in a thermal bath for the cases when the polymer is in the open space R3 and when it is in a bounded domain D ⊂ R3
The basic idea of formalism in the 3D case is followed by two postulates, that is, each conformational state corresponds to the realization of a path described by the stochastic Frenet–Serret Eq 5a and Eq 5b, to introduce a stochastic curvature vector k(s), and a second postulate that gives the manner how κ(s) is distributed according to the thermal fluctuations
Summary
Semiflexible polymers is a term coined to understand a variety of physical systems that involve linear molecules. The most popular polymers are industrial plastics, like polyethylene or polystyrene, with various applications in daily life [1, 2] Another prominent example is the DNA compacted in the nucleus of cells or viral DNA/RNA packed in capsids [3, 4]. These last examples are of particular interest since they are confined semiflexible polymers. A common well-known theoretical framework used to describe the fundamental properties of a semiflexible polymer is the well-known worm-like chain model (WLC), which pictures a polymer as a thin wire with a flexibility given by its bending rigidity constant α [8].
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