From Molecular to Biological Structure and Back

A comparative analysis of the topological structure of molecules and molecular biology networks revealed both similarity and differences in the methods used, as well as in the essential features of the two types of systems. Molecular graphs are static and, due to the limitations in atomic valence, show neither power distribution of vertex degrees nor "small-world" properties, which are typical for dynamic evolutionary networks. Areas of mutual benefits from an exchange of methods and ideas are outlined for the two fields. More specifically, chemical graph theory might make use of some new descriptors of network structure. Of interest for quantitative structure-property relationship/quantitative structure-activity relationship and drug design might be the conclusion that descriptors based on distributions of vertex degrees, distances, and subgraphs seem to be more relevant to biological information than the single-number descriptors. The network concepts of centrality, clustering, and cliques provide a basis for similar studies in theoretical chemistry. The need of dynamic theory of molecular topology is advocated.

[1]  A. P. S. de Moura,et al.  Clustering as a measure of the local topology of networks , 2006 .

[2]  Danail Bonchev,et al.  Generalization of the Graph Center Concept, and Derived Topological Centric Indexes , 1980, J. Chem. Inf. Comput. Sci..

[3]  A. Barabasi,et al.  Network biology: understanding the cell's functional organization , 2004, Nature Reviews Genetics.

[4]  P. Bonacich.  Factoring and weighting approaches to status scores and clique identification , 1972 .

[5]  T. Ideker,et al.  Modeling cellular machinery through biological network comparison , 2006, Nature Biotechnology.

[6]  J. W. Kennedy,et al.  The graph-like state of matter. Part 2.—LCGI schemes for the thermodynamics of alkanes and the theory of inductive inference , 1973 .

[7]  Danail Bonchev,et al.  Complexity of Protein-Protein Interaction Networks, Complexes, and Pathways , 2003 .

[8]  Susumu Goto,et al.  Extraction of phylogenetic network modules from prokayrote metabolic pathways. , 2004, Genome informatics. International Conference on Genome Informatics.

[9]  Danail Bonchev,et al.  Information theoretic indices for characterization of chemical structures , 1983 .

[10]  Albert-László Barabási,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW , 2004 .

[11]  Danail Bonchev,et al.  Novel Indices for the Topological Complexity of Molecules , 1997 .

[12]  P. Bork,et al.  Functional organization of the yeast proteome by systematic analysis of protein complexes , 2002, Nature.

[13]  H. Wiener.  Structural determination of paraffin boiling points. , 1947, Journal of the American Chemical Society.

[14]  G. Whitesides,et al.  Complexity in chemistry. , 1999, Science.

[15]  D. Watts.  The “New” Science of Networks , 2004 .

[16]  Steven H. Bertz,et al.  The first general index of molecular complexity , 1981 .

[17]  Koh-hei Nitta.  A graph‐theoretical approach to statistics and dynamics of tree‐like molecules , 1999 .

[18]  Ricard V. Solé,et al.  Graphs as Models of Large-Scale Biochemical Organization , 2005 .

[19]  D. Promislow.  Protein networks, pleiotropy and the evolution of senescence , 2004, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[20]  J. A. Rodríguez-Velázquez,et al.  Subgraph centrality and clustering in complex hyper-networks , 2006 .

[21]  A. Fronczak,et al.  Higher order clustering coefficients in Barabási–Albert networks , 2002, cond-mat/0212237.

[22]  A. Barabasi,et al.  Functional and topological characterization of protein interaction networks , 2004, Proteomics.

[23]  L. Hall,et al.  Molecular connectivity in chemistry and drug research , 1976 .

[24]  Ernesto Estrada.  Protein bipartivity and essentiality in the yeast protein-protein interaction network. , 2006, Journal of proteome research.

[25]  J. A. Rodríguez-Velázquez,et al.  Subgraph centrality in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Jie Wu,et al.  Small Worlds: The Dynamics of Networks between Order and Randomness , 2003 .

[27]  Steven H. Bertz,et al.  Rigorous mathematical approaches to strategic bonds and synthetic analysis based on conceptually simple new complexity indices , 1997 .

[28]  N. Trinajstic,et al.  Information theory, distance matrix, and molecular branching , 1977 .

[29]  A. Barabasi,et al.  Hierarchical Organization of Modularity in Metabolic Networks , 2002, Science.

[30]  Danail Bonchev,et al.  Quantitative Measures of Network Complexity , 2005 .

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

[32]  Ernesto Estrada.  Virtual identification of essential proteins within the protein interaction network of yeast , 2005, Proteomics.

[33]  J. A. Rodríguez-Velázquez,et al.  Atomic branching in molecules , 2006 .

[34]  Danail Bonchev,et al.  The concept for the centre of a chemical structure and its applications , 1989 .

[35]  D. Bonchev.  On the complexity of directed biological networks , 2003, SAR and QSAR in environmental research.

[36]  R. Karp,et al.  From the Cover : Conserved patterns of protein interaction in multiple species , 2005 .

[37]  Danail Bonchev,et al.  Long chain branch polymer chain dimensions: application of topology to the Zimm–Stockmayer model , 2002 .

[38]  Mark E. J. Newman.  A measure of betweenness centrality based on random walks , 2005, Soc. Networks.

[39]  L. Freeman.  Centrality in social networks conceptual clarification , 1978 .

[40]  Andrey A. Toropov,et al.  The graph of atomic orbitals and its basic properties. 1. Wiener index , 2005 .

[41]  Gerta Rücker,et al.  Substructure, Subgraph, and Walk Counts as Measures of the Complexity of Graphs and Molecules , 2001, J. Chem. Inf. Comput. Sci..

[42]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[43]  Bernhard O Palsson,et al.  Hierarchical thinking in network biology: the unbiased modularization of biochemical networks. , 2004, Trends in biochemical sciences.

[44]  Claude E. Shannon,et al.  A Mathematical Theory of Communications , 1948 .

[45]  T. Došlić.  Bipartivity of fullerene graphs and fullerene stability , 2005 .

[46]  M E J Newman,et al.  Modularity and community structure in networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[47]  S. Shen-Orr,et al.  Network motifs in the transcriptional regulation network of Escherichia coli , 2002, Nature Genetics.

[48]  Danail Bonchev,et al.  Complexity Analysis of Yeast Proteome Network , 2004, Chemistry & biodiversity.

[49]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[50]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[51]  Mark E. J. Newman,et al.  Structure and Dynamics of Networks , 2009 .

[52]  Danail Bonchev,et al.  Iterative procedure for the generalized graph center in polycyclic graphs , 1989, J. Chem. Inf. Comput. Sci..