Ion-dependent DNA configuration in bacteriophage capsids

Abstract

Bacteriophages densely pack their long double-stranded DNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure. Experiments have confirmed that the details of the hexagonal packing depend on the electrochemistry of the capsid and its environment. In this work, we propose a biophysical model that quantifies the relationship between DNA configurations inside bacteriophage capsids and the types and concentrations of ions present in a biological system. We introduce an expression for the free energy that combines the electrostatic energy with contributions from bending of individual segments of DNA and Lennard-Jones-type interactions between these segments. The equilibrium points of this energy solve a partial differential equation that defines the distributions of DNA and the ions inside the capsid. We develop a computational approach that allows us to simulate much larger systems than what is possible using the existing molecular-level methods. In particular, we are able to estimate bending and repulsion between the DNA segments as well as the full electrochemistry of the solution, both inside and outside of the capsid. The numerical results show good agreement with existing experiments and with molecular dynamics simulations for small capsids.

Figure 1

Configuration of packed DNA inside a bacteriophage capsid. (a) Side view parallel to the axial direction. The black circle represents the protein capsid, and the blue curve describes the ordered structure of the DNA chain. The red dots in the center describe the disordered core region. (b) Side view perpendicular to the axial direction; each dot represents the intersection of a DNA segment with the cross section. The dots are locally arranged in a hexagonal lattice structure. Note that the distance between neighboring DNA segments may change in space as a function of the distance to the center of the capsid. To see this figure in color, go online.

Figure 2

Number density (nm⁻³) in the r-z plane. (a) DNA, (b) Na⁺, and (c) Cl⁻. To see this figure in color, go online.

Figure 3

Average radial distribution ${\overline{\rho }}_i$(r) under different ionic conditions. (a) 100 mM NaCl, (b) 166 mM NaCl, and (c) 1 M Na Cl. All the curves are renormalized and dimensionless. To see this figure in color, go online.

Figure 4

Probability distributions for DNA (black), Na⁺ (red), and Cl⁻ (blue) under different ionic conditions. (a) 100 mM NaCl, (b) 1 M NaCl, and (c) 100 mM MgCl₂. To see this figure in color, go online.

Figure 5

Distance between the DNA segments as a function of NaCl concentration at cross-sectional locations (11, 0) and (7, 0) in a capsid with radius r₀ = 12.5 nm centered at the origin. To see this figure in color, go online.

Figure 6

The energy from bending, electrostatic, and Lennard-Jones for increasing NaCl concentrations. To see this figure in color, go online.

Figure 7

Distance between the DNA segments as a function of NaCl concentration at cross-sectional locations (22, 0) and (11, 0) in a capsid with radius r₀ = 22.5 nm centered at the origin. To see this figure in color, go online.

Figure 8

Total energy of the system with different amounts N_p (in basepairs) of DNA packed inside of the capsid. To see this figure in color, go online.