Reverse engineering and identification in systems biology: strategies, perspectives and challenges

The interplay of mathematical modelling with experiments is one of the central elements in systems biology. The aim of reverse engineering is to infer, analyse and understand, through this interplay, the functional and regulatory mechanisms of biological systems. Reverse engineering is not exclusive of systems biology and has been studied in different areas, such as inverse problem theory, machine learning, nonlinear physics, (bio)chemical kinetics, control theory and optimization, among others. However, it seems that many of these areas have been relatively closed to outsiders. In this contribution, we aim to compare and highlight the different perspectives and contributions from these fields, with emphasis on two key questions: (i) why are reverse engineering problems so hard to solve, and (ii) what methods are available for the particular problems arising from systems biology?

[1]  David Maxwell Chickering,et al.  Learning Bayesian Networks is , 1994 .

[2]  M. Girolami,et al.  Inferring Signaling Pathway Topologies from Multiple Perturbation Measurements of Specific Biochemical Species , 2010, Science Signaling.

[3]  Jörg Stelling,et al.  Systems interface biology , 2006, Journal of The Royal Society Interface.

[4]  Jeremy L. Muhlich,et al.  Properties of cell death models calibrated and compared using Bayesian approaches , 2013, Molecular systems biology.

[5]  Jörg Stelling,et al.  Systems analysis of cellular networks under uncertainty , 2009, FEBS letters.

[6]  Carmen G. Moles,et al.  Parameter estimation in biochemical pathways: a comparison of global optimization methods. , 2003, Genome research.

[7]  M. Feinberg,et al.  Structural Sources of Robustness in Biochemical Reaction Networks , 2010, Science.

[8]  Deepak Kumar Subedi,et al.  Signal and Noise: Why So Many Predictions Fail – but Some Don't , 2013 .

[9]  F. H. Adler.  Cybernetics, or Control and Communication in the Animal and the Machine. , 1949 .

[10]  D. Lauffenburger,et al.  Physicochemical modelling of cell signalling pathways , 2006, Nature Cell Biology.

[11]  Patrik D'haeseleer,et al.  Genetic network inference: from co-expression clustering to reverse engineering , 2000, Bioinform..

[12]  Rainer Spang,et al.  Inferring cellular networks – a review , 2007, BMC Bioinformatics.

[13]  A. Butte,et al.  Discovering functional relationships between RNA expression and chemotherapeutic susceptibility using relevance networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[14]  Darren J. Wilkinson,et al.  Bayesian inference for nonlinear multivariate diffusion models observed with error , 2008, Comput. Stat. Data Anal..

[15]  Jing Kong,et al.  Using distance correlation and SS-ANOVA to assess associations of familial relationships, lifestyle factors, diseases, and mortality , 2012, Proceedings of the National Academy of Sciences.

[16]  M. Mesarovic,et al.  Feedback dynamics and cell function: Why systems biology is called Systems Biology. , 2005, Molecular bioSystems.

[17]  Jeffrey D Orth,et al.  What is flux balance analysis? , 2010, Nature Biotechnology.

[18]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[19]  Ken E. Whelan,et al.  The Automation of Science , 2009, Science.

[20]  Satoru Miyano,et al.  Inferring gene networks from time series microarray data using dynamic Bayesian networks , 2003, Briefings Bioinform..

[21]  Mark A. Girolami,et al.  Bayesian inference for differential equations , 2008, Theor. Comput. Sci..

[22]  Eric Walter,et al.  Identification of Parametric Models: from Experimental Data , 1997 .

[23]  Mark A. Girolami,et al.  Bayesian ranking of biochemical system models , 2008, Bioinform..

[24]  Jacob K. White,et al.  Convergence in parameters and predictions using computational experimental design , 2013, Interface Focus.

[25]  J. Ross,et al.  A Test Case of Correlation Metric Construction of a Reaction Pathway from Measurements , 1997 .

