Scaling in Complex Systems: Analytical Theory of Charged Pores
  In this paper we find an analytical solution of the equilibrium ion distribution for a toroidal model of a ionic channel, using the Perfect Screening Theorem (PST). The ions are charged hard spheres, and are treated using a variational Mean Spherical Approximation (VMSA) .   Understanding ion channels is still a very open problem, because of the many exquisite tuning details of real life channels. It is clear that the electric field plays a major role in the channel behaviour, and for that reason there has been a lot of work on simple models that are able to provide workable theories. Recently a number of interesting papers have appeared that discuss models in which the effect of the geometry, excluded volume and non-linear behaviour is considered.   We present here a 3D model of ionic channels which consists of a charged, deformable torus with a circular or elliptical cross section, which can be flat or vertical (close to a cylinder). Extensive comparisons to MC simulations were performed.   The new solution opens new possibilities, such as studying flexible pores, and water phase transformations inside the pores using an approach similar to that used on flat crystal surfaces . 
A. Enriquez and L. Blum