A possibilistic framework for constraint-based metabolic flux analysis

<p>Abstract</p> <p>Background</p> <p>Constraint-based models allow the calculation of the metabolic flux states that can be exhibited by cells, standing out as a powerful analytical tool, but they do not determine which of these are likely to be existing under given circumstances. Typical methods to perform these predictions are (a) flux balance analysis, which is based on the assumption that cell behaviour is optimal, and (b) metabolic flux analysis, which combines the model with experimental measurements.</p> <p>Results</p> <p>Herein we discuss a possibilistic framework to perform metabolic flux estimations using a constraint-based model and a set of measurements. The methodology is able to handle inconsistencies, by considering sensors errors and model imprecision, to provide rich and reliable flux estimations. The methodology can be cast as linear programming problems, able to handle thousands of variables with efficiency, so it is suitable to deal with large-scale networks. Moreover, the possibilistic estimation does not attempt necessarily to predict the actual fluxes with precision, but rather to exploit the available data – even if those are scarce – to distinguish possible from impossible flux states in a gradual way.</p> <p>Conclusion</p> <p>We introduce a possibilistic framework for the estimation of metabolic fluxes, which is shown to be flexible, reliable, usable in scenarios lacking data and computationally efficient.</p

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

Validation of a constraint-based model of Pichia pastoris metabolism under data scarcity

<p>Abstract</p> <p>Background</p> <p>Constraint-based models enable structured cellular representations in which intracellular kinetics are circumvented. These models, combined with experimental data, are useful analytical tools to estimate the state exhibited (the phenotype) by the cells at given pseudo-steady conditions.</p> <p>Results</p> <p>In this contribution, a simplified constraint-based stoichiometric model of the metabolism of the yeast <it>Pichia pastoris</it>, a workhorse for heterologous protein expression, is validated against several experimental available datasets. Firstly, maximum theoretical growth yields are calculated and compared to the experimental ones. Secondly, possibility theory is applied to quantify the consistency between model and measurements. Finally, the biomass growth rate is excluded from the datasets and its prediction used to exemplify the capability of the model to calculate non-measured fluxes.</p> <p>Conclusions</p> <p>This contribution shows how a small-sized network can be assessed following a rational, quantitative procedure even when measurements are scarce and imprecise. This approach is particularly useful in lacking data scenarios.</p

MCR-ALS on metabolic networks: Obtaining more meaningful pathways

[EN] With the aim of understanding the flux distributions across a metabolic network, i.e. within living cells, Principal Component Analysis (PCA) has been proposed to obtain a set of orthogonal components (pathways) capturing most of the variance in the flux data. The problems with this method are (i) that no additional information can be included in the model, and (ii) that orthogonality imposes a hard constraint, not always reasonably. To overcome these drawbacks, here we propose to use a more flexible approach such as Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) to obtain this set of biological pathways through the network. By using this method, different constraints can be included in the model, and the same source of variability can be present in different pathways, which is reasonable from a biological standpoint. This work follows a methodology developed for Pichia pastoris cultures grown on different carbon sources, lately presented in González-Martínez et al. (2014). In this paper a different grey modelling approach, which aims to incorporate a priori knowledge through constraints on the modelling algorithms, is applied to the same case of study. The results of both models are compared to show their strengths and weaknesses.Research in this study was partially supported by the Spanish Ministry of Science and Innovation and FEDER funds from the European Union through grants DPI2011-28112-C04-01 and DPI2011-28112-C04-02. The authors are also grateful to Biopolis SL for supporting this research.Folch-Fortuny, A.; Tortajada Serra, M.; Prats-Montalbán, JM.; Llaneras Estrada, F.; Picó Marco, JA.; Ferrer Riquelme, AJ. (2015). MCR-ALS on metabolic networks: Obtaining more meaningful pathways. Chemometrics and Intelligent Laboratory Systems. 142:293-303. https://doi.org/10.1016/j.chemolab.2014.10.004S29330314

Metabolic flux understanding of Pichia pastoris grown on heterogenous culture media

