Electrostatic Control of Viral Capsid Assembly via Debye Screening Length — E8 Intelligence Research

FINDING: Viral capsid assembly around charged cores is governed by a critical surface charge density set by the Debye screening length, linking electrostatics to icosahedral geometry. | MATH: Debye length \( \lambda_D = \sqrt{\frac{\epsilon_0 \epsilon_r k_B T}{2 n_0 Z^2 e^2}} \) (for symmetric electrolyte); critical charge density \( \sigma_c \propto \frac{\epsilon_0 \epsilon_r k_B T}{e \lambda_D} \cdot f(\text{geometry}) \); in the arxiv paper (0808.2204v2), the equilibrium theory yields a dimensionless control parameter \( \Gamma \sim \frac{Z_{\text{core}} \lambda_B}{\lambda_D} \) where \( \lambda_B = \frac{e^2}{4\pi\epsilon_0\epsilon_r k_B T} \) is the Bjerrum length. The kinetic theory gives an optimal assembly rate at a narrow window of \( \sigma_c \lambda_D^2 / e \approx \text{const} \). | CONNECTION: The critical charge density for a spherical core scales as \( \sigma_c \propto 1/R \) (radius), and the icosahedral capsid's 5-fold and 3-fold symmetry axes align with the lowest-en Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com