Abstract
Graph rewriting has been applied quite successfully to model chemical and biological systems at different levels of abstraction. A particularly powerful feature of rule-based models that are rigorously grounded in category theory, is, that they admit a well-defined notion of rule composition, hence, provide their users with an intrinsic mechanism for compressing trajectories and coarse grained representations of dynamical aspects. The same formal framework, however, also allows the detailed analysis of transitions in which the final and initial states are known, but the detailed stepwise mechanism remains hidden. To demonstrate the general principle we consider here how rule composition is used to determine accurate atom maps for complex enzyme reactions. This problem not only exemplifies the paradigm but is also of considerable practical importance for many down-stream analyses of metabolic networks and it is a necessary prerequisite for predicting atom traces for the analysis of isotope labelling experiments.
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References
Fontana, W., Buss, L.W.: What would be conserved if “the tape were played twice”? Proc. Natl. Acad. Sci. USA 91, 757–761 (1994)
Regev, A., Shapiro, E.: Cells as computation. Nature 419, 343 (2002)
Danos, V.: Formal molecular biology. Theor. Comp. Sci. 325, 69–110 (2004)
Blinov, M.L., Yang, J., Faeder, J.R., Hlavacek, W.S.: Graph theory for rule-based modeling of biochemical networks. In: Priami, C., Ingólfsdóttir, A., Mishra, B., Riis Nielson, H. (eds.) Transactions on Computational Systems Biology VII. LNCS (LNBI), vol. 4230, pp. 89–106. Springer, Heidelberg (2006)
Păun, G.: Computing with membranes. J. Comp. Syst. Sci. 61, 108–143 (2000)
Cardelli, L.: Brane calculi. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 257–278. Springer, Heidelberg (2005)
Arnold, C., Stadler, P.F., Prohaska, S.J.: Chromatin computation: Epigenetic inheritance as a pattern reconstruction problem. J. Theor. Biol. 336, 61–74 (2013)
Hlavacek, W., Faeder, J.R., Blinov, M.L., Posner, R.G., Hucka, M., Fontana, W.: Rules for modeling signal-transduction systems. Sci. STKE 6, 334–336 (2006)
Sekar, J.A., Faeder, J.R.: Rule-based modeling of signal transduction: a primer. Methods Mol. Biol. 880, 139–218 (2012)
Berry, G., Boudol, G.: The chemical abstract machine. In: Proceedings of the 17th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 1990, pp. 81–94. Assoc. Computing Machinery, New York (1990)
Benkö, G., Flamm, C., Stadler, P.F.: A graph-based toy model of chemistry. J. Chem. Inf. Comput. Sci. 43, 1085–1093 (2003)
Danos, V., Feret, J., Fontana, W., Harmer, R., Hayman, J., Krivine, J., Thompson-Walsh, C., Winskel, G.: Graphs, rewriting and pathway reconstruction for rule-based models. In: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), vol. 18, pp. 276–288 (2012)
Beck, M., Benkö, G., Eble, G., Flamm, C., Müller, S., Stadler, P.F.: Graph grammars as models for the evolution of developmental pathways. In: Schaub, H., Detje, F., Brüggemann, U. (eds.) The Logic of Artificial Life: Abstracting and Synthesizing the Principles of Living Systems, pp. 8–15. IOS Press, Akademische Verlagsgesellschaft, Berlin (2004)
Sauer, U.: Metabolic networks in motion: 13C-based flux analysis. Mol. Syst. Biol. 2, 62 (2006)
Zamboni, N.: 13C metabolic flux analysis in complex systems. Curr. Opin. Biotech. 22, 103–108 (2011)
Durot, M., Bourguignon, P.Y., Schachter, V.: Genome-scale models of bacterial metabolisn: reconstruction and applications. FEMS Microbiol. Rev. 33, 164–190 (2009)
Feist, A.M., Herrgård, M.J., Thiele, I., Reed, J.L., Palsson, B.Ø.: Reconstruction of biochemical networks in microorganisms. Nature Rev. Microbiol. 7, 129–143 (2009)
Holliday, G.L., Bartlett, G.J., Almonacid, D.E., O’Boyle, N.M., Murray-Rust, P., Thornton, J.M., Mitchell, J.B.O.: MACiE: a database of enzyme reaction mechanisms. Bioinformatics 21, 4315–4316 (2005)
Holliday, G.L., Andreini, C., Fischer, J.D., Rahman, S.A., Almonacid, D.E., Williams, S.T., Pearson, W.R.: MACiE: exploring the diversity of biochemical reactions. Nucleic Acids Research 40, D783–D789 (2012)
Andersen, J.L., Flamm, C., Merkle, D., Stadler, P.F.: Inferring chemical reaction patterns using graph grammar rule composition. J. Syst. Chem. 4(4) (2013)
Cook, S.A.: The complexity of theorem-proving procedures. In: Proceedings of the Third Annual ACM Symposium on Theory of Computing, STOC 1971, pp. 151–158. ACM, New York (1971)
Weininger, D.: SMILES, a chemical language and information system. 1. Introduction to methodology and encoding rules. J. Chem. Inf. Comput. Sci. 28(1), 31–36 (1988)
Weininger, D., Weininger, A., Weininger, J.L.: SMILES 2. Algorithm for Generation of Unique SMILES Notation. J. Chem. Inf. Comput. Sci. 29(2), 97–101 (1989)
Atanasov, B.P., Mustafi, D., Makinen, M.W.: Protonation of the beta-lactam nitrogen is the trigger event in the catalytic action of class A beta-lactamases. Proc. Natl. Acad. Sci. 97(7), 3160–3165 (2000)
Bar-Even, A., Flamholz, A., Noor, E., Milo, R.: Rethinking glycolysis: on the biochemical logic of metabolic pathways. Nat. Chem. Biol. 8(6), 509–517 (2012)
Entner, N., Doudoroff, M.: Glucose and gluconic acid oxidation of pseudomonas saccharophila. J. Biol. Chem. 196, 853–862 (1952)
Borodina, I., Schöller, C., Eliasson, A., Nielsen, J.: Metabolic network analysis of streptomyces tenebrarius, a streptomyces species with an active entner-doudoroff pathway. Appl. Environ. Microbiol. 71(5), 2294–2302 (2005)
Romano, A.H., Conway, T.: Evolution of carbohydrate metabolic pathways. Res. Microbiol. 147(6/7), 448–455 (1996)
Stettner, A.I., Segré, D.: The cost of efficiency in energy metabolism. PNAS 110(24), 9629–9630 (2013)
Flamholz, A., Noor, E., Bar-Even, A., Liebmeister, W., Milo, R.: Glycolytic stratewgy as a tradeoff between energy yield and protein cost. PNAS 110(24), 10039–10044 (2013)
Benner, S., Kim, H., Ricardo, A.: Planetary organic chemistry and the origins of biomolecules. Cold Spring Harb. Perspect. Biol. 2(7), a003467 (2010)
Breslow, R.: On the mechanism of the formose reaction. Tetrahedron Letters 1(21) (1959)
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Andersen, J.L., Flamm, C., Merkle, D., Stadler, P.F. (2014). 50 Shades of Rule Composition. In: Fages, F., Piazza, C. (eds) Formal Methods in Macro-Biology. FMMB 2014. Lecture Notes in Computer Science(), vol 8738. Springer, Cham. https://doi.org/10.1007/978-3-319-10398-3_9
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DOI: https://doi.org/10.1007/978-3-319-10398-3_9
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