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Controllability and observability of Boolean networks arising from biology
1. I. Shmulevich, E. R. Dougherty, and W. Zhang, “ From Boolean to probabilistic Boolean networks as models of genetic regulatory networks,” Proc. IEEE 90, 1778–1792 (2002).
3. S. Huang and D. E. Ingber, “ Shape-dependent control of cell growth, differentiation, and apoptosis: Switching between attractors in cell regulatory networks,” Exp. Cell Res. 261, 91–103 (2000).
10. 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, 1–18 (2003).
11. S. Kauffman, C. Peterson, B. Samuelsson, and C. Troein, “ Random Boolean network models and the yeast transcriptional network,” Proc. Natl. Acad. Sci. U.S.A. 100, 14796–14799 (2003).
14. A. Chaos, M. Aldana, C. Espinosa-Soto, B. G. P. de León, A. G. Arroyo, and E. R. Alvarez-Buylla, “ From genes to flower patterns and evolution: Dynamic models of gene regulatory networks,” J. Plant Growth Regul. 25, 278–289 (2006).
17. D. Cheng, H. Qi, and Z. Li, Analysis and Control of Boolean Networks: A Semi-Tensor Product Approach ( Springer-Verlag, London, 2011).
31. R. Li, M. Yang, and T. Chu, “ Observability conditions of Boolean control networks,” Int. J. Robust Nonlinear Control 24, 2711–2723 (2014).
32. E. Fornasini and M. E. Valcher, “ Observability, reconstructibility and state observers of Boolean control networks,” IEEE Trans. Autom. Control 58, 1390–1401 (2013).
34. K. Kobayashi, J.-I. Imura, and K. Hiraishi, “ Polynomial-time algorithm for controllability test of a class of Boolean biological networks,” EURASIP J. Bioinf. Syst. Biol. 2010, 210685.
41. D. Nešić and I. M. Y. Mareels, “ Dead beat controllability of polynomial systems: Symbolic computation approaches,” IEEE Trans. Autom. Control 43, 162–175 (1998).
42. A. Veliz-Cuba, “ An algebraic approach to reverse engineering finite dynamical systems arising from biology,” SIAM J. Appl. Dyn. Syst. 11, 31–48 (2012).
43. D. Cox, J. Little, and D. O'Shea, Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3rd ed. ( Springer, New York, 2007).
44. Q. Zhao, “ A remark on ‘scalar equations for synchronous Boolean networks with biological applications’ by C. Farrow, J. Heidel, J. Maloney, and J. Rogers,” IEEE Trans. Neural Networks 16, 1715–1716 (2005).
45. T. Akutsu, M. Hayashida, W.-K. Ching, and M. K. Ng, “ Control of Boolean networks: Hardness results and algorithms for tree structured networks,” J. Theor. Biol. 244, 670–679 (2007).
50. T. Jia, Y.-Y. Liu, E. Csóka, M. Pósfai, J.-J. Slotine, and A.-L. Barabási, “ Emergence of bimodality in controlling complex networks,” Nat. Commun. 4, 2002 (2013).
56. S. Sahasrabudhe and A. E. Motter, “ Rescuing ecosystems from extinction cascades through compensatory perturbations,” Nat. Commun. 2, 170 (2011).
59. A. S. Jarrah and R. Laubenbacher, “ Discrete models of biochemical networks: The toric variety of nested canalyzing functions,” in Algebraic Biology ( Springer, Berlin, Heidelberg, 2007), pp. 15–22.
60. M. Artin, Algebra ( Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1991).
62. B. Faryabi, G. Vahedi, J.-F. Chamberland, A. Datta, and E. R. Dougherty, “ Optimal constrained stationary intervention in gene regulatory networks,” EURASIP J. Bioinf. Syst. Biol. 2008, 620767.
63. E. D. Sontag, “ On the observability of polynomial systems, I: Finite-time problems,” SIAM J. Control Optim. 17, 139–151 (1979).
64. S. Klamt, J. Saez-Rodriguez, J. A. Lindquist, L. Simeoni, and E. D. Gilles, “ A methodology for the structural and functional analysis of signaling and regulatory networks,” BMC Bioinf. 7, 56 (2006).
65. R. Zhang, M. V. Shah, J. Yang, S. B. Nyland, X. Liu, J. K. Yun, R. Albert, and T. P. Loughran, Jr., “ Network model of survival signaling in large granular lymphocyte leukemia,” Proc. Natl. Acad. Sci. U.S.A. 105, 16308–16313 (2008).
67. R. Laubenbacher, F. Hinkelmann, D. Murrugarra, and A. Veliz-Cuba, “ Algebraic models and their use in systems biology,” in Discrete and Topological Models in Molecular Biology ( Springer, Berlin, Heidelberg, 2014), pp. 443–474.
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Boolean networks are currently receiving considerable attention as a computational scheme for system level analysis and modeling of biological systems. Studying control-related problems in Boolean networks may reveal new insights into the intrinsic control in complex biological systems and enable us to develop strategies for manipulating biological systems using exogenous inputs. This paper considers controllability and observability of Boolean biological networks. We propose a new approach, which draws from the rich theory of symbolic computation, to solve the problems. Consequently, simple necessary and sufficient conditions for reachability, controllability, and observability are obtained, and algorithmic tests for controllability and observability which are based on the Gröbner basis method are presented. As practical applications, we apply the proposed approach to several different biological systems, namely, the mammalian cell-cycle network, the T-cell activation network, the large granular lymphocyte survival signaling network, and the Drosophila segment polarity network, gaining novel insights into the control and/or monitoring of the specific biological systems.
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