Twist dominates bending in the liquid crystal organization of bacteriophage DNA

TL;DR

The predicted knot distribution agrees with experimental data from P4, demonstrating consistency between elasticity, topology, and observed genome organization.

Abstract

DNA frequently adopts liquid-crystalline conformations in both cells and viruses. The Oseen--Frank framework provides a powerful continuum description of these phases through three elastic moduli: splay ($K_1$), twist or cholesteric ($K_2$), and bending ($K_3$). While $K_1$ is typically assumed to dominate, the relative magnitude of $K_2$ and $K_3$ in confined DNA remains poorly understood. Here, we combine cryo-electron microscopy, liquid-crystal modeling, and knot theory to quantify this relationship in bacteriophage P4, whose genome is partially organized in a spool-like liquid-crystalline phase. We first show experimentally that the ordered DNA occupies three concentric layers within the capsid. We then formulate an Oseen--Frank model for this geometry and use it, together with the measured layer radii, to estimate the elastic ratio $α= K_3/K_2$. We find $α\approx 0.0064$, indicating that twist elasticity overwhelmingly dominates bending. To validate this result, we perform Langevin dynamics simulations of DNA trajectories and classify the resulting knots. The predicted knot distribution agrees with experimental data from P4, demonstrating consistency between elasticity, topology, and observed genome organization.

Figures (4)

• Figure 1: Concentric layer architecture observed in P4 bacteriophages: A) Central slice along a 5 fold symmetry axis of the 3D cryoEM reconstruction of P4 nucleocapsid B) Same as A) with concentric DNA and capsid layers identified C) Pixel normalized radial intensity profile of image shown in A). D) Chart radial values for concentric layers. Only layers 3 to 6 are consistent across projections.
• Figure 2: Multiple DNA simulations plotted with KnotPlot Scharein2024. Minimizer solution to the Euler-Lagrange equation (a). Simulated trajectories of a $3_1$ knot (b), $4_1$ knot (c) and $5_1$ knot (d)
• Figure 3: Knotting distribution obtained for 3 layers containing 2200 nm of DNA. The value of $\alpha=0.0064$.
• Figure 4: Layer structure observed on P4 bacteriophages: Electron density maps as a function of the distance from the center of the capsid along a 2-fold and 3-fold axis. The inserts show the images of bacteriophage particles projected along a 2 and a 3 fold axis and a cartoon of an icosahedron highlighting these projections.