[26]  Gonzalo Guillén-Gosálbez,et al.  Deterministic global optimization algorithm based on outer approximation for the parameter estimation of nonlinear dynamic biological systems , 2012, BMC Bioinformatics.

[27]  Andrew J. Bulpitt,et al.  A Primer on Learning in Bayesian Networks for Computational Biology , 2007, PLoS Comput. Biol..

[28]  Bruce Tidor,et al.  Sloppy models, parameter uncertainty, and the role of experimental design. , 2010, Molecular bioSystems.

[29]  Drew Endy,et al.  Stimulus Design for Model Selection and Validation in Cell Signaling , 2008, PLoS Comput. Biol..

[30]  G. Szederkényi.  Computing sparse and dense realizations of reaction kinetic systems , 2010 .

[31]  Moon,et al.  Estimation of mutual information using kernel density estimators. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  Carsten O. Daub,et al.  The mutual information: Detecting and evaluating dependencies between variables , 2002, ECCB.

[33]  Goldenfeld,et al.  Simple lessons from complexity , 1999, Science.

[34]  Richard Bonneau,et al.  The Inferelator: an algorithm for learning parsimonious regulatory networks from systems-biology data sets de novo , 2006, Genome Biology.

[35]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[36]  Lance Fortnow,et al.  The status of the P versus NP problem , 2009, CACM.

[37]  Michal Linial,et al.  Using Bayesian Networks to Analyze Expression Data , 2000, J. Comput. Biol..

[38]  Hod Lipson,et al.  Automated reverse engineering of nonlinear dynamical systems , 2007, Proceedings of the National Academy of Sciences.

[39]  Nathan E Lewis,et al.  Analysis of omics data with genome-scale models of metabolism. , 2013, Molecular bioSystems.

[40]  James A. Evans,et al.  Machine Science , 2010, Science.

[41]  G S Michaels,et al.  Cluster analysis and data visualization of large-scale gene expression data. , 1998, Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing.

[42]  Neil D. Lawrence,et al.  Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes , 2008, NIPS.

[43]  A Kremling,et al.  Systems biology--an engineering perspective. , 2007, Journal of biotechnology.

[44]  B. Kholodenko.  Cell-signalling dynamics in time and space , 2006, Nature Reviews Molecular Cell Biology.

[45]  Julio R. Banga,et al.  Optimization in computational systems biology , 2008, BMC Systems Biology.

[46]  Paul Marjoram,et al.  Markov chain Monte Carlo without likelihoods , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[47]  Pedro Larrañaga,et al.  A Guide to the Literature on Inferring Genetic Networks by Probabilistic Graphical Models , 2005, Data Analysis and Visualization in Genomics and Proteomics.

[48]  Darren J. Wilkinson,et al.  Bayesian methods in bioinformatics and computational systems biology , 2006, Briefings Bioinform..

[49]  Linda M. Wills,et al.  Reverse Engineering , 1996, Springer US.

[50]  Annie Z. Tremp.  Malaria: Plasmodium develops in lymph nodes , 2006, Nature Reviews Microbiology.

[51]  D. Kell.  Metabolomics, modelling and machine learning in systems biology – towards an understanding of the languages of cells , 2006, The FEBS journal.

[52]  David Welch,et al.  Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems , 2009, Journal of The Royal Society Interface.

[53]  A. Kirsch.  An Introduction to the Mathematical Theory of Inverse Problems , 1996, Applied Mathematical Sciences.

[54]  D. di Bernardo,et al.  How to infer gene networks from expression profiles , 2007, Molecular systems biology.

[55]  Julio R. Banga,et al.  Scatter search for chemical and bio-process optimization , 2007, J. Glob. Optim..

[56]  Jason A. Papin,et al.  Genome-scale microbial in silico models: the constraints-based approach. , 2003, Trends in biotechnology.

[57]  D. Kell,et al.  Here is the evidence, now what is the hypothesis? The complementary roles of inductive and hypothesis-driven science in the post-genomic era. , 2004, BioEssays : news and reviews in molecular, cellular and developmental biology.

