A director-field model of DNA packaging in viral capsids

Abstract

The present work is concerned with the formulation of a continuum theory of viral DNA packaging based on a director field representation of the encapsidated DNA. The point values of the director field give the local direction and density of the DNA. The continuity of the DNA strand requires that the director field be divergence-free and tangent to the capsid wall. The energy of the DNA is defined as a functional of the director field which accounts for bending, torsion, and for electrostatic interactions through a density-dependent cohesive energy. The operative principle which determines the encapsidated DNA conformation is assumed to be energy minimization. We show that torsionless toroidal solenoids, consisting of planar coils contained within meridional planes and wrapped around a spool core, and fine mixtures of the solenoid and spool phase, beat the inverse spool construction.