Inferring a nonlinear biochemical network model from a heterogeneous single-cell time course data

Mathematical modeling and analysis of biochemical reaction networks are key routines in computational systems biology and biophysics; however, it remains difficult to choose the most valid model. Here, we propose a computational framework for data-driven and systematic inference of a nonlinear biochemical network model. The framework is based on the expectation-maximization algorithm combined with particle smoother and sparse regularization techniques. In this method, a “redundant” model consisting of an excessive number of nodes and regulatory paths is iteratively updated by eliminating unnecessary paths, resulting in an inference of the most likely model. Using artificial single-cell time-course data showing heterogeneous oscillatory behaviors, we demonstrated that this algorithm successfully inferred the true network without any prior knowledge of network topology or parameter values. Furthermore, we showed that both the regulatory paths among nodes and the optimal number of nodes in the network could be systematically determined. The method presented in this study provides a general framework for inferring a nonlinear biochemical network model from heterogeneous single-cell time-course data.

[1]  Kunihiko Kaneko,et al.  Identifying dynamical systems with bifurcations from noisy partial observation. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Araceli M. Huerta,et al.  From specific gene regulation to genomic networks: a global analysis of transcriptional regulation in Escherichia coli. , 1998, BioEssays : news and reviews in molecular, cellular and developmental biology.

[3]  G. Kitagawa.  Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models , 1996 .

[4]  Koichi Takahashi,et al.  Modeling Cellular Noise Underlying Heterogeneous Cell Responses in the Epidermal Growth Factor Signaling Pathway , 2016, PLoS Comput. Biol..

[5]  Ali Shojaie,et al.  Network Reconstruction From High-Dimensional Ordinary Differential Equations , 2016, Journal of the American Statistical Association.

[6]  Christophe Andrieu,et al.  Particle methods for change detection, system identification, and control , 2004, Proceedings of the IEEE.

[7]  Daogang Guan,et al.  An integrative method to decode regulatory logics in gene transcription , 2017, Nature Communications.

[8]  Jerker Nordh,et al.  pyParticleEst: A Python Framework for Particle-Based Estimation Methods , 2017 .

[9]  Joe W. Gray,et al.  Causal network inference using biochemical kinetics , 2014, Bioinform..

[10]  E. Gilles,et al.  Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors , 2002, Nature Biotechnology.

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

[12]  J E Ferrell,et al.  The biochemical basis of an all-or-none cell fate switch in Xenopus oocytes. , 1998, Science.

[13]  M. Tomita,et al.  Conversion of graded phosphorylation into switch-like nuclear translocation via autoregulatory mechanisms in ERK signalling , 2016, Nature Communications.

[14]  E. Klipp,et al.  Information theory based approaches to cellular signaling. , 2011, Biochimica et biophysica acta.

[15]  U Alon,et al.  Generation of oscillations by the p53-Mdm2 feedback loop: a theoretical and experimental study. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Tetsuya J. Kobayashi,et al.  Cortical Polarity of the RING Protein PAR-2 Is Maintained by Exchange Rate Kinetics at the Cortical-Cytoplasmic Boundary. , 2016, Cell reports.

[17]  Shinya Kuroda,et al.  Prediction and validation of the distinct dynamics of transient and sustained ERK activation , 2005, Nature Cell Biology.

[18]  Hana El-Samad,et al.  Using Dynamic Noise Propagation to Infer Causal Regulatory Relationships in Biochemical Networks , 2014, ACS synthetic biology.

[19]  Oguzhan Atay,et al.  Switch-like Transitions Insulate Network Motifs to Modularize Biological Networks. , 2016, Cell systems.

[20]  Xiaodong Wang,et al.  Regularized EM algorithm for sparse parameter estimation in nonlinear dynamic systems with application to gene regulatory network inference , 2014, EURASIP J. Bioinform. Syst. Biol..

[21]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[22]  Rafael Yuste,et al.  Super-multiplex vibrational imaging , 2017, Nature.

