Skip to main content
SpringerLink
Log in

Chemical Graph Transformation with Stereo-Information

  • Conference paper
  • First Online:
Graph Transformation (ICGT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10373))

Included in the following conference series:

Abstract

Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms and their neighbours in space. Stereoisomers of chemical compounds thus cannot be distinguished, even though their chemical activity may differ substantially. In this contribution we propose an extended chemical graph transformation system with attributes that encode information about local geometry. The modelling approach is based on the so-called “ordered list method”, where an order is imposed on the set of incident edges of each vertex, and permutation groups determine equivalence classes of orderings that correspond to the same local spatial embedding. This method has previously been used in the context of graph transformation, but we here propose a framework that also allows for partially specified stereoinformation. While there are several stereochemical configurations to be considered, we focus here on the tetrahedral molecular shape, and suggest general principles for how to treat all other chemically relevant local geometries. We illustrate our framework using several chemical examples, including the enumeration of stereoisomers of carbohydrates and the stereospecific reaction for the aconitase enzyme in the citirc acid cycle.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Akutsu, T.: A new method of computer representation of stereochemistry. Transforming a stereochemical structure into a graph. J. Chem. Inf. Comput. Sci. 31, 414–417 (1991)

    Article  Google Scholar 

  2. Andersen, J.L.: MedØlDatschgerl (MØD) (2016). http://mod.imada.sdu.dk

  3. Andersen, J.L., Flamm, C., Merkle, D., Stadler, P.F.: Inferring chemical reaction patterns using rule composition in graph grammars. J. Syst. Chem. 4(1), 4 (2013)

    Article  Google Scholar 

  4. Andersen, J.L., Flamm, C., Merkle, D., Stadler, P.F.: Generic strategies for chemical space exploration. Int. J. Comput. Biol. Drug Des. 7(2/3), 225–258 (2014). http://arxiv.org/abs/1302.4006

  5. Andersen, J.L., Flamm, C., Merkle, D., Stadler, P.F.: A software package for chemically inspired graph transformation. In: Echahed, R., Minas, M. (eds.) ICGT 2016. LNCS, vol. 9761, pp. 73–88. Springer, Cham (2016). doi:10.1007/978-3-319-40530-8_5

    Chapter  Google Scholar 

  6. Benkö, G., Flamm, C., Stadler, P.F.: A graph-based toy model of chemistry. J. Chem. Inf. Comput. Sci. 43, 1085–1093 (2003)

    Article  Google Scholar 

  7. Cordella, L., Foggia, P., Sansone, C., Vento, M.: A (sub) graph isomorphism algorithm for matching large graphs. IEEE Trans. Pattern Anal. Mach. Intell. 26(10), 1367 (2004)

    Article  Google Scholar 

  8. Cross, L.C., Klyne, W.: Rules for the nomenclature of organic chemistry: section E: stereochemistry. Pure Appl. Chem. 45, 11–30 (1976)

    Google Scholar 

  9. Ehrig, H., Ehrig, K., Prange, U., Taenthzer, G.: Fundamentals of Algebraic Graph Transformation. Springer, Berlin (2006)

    MATH  Google Scholar 

  10. Ehrig, K., Heckel, R., Lajios, G.: Molecular analysis of metabolic pathway with graph transformation. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds.) ICGT 2006. LNCS, vol. 4178, pp. 107–121. Springer, Heidelberg (2006). doi:10.1007/11841883_9

    Chapter  Google Scholar 

  11. Faulon, J.L., Visco Jr., D., Roe, D.: Enumerating Molecules, Reviews in Computational Chemistry, vol. 21, pp. 209–286. Wiley, Hoboken (2005)

    Book  Google Scholar 

  12. Flack, H.D.: Louis Pasteur’s discovery of molecular chirality and spontaneous resolution in 1848, together with a complete review of his crystallographic and chemical work. Acta Crystallogr. Sect. A 65, 371–389 (2009)

    Article  Google Scholar 

  13. Fontana, W., Buss, L.W.: “The arrival of the fittest”: toward a theory of biological organization. Bull. Math. Biol. 56, 1–64 (1994)

    MATH  Google Scholar 

  14. Fontana, W., Buss, L.W.: What would be conserved “if the tape were played twice”. Proc. Natl. Acad. Sci. USA 91, 757–761 (1994)

    Article  Google Scholar 

  15. Gillespie, R.: Fifty years of the VSEPR model. Coord. Chem. Rev. 252, 1315–1327 (2008)

    Article  Google Scholar 

  16. Kerber, A., Laue, R., Meringer, M., Rücker, C., Schymanski, E.: Mathematical Chemistry and Chemoinformatics. De Gruyter (2013)

    Google Scholar 

  17. Kreowski, H.J., Kuske, S.: Graph multiset transformation: a new framework for massively parallel computation inspired by DNA computing. Nat. Comput. 10(2), 961–986 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. de Lara, J., Bardohl, R., Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Attributed graph transformation with node type inheritance. Theor. Comput. Sci. 376(3), 139–163 (2007). http://www.sciencedirect.com/science/article/pii/S0304397507000631

