Team:Valencia UPV/Modeling/fba


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Modeling Pheromone Production Overview

Pheromones production rates can be estimated using constrained-based modeling of metabolic networks.This can be useful to know about the amount of pheromone that can be produced by the synthetic plant.

Constraint-based modeling

Constraint-based modeling use models of the cell metabolism that are derived from a metabolic network (stoicheometry models) and assume steady-state for the intracellular metabolites. These two constraints are the base of Cconstraint-based modeling: the fact that cells are subject to constraints that limit their behaviour [Palsson06]. In principle, if all constraints operating under a given set of circumstances were known, the actual state of a metabolic network could be elucidated. So by imposing the known constraints, it is possible to determine which functional states can and cannot be achieved by a cell.

Principles of the stoichiometric modeling framework. Given a metabolic network, the mass balance around each intracellular metabolite can be mathematically represented with an ordinary differential equation. If we do not consider intracellular dynamics, the mass balances can be described by a homogeneous system of linear equations: the so-called general equation. Other constraints can be also incorporated to further restrict the space of feasible flux states of cells. From: PhD Thesis. F Llaneras. UPV. 2010

Types of contraints

Constraints can be divided in two main types: non adjustable (invariant) and adjustable ones. The former are time-invariant restrictions of possible cell behaviour, whereas the latter depend on environmental conditions, may change through evolution, and may vary from one individual cell to another. Examples of non adjustable constraints are those imposed by thermodynamics (e.g, irreversibility of fluxes) and enzyme or transport capacities (e.g, maximum flux values). Enzyme kinetics, regulation, and experimental measurements are examples of adjustable constraints. To study the invariant properties of a network, only invariant constraints can be used, because they are those that are always satisfied (i.e, they limit the cell capabilities). If adjustable constraints are used, the elucidated cell states will be only valid under the particular set of circumstances in which these constraints operate.

Space of feasible steady-state flux vectors by non-adjustable constraints. From: PhD Thesis. F Llaneras. UPV. 2010

Flux Balance Analysis

Flux balance analysis (FBA) is a methodology that uses optimisation to get predictions from a constraint-based model by invoking an assumption of optimal cell behaviour. Basically, one particular state among those that cells can show, accordingly to a constraint-based model, is chosen based on the assumption that cells have evolved to be optimal, i.e., that cells regulate its fluxes toward optimal flux states. The following procedure is used to develop a flux balance analysis model:

Procedure to develop a flux balance analysis model. From: PhD Thesis. F Llaneras. UPV. 2010

Flux balance analysis is used to investigate hypothesis (e.g., test if a reduced uptake capacity can be the cause of an unexpected cell behaviour) and to evaluate a range of possibilities (e.g, find the best combination of substrates).

Metabolic objectives and optimization

It must be taken into account that FBA predictions, the optimal flux state, may not correspond to the actual fluxes exhibit by cells. To support the assumption of optimal behaviour, it must be hypothesised that: (i) cells, forced by evolutionary pressure, evolved to achieve an optimal behaviour with respect to certain objective, (ii) we know which this objective is, and (iii) the objective can be expressed, at least approximately, in convenient mathematical terms.

Clearly, predictions of flux balance analysis are dependent on the objective function being used. To date, the most commonly used objective function has been the maximisation of biomass, which leaded to predictions consistent with experimental data for different organisms, such as Escherichia coli [Edwards01].

Genome-scale and plant models

FBA is widely used for predicting metabolism, in particular the genome-scale metabolic network reconstructions that have been built in the past decade. These reconstructions contain all of the known metabolic reactions in an organism or plant, and the genes that encode each enzyme. In our case, FBA will calculate the flow of metabolites through our metabolic network to obtain the major production of pheromone. Must be noted that plant genome-scale models are very rare and indeed plant FBA is a very new research topic. One of the only available models is the ARAGem, a genome-scale of Arabidopsis Thaliana.

ARAGem Model of A. Thaliana. From: ARAGem


[Llaneras08] Llaneras F, Picó J (2008). Stoichiometric Modelling of Cell Metabolism. Journal of Bioscience and Bioengineering, 105:1.

[Palsson06] Palsson BO (2006). Systems biology: properties of reconstructed networks. New York, USA: Cambridge University Press New York.

[Edwards01] Edwards JS, Covert M, Palsson B (2002). Metabolic modelling of microbes: the flux-balance approach. Environmental Microbiology, 4:133-140.


The COnstraints Based Reconstruction and Analysis (COBRA) approach to systems biology accepts the fact that we do not possess sufficiently detailed parameter data to precisely model, in the biophysical sense, an organism or plant at the genome scale [1]. The COBRA Toolbox [2] is a freely available Matlab toolbox can be used to perform a variety of COBRA methods, including many FBA-based methods. Models for the COBRA Toolbox are saved in the Systems Biology Markup Language (SBML).

Model Aragem

AraGEM is the genome-scale metabolic network model covering primary metabolism for a compartmentalized plant cell based on the Arabidopsis (Arabidopsis thaliana) genome. AraGEM is a comprehensive literature-based, that accounts for the functions of 1,419 unique open reading frames, 1,748 metabolites, 5,253 gene-enzyme reaction-association entries, and 1,567 unique reactions compartmentalized into the cytoplasm, mitochondrion, plastid, peroxisome, and vacuole.

Using efficient resource utilization as the optimality criterion, AraGEM predicted the classical photorespiratory cycle as well as known key differences between redox metabolism in photosynthetic and nonphotosynthetic plant cells. Hence, we have added to AraGEM in silico the reactions from the network of production pheromone. The optimality criterion finds to maximize the pheromone flux, which is produced by the plant, and it is released into the air to confuse the moths.

AraGEM is a viable framework for in silico functional analysis and can be used to derive new, nontrivial hypotheses for exploring plant metabolism. AraGEM is the genome-scale metabolic network model that better approximates the metabolism model of N. benthamiana.


[Hyduke2009]COBRA Toolbox 2.0 Daniel Hyduke, Jan Schellenberger, Richard Que, Ronan Fleming, Ines Thiele, Jeffery Orth, Adam Feist, Daniel Zielinski, Aarash Bordbar, Nathan Lewis, Sorena Rahmanian, Joseph Kang & Bernhard Palsson. Link:

[Oliveira10] AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. de Oliveira Dal'Molin CG1, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK. NCBI, Plant Physiol. 2010 Feb;152(2):579-89. doi: 10.1104/pp.109.148817. Epub 2009 Dec 31.

[Saha11] Zea mays iRS1563: A Comprehensive Genome-Scale Metabolic Reconstruction of Maize Metabolism Rajib Saha,Patrick F. Suthers, Costas D. Maranas mail Published: July 06, 2011 DOI: 10.1371/journal.pone.0021784

NetLogo is an agent-based programming language and integrated modeling environment. NetLogo is free and open source software, under a GPL license.

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