📝 SummarXiv

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 $\alpha = K_3/K_2$. We find $\alpha \approx 0.0064$, 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.