CSDL Home IEEE/ACM Transactions on Computational Biology and Bioinformatics 2012 vol.9 Issue No.01 - January/February

Subscribe

Issue No.01 - January/February (2012 vol.9)

pp: 52-65

B. Vasic , Dept. of Electr. & Comput. Eng., Univ. of Arizona, Tucson, AZ, USA

V. Ravanmehr , Dept. of Electr. & Comput. Eng., Univ. of Arizona, Tucson, AZ, USA

A. R. Krishnan , Western Digital Corp., Irvine, CA, USA

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TCBB.2011.61

ABSTRACT

We introduce a class of finite systems models of gene regulatory networks exhibiting behavior of the cell cycle. The network is an extension of a Boolean network model. The system spontaneously cycles through a finite set of internal states, tracking the increase of an external factor such as cell mass, and also exhibits checkpoints in which errors in gene expression levels due to cellular noise are automatically corrected. We present a 7-gene network based on Projective Geometry codes, which can correct, at every given time, one gene expression error. The topology of a network is highly symmetric and requires using only simple Boolean functions that can be synthesized using genes of various organisms. The attractor structure of the Boolean network contains a single cycle attractor. It is the smallest nontrivial network with such high robustness. The methodology allows construction of artificial gene regulatory networks with the number of phases larger than in natural cell cycle.

INDEX TERMS

Gene expression, Mathematical model, Proteins, Robustness, Noise, Boolean functions, Logic gates,error correction coding., Gene regulatory networks, Boolean networks, cell cycle, error correction

CITATION

B. Vasic, V. Ravanmehr, A. R. Krishnan, "An Information Theoretic Approach to Constructing Robust Boolean Gene Regulatory Networks",

*IEEE/ACM Transactions on Computational Biology and Bioinformatics*, vol.9, no. 1, pp. 52-65, January/February 2012, doi:10.1109/TCBB.2011.61REFERENCES

