Design and characterization of chemical space networks

Transcription

1 Design and characterization of chemical space networks Martin Vogt B-IT Life Science Informatics Rheinische Friedrich-Wilhelms-University Bonn 16 August 2015

2 Network representations of chemical spaces Vertices represent molecules Edges represent similarity relationships Often based on fingerprints and similarity coefficients Reflect discreteness of chemical space Coordinate-free Binary relationship Network of serotinin 7 (ant)agonists

3 Network visualization/analysis Visualization Elucidation of topology via layout algorithms Network analysis Identify community structures Identify central vertices Study topological properties Identification of hidden commonalities Network of serotinin 7 (ant)agonists

4 Chemical space networks Chemical space networks (CSNs) represent molecules (vertices) and their pairwise Tanimoto (Tc) similarities (unlabeled edges). A single Tc matrix gives rise to many different CSNs each network being associated with a specific threshold value. Tc threshold Density

5 Threshold chemical space networks N t = V, E t, V = molecules v 1, v 2,, v n, E t = edges (v i, v j ) v i, v j E t Sim Tc v i, v j t 0 t 1 + ε Tc threshold Density

6 Threshold selection for different datasets diverse dataset mean Tc value: 0.42 non-diverse dataset mean Tc value: 0.67 Tc threshold: 0.8 density: density: 0.05 Tc threshold: 0.6 density: 0.05 density: 0.9

7 Characteristic network properties Transitivity / clustering coefficient Degree Assortativity Modularity + Average path length ( small world property, ubiquitary property)

8 Network properties: Transitivity or clustering coefficient The transitivity is defined as the ratio of triangles in a network to the total number of connected triplets b t = 3(number of triangles) (number of triplets) The clustering coefficient reflects the local interconnectivity or cliques among the neighbors of a given vertex a c clustering coefficient

9 Network properties: Modularity Modularity quantifies the degree to which a network is organized into a modular or community structure. Modularity Q: Fraction of edges between vertices of the same group Fraction of inner group edges expected by chance Q = 1 2m i,j a ij k ik j 2m δ c i, c j (a ij ): adjacency matrix m: number of edges k i : degree of i c i : group of vertex i δ(c i,c j ): Kronecker delta

10 Network properties: Modularity Modularity quantifies the degree to which a network is organized into a modular or community structure

11 Network properties: Assortativity Assortativity quantifies how well numerical properties of connected vertices correlate Assortativity r: Pearson correlation coefficient of a numerical property x between connected vertices. r = ij a ij k i k j /2m x i x j ij k i δ ij k i k j /2m x i x j

12 Network properties: Assortativity Assortativity quantifies how well numerical properties of connected vertices correlate Assortative mixing by degree: Pearson correlation coefficient of the degrees of connected vertices. r k = a ij k i k j /2m k i k j ij k i δ ij k i k j /2m k i k j ij Degree assortativity quantifies the tendency of vertices of similar degree to be connected

13 biological technological Functional/scale-free social homophilic Global Network properties Network properties of some real networks Network n m l C r α Film actors Company directors Physics coauthorship Biology coauthorship WWW (nd.edu) /2.4 Internet Train routes Electronic circuits Metabolic network Protein interactions Marine food network Neural network n,order; m, size; l average path length; C, clustering coef.; r, assortativity (Newman, 2010)

14 clustering coefficient / threshold modularity / threshold Density dependence Network properties are dominated by the edge density CSN generated from 1000 random ZINC12 compounds at different densities.

15 Degree assortativity Average shortest paths Density dependence Network properties are dominated by the edge density CSN generated from 1000 random ZINC12 compounds at different densities.

16 Density-based threshold selection diverse dataset mean Tc value: 0.42 non-diverse dataset mean Tc value: 0.67 Tc threshold: 0.8 density: density: 0.05 Tc threshold: 0.6 density: 0.05 density: 0.9

17 Data sets ZINC data sets of 1000 compounds using different selection strategies ChEMBL18-21 data sets containing compounds active single protein target High confidence Ki values CSNs were generated using MACCS Tanimoto coefficients

18 Randomized ZINC sets of varying diversity Combining: - random selection - diversity selection - similarity searching around random compounds random sets with almost arbitrary diversity levels as reflected by their pairwise Tc similarities can be selected.

19 Properties of ZINC datasets Fixed density: 0.025

20 Properties of ChEMBL datasets Fixed density: 0.025

21 Conclusions CSNs based on pairwise similarities can be modelled as a series of threshold networks Global properties of networks depend on edge density Network properties like community structures of CSNs are comparable using density-based threshold selection

22 Comparison of bioactive networks ECFP4-CSN Binding affinity - red: low - yellow: medium - green: high Target-specific thresholds yield networks of comparable densities

23 Comparison of different types of CSNs Matched molecular pairs (MMP): Compounds differ at a single site orexin receptor 2 (ant)agonists ECFP4-fingerprint: Compounds share 58% of features Density: ECFP4 Tc: 0.58 Assortativity: 0.92 Cluster coefficient: 0.69 Modularity: 0.78 pki Edge overlap = 0.73 Jaccard cluster index= 0.76 Assortativity: 0.92 Cluster coefficient: 0.71 Modularity: 0.77

24 Percentage Percentage Percentage Percentage CSN comparison of 154 ChEMBL classes MMP-CSNs yield networks of varying density ECFP4-CSNs with adjusted densities yield - similar networks (40%-70% shared edges) - similar properties: clustering coef.,modularity Histogram of x Histogram of x 40% 20% 30% 15% 20% 10% 10% 5% Edge overlap Jaccard cluster Tc index

25 Summary CSNs based on pairwise similarities can be modelled as a series of threshold networks Global properties of networks depend on edge density Network properties like community structures of CSNs are comparable using density-based threshold selection Meaningful network analysis/comparison is possible at (low) density levels at which network structures become apparent

26 Acknowledgments Jürgen Bajorath Gerry Maggiora Bijun Zhang Magdalena Zwierzyna

27 References Albert, R, Barabási, AL. Statistical mechanics of complex networks. Reviews of Modern Physics 74(1): 47 97, (2002). Newman, MEJ, Park, J. Why social networks are different from other types of networks. Physical Review E 68(3): , (2003). Maggiora, G, Bajorath, J. Chemical space networks a powerful new paradigm for the description of chemical space. Journal of Computer- Aided Molecular Design 28: , (2014). Newman, MEJ. Fast algorithm for detecting community structure in networks. Physical Review E 69(6): , (2004). Willett, P. Dissimilarity-based algorithms for selecting structurally diverse sets of compounds. Journal of Computational Biology 6(3/4): , (1999).