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**The Systems Biology Modelling Cycle EBI-BioPreDyn Workshop**

12-15 May, 2014, UK

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**Parameter Estimation in Large-Scale Kinetic Models of Microorganisms**

Alejandro F. Villaverde (Bio)-Process Engineering group IIM-CSIC

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**What is a kinetic model? (I)**

Many biological processes are non-stationary, time-dependent, dynamic. Example: metabolism CCM of E. coli Chassagnole et al, Biotechnol. Bioeng. 79(1), 2002

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**What is a kinetic model? (II)**

Kinetic model: mathematical model of a dynamic system Include mathematical expressions of the rates at which the biochemical reactions take place equations describe fluxes as a function of concentrations

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**Example: kinetic model of E. coli’s CCM**

Mass balance equations:

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

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Why use kinetic models? Think of an example application: industrial fermentation process We would like to understand (and ideally improve), how a particular metabolite is produced in a bioreactor Dynamic process: different events can affect the outcome “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

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**Kinetic models vs. GEMs GEMs = “GEnome-scale Metabolic models”**

GEMs focus on stoichiometry, not dynamics GEMs include a large set of reactions, without kinetic detail Constraint-based methods (FBA…) use GEMs to calculate steady-state fluxes [GEMs are also called constraint-based models] However, GEMs cannot predict how behavior emerges from dynamic concentration changes of cellular components to do this kinetic models are needed GEMs don’t define the kinetics of every rate expression They can make predictions for steady-state, but cannot describe dynamic adaptations. That is, they cannot model the temporal evolution of the concentrations

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**Kinetic models from GEMs**

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

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**What is a “large-scale” kinetic model?**

Large-scale models have (at least): dozens of reactions and species hundreds of parameters Example: E. coli’s CCM model 18 species (= dynamic states) 30 reactions 139 parameters

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**Which models of microorganisms exist, and where to find them?**

Several LS kinetic models of microorganisms have been built, mostly for E. coli and S. cerevisiae Talk by P. Mendes on Thursday: “Large-scale kinetic models of E. coli and yeast ” Model building takes time and resources. Are there (LS) kinetic models available? Yes! See databases, e.g.: Biomodels CellML (although most of these models are not really LS)

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**BioPreDyn-bench Collection of benchmark problems for PE in LS models**

Includes: Yeast, metabolic 2 x E. coli (metabolic, metab. + transcr. regul.) CHO, metabolic D. melanogaster, development Generic signaling network Available at the web (very soon!): Matlab, AMIGO, Copasi, C, SBML Including ready-to-run implementations

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BioPreDyn-bench

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**So why are kinetic models not widely used (yet)?**

Kinetic models: very useful, but… still an exception in biotech applications Problem: incomplete knowledge of Regulatory interactions Kinetic parameters This leads to limited accuracy of predictions parameter estimation (PE) is one of the ways of addressing this problem

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**How to build a kinetic model?**

Model building steps: Define the purpose of the model Establish the network structure (“wiring diagram”) of the model Determine kinetic rate expressions Model structure = network structure + kinetics Determine the parameters Validate the model Purpose: Typical questions are: Why do we model? What do we want to use the model for? What type of behavior should the model be able to explain? “Kinetic models in industrial biotechnology – Improving cell factory performance” J Almquist, M Cvijovic, V Hatzimanikatis, J Nielsen, M Jirstrand. Metabolic Engineering 2014

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**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 estimation methods (PE) Parameter estimation as an optimization problem (previous talk by Eva Balsa Canto)

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Parameter estimation

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**Overview of PE methods Local vs. Global: Deterministic vs. Stochastic:**

Local methods converge to the closest optimum When several optima exist, global optimization methods (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

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**Parameter estimation: Optimization methods**

