Investigation of chemical space networks using graph measures and random matrix theory. (English) Zbl 1492.92154
Summary: Large collections of molecules (chemical libraries) are nowadays routinely screened in the process of designing drugs for specific ailments. Chemical and structural similarities between these molecules can be quantified using molecular descriptors, and these similarities can in turn be used to represent any chemical library as an undirected network called a chemical space network (CSN). Here we study different CSNs using conventional graph measures as well as random matrix theory (RMT). For the conventional graph measures, we focus on the average degree, average path length, graph diameter, degree assortativity, transitivity, average clustering coefficient and modularity. For the RMT analyses, we examine the eigenvalue spectra of adjacency matrices constructed from the molecular similarities for different CSNs, and examine their local fluctuation properties, contrasting them with the predictions of RMT. Changes in the conventional graph measures and RMT statistics with the network structure are examined for three different chemical libraries by varying the edge density (fraction of the actual to the maximum possible number of edges) of the networks. It is found that the assortativity among the conventional graph measures, and long-range fluctuation statistics of RMT in eigenvalue space respond to the changes in global network structure as well as the chemical space. We expect that this investigation of the network characteristics of different kinds of chemical libraries will provide guidance in the design of high-throughput screening libraries for different drug design applications.
MSC:
| 92E10 | Molecular structure (graph-theoretic methods, methods of differential topology, etc.) |
| 05C92 | Chemical graph theory |
| 60B20 | Random matrices (probabilistic aspects) |
Keywords:
chemical space networks; spectral graph theory; graph adjacency matrix; random matrix theoryReferences:
| [1] | Todeschini, R.; Consonni, V., Handbook of Molecular Descriptors (2000), Weinheim: Wiley-VCH, Weinheim |
| [2] | Bohacek, RS; McMartin, C.; Guida, WC, The art and practice of structure-based drug design: a molecular modeling perspective, Med. Res. Rev., 16, 3 (1999) |
| [3] | Kirkpatrick, P.; Ellis, C., Chemical space, Nature, 432, 823 (2004) |
| [4] | Lipinski, C.; Hopkins, A., Navigating chemical space for biology and medicine, Nature, 432, 855 (2004) |
| [5] | Prabhu, G.; Bhattacharya, S.; Krein, MP; Sukumar, N., Investigation of similarity and diversity threshold networks generated from diversity-oriented and focused chemical libraries, J. Math. Chem., 54, 1916 (2016) |
| [6] | Wawer, M.; Peltason, L.; Weskamp, N.; Teckentrup, A.; Bajorath, J., Structure-activity relationship anatomy by network-like similarity graphs and local structure-activity relationship indices, J. Med. Chem., 51, 6075 (2008) |
| [7] | Benz, RW; Swamidass, SJ; Baldi, P., Discovery of power-laws in chemical space, J Chem. Inf. Model., 48, 1138 (2008) |
| [8] | Tanaka, N.; Ohno, K.; Niimi, T.; Moritomo, A.; Mori, K.; Orita, M., Small-world phenomena in chemical library networks: application to fragment-based drug discovery, J. Chem. Inf. Model., 49, 2677 (2009) |
| [9] | Krein, MP; Sukumar, N., Exploration of the topology of chemical spaces with network measures, J. Phys. Chem. A, 115, 12905 (2011) |
| [10] | Maggiora, GM; Bajorath, J., Chemical space networks: a powerful new paradigm for the description of chemical space, J. Comput. Aided Mol. Des., 28, 795 (2014) |
| [11] | Sukumar, N.; Krein, MP; Prabhu, G.; Bhattacharya, S.; Sen, S., Network measures for chemical library design, Drug Dev. Res., 75, 402 (2014) |
