This thesis is concerned with the formulation of a continuum theory of packaging of DNA in bacterial viruses 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 interaction energy. The operative principle which determines the encapsidated DNA conformation is assumed to be energy minimization.The director-field theory is used for the direct formulation and study of two low-energy DNA conformations: the inverse spool and torsionless toroidal solenoids.Analysis of the inverse spool configuration yields predictions of the interaxial spacing and the dependence of the packing force on the packed genome fraction which are found to be in agreement with experiments.Further analysis shows that torsionless toroidal solenoids can achieve lower energy than the inverse spool configuration.Also, the theory is adapted to a framework of numerical optimization, wherein all fields are discretized on a computational lattice, and energy minimizing configurations are sought via simulated annealing and the nonlinear conjugate gradient method.It is shown that the inverse spool conformation is stable in all regions of the virus capsid except in a central core, where the DNA tends to buckle out of the spooling plane.
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A director-field theory of DNA packaging in bacteriophage viruses
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