LOCAL NLP solvers Converge to the closest optimum to the initial guess. May end up in local solutions. GLOBAL NLP solvers Branch and bound (BB or B&B) is a general algorithm for finding optimal solutions of various optimization problems, especially in discrete and combinatorial optimization. A branch-and-bound algorithm consists of a systematic enumeration of all candidate solutions, where large subsets of fruitless candidates are discarded en masse, by using upper and lower estimated bounds of the quantity being optimized. hill climbing is a mathematical optimization technique which belongs to the family of local search. It is an iterative algorithm that starts with an arbitrary solution to a problem, then attempts to find a better solution by incrementally changing a single element of the solution In a genetic algorithm, a population of candidate solutions (called individuals, creatures, or phenotypes) to an optimization problem is evolved toward better solutions. Each candidate solution has a set of properties (its chromosomes or genotype) which can be mutated and altered

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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 Metaheuristic approaches are a particularly efficient class of stochastic GO methods. They combine mechanisms for exploring the search space and exploiting the obtained knowledge

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**PE in LS kinetic models in biology**

The difficult problem of PE of LS kinetic models Nonlinear systems Multi-modal problems (several local minima) Need of time-series data (usually scarce) Lack of identifiability Overfitting Aligning the model with the data… Computational issues (integrators, tolerances, …). Different timescales: Stiffness CPU times can be very large (days, weeks…) Stochastic (or hybrid) GO methods (metaheuristics) Smallbone & Mendes, 2013: Inherent stiffness of genome-scale models. Since cells need to produce some metabolites at a much higher rate than others, metabolic processes will necessarily be taking place at different timescales. As such, systems biology tools are needed that can robustly simulate models of this size and with these numerical instabilities.

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**Some classic, 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) Etc etc …

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**Some classic, stochastic, nature-inspired GO methods**

doi: /j.eee

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**Some classic, stochastic, nature-inspired GO methods**

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**PE methods: the eSS family**

Scatter Search (SS): population-based metaheuristic (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

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**PE methods: eSS Diversification Generation Method: generates solutions**

Improvement Method: enhances solutions RefSet Update 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

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**PE methods: the eSS family**

Enhanced Scatter Search (eSS): Advanced implementation of the SS metaheuristics Combines SS with local methods (hybrid methodology), to accelerate convergence to the optimum Includes several improvements of the original method Developed for parameter estimation in LS biological problems Egea JA, Martí R, Banga JR: An evolutionary method for complex-process optimization. Computers and Operations Research 2010, 37(2):315–324.

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eSS

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**PE methods: the eSS family –extensions and implementations**

CeSS: parallel cooperative version of eSS SSmGO toolbox: eSS in Matlab AMIGO: includes eSS, in Matlab MEIGO: includes eSS & CeSS in Matlab & R (& Python interface to R) COPASI also includes SS in its latest release SS implementation in C presented at this workshop (poster)

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**Example: PE of a LS kinetic model (I)**

LS kinetic model of yeast (UNIMAN) Largest model included in BioPreDyn-bench (B1) 1759 parameters, 285 reactions, 276 species Implementation—difficulties Numerical problems: integration errors (COPASI—LSODA, MATLAB—CVODES)

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**Example: PE of a LS kinetic model (II)**

Ready-to-run implementations in AMIGO and COPASI PE settings: Parameter bounds: [0.2×nominal, 5×nominal] In AMIGO: eSS + DHC Max. Time allowed = 1 week Results: see next slides

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**Example: PE of a LS kinetic model (III)**

FITS

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**Example: PE of a LS kinetic model (IV)**

Convergence curve

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**Example: PE of a LS kinetic model (V)**

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Final remarks Kinetic modeling: adequate modeling framework for dynamic systems LS kinetic models not widely used in systems biology yet, due to uncertainties, which limit applicability Parameter estimation is necessary to address this issue PE in LS kinetic models is problematic (and costly) Stochastic or hybrid GO methods are preferred Tomorrow, 10:30h: practical session on PE and OED

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**Recommended recent 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: On kinetic models Yeast model (and others) PE methods

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**Thanks for your attention**

Now it’s dinner time!

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