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 \(\mathcal{NP}\)-hardness and give an exact algorithm capable of solving practical problem instances to provable optimality in a fraction of a second.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alber, J., Dorn, F., Niedermeier, R.: Experimental evaluation of a tree decomposition-based algorithm for vertex cover on planar graphs. Discrete Applied Mathematics 145(2), 219–231 (2005)
Allen, M.P., Tildesley, D.J.: Computer Simulation of Liquids. Oxford University Press, Oxford (1987)
Arnborg, S., Corneil, D.G., Proskurowski, A.: Complexity of finding embeddings in a k-tree. SIAM J. Algebraic Discrete Methods 8(2), 227–284 (1987)
Berendsen, H.J.C., van der Spoel, D., Van Drunen, R.: GROMACS: a message-passing parallel molecular dynamics implementation. Com. Phys. Comm. 91(1-3), 43–56 (1995)
Beveridge, D.L., DiCapua, F.M.: Free energy via molecular simulation: applications to chemical and biomolecular systems. Annu. Rev. Biophys. Biophys. Chem. 18(1), 431–492 (1989)
Bodlaender, H.L.: NC-Algorithms for Graphs with Small Treewidth. In: van Leeuwen, J. (ed.) WG 1988. LNCS, vol. 344, pp. 1–10. Springer, Heidelberg (1989)
Bodlaender, H.L.: A partial k-arboretum of graphs with bounded treewidth. Theor. Comput. Sci. 209(1-2), 1–45 (1998)
Boggara, M.B.B., Faraone, A., Krishnamoorti, R.: Effect of pH and ibuprofen on the phospholipid bilayer bending modulus. J. Phys. Chem. B 114(24), 8061–8066 (2010)
Brooks, B.R., Brooks III, C.L., Mackerell Jr., A.D., Nilsson, L., Petrella, R.J., Roux, B., Won, Y., Archontis, G., Bartels, C., Boresch, S., Caflisch, A., Caves, L., Cui, Q., Dinner, E.: CHARMM: The Biomolecular Simulation Program. J. Comput. Chem. 30(10, sp. iss. si), 1545–1614 (2009)
Cornell, W.D., Cieplak, P., Bayly, C.I., Gould, I.R., Merz, K.M., Ferguson, D.M., Spellmeyer, D.C., Fox, T., Caldwell, J.W., Kollman, P.A.: A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J. Am. Chem. Soc. 117, 5179–5197 (1995)
Dehof, A.K., Rurainski, A., Bui, Q.B.A., Böcker, S., Lenhof, H.-P., Hildebrandt, A.: Automated bond order assignment as an optimization problem. Bioinformatics 27(5), 619–625 (2011)
Dyer, M., Frieze, A.: On the complexity of partitioning graphs into connected subgraphs. Discrete Applied Mathematics 10(2), 139–153 (1985)
Gerber, P.R.: Charge distribution from a simple molecular orbital type calculation and non-bonding interaction terms in the force field mab. J. Comput.-Aided Mol. Des. 12(1), 37–51 (1998)
Goto, S., Okuno, Y., Hattori, M., Nishioka, T., Kanehisa, M.: LIGAND: database of chemical compounds and reactions in biological pathways. Nucleic Acids Res. 30(1), 402–404 (2002)
Horváth, T., Ramon, J., Wrobel, S.: Frequent subgraph mining in outerplanar graphs. Data Min. Knowl. Discov. 21(3), 472–508 (2010)
Jorgensen, W.L., Maxwell, D.S., Tirado-Rives, J.: Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids. J. Am. Chem. Soc. 118(45), 11225–11236 (1996)
Lemkul, J.A., Allen, W.J., Bevan, D.R.: Practical considerations for building GROMOS-compatible small-molecule topologies. J. Chem. Inf. Model. 50(12), 2221–2235 (2010)
Malde, A.K., Zuo, L., Breeze, M., Stroet, M., Poger, D., Nair, P.C., Oostenbrink, C., Mark, A.E.: An automated force field topology builder (ATB) and repository: version 1.0. J. Chem. Theory Comput. 7(12), 4026–4037 (2011)
Oostenbrink, C., Villa, A., Mark, A.E., van Gunsteren, W.F.: A biomolecular force field based on the free enthalpy of hydration and solvation: The GROMOS force-field parameter sets 53A5 and 53A6. J. Comp. Chem. 25(13), 1656–1676 (2004)
Robertson, N., Seymour, P.D.: Graph minors. II. Algorithmic aspects of tree-width. J. Algorithms 7(3), 309–322 (1986)
Schmid, N., Eichenberger, A., Choutko, A., Riniker, S., Winger, M., Mark, A.E., van Gunsteren, W.F.: Definition and testing of the GROMOS force-field versions 54A7 and 54B7. Eur. Biophys. J. 40, 843–856 (2011)
Schüttelkopf, A.W., van Aalten, D.M.: PRODRG: a tool for high-throughput crystallography of protein-ligand complexes. Acta Crystallogr. 60, 1355–1363 (2004)
Scott, W.R.P., Hunenberger, P.H., Tironi, I.G., Mark, A.E., Billeter, S.R., Fennen, J., Torda, A.E., Huber, T., Kruger, P., van Gunsteren, W.F.: The GROMOS biomolecular simulation program package. J. Phys. Chem. A 103(19), 3596–3607 (1999)
Sharma, M., Khanna, S., Bulusu, G., Mitra, A.: Comparative modeling of thioredoxin glutathione reductase from Schistosoma mansoni: a multifunctional target for antischistosomal therapy. J. Mol. Graphics Model. 27(6), 665–675 (2009)
Uehara, R., Factor, K.T.: The number of connected components in graphs and its applications
van Gunsteren, W.F., Bakowies, D., Baron, R., Chandrasekhar, I., Christen, M., Daura, X., Gee, P., Geerke, D.P., Glttli, A., Hünenberger, P.H., Kastenholz, M.A., Oostenbrink, C., Schenk, M., Trzesniak, D., van der Vegt, N.F.A., Yu, H.B.: Biomolecular modeling: Goals, problems, perspectives. Angew. Chem. Int. Ed. 45(25), 4064–4092 (2006)
Villa, A., Mark, A.E.: Calculation of the free energy of solvation for neutral analogs of amino acid side chains. J. Comp. Chem. 23(5), 548–553 (2002)
Yamaguchi, A., Aoki, K.F., Mamitsuka, H.: Graph complexity of chemical compounds in biological pathways. Genome Inform. 14, 376–377 (2003)
Yang, C., Zhu, X., Li, J., Shi, R.: Exploration of the mechanism for LPFFD inhibiting the formation of beta-sheet conformation of A beta(1-42) in water. J. Mol. Model. 16(4), 813–821 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Canzar, S. et al. (2012). Charge Group Partitioning in Biomolecular Simulation. In: Chor, B. (eds) Research in Computational Molecular Biology. RECOMB 2012. Lecture Notes in Computer Science(), vol 7262. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29627-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-29627-7_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29626-0
Online ISBN: 978-3-642-29627-7
eBook Packages: Computer ScienceComputer Science (R0)