= Solution
Dense <DNA> packaging opposes three main physical effects. The negatively charged <DNA> backbones repel through <electrostatic interactions>, moderated by <electrostatic screening> and <counterion condensation>. At close approach, <hydration forces> and <excluded volume> become important. Bending a semiflexible <DNA> <polymer> on a radius comparable with its <persistence length> stores <elastic energy>. Confinement also removes configurational <entropy>, and concentrating mobile <counterions> can impose an additional <osmotic pressure> and <free energy> cost. Their relative importance depends on geometry and ionic conditions.
A schematic lytic <bacteriophage> life cycle is illustrated below.
\Image[/past-exam-of-the-biological-physics-course-of-the-university-of-oxford/2021-packaging-cycle.png]
{title=Conceptual lytic <bacteriophage> cycle and active <DNA> packaging}
Attachment recognizes a suitable host; delivery brings the genetic information into the host; host resources support production of components; assembly creates progeny that are released. Some <bacteriophages> instead have a latent integrated phase, but that is not a necessary stage of this lytic schematic.
In many double-stranded <DNA> <bacteriophages>, a portal-associated <molecular motor> uses <ATP hydrolysis> to move <DNA> into a preformed <capsid>. Chemical <free energy> pays for bending, repulsion and confinement, so the opposing <force> rises as filling proceeds. This is active packaging rather than spontaneous equilibrium compaction. <Optical tweezers> can infer that opposing <force> from displacement of a trapped bead and monitor packaging through the changing external <DNA> extension. Such measurements establish the mechanical principle without requiring any virus-handling procedure. The <inverse spool model> used below is an idealized packing geometry, not an exact structural claim for every <bacteriophage>.
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