Algebraic models and their use in systems biology

Natural Computing Series

Volumn 48, Issue , 2014, Pages 443-474

  Laubenbacher, Reinhard ^a   Hinkelmann, Franziska ^b   Murrugarra, David ^c   Veliz Cuba, Alan ^d,e  

^a UNIVERSITY OF CONNECTICUT HEALTH CENTER   (United States)

^b C/o Renzelmann ^*  (Germany)

^c GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^d University of Houston   (United States)

^e RICE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85018214593     PISSN: 16197127     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-40193-0_21     Document Type: Chapter

References (80)

1. R. Albert, 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)
2. E.R. Álvarez-Buylla, Á. Chaos, M. Aldana, M. Benítez, Y. Cortes-Poza, C. Espinosa-Soto, D.A. Hartasánchez, R.B. Lotto, D. Malkin, G.J. Escalera Santos, P. Padilla-Longoria, Floral morphogenesis: stochastic explorations of a gene network epigenetic landscape. PLoS ONE 3(11), e3626 (2008)
3. J. Aracena, J. Demongeot, E. Goles, Fixed points and maximal independent sets in AND-OR networks. Discret. Appl. Math. 138(3), 277-288 (2004)
4. R. Bonneau, Learning biological networks: from modules to dynamics. Nat. Chem. Biol. 4(11), 658-664 (2008)
5. D. Bratsun, D. Volfson, L.S. Tsimring, J. Hasty, Delay-induced stochastic oscillations in gene regulation. Proc. Natl. Acad. Sci. U.S.A. 102(41), 14593-14598 (2005)
6. A. Bruex, R.M. Kainkaryam, Y. Wieckowski, Y.H. Kang, C. Bernhardt, Y. Xia, X. Zheng, J.Y. Wang, M.M. Lee, P. Benfey, P.J. Woolf, J. Schiefelbein, A gene regulatory network for root epidermis cell differentiation in arabidopsis. PLoS Genet. 8(1), e1002446 (2012). PMID: 22253603
7. F.J. Bruggeman, H.V. Westerhoff, The nature of systems biology. Trends Microbiol. 15(1), 45-50 (2007)
8. A. Butte, I. Kohane, Mutual information relevance networks: functional genomic clustering using pairwise entropy measurements. Pac. Symp. Biocomput. 5, 415-426 (2000)
9. I. Cantone, L. Marucci, F. Iorio, M. Ricci, V. Belcastro, M. Bansal, S. Santini, M. di Bernardo, D. di Bernardo, M. Cosma, A yeast synthetic network for in vivo assessment of reverseengineering and modeling approaches. Cell 137(1), 172-181 (2009)
10. C. Chaouiya, E. Remy, P.R.D. Thieffry, Qualitative modeling of genetic networks: from logical regulatory graphs to standard Petri nets. Springer Lect. Notes Comput. Sci. 3099, 137-156 (2004)
11. M. Chaves, E. Sontag, R. Albert, Methods of robustness analysis for Boolean models of gene control networks. IET Syst. Biol. 153, 154-167 (2006)
12. J. Chifman, A. Kniss, P. Neupane, I. Williams, B. Leung, Z. Deng, P. Mendes, V. Hower, F.M. Torti, S.A. Akman, S.V. Torti, R. Laubenbacher, The core control system of intracellular iron homeostasis: a mathematical model. J. Theor. Biol. 300, 91-99 (2012). PMID: 22286016
13. D. Cox, J. Little, D. O’Shea, Ideals, Varieties, and Algorithms, 2nd edn. (Springer, New York, 1997)
14. P. Dao, R. Colak, R. Salari, F. Moser, E. Davicioni, A. Schonhuth, M. Ester, Inferring cancer subnetwork markers using density-constrained biclustering. Bioinformatics 26(18), 625-631 (2010)
15. M.I. Davidich, S. Bornholdt, Boolean network model predicts cell cycle sequence of fission yeast. PLoS One 3(2), e1672 (2008)
16. A. de la Fuente, P. Brazhnik, P. Mendes, Linking the genes: inferring quantitative gene networks from microarray data. Trends Genet. 18(8), 395-398 (2002)
