Inferring the helix-helix electrostatic interaction strength from the structure of dense DNA toroids

DNA is often condensed to remarkably dense phases, where one or more chains are curved at scales comparable to their persistence length. This can happen in the presence of highly valent cations, like in the capsids of some bacteriophage viruses, where a long DNA chain is rolled up to nearly crystalline densities with spermidine(3+) and putrescine(2+). Despite their biological relevance, cation-mediated helix-helix electrostatic interactions remain poorly understood and their experimental measurement limited to arrays of locally parallel DNA helices. These forces relying on strong spatial correlations between charges on neighbouring helices, straight DNA chains may interact differently than curved ones. We are able to infer the strength of helix-helix electrostatic forces in a spermine(4+)-condensed DNA toroid, predicting with a minimal model the inter-helical spacing spatial inhomogeneities observed in our recent cryo-electron microscopy experiments. Our results suggest that electrostatic cohesion may be one order of magnitude weaker in toroids than in other DNA condensates with less local curvature. Curvature-reduced electrostatic interactions may facilitate DNA ejection dynamics in bacteriophages.