Graph Transformation in Molecular Biology

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 modelling of higher-dimensional structures of biomolecules, the description of biochemical reactions, and the study of biochemical pathways.

[1]  Wolfgang Banzhaf,et al.  Advances in Artificial Life , 2003, Lecture Notes in Computer Science.

[2]  Aviv Regev,et al.  Representation and Simulation of Biochemical Processes Using the pi-Calculus Process Algebra , 2000, Pacific Symposium on Biocomputing.

[3]  F. Friedler,et al.  Graph-theoretical identification of pathways for biochemical reactions , 2001, Biotechnology Letters.

[4]  Sean R. Eddy,et al.  Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids , 1998 .

[5]  Cayley LVII. On the mathematical theory of isomers , 1874 .

[6]  Rajgopal Srinivasan,et al.  Recursive domains in proteins , 2002, Protein science : a publication of the Protein Society.

[7]  A. Kister,et al.  The theoretical analysis of the process of RNA molecule self-assembly. , 1993, Bio Systems.

[8]  Walter Fontana,et al.  Fast folding and comparison of RNA secondary structures , 1994 .

[9]  Lawrence Hunter,et al.  Pacific symposium on biocomputing 2006 , 2005, PSB 2016.

[10]  Brian P. Kelley,et al.  The Potential of a Chemical Graph Transformation System , 2004, ICGT.

[11]  David B. Searls,et al.  The computational linguistics of biological sequences , 1993, ISMB 1995.

[12]  K. Dill,et al.  ‘‘Sequence space soup’’ of proteins and copolymers , 1991 .

[13]  D Gernert,et al.  Graph grammars as an analytical tool in physics and biology. , 1997, Bio Systems.

[14]  H. Ehrig,et al.  Equational Specifications and Algebras , 1985 .

[15]  公人 船津 “Computer-Oriented Representation of Organic Reactions” , 2002 .

[16]  P. Moore,et al.  Structural motifs in RNA. , 1999, Annual review of biochemistry.

[17]  A. Lindenmayer,et al.  PARALLEL GRAPH GENERATING AND GRAPH RECURRENCE SYSTEMS FOR MULTICELLULAR DEVELOPMENT , 1976 .

[18]  Harald Schaub,et al.  The Logic Of Artificial Life: Abstracting And Synthesizing The Principles Of Living Systems: Proceedings Of The 6th German Workshop On Artificial Life April 14-16, 2004, Bamberg Germany , 2004 .

[19]  David Weininger,et al.  SMILES. 2. Algorithm for generation of unique SMILES notation , 1989, J. Chem. Inf. Comput. Sci..

[20]  Cosimo Laneve,et al.  Graphs for Core Molecular Biology , 2003, CMSB.

[21]  中尾 光輝,et al.  KEGG(Kyoto Encyclopedia of Genes and Genomes)〔和文〕 (特集 ゲノム医学の現在と未来--基礎と臨床) -- (データベース) , 2000 .

[22]  Reiko Heckel,et al.  Algebraic Approaches to Graph Transformation - Part I: Basic Concepts and Double Pushout Approach , 1997, Handbook of Graph Grammars.

[23]  Francesc Rosselló,et al.  Chemical Graphs, Chemical Reaction Graphs, and Chemical Graph Transformation , 2005, GraBaTs.

[24]  David Weininger,et al.  SMILES, 3. DEPICT. Graphical depiction of chemical structures , 1990, J. Chem. Inf. Comput. Sci..

[25]  Shinsaku Fujita Description of organic reactions based on imaginary transition structures. 6. Classification and enumeration of two-string reactions with one common node , 1987, J. Chem. Inf. Comput. Sci..

[26]  Peter F. Stadler,et al.  Generic Properties of Chemical Networks: Artificial Chemistry Based on Graph Rewriting , 2003, ECAL.

[27]  J. Ziegler,et al.  Artificial Chemistries-A Review , 2001 .

[28]  BanzhafWolfgang,et al.  Artificial chemistriesa review , 2001 .

[29]  Pietro Speroni di Fenizio,et al.  Artificial Chemistries , 2002, Bull. EATCS.

[30]  David I. Lewin,et al.  DNA computing , 2002, Comput. Sci. Eng..

[31]  D. Fell,et al.  A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks , 2000, Nature Biotechnology.

[32]  Batey,et al.  Tertiary Motifs in RNA Structure and Folding. , 1999, Angewandte Chemie.

[33]  H. Kitano,et al.  Computational systems biology , 2002, Nature.

[34]  David Weininger,et al.  SMILES, a chemical language and information system. 1. Introduction to methodology and encoding rules , 1988, J. Chem. Inf. Comput. Sci..

[35]  Yves Deville,et al.  An overview of data models for the analysis of biochemical pathways , 2003, Briefings Bioinform..

[36]  Hartmut Ehrig,et al.  Fundamentals of Algebraic Specification 1 , 1985, EATCS Monographs on Theoretical Computer Science.

[37]  Peer Bork,et al.  SMART, a simple modular architecture research tool , 1998 .

[38]  E. Shapiro,et al.  Cellular abstractions: Cells as computation , 2002, Nature.

[39]  V. Brendel,et al.  Genome structure described by formal languages. , 1984, Nucleic acids research.

[40]  M. Waterman,et al.  RNA secondary structure: a complete mathematical analysis , 1978 .

[41]  T. P. Flores,et al.  Protein structural topology: Automated analysis and diagrammatic representation , 2008, Protein science : a publication of the Protein Society.

[42]  Francesc Rosselló,et al.  Analysis of Metabolic Pathways by Graph Transformation , 2004, ICGT.

[43]  D. Sankoff,et al.  RNA secondary structures and their prediction , 1984 .

