Lattice Field Theory Methods in Modern Biophysics

TL;DR

This paper discusses lattice field theory approaches to biophysical Coulomb systems, highlighting the limitations of mean-field theories and proposing lattice formulations and computational methods from lattice QCD to improve accuracy in complex, strongly-coupled environments.

Contribution

It introduces a lattice formulation for biophysical Coulomb systems that overcomes mean-field limitations and applies lattice QCD techniques for efficient electrostatics calculations.

Findings

Lattice formulations can handle strong coupling regimes.

Determinant insertion improves electrostatics in variable dielectric environments.

Lattice QCD methods enhance computational efficiency.

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.