A differential equation for the Generalized Born radii

The Generalized Born (GB) model offers a convenient way of representing electrostatics in complex macromolecules like proteins or nucleic acids. The computation of atomic GB radii is currently performed by different non-local approaches involving volume or surface integrals. Here we obtain a non-linearsecond-order partial differential equation for the Generalized Born radius, which may be solved using to the reaction field obeys Laplace\u2019s equation. The equation admits as particular solutions the correct GB local iterative algorithms. The equation is derived under the assumption that the usual GB approximation radii for the sphere and the plane. The tests performed on a set of 55 different proteins show an overall agreement with other reference GB models and \u2018\u2018perfect\u2019\u2019 Poisson\u2013Boltzmann based values