Fluctuation Assisted Ejection of DNA From Bacteriophage

The role of thermal pressure fluctuations in the ejection of tightly packaged DNA from protein capsid shells is discussed in a model calculation. At equilibrium before ejection we assume the DNA is folded many times into a bundle of parallel segments that forms an equilibrium conformation at minimum free energy, which presses tightly against internal capsid walls. Using a canonical ensemble at temperature T we calculate internal pressure fluctuations against a slowly moving or static capsid mantle for an elastic continuum model of the folded DNA bundle. It is found that fluctuating pressure on the capsid mantle from thermal excitation of longitudinal acoustic vibrations in the bundle may have root-mean-square values which are several tens of atmospheres for typically small phage dimensions.

💡 Research Summary

The paper presents a theoretical investigation into how thermal pressure fluctuations within a bacteriophage capsid might assist the ejection of tightly packed DNA. The authors begin by assuming that, prior to ejection, the viral genome is folded many times into a dense bundle of parallel DNA segments that presses firmly against the inner capsid wall. This configuration corresponds to a minimum‑free‑energy state where bending elasticity dominates over electrostatic repulsion.

To model the mechanical response of the DNA bundle, the authors treat it as an isotropic elastic continuum and focus on longitudinal acoustic vibrations (i.e., sound waves traveling along the bundle axis). The capsid is considered essentially rigid, so the ends of the bundle are taken to be fixed (node) boundary conditions. Under these assumptions the normal‑mode frequencies are given by ωₙ = (nπ/L)·cₛ, where L is the bundle length, cₛ is the longitudinal sound speed in DNA (≈1.5 km s⁻¹), and n is an integer mode number.

Thermal excitation of these modes is handled within a canonical ensemble at temperature T. By the equipartition theorem each quadratic degree of freedom contributes k_B T/2 to the average energy, so each mode possesses an average kinetic and potential energy of k_B T/2. The mean‑square amplitude of mode n follows ⟨|qₙ|²⟩ = k_B T/(mₙ ωₙ²), where mₙ is the effective mass associated with that mode. The pressure exerted on the capsid wall is derived from the force F(t) = –∂U/∂x, with U the elastic energy of the vibrating bundle. Summing the contributions of all modes up to a realistic high‑frequency cutoff (≈10 GHz) yields a root‑mean‑square (RMS) pressure

 ΔP_RMS = √