The Systems Biology Modelling Cycle EBI- BioPreDyn Workshop 12-15 May , 2014, UK

1. The Systems Biology Modelling Cycle EBI-BioPreDyn Workshop 12-15 May, 2014, UK

2. Parameter Estimation in Large-Scale Kinetic Models of Microorganisms Alejandro F. Villaverde (Bio)-ProcessEngineeringgroup IIM-CSIC e-mail: afvillaverde@iim.csic.es

3. What is a kinetic model? (I) Manybiologicalprocessesare non-stationary, time-dependent, dynamic. Example: metabolism CCM of E. coli Chassagnole et al, Biotechnol. Bioeng. 79(1), 2002

4. What is a kinetic model? (II) • Kineticmodel: mathematicalmodel of a dynamicsystem • Includemathematicalexpressions of theratesat whichthebiochemicalreactionstake place •  equations describe fluxes as a function of concentrations

5. Example: kinetic model of E. coli’s CCM Mass balance equations:

6. Example: kinetic model of E. coli’s CCM (in COPASI)

7. Why use kineticmodels? • Think of an example application: industrial fermentationprocess • Wewouldlike to understand (and ideallyimprove), how a particular metaboliteisproduced in a bioreactor • Dynamicprocess: differentevents can affecttheoutcome • “Genome-scale kinetic models of metabolism are important for rational design of the metabolic engineering required for industrial biotechnology applications. They allow one to predict the alterations needed to optimize the flux or yield of the compounds of interest, while keeping the other functions of the host organism to a minimal, but essential, level.” • Large-scale metabolic models: From reconstruction to differential equations K Smallbone, P Mendes. Industrial Biotechnology 2013, 9: 179–184

8. Kinetic models vs. GEMs • GEMs = “GEnome-scaleMetabolicmodels” • GEMsfocusonstoichiometry, notdynamics • GEMsinclude a large set of reactions, withoutkineticdetail • Constraint-basedmethods (FBA…) useGEMs tocalculatesteady-statefluxes [GEMs are alsocalledconstraint-basedmodels] • However, GEMscannotpredicthowbehavior emerges from dynamic concentration changes of cellular components •  to do this kinetic models are needed

9. KineticmodelsfromGEMs • It’s possible to start from a constraint-based model to build a kinetic model • Procedure: • Start with a network stoichiometry • Add generic rate laws (linlog, Michaelis-Menten-like kinetics) • Estimate unknown kinetic constants • Smallbone& Mendes presented a pipeline for creating thermodynamically consistent kinetic models, using limited data and ensuring consistency with known data and kinetic constants • Large-scale metabolic models: From reconstruction to differential equations • K Smallbone, P Mendes. Industrial Biotechnology 2013, 9: 179–184

10. Whatis a “large-scale” kineticmodel? • Large-scalemodelshave (at least): • dozens of reactions and species • hundreds of parameters • Example: E. coli’s CCM model • 18 species (= dynamic states) • 30 reactions • 139 parameters

11. Whichmodelsof microorganisms exist, and where to find them? • Several LS kinetic models of microorganisms have been built, mostly for E. coli and S. cerevisiae • Talk byP. MendesonThursday: “Large-scale kinetic models of E. coli and yeast” • Model building takes time and resources. • Are there (LS) kinetic models available? • Yes! Seedatabases, e.g.: • Biomodelshttp://www.ebi.ac.uk/biomodels-main/ • CellMLhttp://models.cellml.org/cellml • (althoughmost of thesemodels are notreally LS)

12. BioPreDyn-bench • Collection of benchmarkproblemsfor PE in LS models • Includes: • Yeast, metabolic • 2 x E. coli(metabolic, metab. + transcr. regul.) • CHO, metabolic • D. melanogaster, development • Genericsignalingnetwork • Available at the web (verysoon!): http://www.iim.csic.es/~gingproc/biopredynbench/index.html • Matlab, AMIGO, Copasi, C, SBML • Includingready-to-run implementations