- [1] A. Beyer, S. Bandyopadhyay, and T. Ideker, “Integrating Physical and Genetic Maps: From Genomes to Interaction Networks,”
Nature Rev. Genetics, vol. 8, no. 9, pp. 699-710, 2007.- [2] M. Kærn, W.J. Blake, and J.J. Collins, “The Engineering of Gene Regulatory Networks,”
Ann. Review of Biomedical Eng., vol. 5, pp. 176-206, Aug. 2003.- [3] B.P. Kramer, M. Fischer, and M. Fussenegger, “Semi-Synthetic Mammalian Gene Regulatory Networks,”
Metabolic Eng., vol. 7, no. 4, pp. 241-250, 2005.- [4] H. Kobayashi, M. Kærn, M. Araki, K. Chung, T.S. Gardner, C.R. Cantor, and J.J. Collins, “Programmable Cells: Interfacing Natural and Engineered Gene Networks,”
Proc. Nat'l Academy of Sciences USA, vol. 101, no. 22, pp. 8414-8419, 2004.- [5] D.A. Drubin, J.C. Way, and P.A. Silver, “Designing Biological Systems,”
Genes and Development, vol. 21, no. 3, pp. 242-254, 2007.- [6] N. Strelkowa and M. Barahona, “Switchable Genetic Oscillator Operating in Quasi-Stable Mode,”
J. The Royal Soc. Interface, vol. 7, pp. 1071-1082, 2010.- [7] K. Nasmyth, “Evolution of the Cell Cycle,”
Philosophical Trans.: Biological Sciences, vol. 349, pp. 271-281, 1995.- [8] A. Murray and T. Hunt,
The Cell Cycle. Oxford Univ. Press, 1993.- [9] F. Li, T. Long, Y. Lu, Q. Ouyang, and C. Tang, “The Yeast Cell-cycle Network is Robustly Designed,”
Proc. Nat'l Academy of Sciences USA, vol. 101, no. 14, pp. 4781-4786, 2004.- [10] K. Willadsen and J. Wiles, “Robustness and State-Space Structure of Boolean Gene Regulatory Models,”
J. Theoretical Biology, vol. 249, no. 4, pp. 749-765, 2007.- [11] N.W. Trepode, H.A. Armelin, M. Bittner, J. Barrera, M.D. Gubitoso, and R.F. Hashimoto, “A Robust Structural pgn Model for Control of Cell-Cycle Progression Stabilized by Negative Feedbacks,”
EURASIP J. Bioinformatics and Systems Biology, vol. 2007, p. 8, 2007.- [12] W. Lee and J. Huang, “Robustness and Topology of the Yeast Cell Cycle Boolean Network,”
FEBS Letters, vol. 583, no. 5, pp. 927-932, 2009.- [13] E. Remy, P. Ruet, and D. Thieffry, “Graphic Requirements for Multistability and Attractive Cycles in a Boolean Dynamical Framework,”
Advances in Applied Math., vol. 41, no. 3, pp. 335-350, 2008.- [14] M. Davidich and S. Bornholdt, “The Transition from Differential Equations to Boolean Networks: A Case Study in Simplifying a Regulatory Network Model,”
J. Theoretical Biology, vol. 255, no. 3, pp. 269-277, 2008.- [15] K.C. Chen, A. Csikasz-Nagy, B. Gyorffy, J. Val, B. Novak, and J.J. Tyson, “Kinetic Analysis of a Molecular Model of the Budding Yeast Cell Cycle,”
Molecular Biology Cell, vol. 11, no. 1, pp. 369-391, 2000.- [16] D. Irons, “Logical Analysis of the Budding Yeast Cell Cycle,”
J. Theoretical Biology, vol. 257, no. 4, pp. 543-559, 2009.- [17] A. Faure and D. Thieffry, “Logical Modelling of Cell Cycle Control in Eukaryotes: A Comparative Study,”
Molecular BioSystems, vol. 5, pp. 1569-1581, 2009.- [18] R. Pal, I. Ivanov, A. Datta, M.L. Bittner, and E.R. Dougherty, “Generating Boolean Networks with a Prescribed Attractor Structure,”
Bioinformatics, vol. 21, no. 21, pp. 4021-4025, 2005.- [19] P. Smolen, D. Baxter, and J. Byrne, “Mathematical Modeling of Gene Networks,”
Neuron, vol. 26, no. 3, pp. 567-580, 2000.- [20] J. Hasty, D. McMillen, F. Isaacs, and J. Collins, “Computational Studies of Gene Regulatory Networks: In Numero Molecular Biology,”
Nature Rev. Genetics, vol. 2, no. 4, pp. 268-279, 2001.- [21] E. Dougherty, I. Shmulevich, and M. Bittner, “Genomic Signal Processing: The Salient Issues,”
EURASIP J. Applied Signal Processing, pp. 146-153, 2004.- [22] R. Jansen, H. Yu, D. Greenbaum, Y. Kluger, N. Krogan, S. Chung, A. Emili, M. Snyder, J. Greenblatt, and M. Gerstein, “A Bayesian Networks Approach for Predicting Protein-Protein Interactions from Genomic Data,”
