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A statistical theory is presented of the magnesium ion interacting withlysozyme under conditions where the latter is positively charged. Temporarilyassuming magnesium is not noncovalently bound to the protein, I solve thenonlinear Poisson-Boltzmann equation accurately and uniformly in a perturbativefashion. The resulting expression for the effective charge, which is largerthan nominal owing to overshooting, is subtle and cannot be asymptoticallyexpanded at high ionic strengths that are practical. An adhesive potentialtaken from earlier work together with the assumption of possibly boundmagnesium is then fitted to be in accord with measurements of the second virialcoefficient by Tessier et al. The resulting numbers of bound magnesium ions asa function of MgBr2 concentration are entirely reasonable compared withdensitometry measurements.

Mean-field theory of the Interaction of the Magnesium Ion with Biopolymers: The Case of Lysozyme