[58]  James O. Berger,et al.  The interplay of Bayesian and frequentist analysis , 2004 .

[59]  H. Engl,et al.  Inverse problems in systems biology , 2009 .

[60]  Adrian F. M. Smith,et al.  Bayesian computation via the gibbs sampler and related markov chain monte carlo methods (with discus , 1993 .

[61]  M. Girolami,et al.  Riemann manifold Langevin and Hamiltonian Monte Carlo methods , 2011, Journal of the Royal Statistical Society: Series B (Statistical Methodology).

[62]  M. Feinberg.  Complex balancing in general kinetic systems , 1972 .

[63]  Filippo Menolascina,et al.  Engineering and control of biological systems: A new way to tackle complex diseases , 2012, FEBS letters.

[64]  Miroslav Fikar,et al.  Global optimization for parameter estimation of differential-algebraic systems , 2009 .

[65]  Anton Crombach,et al.  Life's attractors : understanding developmental systems through reverse engineering and in silico evolution. , 2012, Advances in experimental medicine and biology.

[66]  Katherine C. Chen,et al.  Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. , 2003, Current opinion in cell biology.

[67]  Eva Balsa-Canto,et al.  An iterative identification procedure for dynamic modeling of biochemical networks , 2010, BMC Systems Biology.

[68]  J. Ross,et al.  MIDER: Network Inference with Mutual Information Distance and Entropy Reduction , 2014, PloS one.

[69]  Maria L. Rizzo,et al.  Measuring and testing dependence by correlation of distances , 2007, 0803.4101.

[70]  Jens Timmer,et al.  Joining forces of Bayesian and frequentist methodology: a study for inference in the presence of non-identifiability , 2012, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[71]  B. Efron.  Bayes' Theorem in the 21st Century , 2013, Science.

[72]  Gheorghe Craciun,et al.  Identifiability of chemical reaction networks , 2008 .

[73]  Christodoulos A. Floudas,et al.  A review of recent advances in global optimization , 2009, J. Glob. Optim..

[74]  J. Schaber,et al.  Model-based inference of biochemical parameters and dynamic properties of microbial signal transduction networks. , 2011, Current opinion in biotechnology.

[75]  P. Pardalos,et al.  Handbook of global optimization , 1995 .

[76]  Katta G. Murty,et al.  Some NP-complete problems in quadratic and nonlinear programming , 1987, Math. Program..

[77]  Michele Ceccarelli,et al.  articleTimeDelay-ARACNE : Reverse engineering of gene networks from time-course data by an information theoretic approach , 2010 .

[78]  A. Kan,et al.  A Stochastic Approach to Global Optimization , 2015 .

[79]  R. Viertl.  On the Future of Data Analysis , 2002 .

[80]  Joshua M. Stuart,et al.  A Gene-Coexpression Network for Global Discovery of Conserved Genetic Modules , 2003, Science.

[81]  L. Hood,et al.  Reverse Engineering of Biological Complexity , 2007 .

[82]  Julio R. Banga,et al.  Reverse Engineering Cellular Networks with Information Theoretic Methods , 2013, Cells.

[83]  J. Sethna,et al.  Comment on "Sloppy models, parameter uncertainty, and the role of experimental design". , 2011, Molecular bioSystems.

[84]  Amitava Roy,et al.  Detection of long-range concerted motions in protein by a distance covariance. , 2012, Journal of chemical theory and computation.

[85]  Reinhard Laubenbacher,et al.  Comparison of Reverse‐Engineering Methods Using an in Silico Network , 2007, Annals of the New York Academy of Sciences.

[86]  Hod Lipson,et al.  Distilling Free-Form Natural Laws from Experimental Data , 2009, Science.

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

[88]  Lennart Ljung,et al.  Perspectives on system identification , 2010, Annu. Rev. Control..

[89]  Fabian J Theis,et al.  A vine-copula based adaptive MCMC sampler for efficient inference of dynamical systems , 2013 .

