By assuming that not only counter-ions but DNA molecules as well are thermally distributed according to a Boltzmann law, we propose a modified Poisson-Boltzmann equation, at the classical level, as a starting point to compute the effects of quantum fluctuations of the electric field on the interaction among DNA-cation complexes. The latter are modeled here as infinite one-dimensional wires (δ-functions). Our goal is to single out such quantum-vacuum-driven interaction from the counterion-induced and water-related interactions. We obtain a universal, frustration-free Casimir-like (codimension 2) interaction that extensive numerical analysis show to be a good candidate to explain the formation and stability of DNA aggregates. Such Casimir energy is computed for a variety of configurations of up to 19 DNA strands in a hexagonal array. It is found to be many-body.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.