  The electrostatic potential in the neighborhood of a biomolecule can be
computed thanks to the non-linear divergence-form elliptic Poisson-Boltzmann
PDE. Dedicated Monte-Carlo methods have been developed to solve its linearized
version (see e.g.Bossy et al 2009, Mascagni & Simonov 2004}). These algorithms
combine walk on spheres techniques and appropriate replacements at the boundary
of the molecule. In the first part of this article we compare recent
replacement methods for this linearized equation on real size biomolecules,
that also require efficient computational geometry algorithms. We compare our
results with the deterministic solver APBS. In the second part, we prove a new
probabilistic interpretation of the nonlinear Poisson-Boltzmann PDE. A Monte
Carlo algorithm is also derived and tested on a simple test case.