17. A. de la Fuente, N. Bing, I. Hoeschele, P. Mendes, Discovery of meaningful associations in genomic data using partial correlation coefficients. Bioinformatics 20(18), 3565-3574 (2004)
18. E. Dimitrova, L.D. Garcia-Puente, F. Hinkelmann, A.S. Jarrah, R. Laubenbacher, B. Stigler, M. Stillman, P. Vera-Licona Polynome (2010). Available at http://polymath.vbi.vt.edu/polynome/
19. E. Dimitrova, L.D. Garcìa-Puente, F. Hinkelmann, A.S. Jarrah, R. Laubenbacher, B. Stigler, M. Stillman, P. Vera-Licona, Parameter estimation for Boolean models of biological networks. Theor. Comput. Sci. 412(26), 2816-2826 (2011)
20. J. Faith, B. Hayete, J. Thaden, I. Mogno, J. Wierzbowski, G. Cottarel, S. Kasif, J. Collins, T. Gardner, Large-scale mapping and validation of Escherichia coli transcriptional regulation from a compendium of expression profiles. PLoS Biol. 5(1), e8 (2007)
21. D. Formanowicz, A. Sackmann, P. Formanowicz, J. Błazewicz, Petri net based model of the body iron homeostasis. J. Biomed. Inform. 40(5), 476-485 (2007). PMID: 17258508
22. T. Gardner, D. di Bernardo, D. Lorenz, J. Collins, Inferring genetic networks and identifying compound mode of action via expression profiling. Science 301(5629), 102-105 (2003)
23. A. Garg, K. Mohanram, A. Di Cara, G. De Micheli, I. Xenarios, Modeling stochasticity and robustness in gene regulatory networks. Bioinformatics 25(12), i101-i109 (2009)
24. D.T. Gillespie, Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340-2361 (1977)
25. D. Gillespie, Stochastic simulation of chemical kinetics. Annu. Rev. Phys. Chem. 58, 35-55 (2007)
26. D.R. Grayson, M.E. Stillman, Macaulay2, a software system for research in algebraic geometry (1992). Available at http://www.math.uiuc.edu/Macaulay2/
27. A. Haury, F. Mordelet, P. Vera-Licona, J. Vert, TIGRESS: trustful inference of gene regulation using stability selection. BMC Syst. Biol. 6, 145 (2012)
28. F. Hinkelmann, A.S. Jarrah, Inferring biologically relevant models: nested canalyzing functions. ISRN Biomath. 2012, 7 (2012)
29. F. Hinkelmann, M. Brandon, B. Guang, R. McNeill, A. Veliz-Cuba, G. Blekherman, R. Laubenbacher, ADAM: analysis of analysis of dynamic algebraic models (2010). Available at http://adam.vbi.vt.edu/
30. F. Hinkelmann, M. Brandon, B. Guang, R. McNeill, G. Blekherman, A. Veliz-Cuba, R. Laubenbacher, ADAM: Analysis of discrete models of biological systems using computer algebra. BMC Bioinform. 12(1), 295 (2011)
31. C. Hong, M. Lee, D. Kim, D. Kim, K.-H. Cho, I. Shin, A checkpoints capturing timing-robust Boolean model of the budding yeast cell cycle regulatory network. BMC Syst. Biol. 6(1), 129 (2012). PMID: 23017186
32. A. Jarrah, B. Raposa, R. Laubenbacher, Nested canalyzing, unate cascade, and polynomial functions. Physica D 233, 167-174 (2007)
33. A.S. Jarrah, R. Laubenbacher, B. Stigler, M. Stillman, Reverse-engineering of polynomial dynamical systems. Adv. Appl. Math. 39(4), 477-489 (2007)
34. A. Jarrah, R. Laubenbacher, A. Veliz-Cuba, The dynamics of conjunctive and disjunctive Boolean network models. Bull. Math. Biol. 72, 1425-1447 (2010)
35. S.A. Kauffman, The large-scale structure and dynamics of gene control circuits: an ensemble approach. J. Theor. Biol. 44, 167 (1973)
36. S. Kauffman, C. Peterson, B. Samuelsson, C. Troein, Random Boolean network models and the yeast transcriptional network. Proc. Natl. Acad. Sci. 100(25), 14796-14799 (2003)