Science, vol. 302, no. 5644, pp. 449-453, 2003.- [23] A. Aytuna, A. Gursoy, and O. Keskin, “Prediction of Protein-Protein Interactions by Combining Structure and Sequence Conservation in Protein Interfaces,”
Bioinformatics, vol. 21, no. 12, pp. 2850-2855, 2005.- [24] A. Hartemink, D. Gifford, T. Jaakkola, and R. Young, “Using Graphical Models and Genomic Expression Data to Statistically Validate Models of Genetic Regulatory Networks,”
Proc. Pacific Symp. Biocomputing, vol. 6, pp. 422-433, 2001.- [25] C. Yeang and T. Jaakkola, “Modeling the Combinatorial Functions of Multiple Transcription Factors,”
J. Computational Biology, vol. 13, no. 2, pp. 463-480, 2006.- [26] N. Friedman, “Inferring Cellular Networks Using Probabilistic Graphical Models,”
Science Signaling, vol. 303, no. 5659, pp. 799-805, 2004.- [27] R. Albert and A. Barabási, “Statistical Mechanics of Complex Networks,”
Rev. of Modern Physics, vol. 74, no. 1, pp. 47-97, 2002.- [28] E. Koonin, Y. Wolf, and G. Karev,
Power Laws, Scale-Free Networks and Genome Biology. Springer Verlag, 2006.- [29] L.A.N. Amaral, A. Scala, M. Barthelemy, and H.E. Stanley, “Classes of Small-world Networks,”
Proc. Nat'l Academy of Sciences USA, vol. 97, no. 21, pp. 11149-11152, 2000.- [30] U. Bastolla and G. Parisi, “The Modular Structure of Kauffman Networks,”
Physica D: Nonlinear Phenomena, vol. 115, nos. 3/4, pp. 219-233, 1998.- [31] P. D'haeseleer, S. Liang, and R. Somogyi, “Genetic Network Inference: From Co-Expression Clustering to Reverse Engineering,”
Bioinformatics, vol. 16, no. 8, pp. 707-726, 2000.- [32] S. Kauffman and S. Levin, “Towards a General Theory of Adaptive Walks on Rugged Landscapes$^\ast$ ,”
J. Theoretical Biology, vol. 128, no. 1, pp. 11-45, 1987.- [33] F. Kschischang, B. Frey, and H. Loeliger, “Factor Graphs and the Sum-Product Algorithm,”
IEEE Trans. Information Theory, vol. 47, no. 2, pp. 498-519, Feb. 2001.- [34] R. Hermsen, S. Tans, P. ten Wolde, and V. Rhodius, “Transcriptional Regulation by Competing Transcription Factor Modules,”
PLoS Computational Biology, vol. 2, p. e164, 2006.- [35] N. Buchler, U. Gerland, and T. Hwa, “On Schemes of Combinatorial Transcription Logic,”
Proc. Nat'l Academy of Sciences USA, vol. 100, no. 9, pp. 5136-5141, 2003.- [36] C. Yuh, H. Bolouri, and E. Davidson, “Genomic Cis-regulatory Logic: Experimental and Computational Analysis of a Sea Urchin Gene,”
Science, vol. 279, no. 5358, pp. 1896-1902, 1998.- [37] J. von Neumann, “Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components,”
Brain Theory: Reprint Volume, p. 110, World Scientific, 1988.- [38]
Coding and Signal Processing for Magnetic Recording Systems, B. Vasic and E. Kurtas, eds. CRC Press, 2004.- [39] N. Pippenger, “Developments in ‘the Synthesis of Reliable Organisms from Unreliable Gates’,”
Proc. Symposia in Pure Math., pp. 311-324, 1990.- [40] S. Kauffman,
The Origins of Order: Self Organization and Selection in Evolution. Oxford Univ. Press, 1993.- [41] A. Garg, K. Mohanram, A. Di Cara, G. De Micheli, and I. Xenarios, “Modeling Stochasticity and Robustness in Gene Regulatory Networks,”
Bioinformatics, vol. 25, no. 12, pp. i101-i109, 2009.- [42] D.T. Gillespie, “Exact Stochastic Simulation of Coupled Chemical Reactions,”
The J. Physical Chemistry, vol. 81, no. 25, pp. 2340-2361, 1977.- [43] H.H. McAdams and A. Arkin, “It's a Noisy Business! Genetic Regulation at the Nanomolar Scale,”
Trends in Genetics, vol. 15, no. 2, pp. 65-69, 1999.- [44] J.M. Pedraza and A. Oudenaarden, “Noise in Gene Regulatory Networks,”
Complex Systems Science in Biomedicine, E. Micheli-Tzanakou, T.S. Deisboeck, and J.Y. Kresh, eds., pp. 211-226, Springer, 2006.- [45] E.R. Alvarez-Buylla, A. Chaos, M. Aldana, M. Benitez, Y. Cortes-Poza, C. Espinosa-Soto, D.A. Hartasanchez, R.B. Lotto, D. Malkin, G.J. Escalera Santos, and P. Padilla-Longoria, “Floral Morphogenesis: Stochastic Explorations of a Gene Network Epigenetic Landscape,”
