Scalable Parameter Estimation for Genome-Scale Biochemical Reaction Networks

Mechanistic mathematical modeling of biochemical reaction networks using ordinary differential equation (ODE) models has improved our understanding of small- and medium-scale biological processes. While the same should in principle hold for large- and genome-scale processes, the computational methods for the analysis of ODE models which describe hundreds or thousands of biochemical species and reactions are missing so far. While individual simulations are feasible, the inference of the model parameters from experimental data is computationally too intensive. In this manuscript, we evaluate adjoint sensitivity analysis for parameter estimation in large scale biochemical reaction networks. We present the approach for time-discrete measurement and compare it to state-of-the-art methods used in systems and computational biology. Our comparison reveals a significantly improved computational efficiency and a superior scalability of adjoint sensitivity analysis. The computational complexity is effectively independent of the number of parameters, enabling the analysis of large- and genome-scale models. Our study of a comprehensive kinetic model of ErbB signaling shows that parameter estimation using adjoint sensitivity analysis requires a fraction of the computation time of established methods. The proposed method will facilitate mechanistic modeling of genome-scale cellular processes, as required in the age of omics.

[1]  C. Chassagnole,et al.  Dynamic modeling of the central carbon metabolism of Escherichia coli. , 2002, Biotechnology and bioengineering.

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

[3]  Andreas Zell,et al.  Path2Models: large-scale generation of computational models from biochemical pathway maps , 2013, BMC Systems Biology.

[4]  Pedro Gonnet,et al.  A specialized ODE integrator for the efficient computation of parameter sensitivities , 2012, BMC Systems Biology.

[5]  Holger Fröhlich,et al.  Modeling ERBB receptor-regulated G1/S transition to find novel targets for de novo trastuzumab resistance , 2009, BMC Systems Biology.

[6]  Otmar Scherzer,et al.  Inverse Problems Light: Numerical Differentiation , 2001, Am. Math. Mon..

[7]  Andreas Griewank,et al.  Evaluating derivatives - principles and techniques of algorithmic differentiation, Second Edition , 2000, Frontiers in applied mathematics.

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

[9]  Julio R. Banga,et al.  Robust and efficient parameter estimation in dynamic models of biological systems , 2015, BMC Systems Biology.

[10]  Xingming Zhao,et al.  Computational Systems Biology , 2013, TheScientificWorldJournal.

[11]  Eva Balsa-Canto,et al.  A consensus approach for estimating the predictive accuracy of dynamic models in biology , 2015, Comput. Methods Programs Biomed..

[12]  Xin-She Yang,et al.  Nature-Inspired Metaheuristic Algorithms , 2008 .

[13]  Eva Balsa-Canto,et al.  BioPreDyn-bench: a suite of benchmark problems for dynamic modelling in systems biology , 2015, BMC Systems Biology.

[14]  Beatriz Peñalver Bernabé,et al.  State–time spectrum of signal transduction logic models , 2012, Physical biology.

[15]  Eva Balsa-Canto,et al.  High-Confidence Predictions in Systems Biology Dynamic Models , 2014, PACBB.

[16]  Luís N. Vicente,et al.  A particle swarm pattern search method for bound constrained global optimization , 2007, J. Glob. Optim..

[17]  G. Corliss,et al.  ATOMFT: solving ODEs and DAEs using Taylor series , 1994 .

[18]  Mudita Singhal,et al.  COPASI - a COmplex PAthway SImulator , 2006, Bioinform..

[19]  Mona Singh,et al.  Computational solutions for omics data , 2013, Nature Reviews Genetics.

[20]  Judith B. Zaugg,et al.  Bacterial adaptation through distributed sensing of metabolic fluxes , 2010, Molecular systems biology.

[21]  Fabian J. Theis,et al.  Data-driven modelling of biological multi-scale processes , 2015, 1506.06392.

[22]  Lincoln Stein,et al.  Reactome: a database of reactions, pathways and biological processes , 2010, Nucleic Acids Res..

[23]  Thomas S. Ligon,et al.  Single-cell mRNA transfection studies: delivery, kinetics and statistics by numbers. , 2014, Nanomedicine : nanotechnology, biology, and medicine.

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

[25]  Melanie I. Stefan,et al.  BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models , 2010, BMC Systems Biology.

[26]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[27]  Jörg Stelling,et al.  Predicting network functions with nested patterns , 2014, Nature Communications.

[28]  Joaquim R. R. A. Martins,et al.  The complex-step derivative approximation , 2003, TOMS.

[29]  Eva Balsa-Canto,et al.  AMIGO, a toolbox for advanced model identification in systems biology using global optimization , 2011, Bioinform..

[30]  Michael P Snyder,et al.  High-throughput sequencing for biology and medicine , 2013, Molecular systems biology.

[31]  Chris Sander,et al.  Emerging landscape of oncogenic signatures across human cancers , 2013, Nature Genetics.

