×

Response of Lyapunov exponents to diffusion state of biological networks. (English) Zbl 1466.92060

Summary: The topologies of protein-protein interaction networks are uncertain and noisy. The network topology determines the reliability of computational knowledge acquired from noisy networks and can impose the deterministic and non-deterministic character of the resulting data. In this study, we analyze the effect of the network topology on Lyapunov exponents and its relationship with network stability. We define the methodology to convert the network data into signal data and obtain the Lyapunov exponents for a variety of networks. We then compare the Lyapunov exponent response and the stability results. Our technique can be applied to all types of network topologies as demonstrated with our experiments, conducted on both synthetic and real networks from public databases. For the first time, this article presents findings where Lyapunov exponents are evaluated under topological mutations and used for network analysis. Experimental results show that Lyapunov exponents have a strong correlation with network stability and both are correlatively affected by the network model. Hence we develop a novel coefficient, termed LEC, to measure the robustness of biological networks. LEC can be applied to real or synthetic biological networks rapidly. Results are a striking indication that the Lyapunov exponent is a potential candidate measure for network analysis.

MSC:

92C42 Systems biology, networks
92C40 Biochemistry, molecular biology
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory

Software:

TISEAN; STRING
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abarbanel, H. (2012). Analysis of Observed Chaotic Data, Springer Science, New York, NY. · Zbl 0843.93004
[2] Abarbanel, H.D., Brown, R., Sidorowich, J.J. and Tsimring, L.S. (1993). The analysis of observed chaotic data in physical systems, Reviews of Modern Physics65(4): 1331.
[3] Albert, R. and Barabási, A.-L. (2002). Statistical mechanics of complex networks, Reviews of Modern Physics74(1): 47. · Zbl 1205.82086
[4] Alm, E. and Arkin, A.P. (2003). Biological networks, Current Opinion in Structural Biology13(2): 193-202.
[5] Altuntaş, V. and Gök, M. (2017). The stability and fragility of biological networks: Eukaryotic model organism saccharomyces cerevisiae, International Conference on Computer Science and Engineering (UBMK), Antalya, Turkey, pp. 116-118.
[6] Altuntaş, V. and Gök, M. (2020). Protein-protein etkileşimi tespit yöntemleri, veri tabanları ve veri güvenilirliği, Avrupa Bilim ve Teknoloji Dergisi (19): 722-733.
[7] Altuntas, V., Gök, M. and Kahveci, T. (2018). Stability analysis of biological networks’ diffusion state, IEEE/ACM Transactions on Computational Biology and Bioinformatics11(4): 1406-1418.
[8] Borgatti, S.P. (2005). Centrality and network flow, Social Networks27(1): 55-71.
[9] Can, T.,Çamoǧlu, O. and Singh, A.K. (2005). Analysis of protein-protein interaction networks using random walks, Proceedings of the 5th International Workshop on Bioinformatics, Chicago, IL, USA, pp. 61-68.
[10] Cao, L. (1997). Practical method for determining the minimum embedding dimension of a scalar time series, Physica D: Nonlinear Phenomena110(1-2): 43-50. · Zbl 0925.62385
[11] Cao, M., Zhang, H., Park, J., Daniels, N.M., Crovella, M.E., Cowen, L.J. and Hescott, B. (2013). Going the distance for protein function prediction: A new distance metric for protein interaction networks, PloS One8(10): e76339.
[12] Chatr-Aryamontri, A., Breitkreutz, B.-J., Oughtred, R., Boucher, L., Heinicke, S., Chen, D., Stark, C., Breitkreutz, A., Kolas, N., O’Donnell, L., Reguly, T., Nixon, J., Ramage, L., Winter, A., Sellam, A., Chang, C., Hirschman, J., Theesfeld, C., Rust, J., Livstone, M.S., Dolinski, K. and Tyers, M. (2015). The BioGRID interaction database: 2015 Update, Nucleic Acids Research43(D1): D470-D478.
[13] Cho, H., Berger, B. and Peng, J. (2015). Diffusion component analysis: Unraveling functional topology in biological networks, International Conference on Research in Computational Molecular Biology, Warsaw, Poland, pp. 62-64.
[14] Erten, S., Bebek, G. and Koyutürk, M. (2011). VAVIEN: An algorithm for prioritizing candidate disease genes based on topological similarity of proteins in interaction networks, Journal of Computational Biology18(11): 1561-1574.
[15] Freeman, L.C. (1977). A set of measures of centrality based on betweenness, Sociometry40(1): 35-41.
[16] Freeman, L.C., Borgatti, S.P. and White, D.R. (1991). Centrality in valued graphs: A measure of betweenness based on network flow, Social Networks13(2): 141-154.
[17] Gabr, H. and Kahveci, T. (2015). Signal reachability facilitates characterization of probabilistic signaling networks, BMC Bioinformatics16(17): S6.
[18] Gabr, H., Rivera-Mulia, J.C., Gilbert, D.M. and Kahveci, T. (2015). Computing interaction probabilities in signaling networks, EURASIP Journal on Bioinformatics and Systems Biology2015(1): 10.
[19] Gao, J. (2012). Multiscale analysis of biological data by scale-dependent Lyapunov exponent, Frontiers in Physiology2: 110.