[90]  J. Arnold,et al.  An ensemble method for identifying regulatory circuits with special reference to the qa gene cluster of Neurospora crassa , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[91]  Biao Huang,et al.  System Identification , 2000, Control Theory for Physicists.

[92]  Gunnar Cedersund,et al.  Conclusions via unique predictions obtained despite unidentifiability – new definitions and a general method , 2012, The FEBS journal.

[93]  A. Tikhonov,et al.  Numerical Methods for the Solution of Ill-Posed Problems , 1995 .

[94]  J. Liao,et al.  Reducing the allowable kinetic space by constructing ensemble of dynamic models with the same steady-state flux. , 2011, Metabolic engineering.

[95]  Satoru Miyano,et al.  Dynamic Bayesian Network and Nonparametric Regression for Nonlinear Modeling of Gene Networks from Time Series Gene Expression Data , 2003, CMSB.

[96]  Diogo M. Camacho,et al.  Wisdom of crowds for robust gene network inference , 2012, Nature Methods.

[97]  G. Szederkényi,et al.  Finding complex balanced and detailed balanced realizations of chemical reaction networks , 2010, 1010.4477.

[98]  Julio R. Banga,et al.  A cooperative strategy for parameter estimation in large scale systems biology models , 2012, BMC Systems Biology.

[99]  P. Mendes,et al.  Multi-scale modelling and simulation in systems biology. , 2011, Integrative biology : quantitative biosciences from nano to macro.

[100]  Dirk Lebiedz,et al.  An optimal experimental design approach to model discrimination in dynamic biochemical systems , 2010, Bioinform..

[101]  E D Sontag,et al.  Some new directions in control theory inspired by systems biology. , 2004, Systems biology.

[102]  O. Milenkovic,et al.  Designing Compressive Sensing DNA Microarrays , 2007, 2007 2nd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing.

[103]  Mauricio Barahona,et al.  Toggling a Genetic Switch Using Reinforcement Learning , 2013, ArXiv.

[104]  A. Lapedes,et al.  Determination of eukaryotic protein coding regions using neural networks and information theory. , 1992, Journal of molecular biology.

[105]  S Fuhrman,et al.  Reveal, a general reverse engineering algorithm for inference of genetic network architectures. , 1998, Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing.

[106]  Hiroaki Kitano,et al.  The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models , 2003, Bioinform..

[107]  Klaus Schittkowski,et al.  Numerical Data Fitting in Dynamical Systems: A Practical Introduction with Applications and Software , 2002 .

[108]  David R. Cox,et al.  PRINCIPLES OF STATISTICAL INFERENCE , 2017 .

[109]  Gregory F. Cooper,et al.  A Bayesian method for the induction of probabilistic networks from data , 1992, Machine Learning.

[110]  Roland Eils,et al.  Optimal Experimental Design for Parameter Estimation of a Cell Signaling Model , 2009, PLoS Comput. Biol..

[111]  Amanda Clare,et al.  An ontology for a Robot Scientist , 2006, ISMB.

[112]  Miguel Rocha,et al.  Modeling formalisms in Systems Biology , 2011, AMB Express.

[113]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[114]  Kamil Erguler,et al.  Practical limits for reverse engineering of dynamical systems: a statistical analysis of sensitivity and parameter inferability in systems biology models. , 2011, Molecular bioSystems.

[115]  Neil D. Lawrence,et al.  Probabilistic inference of transcription factor concentrations and gene-specific regulatory activities , 2006, Bioinform..

[116]  R. Dennis Cook,et al.  Cross-Validation of Regression Models , 1984 .

[117]  H. Chae,et al.  Characterization of diverse natural variants of CYP102A1 found within a species of Bacillus megaterium , 2011, AMB Express.

[118]  Fabian J Theis,et al.  High-dimensional Bayesian parameter estimation: case study for a model of JAK2/STAT5 signaling. , 2013, Mathematical biosciences.

[119]  J. Bailey.  Complex biology with no parameters , 2001, Nature Biotechnology.

[120]  Mihajlo D. Mesarovic,et al.  Systems Theory and Biology­ View of a Theoretician * , 1968 .

