Linear Control Theory for Gene Network Modeling

Systems biology is an interdisciplinary field that aims at understanding complex interactions in cells. Here we demonstrate that linear control theory can provide valuable insight and practical tools for the characterization of complex biological networks. We provide the foundation for such analyses through the study of several case studies including cascade and parallel forms, feedback and feedforward loops. We reproduce experimental results and provide rational analysis of the observed behavior. We demonstrate that methods such as the transfer function (frequency domain) and linear state-space (time domain) can be used to predict reliably the properties and transient behavior of complex network topologies and point to specific design strategies for synthetic networks.

[1]  Albert Y. Zomaya,et al.  Algorithms in Computational Molecular Biology: Techniques, Approaches and Applications , 2011 .

[2]  Guy Karlebach,et al.  Modelling and analysis of gene regulatory networks , 2008, Nature Reviews Molecular Cell Biology.

[3]  Chrystopher L. Nehaniv,et al.  Bio-Logic: Gene Expression and the Laws of Combinatorial Logic , 2008, Artificial Life.

[4]  Farren J. Isaacs,et al.  Computational studies of gene regulatory networks: in numero molecular biology , 2001, Nature Reviews Genetics.

[5]  M. di Bernardo,et al.  How to Turn a Genetic Circuit into a Synthetic Tunable Oscillator, or a Bistable Switch , 2009, PloS one.

[6]  James M. Bower,et al.  Computational modeling of genetic and biochemical networks , 2001 .

[7]  Benjamin L Turner,et al.  Supporting Online Material Materials and Methods Som Text Figs. S1 to S3 Table S1 References Robust, Tunable Biological Oscillations from Interlinked Positive and Negative Feedback Loops , 2022 .

[8]  E. Dougherty,et al.  Gene perturbation and intervention in probabilistic Boolean networks. , 2002, Bioinformatics.

[9]  L. Serrano,et al.  Engineering stability in gene networks by autoregulation , 2000, Nature.

[10]  S. Ramaswamy,et al.  Microarrays for an integrative genomics , 2004 .

[11]  S. Mangan,et al.  Structure and function of the feed-forward loop network motif , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[12]  M. di Bernardo,et al.  Comparing different ODE modelling approaches for gene regulatory networks. , 2009, Journal of theoretical biology.

[13]  A. Oudenaarden,et al.  Nature, Nurture, or Chance: Stochastic Gene Expression and Its Consequences , 2008, Cell.

[14]  D. A. Baxter,et al.  Modeling transcriptional control in gene networks—methods, recent results, and future directions , 2000, Bulletin of mathematical biology.

[15]  and Charles K. Taft Reswick,et al.  Introduction to Dynamic Systems , 1967 .

[16]  E. Andrianantoandro,et al.  Synthetic biology: new engineering rules for an emerging discipline , 2006, Molecular systems biology.

[17]  J. Davies,et al.  Molecular Biology of the Cell , 1983, Bristol Medico-Chirurgical Journal.

[18]  B. P. Lathi Linear systems and signals , 1992 .

[19]  J. Stelling,et al.  A tunable synthetic mammalian oscillator , 2009, Nature.

[20]  R. Thomas,et al.  Boolean formalization of genetic control circuits. , 1973, Journal of theoretical biology.

[21]  Zdzislaw Bubnicki,et al.  Modern Control Theory , 2005 .

[22]  S. Shen-Orr,et al.  Networks Network Motifs : Simple Building Blocks of Complex , 2002 .

[23]  M. Elowitz,et al.  Reconstruction of genetic circuits , 2005, Nature.

[24]  Mehrdad Nourani,et al.  Statecharts for Gene Network Modeling , 2010, PloS one.

[25]  P. Swain,et al.  Intrinsic and extrinsic contributions to stochasticity in gene expression , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[26]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[27]  Nicholas J. Guido,et al.  A bottom-up approach to gene regulation , 2006, Nature.

[28]  James C. W. Locke,et al.  Using movies to analyse gene circuit dynamics in single cells , 2009, Nature Reviews Microbiology.

[29]  James J. Collins,et al.  Next-Generation Synthetic Gene Networks , 2009, Nature Biotechnology.

[30]  Richard Banks,et al.  Qualitatively modelling and analysing genetic regulatory networks: a Petri net approach , 2007, Bioinform..

[31]  Jorge Goncalves,et al.  Control theory and systems biology , 2009 .

[32]  Magda Osman,et al.  Control Systems Engineering , 2010 .

[33]  John B. Moore,et al.  Optimal State Estimation , 2006 .

[34]  G. D. Gatta,et al.  Systems and Synthetic biology: tackling genetic networks and complex diseases , 2009, Heredity.

[35]  M. L. Simpson,et al.  Frequency domain analysis of noise in simple gene circuits. , 2006, Chaos.

[36]  Giovanni De Micheli,et al.  Synchronous versus asynchronous modeling of gene regulatory networks , 2008, Bioinform..

[37]  U. Alon Network motifs: theory and experimental approaches , 2007, Nature Reviews Genetics.

[38]  Robert F. Stengel,et al.  Optimal Control and Estimation , 1994 .

[39]  Gürol M. Süel,et al.  An excitable gene regulatory circuit induces transient cellular differentiation , 2006, Nature.

[40]  M. L. Simpson,et al.  Gene network shaping of inherent noise spectra , 2006, Nature.

[41]  Shane T. Jensen,et al.  The Program of Gene Transcription for a Single Differentiating Cell Type during Sporulation in Bacillus subtilis , 2004, PLoS biology.

[42]  M. L. Simpson,et al.  Frequency domain analysis of noise in autoregulated gene circuits , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[43]  H. Kitano Systems Biology: A Brief Overview , 2002, Science.

[44]  M. Bennett,et al.  A fast, robust, and tunable synthetic gene oscillator , 2008, Nature.

[45]  H. Bolouri Computational Modeling of Gene Regulatory Networks - A Primer , 2008 .

[46]  H. D. Jong,et al.  Qualitative simulation of genetic regulatory networks using piecewise-linear models , 2004, Bulletin of mathematical biology.

[47]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[48]  H. D. Jong,et al.  Piecewise-linear Models of Genetic Regulatory Networks: Equilibria and their Stability , 2006, Journal of mathematical biology.

[49]  Ronald W. Davis,et al.  Quantitative Monitoring of Gene Expression Patterns with a Complementary DNA Microarray , 1995, Science.

[50]  J. Raser,et al.  Noise in Gene Expression: Origins, Consequences, and Control , 2005, Science.

[51]  Eduardo D. Sontag,et al.  Reverse Engineering of Molecular Networks from a Common Combinatorial Approach , 2010, ArXiv.

[52]  M. Elowitz,et al.  Regulatory activity revealed by dynamic correlations in gene expression noise , 2008, Nature Genetics.

[53]  N. Lee,et al.  Computational and experimental approaches for modeling gene regulatory networks. , 2007, Current pharmaceutical design.

[54]  Gilbert Strang,et al.  Computational Science and Engineering , 2007 .