[20] Gök, M., Koçal, O.H. and Genç, S. (2016). Prediction of disordered regions in proteins using physicochemical properties of amino acids, International Journal of Peptide Research and Therapeutics22(1): 31-36.
[21] Hagberg, A., Swart, P. and Schult, D. (2008). Exploring network structure, dynamics, and function using network, Technical report, Los Alamos National Lab., Los Alamos, NM.
[22] Han, Q. and Wang, P. (2007). Estimation of the largest Lyapunov exponent of the HRV signals, Journal of Biomedical Engineering24(4): 732-735.
[23] He, H., Lin, D., Zhang, J., Wang, Y.-P. and Deng, H.-W. (2017). Comparison of statistical methods for subnetwork detection in the integration of gene expression and protein interaction network, BMC Bioinformatics18(1), Article no. 149.
[24] Hegger, R., Kantz, H. and Schreiber, T. (1999). Practical implementation of nonlinear time series methods: The TISEAN package, Chaos: An Interdisciplinary Journal of Nonlinear Science9(2): 413-435. · Zbl 0990.37522
[25] Holme, P., Kim, B.J., Yoon, C.N. and Han, S.K. (2002). Attack vulnerability of complex networks, Physical Review E65(5): 056109.
[26] Jeong, H., Qian, X. and Yoon, B.-J. (2016). Effective comparative analysis of protein-protein interaction networks by measuring the steady-state network flow using a Markov model, BMC Bioinformatics17(13): 395.
[27] Kennel, M.B., Brown, R. and Abarbanel, H.D. (1992). Determining embedding dimension for phase-space reconstruction using a geometrical construction, Physical Review A45(6): 3403.
[28] Koçal, O.H., Yuruklu, E. and Avcibas, I. (2008). Chaotic-type features for speech steganalysis, IEEE Transactions on Information Forensics and Security3(4): 651-661.
[29] Köhler, S., Bauer, S., Horn, D. and Robinson, P.N. (2008). Walking the interactome for prioritization of candidate disease genes, The American Journal of Human Genetics82(4): 949-958.
[30] Li, F., Li, P., Xu, W., Peng, Y., Bo, X. and Wang, S. (2010). Perturbationanalyzer: A tool for investigating the effects of concentration perturbation on protein interaction networks, Bioinformatics26(2): 275-277.
[31] Li, Y., Wang, H. and Meng, X. (2019). Almost periodic synchronization of fuzzy cellular neural networks with time-varying delays via state-feedback and impulsive control, International Journal of Applied Mathematics and Computer Science29(2): 337-349, DOI: 10.2478/amcs-2019-0025. · Zbl 1430.93087
[32] Liu, K., Wang, H. and Xiao, J. (2015). The multivariate largest Lyapunov exponent as an age-related metric of quiet standing balance, Computational and Mathematical Methods in Medicine2015, Article ID 309756. · Zbl 1344.92026
[33] Nazarimehr, F., Jafari, S., Golpayegani, S.M.R.H. and Sprott, J. (2017). Can Lyapunov exponent predict critical transitions in biological systems?, Nonlinear Dynamics88(2): 1493-1500.
[34] Newman, M. (2018). Networks, Oxford University Press, Oxford. · Zbl 1391.94006
[35] Perez, C. and Germon, R. (2016). Graph creation and analysis for linking actors: Application to social data, in R. Layton and P. Watters (Eds), Automating Open Source Intelligence, Elsevier, Waltham, pp. 103-129.
[36] Ruiz, D. and Finke, J. (2019). Lyapunov-based anomaly detection in preferential attachment networks, International Journal of Applied Mathematics and Computer Science29(2): 363-373, DOI: 10.2478/amcs-2019-0027. · Zbl 1430.93089
[37] Sano, M. and Sawada, Y. (1985). Measurement of the Lyapunov spectrum from a chaotic time series, Physical Review Letters55(10): 1082.
[38] Serletis, A., Shahmoradi, A. and Serletis, D. (2007). Effect of noise on estimation of Lyapunov exponents from a time series, Chaos, Solitons & Fractals32(2): 883-887. · Zbl 1170.91399
[39] Stelling, J., Sauer, U., Szallasi, Z., Doyle, F.J. and Doyle, J. (2004). Robustness of cellular functions, Cell118(6): 675-685.
[40] Stumpf, M.P. and Wiuf, C. (2010). Incomplete and noisy network data as a percolation process, Journal of the Royal Society Interface7(51): 1411-1419.
[41] Szklarczyk, D., Franceschini, A., Wyder, S., Forslund, K., Heller, D., Huerta-Cepas, J., Simonovic, M., Roth, A., Santos, A., Tsafou, K.P., Kuhn, M., Bork, P., Jensen, L.J., von Mering, C. (2014). STRING v10: Protein-protein interaction networks, integrated over the tree of life, Nucleic Acids Research43(D1): D447-D452.
[42] Turinsky, A.L., Razick, S., Turner, B., Donaldson, I.M. and Wodak, S.J. (2010). Literature curation of protein interactions: Measuring agreement across major public databases, Database2010: baq026, DOI:10.1093/database /baq026.
[43] Vocaturo, E. and Veltri, P. (2017). On the use of networks in biomedicine, Procedia Computer Science110: 498-503.
[44] Watts, D.J. and Strogatz, S.H. (1998). Collective dynamics of ‘small-world’ networks, Nature393(6684): 440. · Zbl 1368.05139
[45] Yu, D., Kim, M., Xiao, G. and Hwang, T.H. (2013). Review of biological network data and its applications, Genomics & Informatics11(4): 200-210.
[46] Zhang, X., Wang, H. and Yang, Y. (2016). Robustness of indispensable nodes in controlling protein-protein interaction network, arXiv: 1609.02637.
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.