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. 2013 Mar;20(3):188-98.
doi: 10.1089/cmb.2012.0239.

Charge Group Partitioning in Biomolecular Simulation

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Free PMC article

Charge Group Partitioning in Biomolecular Simulation

Stefan Canzar et al. J Comput Biol. .
Free PMC article

Abstract

Molecular simulation techniques are increasingly being used to study biomolecular systems at an atomic level. Such simulations rely on empirical force fields to represent the intermolecular interactions. There are many different force fields available--each based on a different set of assumptions and thus requiring different parametrization procedures. Recently, efforts have been made to fully automate the assignment of force-field parameters, including atomic partial charges, for novel molecules. In this work, we focus on a problem arising in the automated parametrization of molecules for use in combination with the GROMOS family of force fields: namely, the assignment of atoms to charge groups such that for every charge group the sum of the partial charges is ideally equal to its formal charge. In addition, charge groups are required to have size at most k. We show NP-hardness and give an exact algorithm that solves practical problem instances to provable optimality in a fraction of a second.

Figures

FIG. 1.
FIG. 1.
Reduction from planar 3dm (see Definition 2): every formula image corresponds to a node with weight δ(x) = −1, whereas every formula image corresponds to a node with weight δ(T) = 3. There is an edge between nodes formula image and formula image if and only if formula image. In addition to every formula image, a path (formula image) is attached with weights formula image and formula image.
FIG. 2.
FIG. 2.
Illustration of the tree decomposition-based dynamic programming algorithm. A graph G falls apart into connected components (gray regions) by removing the groups (dashed lines) that intersect bag Xi.
FIG. 3.
FIG. 3.
Calculated ΔGhyd values versus experimental ones, showing the effect of the charge group assignment on the simulated hydration-free energy. The labels in the legend are the same as in Table 1. The solid line represents perfect agreement with experiment, dotted lines indicate the ±5 kJ/mol approximate experimental error.
FIG. 4.
FIG. 4.
Charge group assignments for adenosine tri-phosphate (ATP) at pH 5.0. The total molecular charge is −3. The partial charges are shown in gray. (a) Our optimal assignment according to Definition 1, obtained with k = 5, (b) gromos 53A6 assignment, and (c) assignment by the atb. Note that the C–H segments indicated by the rounded boxes are considered as single atom types in the gromos assignment, whereas they comprise two atoms in the other assignments.

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