[121]  Sharon Bertsch McGrayne,et al.  The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy , 2011 .

[122]  D. Lebiedz,et al.  Robust Optimal Design of Experiments for Model Discrimination Using an Interactive Software Tool , 2013, PloS one.

[123]  M. Feinberg,et al.  Understanding bistability in complex enzyme-driven reaction networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[124]  J. Stelling,et al.  Ensemble modeling for analysis of cell signaling dynamics , 2007, Nature Biotechnology.

[125]  Tina Toni,et al.  The ABC of reverse engineering biological signalling systems. , 2009, Molecular bioSystems.

[126]  R. Jackson,et al.  General mass action kinetics , 1972 .

[127]  M. Khammash,et al.  Systems biology: from physiology to gene regulation , 2004, IEEE Control Systems.

[128]  Michael Mitzenmacher,et al.  Detecting Novel Associations in Large Data Sets , 2011, Science.

[129]  Nir Friedman,et al.  Inferring Cellular Networks Using Probabilistic Graphical Models , 2004, Science.

[130]  S. Brenner.  Sequences and consequences , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[131]  Nicholas T. Ingolia,et al.  Systems biology: Reverse engineering the cell , 2008, Nature.

[132]  David Lindley,et al.  The future of statistics-A Bayesian 21st Century , 1974 .

[133]  A. Goldberg.  General System Theory: Foundations, Development, Applications. , 1969 .

[134]  Arild Thowsen,et al.  Structural identifiability , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[135]  D. Noble.  Modeling the Heart--from Genes to Cells to the Whole Organ , 2002, Science.

[136]  Gaudenz Danuser,et al.  Linking data to models: data regression , 2006, Nature Reviews Molecular Cell Biology.

[137]  Guy-Bart Stan,et al.  Reconstruction of arbitrary biochemical reaction networks: A compressive sensing approach , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[138]  Barbara Di Ventura,et al.  From in vivo to in silico biology and back , 2006, Nature.

[139]  Jacky L. Snoep,et al.  BioModels Database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems , 2005, Nucleic Acids Res..

[140]  F. Llaneras,et al.  Stoichiometric modelling of cell metabolism. , 2008, Journal of bioscience and bioengineering.

[141]  U. Alon.  Biological Networks: The Tinkerer as an Engineer , 2003, Science.

[142]  Mark Girolami,et al.  Statistical analysis of nonlinear dynamical systems using differential geometric sampling methods , 2011, Interface Focus.

[143]  Christopher H. Bryant,et al.  Functional genomic hypothesis generation and experimentation by a robot scientist , 2004, Nature.

[144]  N A W van Riel,et al.  Parameter uncertainty in biochemical models described by ordinary differential equations. , 2013, Mathematical biosciences.

[145]  C. Floudas,et al.  Global Optimization for the Parameter Estimation of Differential-Algebraic Systems , 2000 .

[146]  Christopher R. Myers,et al.  Universally Sloppy Parameter Sensitivities in Systems Biology Models , 2007, PLoS Comput. Biol..

[147]  I S Kohane,et al.  Mutual information relevance networks: functional genomic clustering using pairwise entropy measurements. , 1999, Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing.

[148]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[149]  J. Banga,et al.  Exploring multiplicity conditions in enzymatic reaction networks , 2009, Biotechnology progress.

[150]  C.E. Shannon,et al.  Communication in the Presence of Noise , 1949, Proceedings of the IRE.

[151]  Ursula Klingmüller,et al.  Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood , 2009, Bioinform..

[152]  Fei He,et al.  Maximin and Bayesian robust experimental design for measurement set selection in modelling biochemical regulatory systems , 2010 .

[153]  J. Hasty,et al.  Reverse engineering gene networks: Integrating genetic perturbations with dynamical modeling , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[154]  M. Feinberg,et al.  Dynamics of open chemical systems and the algebraic structure of the underlying reaction network , 1974 .