| [12] | Almendral, JA; Díaz-Guilera, A., Dynamical and spectral properties of complex networks, New J. Phys., 9, 187 (2007) |
| [13] | Rodgers, GJ; Austin, K.; Kahng, B.; Kim, D., Eigenvalue spectra of complex networks, J. Phys. A Math. Gen., 38, 9431 (2005) · Zbl 1087.05053 |
| [14] | Bohigas, O.; Giannoni, MJ; Schmit, C., Characterization of chaotic quantum spectra and universality of level fluctuation laws, Phys. Rev. Lett., 52, 1 (1984) · Zbl 1119.81326 |
| [15] | Mehta, ML, Random Matrices (2004), New York: Academic, New York · Zbl 1107.15019 |
| [16] | Haake, F., Quantum Signatures of Chaos (2010), New York: Springer, New York · Zbl 1209.81002 |
| [17] | Guhr, T.; Müller-Groeling, A.; Weidenmüller, HA, Random-matrix theories in quantum physics: common concepts, Phys. Rep., 299, 189 (1998) |
| [18] | Bandyopadhyay, JN; Jalan, S., Universality in complex networks: random matrix analysis, Phys. Rev. E, 76, 026109 (2007) |
| [19] | Jalan, S.; Bandyopadhyay, JN, Random matrix analysis of complex networks, Phys. Rev. E, 76, 046107 (2007) |
| [20] | Jalan, S.; Bandyopadhyay, JN, Random matrix analysis of network Laplacians, Physica A, 387, 667 (2008) |
| [21] | Luo, F.; Zhong, J.; Yang, Y.; Scheuermann, RH; Zhou, J., Application of random matrix theory to biological networks, Phys. Lett. A, 357, 420 (2006) |
| [22] | Rai, A.; Jalan, S.; Banerjee, S.; Rondoni, L., Application of random matrix theory to complex networks, Applications of Chaos and Nonlinear Dynamics in Science and Engineering (2015), Cham: Springer, Cham |
| [23] | Kikkawa, A., Random matrix analysis for gene interaction networks in cancer cells, Sci. Rep., 8, 10607 (2018) |
| [24] | Eom, C.; Oh, G.; Jung, W-S; Jeong, H.; Kim, S., Topologic properties of stock networks based on minimal spanning tree and random matrix theory in financial time series, Physica A, 388, 900 (2009) |
| [25] | Lee, AA; Brenner, MP; Colwell, LJ, Predicting protein-ligand affinity with a random matrix framework, Proc Natl. Acad. Sci. USA, 113, 13564 (2016) |
| [26] | Strogatz, SH, Exploring complex networks, Nature, 410, 268 (2001) · Zbl 1370.90052 |
| [27] | Barabási, A-L, Network science, Philos. Trans. R. Soc. A, 371, 20120375 (2013) |
| [28] | Newman, MEJ, Networks: An introduction (2010), Oxford: Oxford University Press, Oxford · Zbl 1195.94003 |
| [29] | Jalan, Sarika; Yadav, Alok, Assortative and disassortative mixing investigated using the spectra of graphs, Phys. Rev. E, 91, 012813 (2015) |
| [30] | Van Mieghem, P.; Ge, X.; Schumm, P.; Trajanovski, S.; Wang, H., Spectral graph analysis of modularity and assortativity, Phys. Rev. E, 82, 056113 (2010) |
| [31] | A. Hurwitz, Über die Erzeugung der Invarianten durch Integration. Nachr. Ges. Wiss. Göttingen , 71-90 (1897) · JFM 28.0103.03 |
| [32] | Diaconis, P.; Forrester, PJ, Hurwitz and the origins of random matrix theory in mathematics, Random Matrices Theory Appl., 6, 1730001 (2017) · Zbl 1398.11119 |
| [33] | Wigner, EP, Ann. Math., 62, 548 (1955) · Zbl 0067.08403 |
| [34] | Wigner, EP, Ann. Math., 65, 203 (1957) · Zbl 0077.31901 |
| [35] | Wigner, EP, Ann. Math., 67, 325 (1958) · Zbl 0085.13203 |
| [36] | Akemann, G.; Baik, J.; Di Francesco, P., The Oxford Handbook of Random Matrix Theory (2011), Oxford: Oxford University Press, Oxford · Zbl 1225.15004 |
| [37] | Hoskins, RF, Delta Functions: An Introduction to Generalised Functions, 2nd Edition 2009 (2011), Oxford: Woodhead Publishing Limited, Oxford · Zbl 1186.46001 |
| [38] | Huse, DA; Oganesyan, V., Localization of interacting fermions at high temperature, Phys. Rev. B, 75, 155111 (2007) |
| [39] | Atas, YY; Bogomolny, E.; Giraud, O.; Roux, G., Distribution of the ratio of consecutive level spacings in random matrix ensembles, Phys. Rev. Lett., 110, 084101 (2013) |
