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Open Access Research article

Long range Debye-Hückel correction for computation of grid-based electrostatic forces between biomacromolecules

Paolo Mereghetti12, Michael Martinez1 and Rebecca C Wade13*

Author Affiliations

1 Molecular and Cellular Modeling Group, Heidelberg Institute for Theoretical Studies (HITS), Schloß-Wolfsbrunnenweg 35, 69118 Heidelberg, Germany

2 Center for Nanotechnology Innovation@NEST, Italian Institute of Technology, Piazza San Silvestro 12, Pisa, Italy

3 Center for Molecular Biology (ZMBH), University of Heidelberg, Im Neuenheimer Feld 282, 69120 Heidelberg, Germany

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BMC Biophysics 2014, 7:4  doi:10.1186/2046-1682-7-4

Published: 17 June 2014



Brownian dynamics (BD) simulations can be used to study very large molecular systems, such as models of the intracellular environment, using atomic-detail structures. Such simulations require strategies to contain the computational costs, especially for the computation of interaction forces and energies. A common approach is to compute interaction forces between macromolecules by precomputing their interaction potentials on three-dimensional discretized grids. For long-range interactions, such as electrostatics, grid-based methods are subject to finite size errors. We describe here the implementation of a Debye-Hückel correction to the grid-based electrostatic potential used in the SDA BD simulation software that was applied to simulate solutions of bovine serum albumin and of hen egg white lysozyme.


We found that the inclusion of the long-range electrostatic correction increased the accuracy of both the protein-protein interaction profiles and the protein diffusion coefficients at low ionic strength.


An advantage of this method is the low additional computational cost required to treat long-range electrostatic interactions in large biomacromolecular systems. Moreover, the implementation described here for BD simulations of protein solutions can also be applied in implicit solvent molecular dynamics simulations that make use of gridded interaction potentials.

Continuum solvent electrostatics; Ionic strength; Debye-Hückel; Poisson-Boltzmann equation; Brownian dynamics simulation; Protein diffusion; Discretization grid; Finite difference; Second virial coefficient; Small angle scattering intensity