13. BioPreDyn-bench

14. So why are kineticmodelsnotwidelyused (yet)? • Kineticmodels: veryuseful, but… stillanexception in biotechapplications • Problem: incompleteknowledgeof • Regulatoryinteractions • Kineticparameters • This leads to limitedaccuracy of predictions •  parameterestimation (PE) isone of theways of addressingthisproblem

15. How to build a kineticmodel? Modelbuildingsteps: Define thepurpose of themodel Establishthenetworkstructure(“wiringdiagram”) of themodel Determine kineticrateexpressions Modelstructure= networkstructure + kinetics Determine theparameters Validatethemodel “Kinetic models in industrial biotechnology – Improving cell factory performance” J Almquist, M Cvijovic, V Hatzimanikatis, J Nielsen, M Jirstrand. Metabolic Engineering 2014

16. Parameter determination • Parameter values are sometimes established one by one, either from targeted experiments measuring them directly or from other types of a priori information on individual parameter values. • In contrast, parameter values can also be determined simultaneously using parameter estimationmethods (PE) • Parameterestimation as anoptimizationproblem (previoustalkby Eva Balsa Canto)

17. Parameterestimation

18. Overview of PE methods • Local vs. Global: • Localmethods converge to theclosestoptimum • Whenseveral optima exist, globaloptimizationmethods (GO) must be used • Deterministic vs. Stochastic: • Deterministic GO methods guarantee that the solution is the global optimum, but the computational effort is very high • Stochastic GO methods do not guarantee the global optimality of the solution, but they are frequently capable of finding excellent solutions in reasonable computation times

19. Parameterestimation: Optimizationmethods LOCAL NLP solvers Converge to theclosestoptimum to theinitialguess. Mayend up in local solutions. GLOBAL NLP solvers

20. Metaheuristics • Heuristic: procedure based on expert knowledge, not on formal analysis • Metaheuristic: general-purpose heuristic method designed to guide an underlying problem-specific heuristic • A metaheuristic is therefore a general algorithmic framework which can be applied to different optimization problems with relative few modifications Metaheuristicapproaches are a particularlyefficient class of stochastic GO methods. They combine mechanisms for exploring the search space and exploiting the obtained knowledge

21. PE in LS kineticmodels in biology • Thedifficultproblem of PE of LS kineticmodels • Nonlinearsystems • Multi-modal problems(several local minima) • Need of time-series data (usuallyscarce) • Lack of identifiability • Overfitting • Aligningthemodelwiththe data… • Computationalissues (integrators, tolerances, …). Differenttimescales: Stiffness • CPU times can be verylarge (days, weeks…) •  Stochastic (orhybrid) GO methods (metaheuristics)

22. Someclassic, stochastic, nature-inspired GO methods • Genetic Algorithms A population of candidate solutions is evolved toward better solutions. Each candidate solution has a set of properties (chromosomes) which can be mutated • Swarm intelligence: Ant Colony Optimization, Particle Swarm… mimic the movement of agents in a swarm • Simulated Annealing mimics the annealing process in metallurgy: slow cooling of a material to produce crystals (temperature = probability of accepting worse solutions) • Etcetc …

23. Someclassic, stochastic, nature-inspired GO methods doi: 10.5923/j.eee.20120204.09

24. Someclassic, stochastic, nature-inspired GO methods

25. PE methods: theeSSfamily ScatterSearch(SS): population-basedmetaheuristic (Glover 1977). Main differences with GA: • SS orients its exploration systematically, relative to a set of reference points (RefSet). This allows to exploit the information gathered by each solution. • Besides, SS includes the Improvement Method (local search ) Five-method template: • Diversification Generation Method: • Improvement Method • Reference Set Update Method • Subset Generation Method • Solution Combination Method

26. PE methods: eSS Diversification Generation Method: generates solutions Improvement Method: enhances solutions RefSetUpdate Method: selects a ref. set of solutions (according to quality or diversity) Subset Generation Method: produces subsets of solutions from the RefSet Solution Combination Method “Scatter search for chemical and bio-process optimization” JA Egea, M Rodríguez-Fernández, JR Banga, R Martí. J Glob Optim (2007) 37:481–503

27. PE methods: theeSSfamily EnhancedScatterSearch (eSS): • Advancedimplementation of the SS metaheuristics • Combines SS with local methods (hybridmethodology), to accelerateconvergence to theoptimum • Includesseveralimprovements of the original method • Developedforparameterestimation in LS biologicalproblems Egea JA, MartíR, Banga JR: An evolutionary method for complex-process optimization. Computers and Operations Research 2010, 37(2):315–324.

