NOTICE: Scitation Maintenance Sunday, March 1, 2015.

Scitation users may experience brief connectivity issues on Sunday, March 1, 2015 between 12:00 AM and 7:00 AM EST due to planned network maintenance.

Thank you for your patience during this process.

banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
An effective network reduction approach to find the dynamical repertoire of discrete dynamic networks
Rent this article for
Access full text Article
1. A. L. Barabási and Z. N. Oltvai, “Network biology: Understanding the cell's functional organization,” Nat. Rev. Genet. 5, 101113 (2004).
2. S. Bornholdt, “Systems biology: Less is more in modeling large genetic networks,” Science 310(5747), 449451 (2005).
3. A. Mogilner, J. Allard, and R. Wollman, “Cell polarity: Quantitative modeling as a tool in cell biology,” Science 336(6078), 175179 (2012).
4. J. J. Tyson, K. C. Chen, and B. Novak, “Network dynamics and cell physiology,” Nat. Rev. Mol. Cell Biol. 2(12) 908916 (2001).
5. J. J. Tyson, K. C. Chen, and B. Novak, “Sniffers, buzzers, toggles and blinkers: Dynamics of regulatory and signaling pathways in the cell,” Curr. Opin. Cell Biol. 15, 221231 (2003).
6. A. Mogilner, R. Wollman, and W. F. Marshall, “Quantitative modeling in cell biology: What is it good for?,” Develop. Cell 11(3), 279287 (2006).
7. B. B. Aldridge, J. M. Burke, D. A. Lauffenburger, and P. K. Sorger, “Physicochemical modeling of cell signaling pathways,” Nat. Cell Biol. 8, 11951203 (2006).
8. R. Albert and H. G. Othmer, “The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster,” J. Theor. Biol. 223(1), 118 (2003).
9. C. Espionza-Soto, P. Padilla-Longoria, and E. R. Alvarez-Buylla, “A gene regulatory network model for cell-fate determination during Arabidopsis thaliana flower development that is robust and recovers experimental gene expression profiles,” Plant Cell 16, 29232939 (2004).
10. D. A. Orlando, C. Y. Lin, A. Bernard, J. Y. Wang, J. E. S. Socolar, E. S. Iversen, A. J. Hartemink, and S. B. Haase, “Global control of cell-cycle transcription by coupled CDK and network oscillators,” Nature 453, 944947 (2008).
11. R. Zhang, M. V. Shah, J. Yang, S. B. Nyland, X. Liu, J. K. Yun, R. Albert, and T. P. Loughran, “Network model of survival signaling in LGL leukemia,” Proc. Natl. Acad. Sci. 105, 1630816313 (2008).
12. J. Saez-Rodriguez, L. Simeoni, J. A. Lindquist, R. Hemenway, U. Bommhardt, B. Arndt, U. U. Haus, R. Weismantel, E. D. Gilles, S. Klamt, and B. Schraven, “A logical model provides insights into T cell receptor signaling,” PLoS Comput. Biol. 3, e163 (2007).
13. R. S. Wang and R. Albert, “Discrete dynamic modeling of cellular signaling networks,” Methods Enzymol. 467, 281306 (2009).
14. R. Albert and H. G. Othmer, “But no kinetic details are needed,” SIAM News 36(10) (2003).
15. F. Jacob and J. Monod, “Genetic regulatory mechanisms in the synthesis of proteins,” J. Mol. Biol. 3, 318356 (1961).
16. R. Thomas, “Boolean formalization of genetic control circuits,” J. Theor. Biol. 42, 563585 (1973).
17. S. A. Kauffman, “Metabolic stability and epigenesis in randomly constructed genetic nets,” J. Theor. Biol. 22, 437467 (1969).
18. L. Glass and S. A. Kauffman, “The logical analysis of continous, nonlinear biochemical control networks,” J. Theor. Biol. 39, 103129 (1973).
19. R. Thomas, On the Relation Between the Logical Structure of Systems and Their Ability to Generate Multiple Steady States and Sustained Oscillations, Series in Synergetics Vol. 9 (Springer, 1981), pp. 180193.
20. E. Plahte, “Feedback loops, stability and multistationarity in dynamical systems,” J. Biol. Syst. 3, 409413 (1995).
21. E. H. Snoussi, “Necessary conditions for multistationarity and stable periodicity,” J. Biol. Syst. 6, 39 (1998).
22. J. L. Gouzé, “Positive and negative circuits in dynamical systems,” J. Biol. Syst. 6, 1115 (1998).
