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Node-independent elementary signaling modes: A measure of redundancy in Boolean signaling transduction networks

  • ZHONGYAO SUN (a1) and RÉKA ALBERT (a1) (a2)


The redundancy of a system denotes the amount of duplicate components or mechanisms in it. For a network, especially one in which mass or information is being transferred from an origin to a destination, redundancy is related to the robustness of the system. Existing network measures of redundancy rely on local connectivity (e.g. clustering coefficients) or the existence of multiple paths. As in many systems there are functional dependencies between components and paths, a measure that not only characterizes the topology of a network, but also takes into account these functional dependencies, becomes most desirable.

We propose a network redundancy measure in a prototypical model that contains functionally dependent directed paths: a Boolean model of a signal transduction network. The functional dependencies are made explicit by using an expanded network and the concept of elementary signaling modes (ESMs). We define the redundancy of a Boolean signal transduction network as the maximum number of node-independent ESMs and develop a methodology for identifying all maximal node-independent ESM combinations. We apply our measure to a number of signal transduction network models and show that it successfully distills known properties of the systems and offers new functional insights. The concept can be easily extended to similar related forms, e.g. edge-independent ESMs.



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Adelson-Velsky, G. M., Gelbukh, A., & Levner, E. (2002). On fast path-finding algorithms in AND-OR graphs. Mathematical Problems in Engineering, 8 (4/5), 283293.
Adelson-Velsky, G. M., & Levner, E. (2002). Project scheduling in AND-OR graphs: A generalization of Dijkstra's algorithm. Mathematics of Operations Research, 27 (3), 504517.
Albert, R., & Othmer, H. G. (2003). The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster. Journal of Theoretical Biology, 223, 118.
Albert, R., & Thakar, J. (2014). Boolean modeling: A logic-based dynamic approach for understanding signaling and regulatory networks and for making useful predictions. Wiley Interdisciplinary Reviews Systems Biology and Medicine, 6, 353369.
Balabanian, N., & Carlson, B. (2001). Digital logic design principles (pp. 3940). New York: John Wiley. ISBN 978-0-471-29351-4.
Bondy, J. A., & Murty, U. S. R. (1976). Graph theory with applications (pp. 131133). New York: Elsevier Science Publishing Co., Inc.
Bron, C., & Kerbosch, J. (1973). Algorithm 457: Finding all cliques of an undirected graph. Communications of the ACM, 16 (9), 575577.
Buldyrev, S., Parshani, R., Paul, G., Stanley, H. E., & Havlin, S. (2010). Catastrophic cascade of failures in interdependent networks. Nature, 464, 10251028.
Camarinha-Matos, L. M., & Afsarmanesh, H. (2003). Elements of a base VE infrastructure. Journal of Computers in Industry, 51 (2), 139163.
Cazals, F., & Karande, C. (2008). A note on the problem of reporting maximal cliques. Theoretical Computer Science, 407 (1–3), 564568.
Dinic, E. A. (1990). The fastest algorithm for PERT problem with AND- and OR-nodes. In Proceedings of Integer Programming/Combinatorial Optimization Conference (IPCO) (pp. 185187). Waterloo: University of Waterloo Press.
Ford, L. R., & Fulkerson, D. R. (1956). Maximal flow through a network. Canadian Journal of Mathematics, 8, 399.
Goemann, B., Wingender, E., & Potapov, A. P. (2009). An approach to evaluate the topological significance of motifs and other patterns in regulatory networks. BMC Systems Biology, 3, 53.
Goldberg, A. V., & Tarjan, R. E. (1986). A new approach to the maximum flow problem. Proceedings of the Eighteenth Annual ACM Symposium on Theory of Computing - STOC '86 (p. 136). New York, NY, USA.
Hagberg, A. A., Schult, D. A., & Swart, P. J. (2008). Exploring network structure, dynamics, and function using NetworkX. In Varoquaux, G., Vaught, T., & Millman, J. (Eds.), Proceedings of the 7th Python in Science Conference (SciPy2008) (pp. 1115). Pasadena, CA USA.
Kato, M., Hata, N., Banerjee, N., Futcher, B., & Zhang, M. Q. (2004). Identifying combinatorial regulation of transcription factors and binding motifs. Genome Biology, 5, R56.
Klamt, S., Saez-Rodriguez, J., & Gilles, E. D. (2007). Structural and functional analysis of cellular networks with CellNetAnalyzer. BMC Systems Biology, 1, 2.
