This article presents a fast adaptive method for the computation of long‐range
electrostatic interactions in computer simulations of polyelectrolyte DNA. Classically,
the computation of electrostatic energy involves a direct summation of all pairwise in
teractions due to the charged phosphate groups in the molecule. This results in an
N‐body interaction problem with an asymptotic time complexity of
O(N2) which is computationally very expensive and limits the
number of phosphate groups that can be used in computer simulations of polyelectrolyte
DNA to at most several hundred. We describe an effort to speed up computer simulations
of polyelectrolyte DNA with the use of a fast adaptive hierarchical algorithm for the
computation of electrostatic energy (i.e., modified Debye–Hückel energy).
The asymptotic time complexity is reduced to O(N) with the implementation
of the fast hierarchical algorithm on serial computers. This is achieved by grouping
phosphate groups into an adaptive hierarchical data structure and computing the
interactions between groups using low order multipole and Taylor series expansions
expressed in Cartesian coordinates. We first examine the accuracy and speed
enhancements of the fast hierarchical method in the computation of the electrostatic
energy of circular DNA at zero and high salt concentrations. The fast hierarchical
method is further tested in a one‐step Monte Carlo (MC) simulated annealing algorithm
for closed circular supercoiled DNA. In all cases, we observe order of magnitude
reductions in the computation time with negligible loss of numerical accuracy in the
electrostatic energy computation. © 1996 by John Wiley & Sons, Inc.