| [40] | Sarkar, A.; Kothiyal, M.; Kumar, S., Distribution of the ratio of two consecutive level spacings in orthogonal to unitary crossover ensembles, Phys. Rev. E, 101, 012216 (2020) |
| [41] | Berry, MV; Tabor, M., Level clustering in the regular spectrum, Proc. R. Soc. A, 356, 375 (1977) · Zbl 1119.81395 |
| [42] | Dyson, FJ; Mehta, ML, Statistical theory of the energy levels of complex systems. IV, J. Math. Phys., 4, 701 (1963) · Zbl 0133.45201 |
| [43] | Berry, MV, Semicalssical theory of spectral rigidity, Proc. R. Soc. Lond. A, 400, 229 (1985) · Zbl 0875.35061 |
| [44] | Katt, WP; Lukey, MJ; Cerione, RA, A tale of two glutaminases: homologous enzymes with distinct roles in tumorigenesis, Future Med. Chem., 9, 223 (2017) |
| [45] | Milano, SK; Huang, Q.; Nguyen, T-TT; Ramachandran, S.; Finke, A.; Kriksunov, I.; Schuller, D.; Szebenyi, M.; Arenholz, E.; McDermott, LA; Sukumar, N.; Cerione, RA; Katt, WP, New insights into the molecular mechanisms of glutaminase C inhibitors in cancer cells using serial room temperature crystallography, J. Biol. Chem., 298, 101535 (2022) |
| [46] | Whitehead, CE; Breneman, CM; Sukumar, N.; Dominic Ryan, M., Transferable atom equivalent multicentered multipole expansion method, J. Comput. Chem., 24, 512 (2003) |
| [47] | Sukumar, N.; Breneman, CM; Matta, CF; Boyd, RJ, QTAIM in drug discovery and protein modeling, The Quantum Theory of Atoms in Molecules: From Solid State to DNA and Drug Design (2007), Weinheim: Wiley-VCH, Weinheim |
| [48] | N. Sukumar, D. Zhuang, W.P. Katt, C.E. Whitehead, C.M. Breneman, Transferable atom equivalent reconstruction. http://reccr.chem.rpi.edu/Software/RECON/recondoc/WinRecon.html |
| [49] | Labute, P., A widely applicable set of descriptors, J. Mol. Graph. Model., 18, 464 (2000) |
| [50] | Chemical Computing Group, Molecular operating environment (2021) https://www.chemcomp.com/ |
| [51] | Bader, RFW, Atoms in Molecules: A Quantum Theory (1990), Oxford: Oxford University Press, Oxford |
| [52] | Chen, CY-C, TCM Database@ Taiwan: the world’s largest traditional Chinese medicine database for drug screening in silico, PLoS One, 6, e15939 (2011) |
| [53] | Mangal, M.; Sagar, P.; Singh, H.; Raghava, GPS; Agarwal, SM, NPACT: naturally occurring plant-based anti-cancer compound-activity-target database, Nucleic Acids Res., 41, 1124 (2013) |
| [54] | Sterling, T.; Irwin, JJ, J. Chem. Inf. Model, 55, 2324 (2015) |
| [55] | G. Csardi, T. Nepusz, The igraph software package for complex network research. Int. J. Complex Syst., 1695 (2006). https://igraph.org |
| [56] | R Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2020). https://www.R-project.org/ |
| [57] | Wolfram Research Inc. 2020 Mathematica Version 12.1.1 |
| [58] | Zwierzyna, M.; Vogt, M.; Maggiora, GM; Bajorath, J., Design and characterization of chemical space networks for different compound data sets, J. Comput. Aided Mol. Des., 29, 113-125 (2015) |
| [59] | Marrec, L.; Jalan, S., Analysing degeneracies in networks spectra, Europhys. Lett., 117, 48001 (2017) |
| [60] | Chung, FRK, Spectral Graph Theory (1997), Providence, RI: American Mathematical Society, Providence, RI · Zbl 0867.05046 |
| [61] | Dorogovtsev, SN; Goltsev, AV; Mendes, JFF; Samukhin, AN, Spectra of complex networks, Phys. Rev. E, 68, 046109 (2003) |
| [62] | Albert, R.; Barabási, A-L, Statistical mechanics of complex networks, Rev. Mod. Phys., 74, 47 (2002) · Zbl 1205.82086 |
| [63] | Yap, CW, PaDEL-descriptor: an open source software to calculate molecular descriptors and fingerprints, J. Comput. Chem., 32, 1466 (2011) |
| [64] | S. Craw, Manhattan distance. Encycl. Mach. Learn. Data Min. 790-791 (2017) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
