The mechanics of viral DNA packaging

DNA is packaged by a portal motors within viral capsids of size comparable to the persistence length of the DNA, and thus the packaging carries a steep cost in terms of elastic energy. The scale of the process is equivalent to packing 20 Km of thread in a tennis ball (Alberts et al., Essential Cell Biology, 1997). A number of novel experimental procedures provide data and insight into the packaging process. For instance, Smith et al.~(Nature, 413 (2001) 748) have measured the force required to package the DNA into a Phi29 bacteriophage as a function of the fraction of genome packed. Cryo-electron microscopy experiments have revealed the concentric arrangements of DNA within viral capsids (Ceterelli et al., Cell, 91 (1997) 271; Olson et al., Virology, 279 (2001) 385).

The objective of the present work is to formulate a continuum model of viral DNA packaging. The conformations of the DNA are described in terms of a director field whose point values give the local direction and density of the DNA. The continuity of the DNA strand requires the director field to be divergence-free and tangent to the capsid wall. The operative principle which determines the DNA conformation is assumed to be energy minimization. The energy of the DNA is defined as a functional of the director field which accounts for the bending and torsion of the DNA strand, as well as for charge and hydration forces. The central problem concerns the determination of the energy-minimizing DNA conformations as a function of fraction of genome packed. A baseline conformation is furnished by a simple inverse-spool geometry. We show that the energy of the inverse-spool conformation may be lowered by a construction consisting of the packing of toroidal coils. The predictions of the theory are compared against the available experimental evidence.