  The classical electrostatic interaction between DNA molecules in water in the
presence of counterions is reconsidered and we propose it is governed by a
modified Poisson-Boltzmann equation. Quantum fluctuations are then studied and
shown to lead to a vacuum interaction that is numerically computed for several
configurations of many DNA strands and found to be strongly many-body. This
Casimir vacuum interaction can be the ``glue'' holding together DNA molecules
into aggregates.