37. S. Kauffman, C. Peterson, B. Samuelsson, C. Troein, Genetic networks with canalyzing Boolean rules are always stable. Proc. Natl. Acad. Sci. 101(49), 17102-17107 (2004)
38. J.G. Klotz, R. Heckel, S. Schober, Bounds on the average sensitivity of nested canalizing functions. PLoS ONE 8(5), e64371 (2013)
39. N. Kramer, J. Schafer, A. Boulesteix, Regularized estimation of large-scale gene association networks using graphical Gaussian models. BMC Bioinform. 10, 384 (2009)
40. R. Küffner, T. Petri, P. Tavakkolkhah, L. Windhager, R. Zimmer, Inferring gene regulatory networks by ANOVA. Bioinformatics 28(10), 1376-1382 (2012)
41. R. Laubenbacher, B. Stigler, A computational algebra approach to the reverse engineering of gene regulatory networks. J. Theor. Biol. 229, 523-537 (2004)
42. R. Layek, A. Datta, R. Pal, E.R. Dougherty, Adaptive intervention in probabilistic Boolean networks. Bioinformatics 25(16), 2042-2048 (2009)
43. Y. Li, J.O. Adeyeye, D. Murrugarra, B. Aguilar, R. Laubenbacher, Boolean nested canalizing functions: a comprehensive analysis. Theor. Comput. Sci. 481(0), 24-36 (2013)
44. J. Liang, J. Han, Stochastic Boolean networks: an efficient approach to modeling gene regulatory networks. BMC Syst. Biol. 6(1), 113 (2012)
45. R. Lidl, H. Niederreiter, Finite Fields (Cambridge University Press, New York, 1997)
46. A. Madar, A. Greenfield, E. Vanden-Eijnden, R. Bonneau, DREAM3: network inference using dynamic context likelihood of relatedness and the Inferelator. PLoS ONE 5(3), e9803 (2010)
47. D. Murrugarra, R. Laubenbacher, Regulatory patterns in molecular interaction networks. J. Theor. Biol. 288(0), 66-72 (2011)
48. D. Murrugarra, R. Laubenbacher, Multi-states nested canlyzing functions. Phys. D Nonlinear Phenom. 241, 921-938 (2012)
49. D. Murrugarra, A. Veliz-Cuba, B. Aguilar, S. Arat, R. Laubenbacher, Modeling stochasticity and variability in gene regulatory networks. EURASIP J. Bioinform. Syst. Biol. 2012, 5 (2012)
50. C. Müssel, M. Hopfensitz, H.A. Kestler, BoolNet-an R package for generation, reconstruction and analysis of Boolean networks. Bioinformatics 26(10), 1378-1380 (2010)
51. A. Naldi, D. Berenguier, A. Fauré, F. Lopez, D. Thieffry, C. Chaouiya, Logical modelling of regulatory networks with GINsim 2.3. Biosystems 97(2), 134-139 (2009)
52. A. Naldi, E. Remy, D. Thieffry, C. Chaouiya, A reduction of logical regulatory graphs preserving essential dynamical properties, in Computational Methods in Systems Biology, ed. by P. Degano, R. Gorrieri. Volume 5688 of Lecture Notes in Computer Science (Springer, Berlin/Heidelberg, 2009), pp. 266-280
53. R. Porreca, E. Cinquemani, J. Lygeros, G. Ferrari-Trecate, Identification of genetic network dynamics with unate structure. Bioinformatics 26(9), 1239-1245 (2010)
54. L. Raeymaekers, Dynamics of Boolean networks controlled by biologically meaningful functions. J. Theor. Biol. 218(3), 331-341 (2002)
55. A.S. Ribeiro, Stochastic and delayed stochastic models of gene expression and regulation. Math. Biosci. 223(1), 1-11 (2010)
56. A.S. Ribeiro, S.A. Kauffman, Noisy attractors and ergodic sets in models of gene regulatory networks. J. Theor. Biol. 247(4), 743-755 (2007)
57. A. Ribeiro, R. Zhu, S.A. Kauffman, A general modeling strategy for gene regulatory networks with stochastic dynamics. J. Comput. Biol. 13(9), 1630-1639 (2006)
58. C. Rohr, W. Marwan, M. Heiner, Snoopy-a unifying Petri net framework to investigate biomolecular networks. Bioinformatics 26(7), 974-975 (2010)
