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Abstract
Introduction
Analysis of Metabolic Pathways
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Biology
Molecular Biology

Graph transformation in molecular biology

Profile image of Francesc RossellóFrancesc Rosselló

2005, Formal Methods in Software and Systems …

https://doi.org/10.1007/978-3-540-31847-7_7
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16 pages

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Abstract

In the beginning, one of the main fields of application of graph transformation was biology, and more specifically morphology. Later, however, it was like if the biological applications had been left aside by the graph transformation community, just to be moved back into the mainstream these very last years with a new interest in molecular biology. In this paper, we review several fields of application of graph grammars in molecular biology, including: the modeling higherdimensional structures of biomolecules, the description of biochemical reactions, the analysis of metabolic pathways, and their potential use in computational systems biology.

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References (54)

  1. Culik II, K., Lindenmayer, A.: Parallel rewriting on graphs and multidimensional development. Int. Journ. of General Systems 3 (1976) 53-66
  2. Mayoh, B.: Multidimensional Lindemayer organisms. In: L-systems. Volume 15 of Lecture Notes in Computer Science., Springer-Verlag (1974) 302-326
  3. Beck, M., Benkö, G., G. Eble, C.F., Müller, S., Stadler, P.: Graph grammars as models for the evolution of developmental pathways. In: The Logic of Artificial Life: Abstracting and Synthesizing the Principles of Living Systems (Proceedings of GWAL 2004), IOS Press (2004) 8-15
  4. Gernert, D.: Graph grammars as an analytical tool in physics and biology. Biosys- tems 43 (1997) 179-187
  5. Mayoh, B.: On patterns and graphs. Preprint (1995)
  6. Cayley, A.: On the mathematical theory of isomers. Philosophical Magazine 47 (1874) 444-446
  7. Waterman, M.S., Smith, T.F.: RNA secondary structure: a complete mathematical analysis. Math. Biosci. 42 (1978) 257-266
  8. Fujita, S.: Computer-Oriented Representation of Organic Reactions. Yoshioka Shoten, Kyoto (2001)
  9. Michal, G., ed.: Biological Pathways: An Atlas of Biochemistry and Molecular Biology. John Wiley & Sons, New York (1999)
  10. Ehrig, H., Mahr, B.: Fundamentals of algebraic specification I: Equations and initial semantics. Springer Verlag (1985)
  11. Reidys, C., Stadler, P.F.: Bio-molecular shapes and algebraic structures. Comput- ers & Chemistry 20 (1996) 85-94
  12. Chan, H.S., Dill, K.A.: Compact polymers. Macromolecules 22 (1989) 4559-4573
  13. Zuker, M., Sankoff, D.: RNA secondary structures and their prediction. Bull. Math. Biol. 46 (1984) 591-621
  14. Westhof, E., L. Jaeger, L.: RNA pseudoknots. Curr. Opinion Struct. Biol. 2 (1992) 327-333
  15. Batey, R.T., Rambo, R.P., Doudna, J.A.: Tertiary motifs and folding of RNA. Angew. Chem. Int. Ed. 38 (1999) 2326-2343
  16. Moore, P.B.: Structural motifs in RNA. Annu. Rev. Biochem. 68 (1999) 287-300
  17. Chan, H.S., Dill, K.A.: Sequence space soup of proteins and copolymers. J. Chem. Phys. 95 (1991) 3775-3779
  18. Dill, K.A., Bromberg, S., Yue, K., Fiebig, K.M., Yeo, D.P., Thomas, P.D., Chan, H.S.: Principles of protein folding: A perspective from simple exact models. Protein Science 4 (1995) 561-602
  19. Brendel, V., Busse, H.G.: Genome structure described by formal languages. Nucleic Acid Research 12 (1984) 2561-2568
  20. Searls, D.: Formal language and biological macromolecules. In: Mathematical Sup- port for Molecular Biology. Volume 47 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science., AMS (1999) 128-141
  21. Searls, D.: The computational linguistics of biological sequences. In: Artificial Intelligence and Molecular Biology, AAAI Press (1993) 47-120
  22. Rivas, E., Eddy, S.R.: The language of RNA: a formal grammar that includes pseudoknots. Bioinformatics 16 (2000) 334-340
  23. Schultz, J., Milpetz, F., Bork, P., Ponting, C.: SMART, a simple molecular archi- tecture research tool. PNAS 95 (1998) 5857-5864
  24. Westhead, D., Slidel, T., Flores, T., Thornton, J.: Protein structural topology: automated analysis and diagrammatic representation. Protein Science 8 (1999) 897-904