Klamt, S., Saez-Rodriguez, J., Lindquist, J. A., Simeoni, L., & Gilles, E. D. (2006). A methodology for the structural and functional analysis of signaling and regulatory networks. BMC Bioinformatics, 7, 56.
Li, S., Assmann, S. M., & Albert, R. (2006). Predicting essential components of signal transduction networks: A dynamic model of guard cell abscisic acid signaling. PLoS Biology, 4, e312.
Lipshtat, A., Purushothaman, S. P., Iyengar, R. & Ma'ayan, A. (2008). Functions of bifans in context of multiple regulatory motifs in signaling networks. Biophysical Journal, 94, 14.
Ma'ayan, A., Jenkins, S. L., Neves, S., Hasseldine, A., Grace, E., Dubin-Thaler, B., . . . Iyengar, R. (2005). Formation of regulatory patterns during signal propagation in a Mammalian cellular network. Science, 309, 10781083.
Martínez-Sosa, P., & Mendoza, L. (2013). The regulatory network that controls the differentiation of T lymphocytes. Bio Systems, 8, 96103.
Menger, K. (1927). Zur allgemeinen Kurventheorie. Fundamenta Mathematicae, 10, 96115.
Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., & Alon, U. (2002). Network motifs: Simple building blocks of complex networks. Science, 298, 824827.
Miskov-Zivanov, N., Turner, M. S., Kane, L. P., Morel, P. A., & Faeder, J. R. (2013). The duration of T cell stimulation is a critical determinant of cell fate and plasticity. Science Signaling, 6, ra97.
Parshani, R., Buldyrev, S. V., & Havlin, S. (2011). Critical effect of dependency groups on the function of networks. PNAS USA, 108 (3), 10071010.
Rajaraman, & Radhakrishnan, (2004). Introduction To Digital Computer Design An 5Th Ed. (p. 65). New Delhi, India: PHI Learning Pvt. Ltd. ISBN 978-81-203-3409-0.
Remenyi, A., Scholer, H. R., & Wilmanns, M. (2004). Combinatorial control of gene expression. Nature Structural & Molecular Biology, 11 (9), 812815.
Saez-Rodriguez, J., Simeoni, L., Lindquist, J. A., Hemenway, R., Bommhardt, U., Arndt, B., . . . Schraven, B. (2007). A logical model provides insights into T cell receptor signaling. PLoS Computational Biology, 3, e163.
Samaga, R., Saez-Rodriguez, J., Alexopoulos, L. G., Sorger, P. K., & Klamt, S. (2009). The logic of EGFR/ErbB signaling: Theoretical properties and analysis of high-throughput data. PLoS Computational Biology, 5, e1000438.
Steinway, S. N., Zanudo, J. G., Ding, W., Rountree, C. B., Feith, D. J., Loughran, T.P. Jr., & Albert, R. (2014). Network modeling of TGFbeta signaling in hepatocellular carcinoma epithelial-to-mesenchymal transition reveals joint sonic hedgehog and Wnt pathway activation. Cancer Research, 74, 59635977.
Steinway, S. N., Zanudo, J. G., Michel, P. J., Feith, D. J., Loughran, T. P., & Albert, R. (2015). Combinatorial interventions inhibit TGFβ-driven epithelial-to-mesenchymal transition and support hybrid cellular phenotypes. npj Systems Biology and Applications, 1, 15014.
Sun, Z., Jin, X., Albert, R., & Assmann, S. M. (2014). Multi-level modeling of light-induced stomatal opening offers new insights into its regulation by drought. PLoS Computational Biology, 10, e1003930.
Thakar, J., Pilione, M., Kirimanjeswara, G., Harvill, E. T., & Albert, R. (2007). Modeling systems-level regulation of host immune responses. PLoS Computational Biology, 3, e109.
Tomita, E., Tanaka, A., & Takahashi, H. (2006). The worst-case time complexity for generating all maximal cliques and computational experiments. Theoretical Computer Science, 363 (1), 2842. Computing and Combinatorics, 10th Annual International Conference on Computing and Combinatorics (COCOON 2004).
Wang, R. S., & Albert, R. (2011). Elementary signaling modes predict the essentiality of signal transduction network components. BMC Systems Biology, 5, 44.
Wang, R., Sun, Z., & Albert, R. (2013). Minimal functional routes in directed graphs with dependent edges. International Transactions in Operational Research, 20, 19.
Wunderlich, Z., & Mirny, L. A. (2006). Using the topology of metabolic networks to predict viability of mutant strains. Biophys J., 91, 23042311.
Zanudo, J. G., & Albert, R. (2013). An effective network reduction approach to find the dynamical repertoire of discrete dynamic networks. Chaos, 23, 025111.
Zhang, R., Shah, M. V., Yang, J., Nyland, S. B., Liu, X. et al. (2008). Network model of survival signaling in large granular lymphocyte leukemia. Proceedings of the National Academy of Sciences of the United States of America, 105, 1630816313.


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Node-independent elementary signaling modes: A measure of redundancy in Boolean signaling transduction networks

  • ZHONGYAO SUN (a1) and RÉKA ALBERT (a1) (a2)


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