59. A. Saadatpour, I. Albert, R. Albert, Attractor analysis of asynchronous Boolean models of signal transduction networks. J. Theor. Biol. 266(4), 641-656 (2010)
60. A. Sackmann, M. Heiner, I. Koch, Application of Petri net based analysis techniques to signal transduction pathways. BMC Bioinform. 7(1), 482 (2006)
61. I. Shmulevich, E.R. Dougherty, Probabilistic Boolean Networks: The Modeling and Control of Gene Regulatory Networks (SIAM, Philadelphia, 2010)
62. I. Shmulevich, E.R. Dougherty, S. Kim, W. Zhang, Probabilistic Boolean networks: a rulebased uncertainty model for gene regulatory networks. Bioinformatics 18(2), 261-274 (2002)
63. B. Stigler, D. Camacho, A. Martins, W. Sha, E.S. Dimitrova, P. Vera-Licona, V. Shulaev, P. Mendes, R. Laubenbacher, Reverse engineering a yeast oxidative stress response network. Under review (2013)
64. S. Teraguchi, Y. Kumagai, A. Vandenbon, S. Akira, D.M. Standley, Stochastic binary modeling of cells in continuous time as an alternative to biochemical reaction equations. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 84(6 Pt 1), 062903 (2011)
65. D. Thieffry, R. Thomas, Qualitative analysis of gene networks. Pac. Symp. Biocomput. 3, 77-88 (1998)
66. R. Thomas, Regulatory networks seen as asynchronous automata: a logical description. J. Theor. Biol. 153, 1-23 (1991)
67. T. Toulouse, P. Ao, I. Shmulevich, S. Kauffman, Noise in a small genetic circuit that undergoes bifurcation. Complexity 11(1), 45-51 (2005)
68. A. Veliz-Cuba, Reduction of Boolean network models. J. Theor. Biol. 289, 167-172 (2011)
69. A. Veliz-Cuba, An algebraic approach to reverse engineering finite dynamical systems arising from biology. SIAM J. Appl. Dyn. Syst. 11(1), 31-48 (2012)
70. A. Veliz-Cuba, R. Laubenbacher, On the computation of fixed points in Boolean networks. J. Appl. Math. Comput. accepted (2011)
71. A. Veliz-Cuba, B. Stigler, Boolean models can explain bistability in the lac operon. J. Comput. Biol. 18(6), 783-794 (2011)
72. A. Veliz-Cuba, A.S. Jarrah, R. Laubenbacher, Polynomial algebra of discrete models in systems biology. Bioinformatics 26(13), 1637-1643 (2010)
73. A. Veliz-Cuba, J. Arthur, L. Hochstetler, V. Klomps, E. Korpi, On the relationship of steady states of continuous and discrete models arising from biology. Bull. Math. Biol. accepted (2012)
74. A. Veliz-Cuba, K. Buschur, R. Hamershock, A. Kniss, E. Wolff, R. Laubenbacher, AND-NOT logic framework for steady state analysis of Boolean network models (2012). arXiv:1211.5633
75. M. Vignes, J. Vandel, D. Allouche, N. Ramadan-Alban, C. Cierco-Ayrolles, T. Schiex, B. Mangin, S. de Givry, Gene regulatory network reconstruction using Bayesian networks, the Dantzig selector, the Lasso and their meta-analysis. PLoS ONE 6(12), e29165 (2011)
76. C.H. Waddington, Canalisation of development and the inheritance of acquired characters. Nature 150, 563-564 (1942)
77. H. Wang, L. Qian, E. Dougherty, Inference of gene regulatory networks using S-system: a unified approach. IET Syst. Biol. 4(2), 145-156 (2010)
78. D. Wilkinson, Stochastic Modeling for Systems Biology (Chapman and Hall/CRC, Boca Raton, 2006)
79. K. Willadsen, J. Wiles, Robustness and state-space structure of Boolean gene regulatory models. J. Theor. Biol. 249(4), 749-765 (2007)
80. P. Zoppoli, S. Morganella, M. Ceccarelli, TimeDelay-ARACNE: reverse engineering of gene networks from time-course data by an information theoretic approach. BMC Bioinform. 11(1), 154 (2010)