PLoS ONE, vol. 3, no. 11, p. e3626, 2008.- [46] M.I. Davidich and S. Bornholdt, “Boolean Network Model Predicts Cell Cycle Sequence of Fission Yeast,”
PLoS ONE, vol. 3, no. 2, p. e1672, http://dx.plos.org10.1371%2Fjournal. pone.0001672 , Feb. 2008.- [47] E. Fredkin and T. Toffoli,
Conservative Logic, pp. 47-81. Springer-Verlag, 2002.- [48] D. Harlan Wood and J. Chen, “Fredkin Gate Circuits via Recombination Enzymes,”
Proc. IEEE Congress Evolutionary Computation, vol. 2, pp. 1896-1900, June 2004.- [49] H. Thapliyal and M.B. Srinivas, “An Extension to DNA Based Fredkin Gate Circuits: Design of Reversible Sequential Circuits Using Frekin Gates,”
Proc. CoRR, vol. abs/cs/0603092, http://arxiv.org/abs/cs0603092, 2006.- [50] S. Kauffman, P. Carsten, B. Samuelsson, and C. Troein, “Genetic Networks with Canalyzing Boolean Rules are Always Stable,”
Proc. Nat'l Academy of Sciences USA, vol. 101, no. 49, pp. 17102-17107, http://www.pnas.org/cgi/doi/10.1073pnas.0407783101 , Dec. 2004.- [51] M. Terzer, M. Jovanovic, A. Choutko, O. Nikolayeva, A. Korn, D. Brockhoff, F. Zurcher, M. Freidmann, R. Schutze, E. Zitzler, J. Stelling, and S. Panke, “Design of a Biological Half Adder,”
IET Synthetic Biology, vol. 1, no. 1.2, pp. 53-58, June 2007.- [52] R. Weiss, G.E. Homsy, and T.F. KnightJr., “Toward in Vivo Digital Circuits,”
Proc. DIMACS Workshop Evolution as Computation, vol. 349, pp. 271-281, 1995.- [53] K. Mangla, D.L. Dill, and M.A. Horowitz, “Timing Robustness in the Budding and Fission Yeast Cell Cycles,”
PLoS ONE, vol. 5, no. 2, p. e8906, http://www.plosone.org/articleinfo%3A doi%2F10.1371%2Fjournal.pone.0008%906 , Feb. 2010.- [54] S. Lin and D.J. CostelloJr.,
Error Control Coding: Fundamentals and Applications. Prentice-Hall, 1983.- [55] R.M. Tanner, “A Recursive Approach to Low Complexity Codes,”
IEEE Trans. Information Theory, vol. IT-27, no. 5, pp. 533-547, Sept. 1981.- [56] S.K. Chilappagari and B. Vasic, “Error Correction Capability of Column-Weight-Three LDPC Codes,”
IEEE Trans. Information Theory, vol. 55, no. 5, pp. 2055-2061, May 2009.- [57] L. Rudolph, “A Class of Majority Logic Decodable Codes,”
IEEE Trans. Information Theory, vol. IT-13, no. 2, pp. 305-307, Apr. 1967.- [58] A. Roguev, S. Bandyopadhyay, M. Zofall, K. Zhang, T. Fischer, S. Collins, H. Qu, M. Shales, H. Park, J. Hayles, K. Hoe, D. Kim, T. Ideker, S. Grewal, J. Weissman, and N. Krogan, “Conservation and Rewiring of Functional Modules Revealed by an Epistasis Map in Fission Yeast,”
Science, vol. 322, pp. 405-410, 2008.- [59] S. Bandyopadhyay, M. Mehta, D. Kuo, M. Sung, R. Chuang, E. Jaehnig, B. Bodenmiller, K. Licon, W. Copeland, M. Shales, D. Fiedler, J. Dutkowski, A. Guenole, H. van Attikum, K. Shokat, R. Kolodner, W. Huh, R. Aebersold, M. Keogh, N. Krogan, and T. Ideker, “Rewiring of Genetic Networks in Response to DNA Damage,”
Science, vol. 330, pp. 1385-1389, 2010.- [60] C. Harbison et al., “Transcriptional Regulatory Code of a Eukaryotic Genome,”
Nature, vol. 431, no. 7004, pp. 99-104, 2004.- [61] B. Vasic, S.K. Chilappagari, S. Sankaranarayanan, and R. Radhakrishnan, “Failures of the Gallager B Decoder: Analysis and Applications,”
Proc. Second Information Theory and Applications Workshop, 2006.- [62] E.F. AssmusJr. and J.D. Key,
Design and Their Codes. Cambridge Univ. Press, 1992.- [63] J. Colbourn and J.H. Dinitz,
The Handbook of Combinatorial Designs. CRC Press, 1996.- [64] Y. Kou, S. Lin, and M.P.C. Fossorier, “Low-Density Parity-Check Codes Based on Finite Geometries: A Rediscovery and New Results,”
IEEE Trans. Information Theory, vol. 47, no. 7, pp. 2711-2736, Nov. 2001. |