[32]  David Henriques,et al.  MEIGO: an open-source software suite based on metaheuristics for global optimization in systems biology and bioinformatics , 2013, BMC Bioinformatics.

[33]  Damian Szklarczyk,et al.  STRING v9.1: protein-protein interaction networks, with increased coverage and integration , 2012, Nucleic Acids Res..

[34]  Mudita Singhal,et al.  Simulation of Biochemical Networks using Copasi - A Complex Pathway Simulator , 2006, Proceedings of the 2006 Winter Simulation Conference.

[35]  D. Goldfarb A family of variable-metric methods derived by variational means , 1970 .

[36]  Daryl P. Shanley,et al.  Computational modelling of the regulation of Insulin signalling by oxidative stress , 2013, BMC Systems Biology.

[37]  S. Linnainmaa Taylor expansion of the accumulated rounding error , 1976 .

[38]  Fabian J. Theis,et al.  Radial Basis Function Approximations of Bayesian Parameter Posterior Densities for Uncertainty Analysis , 2014, CMSB.

[39]  Fabian J. Theis,et al.  Data2Dynamics: a modeling environment tailored to parameter estimation in dynamical systems , 2015, Bioinform..

[40]  Hugo Y. K. Lam,et al.  Personal Omics Profiling Reveals Dynamic Molecular and Medical Phenotypes , 2012, Cell.

[41]  D. Lauffenburger,et al.  Input–output behavior of ErbB signaling pathways as revealed by a mass action model trained against dynamic data , 2009, Molecular systems biology.

[42]  Derya B. Özyurt,et al.  Cheap Second Order Directional Derivatives of Stiff ODE Embedded Functionals , 2005, SIAM J. Sci. Comput..

[43]  P. Mendes,et al.  Large-Scale Metabolic Models: From Reconstruction to Differential Equations , 2013 .

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

[45]  Krzysztof Fujarewicz,et al.  On fitting of mathematical models of cell signaling pathways using adjoint systems. , 2005, Mathematical biosciences and engineering : MBE.

[46]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[47]  Hiroyuki Ogata,et al.  KEGG: Kyoto Encyclopedia of Genes and Genomes , 1999, Nucleic Acids Res..

[48]  Andreas Zell,et al.  SBMLsqueezer 2: context-sensitive creation of kinetic equations in biochemical networks , 2015, BMC Systems Biology.

[49]  Carol S. Woodward,et al.  Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers , 2020, ACM Trans. Math. Softw..

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

[51]  Radford M. Neal MCMC Using Hamiltonian Dynamics , 2011, 1206.1901.

[52]  Fabian J Theis,et al.  Lessons Learned from Quantitative Dynamical Modeling in Systems Biology , 2013, PloS one.

[53]  R. Plessix A review of the adjoint-state method for computing the gradient of a functional with geophysical applications , 2006 .

[54]  Mark A. Girolami,et al.  Emulation of higher-order tensors in manifold Monte Carlo methods for Bayesian Inverse Problems , 2015, J. Comput. Phys..

[55]  N. Longford A fast scoring algorithm for maximum likelihood estimation in unbalanced mixed models with nested random effects , 1987 .

[56]  Roger Fletcher,et al.  A Rapidly Convergent Descent Method for Minimization , 1963, Comput. J..

[57]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[58]  M. Guay,et al.  Optimization and sensitivity analysis for multiresponse parameter estimation in systems of ordinary , 1995 .

[59]  P. Mendes,et al.  Systematic Construction of Kinetic Models from Genome-Scale Metabolic Networks , 2013, PloS one.

[60]  Mats Jirstrand,et al.  Systems biology Systems Biology Toolbox for MATLAB : a computational platform for research in systems biology , 2006 .

[61]  Ronan M. T. Fleming,et al.  A community-driven global reconstruction of human metabolism , 2013, Nature Biotechnology.

[62]  Kate Smith-Miles,et al.  Stochastic modelling of biochemical systems of multi-step reactions using a simplified two-variable model , 2013, BMC Systems Biology.

[63]  Antje Chang,et al.  BRENDA, AMENDA and FRENDA the enzyme information system: new content and tools in 2009 , 2008, Nucleic Acids Res..

[64]  Eva Balsa-Canto,et al.  Hybrid optimization method with general switching strategy for parameter estimation , 2008, BMC Systems Biology.

[65]  Edda Klipp,et al.  Monte Carlo analysis of an ODE Model of the Sea Urchin Endomesoderm Network Supplementary Table 1: Differential Equations , 2009 .

[66]  Lei Shi,et al.  SABIO-RK—database for biochemical reaction kinetics , 2011, Nucleic Acids Res..

[67]  Radu Serban,et al.  User Documentation for CVODES: An ODE Solver with Sensitivity Analysis Capabilities , 2002 .

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