Extended GT-STAF information indices based on Markov approximation models

Abstract A series of novel information theory-based molecular parameters derived from the insight of a molecular structure as a chemical communication system were recently presented and usefully employed in QSAR/QSPRs (J. Comp. Chem, 2013, 34, 259; SAR and QSAR in Environ. Res. 2013, 24). This approach permitted the application of Shannon’s source and channel coding entropic measures to a chemical information source comprised of molecular ‘fragments’, using the zero-order Markov approximation model (atom-based approach). This report covers the theoretical aspects of the extensions of this approach to higher-order models, introducing the first, second and generalized-order Markov approximation models.

[1]  E. Trucco A note on the information content of graphs , 1956 .

[2]  Ernesto Estrada,et al.  Molecular Connectivity Indices of Iterated Line Graphs. A New Source of Descriptors for QSPR and QSAR Studies , 1998 .

[3]  Francisco Torrens,et al.  Relations frequency hypermatrices in mutual, conditional, and joint entropy‐based information indices , 2013, J. Comput. Chem..

[4]  L B Kier,et al.  Molecular connectivity and substructure analysis. , 1978, Journal of pharmaceutical sciences.

[5]  Ernesto Estrada,et al.  A Topological Index Based on Distances of Edges of Molecular Graphs , 1996, J. Chem. Inf. Comput. Sci..

[6]  Ernesto Estrada,et al.  Extension of Edge Connectivity Index. Relationships to Line Graph Indices and QSPR Applications , 1998, J. Chem. Inf. Comput. Sci..

[7]  Francisco Torrens,et al.  Shannon's, mutual, conditional and joint entropy information indices: generalization of global indices defined from local vertex invariants. , 2013, Current computer-aided drug design.

[8]  Ernesto Estrada,et al.  Edge Adjacency Relationships and a Novel Topological Index Related to Molecular Volume , 1995, J. Chem. Inf. Comput. Sci..

[9]  Ernesto Estrada,et al.  Spectral Moments of the Edge Adjacency Matrix in Molecular Graphs, 1. Definition and Applications to the Prediction of Physical Properties of Alkanes , 1996, J. Chem. Inf. Comput. Sci..

[10]  Sonja Nikolic,et al.  Comparison between the Vertex- and Edge-Connectivity Indices for Benzenoid Hydrocarbons , 1998, J. Chem. Inf. Comput. Sci..

[11]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[12]  Danail Bonchev,et al.  Trends in information theory-based chemical structure codification , 2014, Molecular Diversity.

[13]  I. Rigoutsos,et al.  The emergence of pattern discovery techniques in computational biology. , 2000, Metabolic engineering.

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

[15]  Lemont B. Kier,et al.  The E-State as the Basis for Molecular Structure Space Definition and Structure Similarity , 2000, J. Chem. Inf. Comput. Sci..

[16]  James G. Nourse,et al.  Reoptimization of MDL Keys for Use in Drug Discovery , 2002, J. Chem. Inf. Comput. Sci..

[17]  Igor I. Baskin,et al.  Chapter 1:Fragment Descriptors in SAR/QSAR/QSPR Studies, Molecular Similarity Analysis and in Virtual Screening , 2008 .

[18]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

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

[20]  Ernesto Estrada,et al.  Topological Indices Based on the Line Graph of the Molecular Graph , 1996, J. Chem. Inf. Comput. Sci..

[21]  E. Trucco,et al.  On the information content of graphs: Compound symbols; Different states for each point , 1956 .

[22]  Richard W. Hamming,et al.  Coding and Information Theory , 1980 .

[23]  CHUN WEI YAP,et al.  PaDEL‐descriptor: An open source software to calculate molecular descriptors and fingerprints , 2011, J. Comput. Chem..

[24]  Ernesto Estrada,et al.  Edge-Connectivity Indices in QSPR/QSAR Studies, 2. Accounting for Long-Range Bond Contributions , 1999, J. Chem. Inf. Comput. Sci..

[25]  Ernesto Estrada,et al.  Generalization of topological indices , 2001 .

[26]  Claude E. Shannon,et al.  The mathematical theory of communication , 1950 .

[27]  J. Gálvez,et al.  Event-based criteria in GT-STAF information indices: theory, exploratory diversity analysis and QSPR applications , 2013, SAR and QSAR in environmental research.

[28]  Emmanuel Desurvire Classical and Quantum Information Theory , 2013 .

[29]  Mark Nelson,et al.  The Data Compression Book , 2009 .

[30]  Ernesto Estrada,et al.  Edge Adjacency Relationships and Molecular Topographic Descriptors. Definition and QSAR Applications , 1996, J. Chem. Inf. Comput. Sci..

[31]  Gregory Stephanopoulos,et al.  A linguistic model for the rational design of antimicrobial peptides , 2006, Nature.