23. C. Soulé, “Graphic requirements for multistationarity,” ComPlexUs 1, 123133 (2003).
24. J. Aracena, J. Demongeot, and E. Goles, “On limit cycles of monotone functions with symmetric connection graph,” Theor. Comput. Sci. 322, 237244 (2004).
25. É. Remy and P. Ruet, “On differentiation and homeostatic behaviours of Boolean dynamical systems,” in Transactions on Computational Systems Biology, Lecture Notes in Computer Science Vol. 4780 (Springer, 2007), pp. 92101.
26. É. Remy, P. Ruet, and D. Thieffry, “Graphic requirements for multistability and attractive cycles in a Boolean dynamical framework,” Adv. Appl. Math. 41(3), 335350 (2008).
27. É. Remy and P. Ruet, “From minimal signed circuits to the dynamics of Boolean regulatory networks,” Bioinformatics 24(16), 220226 (2008).
28. H. Siebert, “Deriving behavior of Boolean bioregulatory networks from subnetwork dynamics,” Math. Comput. Sci. 2, 421442 (2009).
29. I. Harvey and T. Bossomaie, “Time out of join: Attractors in asynchronous random Boolean networks,” in Proceedings of the Fourth European Conferences on Artificial Life (Cambridge, UK, 1997), pp. 6775.
30. M. Chaves, R. Albert, and E. D. Sontag, “Robustness and fragility of Boolean models for genetic regulatory networks,” J. Theor. Biol. 235, 431449 (2005).
31. L. Glass, “Classification of biological networks by their qualitative dynamics,” J. Theor. Biol. 54(1), 85107 (1975).
32. R. Thomas, D. Thieffry, and M. Kaufman, “Dynamical behaviour of biological regulatory networks–I. Biological role of feedback loops and practical use of the concept of the loop-characteristic state,” Bull. Math. Biol. 57(2), 247276 (1995).
33. V. Sevim, X. Gong, and J. E. Socolar, “Reliability of transcriptional cycles and the yeast cell-cycle oscillator,” PLoS Comput. Biol. 6(7), e1000842 (2010).
34. M. Chaves, E. D. Sontag, and R. Albert, “Methods of robustness analysis for Boolean models of gene control networks,” Syst. Biol. (Stevenage) 153(4), 154167 (2006).
35. A. Saadatpour, I. Albert, and R. Albert, “Attractor analysis of asynchronous Boolean models of signal transduction networks,” J. Theor. Biol. 266, 641656 (2010).
36. A. Naldi, É. Remy, D. Thieffry, and C. Chaouiya, “Dynamically consistent reduction of logical regulatory graphs,” Theor. Comput. Sci. 412, 22072218 (2011).
37. A. Veliz-Cuba, “Reduction of Boolean network models,” J. Theor. Biol. 289, 167172 (2011).
38. S. Bilke and F. Sjunnesson, “Stability of the Kauffman model,” Phys. Rev. E 65, 016129 (2001).
39. J. E. Socolar and S. A. Kauffman, “Scaling in ordered and critical random Boolean networks,” Phys. Rev. Lett. 90, 068702 (2003).
40. T. Mihaljev and B. Drossel, “Scaling in a general class of critical random Boolean networks,” Phys. Rev. E 74, 046101 (2006).
41. A. Saadatpour, R.-S. Wang, A. Liao, X. Liu, T. P. Loughran, I. Albert, and R. Albert, “Dynamical and structural analysis of a T cell survival network identifies novel candidate therapeutic targets for large granular lymphocyte leukemia,” PLoS Comput. Biol. 7(11), e1002267 (2011).
42. R. S. Wang and R. Albert, “Elementary signaling modes predict the essentiality of signal transduction network components,” BMC Syst. Biol. 5, 44 (2011).
43. E. H. Snoussi and R. Thomas, “Logical identification of all steady states: The concept of feedback loop characteristic states,” Bull. Math. Biol. 55(5), 973991 (1993).
44. S. Klamt, J. Saez-Rodriguez, and E. D. Gilles, “Structural and functional analysis of cellular networks with CellNetAnalyzer,” BMC Syst. Biol. 1, 2 (2007).
45. D. B. Johnson, “Finding all the elementary circuits of a directed graph,” SIAM J. Comput. 4(1), 7784 (1975).
46. M. Aldana-Gonzalez, S. Coppersmith, and L. P. Kadanoff, “Boolean dynamics with random couplings,” in Perspectives and Problems in Nonlinear Science, A celebratory volume in honor of Lawrence Sirovich, Springer Applied Mathematical Sciences Series, edited by Ehud Kaplan, Jerrold E. Marsden, and Katepalli R. Sreenivasan (2003), pp. 2389.
