# Modeling metabolic networks in C. glutamicum: a comparison of rate laws in combination with various parameter optimization strategies

### Abstract

Background: To understand the dynamic behavior of cellular systems, mathematical modeling is often necessary and comprises three steps: (1) experimental measurement of participating molecules, (2) assignment of rate laws to each reaction, and (3) parameter calibration with respect to the measurements. In each of these steps the modeler is confronted with a plethora of alternative approaches, e.g., the selection of approximative rate laws in step two as specific equations are often unknown, or the choice of an estimation procedure with its specific settings in step three. This overall process with its numerous choices and the mutual influence between them makes it hard to single out the best modeling approach for a given problem.

Results: We investigate the modeling process using multiple kinetic equations together with various parameter optimization methods for a well-characterized example network, the biosynthesis of valine and leucine in C. glutamicum. For this purpose, we derive seven dynamic models based on generalized mass action, Michaelis-Menten and convenience kinetics as well as the stochastic Langevin equation. In addition, we introduce two modeling approaches for feedback inhibition to the mass action kinetics. The parameters of each model are estimated using eight optimization strategies. To determine the most promising modeling approaches together with the best optimization algorithms, we carry out a two-step benchmark: (1) coarse-grained comparison of the algorithms on all models and (2) fine-grained tuning of the best optimization algorithms and models. To analyze the space of the best parameters found for each model, we apply clustering, variance, and correlation analysis.

Conclusion: A mixed model based on the convenience rate law and the Michaelis-Menten equation, in which all reactions are assumed to be reversible, is the most suitable deterministic modeling approach followed by a reversible generalized mass action kinetics model. A Langevin model is advisable to take stochastic effects into account. To estimate the model parameters, three algorithms are particularly useful: For first attempts the settings-free Tribes algorithm yields valuable results. Particle swarm optimization and differential evolution provide significantly better results with appropriate settings.

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### BibTeX

@article{Draeger2009a,
author = {Dr\"ager, Andreas and Kronfeld, Marcel and Ziller, Michael J. and
Supper, Jochen and Planatscher, Hannes and Magnus, J{\o}rgen B. and
Oldiges, Marco and Kohlbacher, Oliver and Zell, Andreas},
title = {{Modeling metabolic networks in \emph{C.~glutamicum}: a comparison
of rate laws in combination with various parameter optimization strategies}},
journal = {BMC Systems Biology},
year = {2009},
volume = {3},
pages = {5},
number = {5},
month = jan,
abstract = {Background:
To understand the dynamic behavior of cellular systems, mathematical
modeling is often necessary and comprises three steps: (1) experimental
measurement of participating molecules, (2) assignment of rate laws to each
reaction, and (3) parameter calibration with respect to the measurements.
In each of these steps the modeler is confronted with a plethora of
alternative approaches, e.g., the selection of approximative rate laws in
step two as specific equations are often unknown, or the choice of an
estimation procedure with its specific settings in step three. This overall
process with its numerous choices and the mutual influence between them
makes it hard to single out the best modeling approach for a given problem.

Results:
We investigate the modeling process using multiple kinetic equations
together with various parameter optimization methods for a
well-characterized example network, the biosynthesis of valine and leucine
in \emph{C.~glutamicum}. For this purpose, we derive seven dynamic models
based on generalized mass action, Michaelis-Menten and convenience kinetics
as well as the stochastic Langevin equation. In addition, we introduce two
modeling approaches for feedback inhibition to the mass action kinetics. The
parameters of each model are estimated using eight optimization strategies.
To determine the most promising modeling approaches together with
the best optimization algorithms, we carry out a two-step benchmark:
(1) coarse-grained comparison of the algorithms on all models and
(2) fine-grained tuning of the best optimization algorithms and models.
To analyze the space of the best parameters found for each model,
we apply clustering, variance, and correlation analysis.

Conclusion:
A mixed model based on the convenience rate law and the Michaelis-Menten
equation, in which all reactions are assumed to be reversible, is
the most suitable deterministic modeling approach followed by a reversible
generalized mass action kinetics model. A Langevin model is advisable
to take stochastic effects into account. To estimate the model parameters,
three algorithms are particularly useful: For first attempts the
settings-free Tribes algorithm yields valuable results. Particle
swarm optimization and differential evolution provide significantly
better results with appropriate settings.},
doi = {10.1186/1752-0509-3-5},
pdf = {http://www.biomedcentral.com/content/pdf/1752-0509-3-5.pdf},
url = {http://www.biomedcentral.com/1752-0509/3/5}
}