[155]  J. Collins,et al.  Large-Scale Mapping and Validation of Escherichia coli Transcriptional Regulation from a Compendium of Expression Profiles , 2007, PLoS biology.

[156]  Antonis Papachristodoulou,et al.  Discriminating between rival biochemical network models: three approaches to optimal experiment design , 2010, BMC Systems Biology.

[157]  George A. Bekey,et al.  Identification of Biological Systems : a Survey * , 2002 .

[158]  Jerome T. Mettetal,et al.  The Frequency Dependence of Osmo-Adaptation in Saccharomyces cerevisiae , 2008, Science.

[159]  Michael P. H. Stumpf,et al.  Maximizing the Information Content of Experiments in Systems Biology , 2013, PLoS Comput. Biol..

[160]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[161]  J. Tyson,et al.  Design principles of biochemical oscillators , 2008, Nature Reviews Molecular Cell Biology.

[162]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[163]  N. D. Clarke,et al.  Towards a Rigorous Assessment of Systems Biology Models: The DREAM3 Challenges , 2010, PloS one.

[164]  Eva Balsa-Canto,et al.  Parameter estimation and optimal experimental design. , 2008, Essays in biochemistry.

[165]  Mustafa Khammash,et al.  Parameter Estimation and Model Selection in Computational Biology , 2010, PLoS Comput. Biol..

[166]  Kevin Kontos,et al.  Information-Theoretic Inference of Large Transcriptional Regulatory Networks , 2007, EURASIP J. Bioinform. Syst. Biol..

[167]  Bruce Tidor,et al.  Reply to Comment on "Sloppy models, parameter uncertainty, and the role of experimental design" , 2011, Molecular bioSystems.

[168]  T. Ideker,et al.  Modeling cellular machinery through biological network comparison , 2006, Nature Biotechnology.

[169]  José Eduardo Ribeiro Cury,et al.  Systems Biology, Synthetic Biology and Control Theory: A promising golden braid , 2013, Annu. Rev. Control..

[170]  Adam P. Arkin,et al.  Statistical Construction of Chemical Reaction Mechanisms from Measured Time-Series , 1995 .

[171]  H. Kitano.  International alliances for quantitative modeling in systems biology , 2005, Molecular systems biology.

[172]  Franca Fraternali,et al.  Handbook of Statistical Systems Biology , 2011 .

[173]  Neil D. Lawrence,et al.  Learning and Inference in Computational Systems Biology , 2010, Computational molecular biology.

[174]  D. Floreano,et al.  Revealing strengths and weaknesses of methods for gene network inference , 2010, Proceedings of the National Academy of Sciences.

[175]  D. Husmeier,et al.  Dynamic Bayesian networks in molecular plant science: inferring gene regulatory networks from multiple gene expression time series , 2012, Euphytica.

[176]  S. Schuster,et al.  Metabolic network structure determines key aspects of functionality and regulation , 2002, Nature.

[177]  K. S. Brown,et al.  Statistical mechanical approaches to models with many poorly known parameters. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[178]  Rudiyanto Gunawan,et al.  Parameter identifiability of power-law biochemical system models. , 2010, Journal of biotechnology.

[179]  Christopher A. Penfold,et al.  How to infer gene networks from expression profiles, revisited , 2011, Interface Focus.

[180]  Bradley P. Carlin,et al.  BAYES AND EMPIRICAL BAYES METHODS FOR DATA ANALYSIS , 1996, Stat. Comput..

[181]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[182]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

[183]  M. Bennett,et al.  Metabolic gene regulation in a dynamically changing environment , 2008, Nature.

[184]  Paul P. Wang,et al.  Advances to Bayesian network inference for generating causal networks from observational biological data , 2004, Bioinform..

[185]  J. Banga,et al.  Structural Identifiability of Systems Biology Models: A Critical Comparison of Methods , 2011, PloS one.

[186]  J. Rothberg,et al.  Gaining confidence in high-throughput protein interaction networks , 2004, Nature Biotechnology.