  25. Durbin, R., Krogh., A., Mitchison, G., Eddy, S.: Biological sequence analysis: Prob- abilistic models of proteins and nucleic acids. Cambridge Univ. Press, Cambridge (1998)
  26. Sakakibara, Y., Brown, M., Hughey, R., Mian, I., Sjolander, K., Underwood, R., Haussler, D.: Stochastic context-free grammars for tRNA modeling. Nucleic Acids Research 22 (1994) 5112-5128
  27. Searls, D.: The language of genes. Nature 420 (2002) 211-217
  28. Mayoh, B.: DNA pattern multigrammars. Preprint (1995)
  29. Przytycka, T., Srinivasan, T., Rose, G.: Recursive domains in proteins. Protein Science 11 (2002) 409-417
  30. Richardson, J.: β-sheet topology and the relatedness of proteins. Nature 268 (1977) 495-500
  31. Lesk, A.M.: Systematic representation of protein folding patterns. J. Mol. Graph. 13 (1995) 159-164
  32. Hofacker, I., Fontana, W., Stadler, P., Bonhoeffer, L., Tacker, M., Schuster, P.: Fast folding and comparison of RNA secondary structures. Monatsh. Chem. 125 (1994) 167-188
  33. Kister, A., Magarshak, Y., Malinsky, J.: The theoretical analysis of the process of RNA molecule self-assembly. BioSystems 30 (1993) 31-48
  34. Abe, N., Mamitsuka, H.: Predicting protein secondary structure using stochastic tree grammars. Machine learning 29 (1997) 275-301
  35. Dittrich, P., Ziegler, J., Banzhaff, W.: Artificial chemistries-a review. Artificial life 7 (2001) 225-275
  36. Speroni, P.: Artificial chemistries. Bulletin EATCS 76 (2002) 128-141
  37. Fontana, W.: Algorithmic chemistry. In: Artificial life II. Volume 47 of Santa Fe Institute Studies in the Sciences of Complexity., Addison-Wesley (1992) 159-210
  38. Kanehisa, M., Goto, S.: KEGG: Kyoto encyclopedia of genes and genomes. Nucleic Acids Research 28 (2000) 27-30
  39. Benkö, G., Flamm, C., Stadler, P.F.: A graph-based toy model of chemistry. Journal of Chemical Information and Computer Sciences 43 (2003) 1085-1093
  40. McCaskill, J., Niemann, U.: Graph replacement chemistry for DNA processing. In: DNA 2000. Volume 2054 of Lecture Notes in Computer Science., Springer-Verlag (2001) 103-116
  41. Ehrig, H., Heckel, R., Korff, M., Löwe, M., Ribeiro, L., Wagner, A., Corradini, A.: Algebraic approaches to graph transformation. part II: Single pushout approach and comparison with double pushout approach. In Rozenberg, G., ed.: Handbook of Graph Grammars and Computing by Graph Transformation. Volume 1: Foun- dations. World Scientific (1997) 247-312
  42. Benkö, G., Flamm, C., Stadler, P.F.: Generic properties of chemical networks: Ar- tificial chemistry based on graph rewriting. In: Proc. 7th European Conf. Advances in Artificial Life. Volume 2801 of Lecture Notes in Computer Science., Springer- Verlag (2003) 10-19
  43. Benkö, G., Flamm, C., Stadler, P.F.: Multi-pase artificial chemistry. Submitted (2004)
  44. Polanski, O.: Graphs in quantum chemistry. MATCH 1 (1975) 183-195
  45. 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, Volume 1: Foundations. World Scientific (1997) 163-246
  46. Fringuelli, F., Taticchi, A.: The Diels-Alder Reaction: Selected Practical Methods. John Wiley & Sons, Chichester, England (2002)
  47. Rosselló, F., Valiente, G.: Analysis of metabolic pathways by graph transforma- tion. In: Proc. 2nd Int. Conf. Graph Transformation. Lecture Notes in Computer Science, Springer-Verlag (2004) to appear
  48. Rosselló, F., Valiente, G.: Chemical graphs, chemical reaction graphs, and chemical graph transformation. Electronic Notes in Theoretical Computer Science (2004) to appear
  49. Fujita, S.: Description of organic reactions based on imaginary transition struc- tures. Part 1-5. Journal of Chemical Information and Computer Sciences 26 (1986) 205-242
  50. Fujita, S.: Description of organic reactions based on imaginary transition struc- tures. Part 6-9. Journal of Chemical Information and Computer Sciences 27 (1987) 99-120
  51. Schuster, S., Fell, D.A., Dandekar, T.A.: A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks. Nature Biotechnology 18 (2000) 326-332
  52. Berry, G.: The chemical abstract machine. Theoretical Computer Science 96 (1992) 217-248
  53. Danos, V., Laneve, C.: Graphs for core molecular biology. In: Proc. 1st Int. Workshop Computational Methods in Systems Biology. Volume 2602 of Lecture Notes in Computer Science., Springer-Verlag (2003) 34-46
  54. Danos, V., Laneve, C.: Formal molecular biology. Theoretical Computer Science (2004) in press

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