Mechanics of DNA packaging in viruses

Abstract

A new generation of single-molecule experiments has opened up the possibility of reexamining many of the fundamental processes of biochemistry and molecular biology from a unique and quantitative perspective. One technique producing a host of intriguing results is the use of optical tweezers to measure the mechanical forces exerted by molecular motors during key processes such as the transcription of DNA or the packing of a viral genome into its capsid. The objective of the current article is to respond to such measurements on viruses and to use the theory of elasticity and a simple model of charge and hydration forces to derive the force required to pack DNA into a viral capsid as a function of the fraction of the viral genome that has been packed. The results are found to be in excellent accord with recent measurements and complement previous theoretical work. Because the packing of DNA in viral capsids occurs under circumstances of high internal pressure, we also compute how much pressure a capsid can sustain without rupture.

Fig 1.

Three simplified models of the viral capsid used to illustrate the calculation of the packing energy. These models are a cross-sectional cut through the capsid and the shaded circles represent the strands of DNA that point into and emerge from the page.

Fig 2.

Spacing between DNA strands as a function of the percent of genome packed for cylindrical and spherical capsid geometries. We assume repulsive solvent conditions with F₀ = 2 × 55,000 pN/nm² (a) or F₀ = 4.1 × 55,000 pN/nm² (b). The capsid dimensions are chosen so their volumes coincide with the φ29 virus. Curve c is the spacing between strands assuming a uniform packing of the capsid.

Fig 3.

Force as a function of the percent packed for a cylindrical capsid under purely repulsive solvent conditions. The dimensions of the capsid and the length of genome packed were chosen to correspond to the φ29 phage: R_out = 19.4 nm, z = 37.9 nm, and L = 6.58 μm. Curve b shows the experimental results of Smith et al. (7), while theoretical curves a, c, and d are given by Eq. 19, with F₀ = 2 × 55,000, 4.1 × 55,000, and 6 × 55,000 pN/nm², respectively.

Fig 4.

Rupture pressure as a function of capsid radius for x* = 0.3 nm (upper curve) and x* = 0.4 nm (lower curve). The width of the capsid walls was set to ΔR = 1.5 nm, while V₀ = 125 pN/nm. CCMV, cowpea chlorotic mottle virus. (Inset) The radial and circumferential stress on a capsid wall element.