Filling the void in confined polymer nematics: Phase transitions in a minimal model of dsDNA packing

Inspired to understand the complex spectrum of space-filling organizations of the dsDNA genome within the capsid of bacterial viruses, we study a minimal, coarse-grained model of single chains densely packed into a finite spherical volume. We build the three basic elements of the model i) the absence of chain ends, ii) the tendency of parallel-strand alignment and iii) a preference of uniform areal density of chain segments- into a polymer nematic theory for confined chains. Given the geometric constraints of the problem, we show that axially symmetric packings fall into one of three topologies: the coaxial spool; the simple solenoid; and the twisted solenoid. Among these, only the twisted solenoid fills the volume without the presence of line-like disclinations, or voids, and is therefore generically preferred in the incompressible limit. An analysis of the thermodynamics behavior of this simple model reveals a rich behavior, a generic sequence of phases from the empty state for small container sizes, to the coaxial spool configuration at intermediate sizes, ultimately giving way, via a second-order, symmetry-breaking transition, to the twisted-solenoid structure above a critical sphere size. Copyright (C) EPLA, 2011