Lattice Field Theory Methods in Modern Biophysics

Abstract

An effective field theory exists describing a very large class of biophysically interesting Coulomb gas systems: the lowest order (mean-field) version of this theory takes the form of a generalized Poisson-Boltzmann theory. Interaction terms depend on details (finite-size effects, multipole properties, etc). Convergence of the loop expansion holds only if mutual interactions of mobile charges are small compared to their interaction with the fixed-charge environment, which is frequently not the case. Problems with the strongly- coupled effective theory can be circumvented with an alternative local lattice formulation, with real positive action. In realistic situations, with variable dielectric, a determinant of the Poisson operator must be inserted to generate correct electrostatics. Methods adopted from unquenched lattice QCD do this very efficiently.