47. M. Aldana, “Dynamics of Boolean networks with scale free topology,” Physica D 185(1), 4566 (2003).
48. S. E. Harris, B. K. Sawhill, A. Wuensche, and S. Kauffman, “A model of transcriptional regulatory networks based on biases in the observed regulation rules,” Complexity 7(4), 2340 (2002).
49. J. G. T. Zañudo, M. Aldana, and G. Martinez-Mekler, “Boolean threshold networks: Virtues and limitations for biological modeling,” in Information Processing and Biological Systems (Springer, Berlin, 2011), pp. 113151.
50. D. M. Wittmann, C. Marr, and F. J. Theis, “Biologically meaningful update rules increase the critical connectivity of generalized Kauffman networks,” J. Theor. Biol. 266(3), 436448 (2010).
51. I. Shmulevich, S. A. Kauffman, and M. Aldana, “Eukaryotic cells are dynamically ordered or critical but not chaotic,” Proc. Natl. Acad. Sci. U.S.A. 102, 1343913444 (2005).
52. M. Nykter, N. D. Price, M. Aldana, S. A. Ramsey, S. A. Kauffman et al., “Gene expression dynamics in the macrophage exhibit criticality,” P roc. Natl. Acad. Sci. U.S.A. 105, 18971900 (2008).
53. M. V. Shah, R. Zhang, R. Irby, R. Kothapalli, X. Liu et al., “Molecular profiling of LGL leukemia reveals role of sphingolipid signaling in survival of cytotoxic lymphocytes,” Blood 112, 770781 (2008).
54. T. P. Loughran, Jr., J. A. Aprile, and F. W. Ruscetti, “Anti-CD3 monoclonal antibody-mediated cytotoxicity occurs through an interleukin-2-independent pathway in CD3+ large granular lymphocytes,” Blood 75, 935940 (1990).
55. R. Kothapalli, S. B. Nyland, I. Kusmartseva, R. D. Bailey, T. M. McKeown et al., “Constitutive production of proinflammatory cytokines RANTES, MIP-1, and IL-18 characterizes LGL leukemia,” Int. J. Oncol. 26(2), 529535 (2005).
56. A. Saadatpour, R. Albert, and T. Reluga, “A reduction method for Boolean network models proven to conserve attractors,” SIAM J. Appl. Dyn. Syst. (submitted).
57. R. S. Wang and R. Albert, “Effects of community structure on the dynamics of random threshold networks,” Phys. Rev. E 87, 012810 (2013).
58. F. Greil and B. Drossel, “Dynamics of critical Kauffman networks under asynchronous stochastic update,” Phys. Rev. Lett. 95, 048701 (2005).
59. G. Y. Vichniac, “Boolean derivatives on cellular automata,” Physica D 45(1), 6374 (1990).

Data & Media loading...


Article metrics loading...



Discrete dynamic models are a powerful tool for the understanding and modeling of large biological networks. Although a lot of progress has been made in developing analysis tools for these models, there is still a need to find approaches that can directly relate the network structure to its dynamics. Of special interest is identifying the stable patterns of activity, i.e., the attractors of the system. This is a problem for large networks, because the state space of the system increases exponentially with network size. In this work, we present a novel network reduction approach that is based on finding network motifs that stabilize in a fixed state. Notably, we use a topological criterion to identify these motifs. Specifically, we find certain types of strongly connected components in a suitably expanded representation of the network. To test our method, we apply it to a dynamic network model for a type of cytotoxic T cell cancer and to an ensemble of random Boolean networks of size up to 200. Our results show that our method goes beyond reducing the network and in most cases can actually predict the dynamical repertoire of the nodes (fixed states or oscillations) in the attractors of the system.


Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: An effective network reduction approach to find the dynamical repertoire of discrete dynamic networks