Bacteriophages are made from self-assembly of DNA and coat

proteins. The DNA is arranged in spool-like fashion within the shell, or capsid, made from coat proteins, that protect genetic content from external

degradation. Recent in vitro studies highlighted the pressurized state of DNA within capsid, allowing this stored energy to be released as an ejecting force when the phage binds to its specific receptor. These studies also show that this ejecting force can be modulated by the presence of multivalent cations. A striking result of these works is the non-monotonicity of ejecting forces as salt content is increased. This is in apparent conflict with naive physical intuition which claims that increasing ionic strength of the solution screens electrostatic repulsions, partly responsible of DNA pressurization. In order to understand more precisely this phenomenon, we set up a model based on the thermodynamics of two classical and well-known effects in physical chemistry: the Gibbs-Donnan equilibrium and the Langmuir adsorption statistics. The coupling between these two effects, as applied in a translocation geometry, leads to predictions that are qualitatively consistent with experimental results. In particular, the non-monotonicity of the ejecting force is produced, and the location of the minimum decreases with the valency of cations, in accordance to observations.

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