28. eSS

29. PE methods: theeSSfamily –extensions and implementations CeSS: parallelcooperativeversion of eSS • SSmGOtoolbox: eSS in Matlabhttp://www.iim.csic.es/~gingproc/ssmGO.html • AMIGO: includeseSS, in Matlabhttp://www.iim.csic.es/~amigo/ • MEIGO: includeseSS & CeSS in Matlab & R (& Python interface to R) http://www.iim.csic.es/~gingproc/meigo.html • COPASIalsoincludes SS in itslatestrelease • SS implementation in C presented at this workshop (poster)

30. Example: PE of a LS kineticmodel (I) • LS kineticmodel of yeast (UNIMAN) • Largestmodelincluded in BioPreDyn-bench (B1) • 1759 parameters, 285 reactions, 276 species • Implementation—difficulties • Numericalproblems: integration errors (COPASI—LSODA, MATLAB—CVODES)

31. Example: PE of a LS kineticmodel (II) • Ready-to-run implementations in AMIGO and COPASI • PE settings: • Parameterbounds: [0.2×nominal, 5×nominal] • In AMIGO: eSS + DHC • Max. Time allowed = 1 week • Results: seenextslides

32. Example: PE of a LS kineticmodel (III) FITS

33. Example: PE of a LS kineticmodel (IV) Convergence curve

34. Example: PE of a LS kineticmodel (V)

35. Final remarks • Kinetic modeling: adequate modeling frameworkfordynamicsystems • LS kineticmodelsnotwidelyused in systemsbiologyyet, due to uncertainties, whichlimitapplicability • Parameterestimationisnecessaryto addressthisissue • PE in LS kineticmodelsisproblematic (and costly) • StochasticorhybridGOmethods are preferred • Tomorrow, 10:30h: practicalsessionon PE and OED

36. Recommendedrecent bibliography: • “Kinetic models in industrial biotechnology – Improving cell factory performance” J Almquist, M Cvijovic, V Hatzimanikatis, J Nielsen, M Jirstrand. Metabolic Engineering 2014 • “Advancing metabolic models with kinetic information” H Link, D Christodoulou, U Sauer. Current Opinion in Biotechnology 2014, 29:8–14 • “Modeling metabolic systems: the need for dynamics” H-S Song, F DeVilbiss, D Ramkrishna. Current Opinion in Chemical Engineering 2013, 2:373–382 • “Yeast 5–an expanded reconstruction of the saccharomyces cerevisiae metabolic network” BD Heavner, K Smallbone, B Barker, P Mendes, LP Walker. BMC Systems Biology 2012, 6: 55. • “Large-scale metabolic models: From reconstruction to differential equations” K Smallbone, P Mendes. Industrial Biotechnology 2013, 9: 179–184 • “BioPreDyn-bench: a suite of benchmark problems for dynamic modelling in systems biology” AF Villaverde, D Henriques, K Smallbone, S Bongard et al. in preparation • “An evolutionary method for complex-process optimization” JA Egea, R Martí, JR Banga. Computers and Operations Research 2010, 37(2):315–324 • “A cooperative strategy for parameter estimation in large scale systems biology models”. AF Villaverde, JA Egea, JR Banga. BMC Systems Biology 2012, 6: 75 • “MEIGO: an open-source software suite based on metaheuristics for global optimization in systems biology and bioinformatics” JA Egea, D Henriques, T Cokelaer, AF Villaverde et al. BMC Bioinformatics 2014 arXiv:1311.5735 On kinetic models Yeast model (and others) PE methods

37. Thanksforyourattention Now it’sdinner time!