[44]  K. Tomita,et al.  Graph automata: natural expression of self-reproduction , 2002 .

[45]  Luca Cardelli,et al.  Brane Calculi , 2004, CMSB.

[46]  Ion Petre,et al.  Computation in Living Cells: Gene Assembly in Ciliates (Natural Computing Series) , 2003 .

[47]  Alan Bundy,et al.  Constructing Induction Rules for Deductive Synthesis Proofs , 2006, CLASE.

[48]  Shinsaku Fujita Description of organic reactions based on imaginary transition structures. 7. Classification and enumeration of two-string reactions with two or more common nodes , 1987, J. Chem. Inf. Comput. Sci..

[49]  Lawrence Hunter,et al.  Artificial Intelligence and Molecular Biology , 1992, AI Mag..

[50]  Cosimo Laneve,et al.  Formal molecular biology , 2004, Theor. Comput. Sci..

[51]  Botond Bertók,et al.  A Graph-theoretic Method to Identify Candidate Mechanisms for Deriving the Rate Law of a Catalytic Reaction , 2002, Comput. Chem..

[52]  Grzegorz Rozenberg,et al.  Handbook of Graph Grammars and Computing by Graph Transformations, Volume 1: Foundations , 1997 .

[53]  José Meseguer,et al.  Pathway Logic: Symbolic Analysis of Biological Signaling , 2001, Pacific Symposium on Biocomputing.

[54]  Hue Sun Chan,et al.  Compact Polymers , 2001 .

[55]  Reiko Heckel,et al.  Algebraic Approaches to Graph Transformation - Part II: Single Pushout Approach and Comparison with Double Pushout Approach , 1997, Handbook of Graph Grammars.

[56]  J. Richardson,et al.  β-Sheet topology and the relatedness of proteins , 1977, Nature.

[57]  Brian H. Mayoh,et al.  Multidimensional Lindenmayer Organisms , 1974, L Systems.

[58]  Naoki Abe,et al.  Predicting Protein Secondary Structure Using Stochastic Tree Grammars , 1997, Machine Learning.

[59]  Christian M. Reidys,et al.  Bio-molecular Shapes and Algebraic Structures , 1996, Comput. Chem..

[60]  Luc Jaeger,et al.  RNA pseudoknots , 1992, Current Biology.

[61]  Shinsaku Fujita Description of organic reactions based on imaginary transition structures. 2. Classification of one-string reactions having an even-membered cyclic reaction graph , 1986, J. Chem. Inf. Comput. Sci..

[62]  John S. McCaskill,et al.  Graph Replacement Chemistry for DNA Processing , 2000, DNA Computing.

[63]  R. C. Underwood,et al.  Stochastic context-free grammars for tRNA modeling. , 1994, Nucleic acids research.

[64]  Peter F. Stadler,et al.  Multi-Phase Artificial Chemistry , 2004 .

[65]  Grzegorz Rozenberg,et al.  L Systems , 1974, Handbook of Formal Languages.

[66]  Gérard Berry,et al.  The chemical abstract machine , 1989, POPL '90.

[67]  David B. Searls Formal language theory and biological macromolecules , 1998, Mathematical Support for Molecular Biology.

[68]  Charles E. Taylor,et al.  Artificial Life II , 1991 .

[69]  Stefan Schuster,et al.  Topological analysis of metabolic networks based on Petri net theory , 2003, Silico Biol..

[70]  H. Lehmann,et al.  Nucleic Acid Research , 1967 .

[71]  Pierpaolo Degano,et al.  Causal pi-Calculus for Biochemical Modelling , 2003, CMSB.

[72]  J Schultz,et al.  SMART, a simple modular architecture research tool: identification of signaling domains. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[73]  D. Yee,et al.  Principles of protein folding — A perspective from simple exact models , 1995, Protein science : a publication of the Protein Society.

[74]  P. Schuster,et al.  RNA folding at elementary step resolution. , 1999, RNA.

[75]  Shinsaku Fujita Description of organic reactions based on imaginary transition structures. 3. Classification of one-string reactions having an odd-membered cyclic reaction graph , 1986, J. Chem. Inf. Comput. Sci..

[76]  P J Goss,et al.  Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[77]  Cosimo Laneve,et al.  Core Formal Molecular Biology , 2003, ESOP.

[78]  James M. Bower,et al.  Computational modeling of genetic and biochemical networks , 2001 .

[79]  Peter F. Stadler,et al.  A Graph-Based Toy Model of Chemistry , 2003, J. Chem. Inf. Comput. Sci..

[80]  Hartmut Ehrig,et al.  Handbook of graph grammars and computing by graph transformation: vol. 3: concurrency, parallelism, and distribution , 1999 .

[81]  Vincent Danos,et al.  Formal Molecular Biology done in CCS , 2003 .

[82]  Francesc Rosselló,et al.  Artificial Chemistries and Metabolic Pathways , 2004, Spanish Bioinformatics Conference.

[83]  D. Searls,et al.  Robots in invertebrate neuroscience , 2002, Nature.

[84]  Elena Rivas,et al.  The language of RNA: a formal grammar that includes pseudoknots , 2000, Bioinform..

[85]  A. Arkin,et al.  It's a noisy business! Genetic regulation at the nanomolar scale. , 1999, Trends in genetics : TIG.

[86]  Reiko Heckel,et al.  Stochastic Graph Transformation Systems , 2004, Fundam. Informaticae.

[87]  A M Lesk,et al.  Systematic representation of protein folding patterns. , 1995, Journal of molecular graphics.

[88]  P. Stadler,et al.  Graph Grammars as Models for the Evolution of Developmental Pathways , 2004 .