Interval and Possibilistic Methods for Constraint-Based Metabolic Models

This thesis is devoted to the study and application of constraint-based metabolic models. The objective was to find simple ways to handle the difficulties that arise in practice due to uncertainty (knowledge is incomplete, there is a lack of measurable variables, and those available are imprecise). With this purpose, tools have been developed to model, analyse, estimate and predict the metabolic behaviour of cells. The document is structured in three parts. First, related literature is revised and summarised. This results in a unified perspective of several methodologies that use constraint-based representations of the cell metabolism. Three outstanding methods are discussed in detail, network-based pathways analysis (NPA), metabolic flux analysis (MFA), and flux balance analysis (FBA). Four types of metabolic pathways are also compared to clarify the subtle differences among them. The second part is devoted to interval methods for constraint-based models. The first contribution is an interval approach to traditional MFA, particularly useful to estimate the metabolic fluxes under data scarcity (FS-MFA). These estimates provide insight on the internal state of cells, which determines the behaviour they exhibit at given conditions. The second contribution is a procedure for monitoring the metabolic fluxes during a cultivation process that uses FS-MFA to handle uncertainty. The third part of the document addresses the use of possibility theory. The main contribution is a possibilistic framework to (a) evaluate model and measurements consistency, and (b) perform flux estimations (Poss-MFA). It combines flexibility on the assumptions and computational efficiency. Poss-MFA is also applied to monitoring fluxes and metabolite concentrations during a cultivation, information of great use for fault-detection and control of industrial processes. Afterwards, the FBA problem is addressed.Llaneras Estrada, F. (2011). Interval and Possibilistic Methods for Constraint-Based Metabolic Models [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/10528Palanci

Dynamic estimations of metabolic fluxes with constraint-based models and possibility theory

Living cells can be modelled by successively imposing known constraints that limit their behaviour, such as mass balances, thermodynamic laws or enzyme capacities. The resulting constraint-based models enclose all the functional states that the modelled cells may exhibit. Then, predictions can be obtained from the models in two main ways: adding experimental data to determine the state of cells at given conditions (MFA) or invoking an assumption of evolved optimal behaviour (FBA). Both MFA and FBA predictions are typically performed at steady state. However, it is easy to take extracellular dynamics into account. This work explores the benefits of using possibility theory to get these dynamic predictions. It will be shown that the possibilistic methods (a) provide rich estimates for time-varying fluxes and metabolite concentrations, (b) account for uncertainty and data scarcity, and (c) give predictions relaxing the optimality assumption of FBA. On the other hand, these methods could serve as basis for monitoring and fault detection systems in industrial bioprocesses.This research has been partially supported by the Spanish Government MINECO (1st and 3rd authors are grateful to grant CICYT DPI2011-28112-C04-01, and A. Sala is grateful to grant DPI2011-27845-C02-01).Llaneras Estrada, F.; Sala, A.; Picó Marco, JA. (2012). Dynamic estimations of metabolic fluxes with constraint-based models and possibility theory. Journal of Process Control. 22(10):1946-1955. https://doi.org/10.1016/j.jprocont.2012.09.00119461955221

Estimation of recombinant protein production in Pichia pastoris base don a constraint-based model

[EN] A previously validated constraint based model and possibilistic MFA have been used to design a simple estimator of protein production rate in Pichia pastoris cultures. A structured model of the yeast P. pastoris metabolism is used to predict the balance of key energetic equivalents such as ATP from available measurements, mainly substrate consumption, gases exchange rates and biomass specific growth. It has been shown that ATP flux can be related to biomass growth and protein productivity specific rates by linear regression. Cross-validation has been applied for robust parameter fitting on the basis of chemostat, steady-state experimental conditions. In this way, protein estimation can be integrated in the constraint-based model, and possibilistic protein productivity prediction can be given even if only a few extracellular rates are known. Complimentary estimation of biomass growth and intracellular rates are also shown in different lacking-data conditions, frequent in industrial environment. © 2012 Elsevier Ltd.This research has been partially supported by the Spanish Government (2nd and 4th authors are grateful to grants DPI2008-06880-C03-01 and Feder-Cicyt DPI2011-28112-C04-01). The authors are also grateful to the Company Biopolis for his support to this research.Tortajada Serra, M.; Llaneras Estrada, F.; Ramón, D.; Picó, J. (2012). Estimation of recombinant protein production in Pichia pastoris base don a constraint-based model. Journal of Process Control. 22(6):1139-1151. https://doi.org/10.1016/j.jprocont.2012.03.009S1139115122

PFA toolbox: a MATLAB tool for Metabolic Flux Analysis

Metabolic Flux Analysis (MFA) is a methodology that has been successfully applied to estimate metabolic fluxes in living cells. However, traditional frameworks based on this approach have some limitations, particularly when measurements are scarce and imprecise. This is very common in industrial environments. The PFA Toolbox can be used to face those scenarios. Results Here we present the PFA (Possibilistic Flux Analysis) Toolbox for MATLAB, which simplifies the use of Interval and Possibilistic Metabolic Flux Analysis. The main features of the PFA Toolbox are the following: (a) It provides reliable MFA estimations in scenarios where only a few fluxes can be measured or those available are imprecise. (b) It provides tools to easily plot the results as interval estimates or flux distributions. (c) It is composed of simple functions that MATLAB users can apply in flexible ways. (d) It includes a Graphical User Interface (GUI), which provides a visual representation of the measurements and their uncertainty. (e) It can use stoichiometric models in COBRA format. In addition, the PFA Toolbox includes a User’s Guide with a thorough description of its functions and several examples. Conclusions The PFA Toolbox for MATLAB is a freely available Toolbox that is able to perform Interval and Possibilistic MFA estimation