Abstract
The Double Pushout (DPO) approach for graph transformation naturally allows an abstraction level of biochemical systems in which individual atoms of molecules can be traced automatically within chemical reaction networks. Aiming at a mathematical rigorous approach for isotopic labeling design we convert chemical reaction networks (represented as directed hypergraphs) into transformation semigroups. Symmetries within chemical compounds correspond to permutations whereas (not necessarily invertible) chemical reactions define the transformations of the semigroup. An approach for the automatic inference of informative labeling of atoms is presented, which allows to distinguish the activity of different pathway alternatives within reaction networks. To illustrate our approaches, we apply them to the reaction network of glycolysis, which is an important and well understood process that allows for different alternatives to convert glucose into pyruvate.
Supported in part by the Independent Research Fund Denmark, Natural Sciences, grant DFF-7014-00041.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Note: The linearisation ids are 1-indexed since they will be used in a semigroup where the tradition is to use the range 1 to n.
References
Andersen, J.L., Flamm, C., Merkle, D., Stadler, P.F.: Inferring chemical reaction patterns using graph grammar rule composition. J. Syst. Chem. 4(1), 4 (2013)
Andersen, J.L., Flamm, C., Merkle, D., Stadler, P.F.: 50 shades of rule composition. In: Fages, F., Piazza, C. (eds.) FMMB 2014. LNCS, vol. 8738, pp. 117–135. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10398-3_9
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). https://doi.org/10.1007/978-3-319-40530-8_5
Andersen, J.L., Flamm, C., Merkle, D., Stadler, P.F.: Chemical transformation motifs – modelling pathways as integer hyperflows. IEEE/ACM Trans. Comput. Biol. Bioinform. (2018)
Andersen, J.L., Merkle, D.: A generic framework for engineering graph canonization algorithms. In: 2018 Proceedings of the 20th Workshop on Algorithm Engineering and Experiments (ALENEX), pp. 139–153 (2018). https://doi.org/10.1137/1.9781611975055.13
Brim, L., Češka, M., Šafránek, D.: Model checking of biological systems. In: Bernardo, M., de Vink, E., Di Pierro, A., Wiklicky, H. (eds.) SFM 2013. LNCS, vol. 7938, pp. 63–112. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38874-3_3
Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., Löwe, M.: Algebraic approaches to graph transformation - part i: basic concepts and double pushout approach. In: Rozenberg, G. (ed.) Handbook of Graph Grammars and Computing by Graph Transformation, chap. 3, pp. 163–245. World Scientific (1997)
East, J., Egri-Nagy, A., Mitchell, J.D., Péresse, Y.: Computing finite semigroups. J. Symb. Comput. (2018, in press). Early access online
Egri-Nagy, A., Nehaniv, C.L.: Hierarchical coordinate systems for understanding complexity and its evolution, with applications to genetic regulatory networks. Artif. Life 14(3), 299–312 (2008). https://doi.org/10.1162/artl.2008.14.3.14305
Egri-Nagy, A., Nehaniv, C.L., Rhodes, J.L., Schilstra, M.J.: Automatic analysis of computation in biochemical reactions. BioSystems 94(1–2), 126–134 (2008). https://doi.org/10.1016/j.biosystems.2008.05.018
Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. Springer-Verlag, Berlin (2006). https://doi.org/10.1007/3-540-31188-2
Flamholz, A., Noor, E., Bar-Even, A., Liebermeister, W., Milo, R.: Glycolytic strategy as a tradeoff between energy yield and protein cost. Proc. Natl. Acad. Sci. 110(24), 10039–10044 (2013)
Ganyushkin, O., Mazorchuk, V.: Classical Finite Transformation Semigroups, vol. 9. Springer, Heidelberg (2009). https://doi.org/10.1007/978-1-84800-281-4
Ginzburg, A.: Algebraic Theory of Automata. Academic Press, Cambridge (1968)
Nehaniv, C.L., et al.: Symmetry structure in discrete models of biochemical systems: natural subsystems and the weak control hierarchy in a new model of computation driven by interactions. Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 373(2046) (2015). https://doi.org/10.1098/rsta.2014.0223
Orth, J.D., Thiele, I., Palsson, B.Ø.: What is flux balance analysis? Nat. Biotech. 28, 245–248 (2010)
Rhodes, J., Nehaniv, C.L., Hirsch, M.W.: Applications of Automata Theory and Algebra. World Scientific, September 2009. https://doi.org/10.1142/7107
Sanders, P.: Algorithm engineering – an attempt at a definition. In: Albers, S., Alt, H., Näher, S. (eds.) Efficient Algorithms. LNCS, vol. 5760, pp. 321–340. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03456-5_22
Schuster, S., Hilgetag, C.: On elementary flux modes in biochemical reaction systems at steady state. J. Biol. Syst. 2(02), 165–182 (1994)
Zeigarnik, A.V.: On hypercycles and hypercircuits in hypergraphs. Discrete Math. Chem. 51, 377–383 (2000)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Andersen, J.L., Merkle, D., Rasmussen, P.S. (2019). Graph Transformations, Semigroups, and Isotopic Labeling. In: Cai, Z., Skums, P., Li, M. (eds) Bioinformatics Research and Applications. ISBRA 2019. Lecture Notes in Computer Science(), vol 11490. Springer, Cham. https://doi.org/10.1007/978-3-030-20242-2_17
Download citation
DOI: https://doi.org/10.1007/978-3-030-20242-2_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-20241-5
Online ISBN: 978-3-030-20242-2
eBook Packages: Computer ScienceComputer Science (R0)