    Article  MathSciNet  MATH  Google Scholar 

  19. Lewis, G.N.: The atom and the molecule. J. Am. Chem. Soc. 38, 762–785 (1916)

    Article  Google Scholar 

  20. Petrarca, A.E., Lynch, M.F., Rush, J.E.: A method for generating unique computer structural representation of stereoisomers. J. Chem. Doc. 7, 154–165 (1967)

    Article  Google Scholar 

  21. Pólya, G.: Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen. Acta Mathematica 68(1), 145–254 (1937)

    Article  MathSciNet  MATH  Google Scholar 

  22. Pólya, G., Read, R.: Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds. Springer, New York (1987)

    Book  Google Scholar 

  23. Redfield, J.: The theory of group-reduced distributions. Am. J. Math. 49(3), 433–455 (1927)

    Article  MathSciNet  MATH  Google Scholar 

  24. Rosselló, F., Valiente, G.: Graph transformation in molecular biology. In: Kreowski, H.-J., Montanari, U., Orejas, F., Rozenberg, G., Taentzer, G. (eds.) Formal Methods in Software and Systems Modeling. LNCS, vol. 3393, pp. 116–133. Springer, Heidelberg (2005). doi:10.1007/978-3-540-31847-7_7

    Chapter  Google Scholar 

  25. Satoh, H., Koshino, H., Funatsu, K., Nakata, T.: Novel canonical coding method for representation of three-dimensional structures. J. Chem. Inf. Comput. Sci. 40, 622–630 (2000)

    Article  Google Scholar 

  26. Taentzer, G.: AGG: a graph transformation environment for modeling and validation of software. In: Pfaltz, J.L., Nagl, M., Böhlen, B. (eds.) Applications of Graph Transformations with Industrial Relevance: Second International Workshop, AGTIVE 2003. LNCS, vol. 3062, pp. 446–453. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  27. Weininger, D.: SMILES, a chemical language and information system. 1. Introduction to methodology and encoding rules. J. Chem. Inf. Model. 28, 31–36 (1988)

    Article  Google Scholar 

  28. Wipke, W.T., Dyott, T.M.: Simulation and evaluation of chemical synthesis-computer representation and manipulation of stereochemistry. J. Am. Chem. Soc. 96, 4825–4834 (1974)

    Article  Google Scholar 

  29. Yadav, M.K., Kelley, B.P., Silverman, S.M.: The potential of a chemical graph transformation system. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds.) ICGT 2004. LNCS, vol. 3256, pp. 83–95. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30203-2_8

    Chapter  Google Scholar 

Download references

Acknowledgements

This work is supported by the Danish Council for Independent Research, Natural Sciences, the COST Action CM1304 “Emergence and Evolution of Complex Chemical Systems”, and the ELSI Origins Network (EON), which is supported by a grant from the John Templeton Foundation. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation.

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Southern Denmark, 5230, Odense, Denmark

    Jakob Lykke Andersen & Daniel Merkle

  2. Institute for Theoretical Chemistry, University of Vienna, 1090, Wien, Austria

    Christoph Flamm & Peter F. Stadler

  3. Bioinformatics Group, Department of Computer Science, and Interdisciplinary Center for Bioinformatics, University of Leipzig, 04107, Leipzig, Germany

    Peter F. Stadler

  4. Max Planck Institute for Mathematics in the Sciences, 04103, Leipzig, Germany

    Peter F. Stadler

  5. Fraunhofer Institute for Cell Therapy and Immunology, 04103, Leipzig, Germany

    Peter F. Stadler

  6. Center for Non-coding RNA in Technology and Health, University of Copenhagen, 1870, Frederiksberg, Denmark

    Peter F. Stadler

  7. Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, NM, 87501, USA

    Peter F. Stadler

  8. Research Network Chemistry Meets Microbiology, University of Vienna, 1090, Wien, Austria

    Christoph Flamm

  9. Tokyo Institute of Technology, Earth-Life Science Institute, Tokyo, 152-8550, Japan

    Jakob Lykke Andersen

Authors
  1. Jakob Lykke Andersen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christoph Flamm
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daniel Merkle
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Peter F. Stadler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Jakob Lykke Andersen or Daniel Merkle .

Editor information

Editors and Affiliations

  1. Universidad Autónoma de Madrid, Madrid, Spain

    Juan de Lara

  2. University of York, York, United Kingdom

    Detlef Plump

A Code Examples

A Code Examples

The following code shows how to use the stereochemical extension of MØD, in the context of the three application examples. The code is also available as modifiable scripts in the live version of the software, accessible at http://mod.imada.sdu.dk/playground.html.

1.1 A.1 Stereospecific Aconitase

Executing the following code creates the figures for Fig. 7.

figure c

1.2 A.2 Stereoisomers of Tartaric Acid

Executing the following code creates the figures for Figs. 8 and 9.

figure d

1.3 A.3 Non-trivial Stereoisomers

Executing the following code creates the figures for Figs. 8 and 10.

figure e

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Andersen, J.L., Flamm, C., Merkle, D., Stadler, P.F. (2017). Chemical Graph Transformation with Stereo-Information. In: de Lara, J., Plump, D. (eds) Graph Transformation. ICGT 2017. Lecture Notes in Computer Science(), vol 10373. Springer, Cham. https://doi.org/10.1007/978-3-319-61470-0_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-61470-0_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61469-4

  • Online ISBN: 978-3-319-61470-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation