Forces during bacteriophage DNA packaging and ejection

Abstract

The conjunction of insights from structural biology, solution biochemistry, genetics, and single-molecule biophysics has provided a renewed impetus for the construction of quantitative models of biological processes. One area that has been a beneficiary of these experimental techniques is the study of viruses. In this article we describe how the insights obtained from such experiments can be utilized to construct physical models of processes in the viral life cycle. We focus on dsDNA bacteriophages and show that the bending elasticity of DNA and its electrostatics in solution can be combined to determine the forces experienced during packaging and ejection of the viral genome. Furthermore, we quantitatively analyze the effect of fluid viscosity and capsid expansion on the forces experienced during packaging. Finally, we present a model for DNA ejection from bacteriophages based on the hypothesis that the energy stored in the tightly packed genome within the capsid leads to its forceful ejection. The predictions of our model can be tested through experiments in vitro where DNA ejection is inhibited by the application of external osmotic pressure.

FIGURE 1

Life cycle of a bacterial virus. The ejection of the genome into the host cell happens within a minute for phage like λ and T4 (Novick and Baldeschwieler, 1988; Letellier et al., 2004). The eclipse period (time between the viral adsorption and the first appearance of the progeny) can be as short as ∼10–15 min (Endy et al., 1997). The packaging of the genome into a single capsid takes ∼5 min (Smith et al., 2001). Lysis of the bacterial cell is completed in <1 h (Endy et al., 1997).

FIGURE 2

Pressure in a hexagonal lattice of DNA, according to experiment and Poisson-Boltzmann theory. Experimental data points are from the data of Rau et al. (1984) for 25 mM and 5 mM Mg²⁺ concentrations. Our theoretical calculations follow from a discrete one-dimensional Poisson-Boltzmann solver, assuming cylindrical symmetry. The free energy was calculated as a sum of the Shannon entropy of the ions and the electrostatic energy of ions and DNA, with the zero point for the potential set so that internal and external ionic concentrations were related by a Boltzmann factor. The theoretical predictions differ from the experimental points by a factor of 10, although the slopes are approximately correct and it is difficult to distinguish between the data for the two different concentrations. Also shown is a least-squares fit to the empirical datapoints, resulting in the parameters c = 0.30 nm and F₀ = 1.2 × 10⁴ pN/nm².

FIGURE 3

Idealized geometries of viral capsids.

FIGURE 4

The spacing d_s in five different phage under fully repulsive conditions with F₀ = 2.3 × 10⁵ pN/nm² and c = 0.27 nm. These values of F₀ and c result in the best visual fit to the data in the experiment on φ29 by Smith et al. (2001) (5 mM MgCl₂ and 50 mM NaCl). The graphs show d_s monotonically decreasing as more of the genome is packaged. T7 is the most tightly packed whereas T4 is most loosely packed. The value λ and HK97 show an almost identical history of d_s versus fraction of genome packed, since the two are closely related structurally.

FIGURE 5

The spacing d_s under repulsive-attractive conditions. We use F₀ = 0.5 pN/nm², d₀ = 2.8 nm and c = 0.14 nm. This corresponds to a solution containing 5 mM Co(NH₃)₆Cl₃, 0.1 M NaCl, 10 mM TrisCl (Kindt et al., 2001; Rau and Parsegian, 1992). The spacing remains at the preferred value of 2.8 nm for most of the packaging process, except in the end when volumetric constraints lead to smaller spacings as a consequence of high energy costs for maintaining this d_s.

FIGURE 6

Comparison of measured spacings d_s with scaling law. The circles correspond to interstrand spacing in T7 obtained by Cerritelli et al. (1997). The stars represent data from Earnshaw and Harrison (1977) for mutants of λ-phage. We fit straight lines to both these data sets to show that the spacing scales with the inverse square-root of the packaged length in capsids that are nearly full.

FIGURE 7

Comparison of forces during DNA packing process for different phage under fully repulsive conditions. T7 requires the largest force to package since it is most densely packed. T4 is at the other end of the spectrum requiring the smallest force. The data above corresponds to F₀ = 2.3 × 10⁵ pN/nm² and c = 0.27 nm obtained by a visual fit to the data of Smith et al. (2001), who conducted the packaging experiment for phage φ29 in a solution containing 5 mM MgCl₂ and 50 mM NaCl.

FIGURE 8

Maximum resistive force in different phage under three different repulsive conditions. a corresponds to F₀ = 1.1 × 10⁵ pN/nm² and c = 0.27 nm; b corresponds to F₀ = 2.3 × 10⁵ pN/nm² and c = 0.27 nm; and c corresponds to F₀ = 3.3 × 10⁵ pN/nm² and c = 0.27 nm. The forces increase with the packing density ρ_pack and also with increasing F₀.

FIGURE 9

Maximum resistive force in φ29 for different salt concentrations. The maximum force increases as the salt concentration decreases since the DNA interstrand repulsion becomes larger as the solution becomes more dilute. The values of F₀ and c for the salt solutions >50 mM used in this figure were obtained from fits to the data of Rau et al. (1984). The leftmost bar represents the data of Smith et al. (2001), and the 50 mM Na⁺ bar was obtained from data communicated privately by D. Rau (2004).

FIGURE 10

Comparison of forces during DNA packing process for different phage under repulsive-attractive conditions with F₀ = 0.5 pN/nm², d₀ = 2.8 nm, and c = 0.14 nm. This corresponds to a solution containing 5 mM CO(NH₃)₆Cl₃, 0.1 M NaCl, 10 mM TrisCl (Kindt et al., 2001; Rau and Parsegian, 1992). The trends seen here are no different from those in the fully repulsive conditions—T7 requires large forces and T4 requires small forces for packaging. The maximum force, however, is significantly smaller than that seen for fully repulsive conditions.

FIGURE 11

Force and interaxial spacing as functions of the amount of DNA packed in bacteriophage φ29. The hexagons correspond to the experimental data of Smith et al. (2001). The continuous lines are the results of the continuum model, and the circles/asterisks are obtained from the discrete model.

FIGURE 12

Fractional DNA ejection in λ-phage as a function of osmotic pressure corresponding to experimental conditions in Evilevitch et al. (2003) (10 mM MgSO₄). The inset shows the best visual fit to the experimental data of Evilevitch et al. (2003) for λ with genome size 41.5 kbp using parameters F₀ and c, and also a parameter free curve obtained from the data of Rau et al. (1984). We see a good match between the experimental findings and the theoretical results. Also shown are the predictions for ejection behavior of λ-phage for genome sizes of 37.4 Kbp, 45 Kbp, 48.5 Kbp, and 51 Kbp under similar experimental conditions.

FIGURE 13

DNA ejection as a function of osmotic pressure for various wild-type species of bacteriophages for ionic conditions similar to the experiments of Evilevitch et al. (2003) (10 mM MgSO₄). The lines show the DNA ejection behavior for T4, HK97, φ29, T7, and λ. Osmotic pressures as high as 35–55 atm are required to inhibit ejection in these bacteriophages.