[187]  Mark A. Girolami,et al.  Bayesian ranking of biochemical system models , 2008, Bioinform..

[188]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

[189]  A. Tarantola.  Popper, Bayes and the inverse problem , 2006 .

[190]  J. Collins,et al.  Size matters: network inference tackles the genome scale , 2007, Molecular systems biology.

[191]  B. Efron.  A 250-year argument: Belief, behavior, and the bootstrap , 2012 .

[192]  Jay D. Keasling,et al.  Engineering Static and Dynamic Control of Synthetic Pathways , 2010, Cell.

[193]  D. Bernardo,et al.  A Yeast Synthetic Network for In Vivo Assessment of Reverse-Engineering and Modeling Approaches , 2009, Cell.

[194]  Albert Tarantola,et al.  Inverse problem theory - and methods for model parameter estimation , 2004 .

[195]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[196]  Peter V Coveney,et al.  Modelling biological complexity: a physical scientist's perspective , 2005, Journal of The Royal Society Interface.

[197]  H. D. Jong,et al.  On the identifiability of metabolic network models , 2013, Journal of mathematical biology.

[198]  Darren J. Wilkinson.  Stochastic Modelling for Systems Biology , 2006 .

[199]  Anton Crombach,et al.  Efficient Reverse-Engineering of a Developmental Gene Regulatory Network , 2012, PLoS Comput. Biol..

[200]  Yu-Chi Ho.  The no free lunch theorem and the human-machine interface , 1999 .

[201]  Wenxing Zhu.  Unsolvability of some optimization problems , 2006, Appl. Math. Comput..

[202]  J. Hadamard.  Sur les problemes aux derive espartielles et leur signification physique , 1902 .

[203]  Frank Emmert-Streib,et al.  Influence of Statistical Estimators of Mutual Information and Data Heterogeneity on the Inference of Gene Regulatory Networks , 2011, PloS one.

[204]  Gregory R. Grant,et al.  Bioinformatics - The Machine Learning Approach , 2000, Comput. Chem..

[205]  Concha Bielza,et al.  Machine Learning in Bioinformatics , 2008, Encyclopedia of Database Systems.

[206]  F. Fages,et al.  Long-term model predictive control of gene expression at the population and single-cell levels , 2012, Proceedings of the National Academy of Sciences.

[207]  Mario di Bernardo,et al.  Analysis, design and implementation of a novel scheme for in-vivo control of synthetic gene regulatory networks , 2011, Autom..

[208]  Peter J. Woolf,et al.  Learning transcriptional regulatory networks from high throughput gene expression data using continuous three-way mutual information , 2008, BMC Bioinformatics.

[209]  F. Doyle,et al.  A benchmark for methods in reverse engineering and model discrimination: problem formulation and solutions. , 2004, Genome research.

[210]  Robert J. Flassig,et al.  Optimal design of stimulus experiments for robust discrimination of biochemical reaction networks , 2012, Bioinform..

[211]  Jesper Tegnér,et al.  Reverse engineering gene networks using singular value decomposition and robust regression , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[212]  Mark Girolami,et al.  Handbook of Statistical Systems Biology: Stumpf/Handbook of Statistical Systems Biology , 2011 .

[213]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[214]  C. Cobelli,et al.  Parameter and structural identifiability concepts and ambiguities: a critical review and analysis. , 1980, The American journal of physiology.

[215]  Jörg Stelling,et al.  Automatic Design of Digital Synthetic Gene Circuits , 2011, PLoS Comput. Biol..

[216]  Eduardo D. Sontag,et al.  Monotone and near-monotone biochemical networks , 2007, Systems and Synthetic Biology.

[217]  Martin Feinberg,et al.  Multiple Equilibria in Complex Chemical Reaction Networks: Semiopen Mass Action Systems * , 2022 .

[218]  P. Rapp,et al.  Statistical validation of mutual information calculations: comparison of alternative numerical algorithms. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[219]  M. Girolami,et al.  Inferring Signaling Pathway Topologies from Multiple Perturbation Measurements of Specific Biochemical Species , 2010, Science Signaling.