[23]  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.

[24]  Jürgen Kurths,et al.  Unraveling gene regulatory networks from time-resolved gene expression data -- a measures comparison study , 2011, BMC Bioinformatics.

[25]  James E. Ferrell,et al.  A positive-feedback-based bistable ‘memory module’ that governs a cell fate decision , 2007, Nature.

[26]  Timothy K Lee,et al.  Single-cell NF-κB dynamics reveal digital activation and analogue information processing , 2010, Nature.

[27]  Hulin Wu,et al.  Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling , 2014, Journal of the American Statistical Association.

[28]  Xiaofan Wang,et al.  Reconstruction of Complex Directional Networks with Group Lasso Nonlinear Conditional Granger Causality , 2017, Scientific Reports.

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

[30]  K. Lage,et al.  Quantitative maps of protein phosphorylation sites across 14 different rat organs and tissues , 2012, Nature Communications.

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

[32]  B. Kholodenko,et al.  Quantification of Short Term Signaling by the Epidermal Growth Factor Receptor* , 1999, The Journal of Biological Chemistry.

[33]  Alessandro Chiuso,et al.  Convex vs non-convex estimators for regression and sparse estimation: the mean squared error properties of ARD and GLasso , 2014, J. Mach. Learn. Res..

[34]  David A. Rand,et al.  Measurement of single-cell dynamics , 2010, Nature.

[35]  Jimmy Omony,et al.  Biological Network Inference: A Review of Methods and Assessment of Tools and Techniques , 2014 .

[36]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[37]  Cesare Furlanello,et al.  A promoter-level mammalian expression atlas , 2015 .

[38]  M. Yuan,et al.  Model selection and estimation in regression with grouped variables , 2006 .

[39]  L. Pelkmans,et al.  Passive Noise Filtering by Cellular Compartmentalization , 2016, Cell.

[40]  M. di Bernardo,et al.  A comparative analysis of synthetic genetic oscillators , 2010, Journal of The Royal Society Interface.

[41]  Masao Nagasaki,et al.  Inference of Gene Regulatory Networks Incorporating Multi-Source Biological Knowledge via a State Space Model with L1 Regularization , 2014, PloS one.

[42]  Jeanne M O Eloundou-Mbebi,et al.  Gene regulatory network inference using fused LASSO on multiple data sets , 2016, Scientific Reports.

[43]  Shinya Kuroda,et al.  Robustness and Compensation of Information Transmission of Signaling Pathways , 2013, Science.

[44]  U. Alon.  An introduction to systems biology : design principles of biological circuits , 2019 .

[45]  Ryan A. Kellogg,et al.  Noise Facilitates Transcriptional Control under Dynamic Inputs , 2015, Cell.

[46]  Andrew Mugler,et al.  Cooperative Clustering Digitizes Biochemical Signaling and Enhances its Fidelity. , 2016, Biophysical journal.

[47]  Kohei Hayashi,et al.  Bayesian Masking: Sparse Bayesian Estimation with Weaker Shrinkage Bias , 2015, ACML.

[48]  Georgios B. Giannakis,et al.  Inference of Gene Regulatory Networks with Sparse Structural Equation Models Exploiting Genetic Perturbations , 2013, PLoS Comput. Biol..

[49]  Honeycutt,et al.  Stochastic Runge-Kutta algorithms. I. White noise. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[50]  Michio Hiroshima,et al.  Positive Feedback Within a Kinase Signaling Complex Functions as a Switch Mechanism for NF-κB Activation , 2014, Science.

[51]  Steven L. Brunton,et al.  Inferring Biological Networks by Sparse Identification of Nonlinear Dynamics , 2016, IEEE Transactions on Molecular, Biological and Multi-Scale Communications.

[52]  Steven L. Brunton,et al.  Sparse Identification of Nonlinear Dynamics (SINDy) , 2016 .