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

The Systems Biology Modelling Cycle EBI-BioPreDyn Workshop

12-15 May, 2014, UK

Alejandro F. Villaverde

(Bio)-Process Engineering groupIIM-CSICe-mail: [email protected]

Parameter Estimation in Large-Scale Kinetic Models of Microorganisms

What is a kinetic model? (I)Many biological processes are non-stationary, time-dependent,dynamic.

Chassagnole et al, Biotechnol. Bioeng. 79(1), 2002

Example: metabolismCCM of E. coli

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

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

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

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

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

Kinetic models from GEMs

• It’s possible to start from a constraint-based model to build a kinetic model

• Procedure:1. Start with a network stoichiometry2. Add generic rate laws (linlog,

Michaelis-Menten-like kinetics)3. 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 equationsK Smallbone, P Mendes. Industrial Biotechnology 2013, 9: 179–184

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

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 http://www.ebi.ac.uk/biomodels-main/• CellML http://models.cellml.org/cellml (although most of these models are not really LS)

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!): http://www.iim.csic.es/~gingproc/biopredynbench/index.html

• Matlab, AMIGO, Copasi, C, SBML• Including ready-to-run implementations

BioPreDyn-bench

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

How to build a kinetic model?

Model building steps:

1. Define the purpose of the model2. Establish the network structure

(“wiring diagram”) of the model3. Determine kinetic rate expressions4. Model structure =

network structure + kinetics5. Determine the parameters6. Validate the model

“Kinetic models in industrial biotechnology – Improving cell factory performance”J Almquist, M Cvijovic, V Hatzimanikatis, J Nielsen, M Jirstrand. Metabolic Engineering 2014

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)

Parameter estimation

Overview of PE methods

• Local vs. Global: – 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

Parameter estimation: Optimization methods

Converge to the closest optimum to the initial guess.

May end up in local solutions.

LOCAL NLP solvers

GLOBAL NLP solvers

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

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)

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 …

Some classic, stochastic, nature-inspired GO methods

doi: 10.5923/j.eee.20120204.09

Some classic, stochastic, nature-inspired GO methods

PE methods: the eSS familyScatter 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:1. Diversification Generation Method:2. Improvement Method3. Reference Set Update Method4. Subset Generation Method5. Solution Combination Method

PE methods: eSS

“Scatter search for chemical and bio-process optimization”JA Egea, M Rodríguez-Fernández, JR Banga, R Martí. J Glob Optim (2007) 37:481–503

1. Diversification Generation Method: generates solutions

2. Improvement Method: enhances solutions

3. RefSet Update Method: selects a ref. set of solutions (according to quality or diversity)

4. Subset Generation Method: produces subsets of solutions from the RefSet

5. Solution Combination Method

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.

eSS

PE methods: the eSS family –extensions and implementations

CeSS: parallel cooperative version of eSS

• SSmGO toolbox: eSS in Matlab http://www.iim.csic.es/~gingproc/ssmGO.html

• AMIGO: includes eSS, in Matlab http://www.iim.csic.es/~amigo/

• MEIGO: includes eSS & CeSS in Matlab & R (& Python interface to R) http://www.iim.csic.es/~gingproc/meigo.html

• COPASI also includes SS in its latest release • SS implementation in C presented at this workshop (poster)

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)

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

Example: PE of a LS kinetic model (III)

FITS

Example: PE of a LS kinetic model (IV)

Convergencecurve

Example: PE of a LS kinetic model (V)

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

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:1311.5735

On kinetic models

Yeast model (and others)

PE methods

Thanks for your attention

Now it’s dinner time!