[220]  Martin Feinberg,et al.  Design principles for robust biochemical reaction networks: what works, what cannot work, and what might almost work. , 2011, Mathematical biosciences.

[221]  Julio R. Banga,et al.  Inference of complex biological networks: distinguishability issues and optimization-based solutions , 2011, BMC Systems Biology.

[222]  Richard Bonneau,et al.  DREAM4: Combining Genetic and Dynamic Information to Identify Biological Networks and Dynamical Models , 2010, PloS one.

[223]  Susana Vinga,et al.  A Survey on Methods for Modeling and Analyzing Integrated Biological Networks , 2011, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[224]  J. Lopreato,et al.  General system theory : foundations, development, applications , 1970 .

[225]  Jonathan R. Karr,et al.  A Whole-Cell Computational Model Predicts Phenotype from Genotype , 2012, Cell.

[226]  Ron Kohavi,et al.  A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection , 1995, IJCAI.

[227]  Mark M. Tanaka,et al.  Sequential Monte Carlo without likelihoods , 2007, Proceedings of the National Academy of Sciences.

[228]  D. Pincus,et al.  In silico feedback for in vivo regulation of a gene expression circuit , 2011, Nature Biotechnology.

[229]  Richard H. Sherman,et al.  Chaotic communications in the presence of noise , 1993, Optics & Photonics.

[230]  L. López-Kleine,et al.  Biostatistical approaches for the reconstruction of gene co-expression networks based on transcriptomic data. , 2013, Briefings in functional genomics.

[231]  I. E. Nikerel,et al.  Model reduction and a priori kinetic parameter identifiability analysis using metabolome time series for metabolic reaction networks with linlog kinetics. , 2009, Metabolic engineering.

[232]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[233]  Oliver Kotte,et al.  A divide-and-conquer approach to analyze underdetermined biochemical models , 2009, Bioinform..

[234]  Eduardo Sontag,et al.  On the number of steady states in a multiple futile cycle , 2008, Journal of mathematical biology.

[235]  D. Balding,et al.  Approximate Bayesian computation in population genetics. , 2002, Genetics.

[236]  A. Lapedes,et al.  Covariation of mutations in the V3 loop of human immunodeficiency virus type 1 envelope protein: an information theoretic analysis. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[237]  J. Stelling.  Mathematical models in microbial systems biology. , 2004, Current opinion in microbiology.

[238]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[239]  Maksat Ashyraliyev,et al.  Systems biology: parameter estimation for biochemical models , 2009, The FEBS journal.

[240]  D. Noble.  Systems: What's in a name? , 2011, Physiology.

[241]  Martin Mönnigmann,et al.  Systematic identifiability testing for unambiguous mechanistic modeling – application to JAK-STAT, MAP kinase, and NF-κB signaling pathway models , 2009, BMC Systems Biology.

[242]  Sorin Draghici,et al.  Machine Learning and Its Applications to Biology , 2007, PLoS Comput. Biol..

[243]  Michael P. H. Stumpf,et al.  Simulation-based model selection for dynamical systems in systems and population biology , 2009, Bioinform..

[244]  Eduardo F. Camacho,et al.  Model predictive control techniques for hybrid systems , 2010, Annu. Rev. Control..

[245]  Adam A. Margolin,et al.  Reverse engineering cellular networks , 2006, Nature Protocols.

[246]  J. Nemcová.  Structural identifiability of polynomial and rational systems. , 2008, Mathematical biosciences.

[247]  Julio R. Banga,et al.  Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems , 2006, BMC Bioinformatics.

[248]  J. Banga,et al.  Computational procedures for optimal experimental design in biological systems. , 2008, IET systems biology.

[249]  B. Palsson,et al.  Genome-scale reconstruction of the Saccharomyces cerevisiae metabolic network. , 2003, Genome research.

[250]  Riet De Smet,et al.  Advantages and limitations of current network inference methods , 2010, Nature Reviews Microbiology.