[EN] Within the emergent field of Systems Biology, mathematical models obtained from physical chemical laws (the so-called first principles-based models) of microbial systems are employed to discern the principles that govern cellular behaviour and achieve a predictive understanding of cellular functions. The reliance on this biochemical knowledge has the drawback that some of the assumptions (specific kinetics of the reaction system, unknown dynamics and values of the model parameters) may not be valid for all the metabolic possible states of the network. In this uncertainty context, the combined use of fundamental knowledge and data measured in the fermentation that describe the behaviour of the microorganism in the manufacturing process is paramount to overcome this problem. In this paper, a grey modelling approach is presented combining data-driven and first principles information at different scales, developed for Pichia pastoris cultures grown on different carbon sources. This approach will allow us to relate patterns of recombinant protein production to intracellular metabolic states and correlate intra and extracellular reactions in order to understand how the internal state of the cells determines the observed behaviour in P. pastoris cultivations.Research in this study was partially supported by the Spanish Ministry of Science and Innovation and FEDER funds from the European Union through grants DPI2011-28112-C04-01 and DPI2011-28112-C04-02. The authors are also grateful to Biopolis SL for supporting this research. We also gratefully acknowledge Associate Professor Jose Camacho for providing the Exploratory Data Analysis Toolbox.González Martínez, JM.; Folch-Fortuny, A.; Llaneras Estrada, F.; Tortajada Serra, M.; Picó Marco, JA.; Ferrer, A. (2014). Metabolic flux understanding of Pichia pastoris grown on heterogenous culture media. Chemometrics and Intelligent Laboratory Systems. 134:89-99. https://doi.org/10.1016/j.chemolab.2014.02.003S899913

Process development for the obtention and use of recombinant glycosidases: expression, modelling and immobilisation

El objetivo general de la presente tesis doctoral es el desarrollo de herramientas para la obtencion, produccion y aplicacion de dos enzimas glicosidicas: �¿-L-arabinofuranosidasa proveniente del hongo Aspergillus niger (Abf) y �À-D-glucosidasa (Bgl), proveniente de la levadura Candida molischiana. Estas hidrolasas se emplean en la liberacion de azucares en procesos de conversion de biomasa y en la industria alimentaria, pero tambien en la sintesis de aminoglicosidos, glicoconjugados y oligosacaridos, compuestos de alto valor anadido para la industria quimico-farmaceutica. Las enzimas se han expresado en la levadura metilotrofica Pichia pastoris, y se han purificado para caracterizar sus propiedades bioquimicas. Asimismo, se ha comprobado su capacidad para catalizar reacciones de transglicosilacion con alto rendimiento. En relacion a su produccion, se ha establecido y validado un modelo basado en restricciones del metabolismo de Pichia pastoris, evaluando su consistencia mediante analisis de flujos metabolicos posibilistico. El modelo permite estimar la tasa de crecimiento y la distribucion de flujos intracelulares a partir de unos pocos flujos extracelulares medidos experimentalmente. Adicionalmente, el modelo se ha extendido para estimar la productividad de proteina recombinante, y se ha empleado para analizar diferentes condiciones de cultivo de las cepas transgenicas que sobreproducen las enzimas Abf y Bgl. Finalmente, las enzimas se han inmobilizado en organosilicas bimodales de la familia UVM-7. Los biocatalizadores resultantes se han caracterizado bioquimica y fisico-quimicamente y se han evaluado en diferentes aplicaciones de interes biotecnologico.Tortajada Serra, M. (2012). Process development for the obtention and use of recombinant glycosidases: expression, modelling and immobilisation [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/16800Palanci

PFA toolbox: a MATLAB tool for Metabolic Flux Analysis

Background: 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 estimations.This research has been partially supported by the Spanish Government (FEDER-CICYT: DPI 2014-55276-C5-1-R). Yeimy Morales is grateful for the BR Grants of the University of Girona (BR2012/26). Gabriel Bosque Chacon is recipient of a doctoral fellowship from the Spanish Government (BES-2012-053772).Morales, Y.; Bosque Chacón, G.; Vehi, J.; Picó Marco, JA.; Llaneras, F. (2016). PFA toolbox: a MATLAB tool for Metabolic Flux Analysis. 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CONTROL OF CONSTRAINED BIOSYSTEMS

Biological systems (biosystems), due to their complexity and multidisplinary character, are becoming one of the challenging research topics in the field of systems and control. In this work, several tools for dealing with control subject to constraints in the area of biosystems have been explored.Revert Tomás, A. (2011). CONTROL OF CONSTRAINED BIOSYSTEMS. http://hdl.handle.net/10251/12873Archivo delegad

Validation of a FBA model for Pichia pastoris in chemostat cultures

Background: Constraint-based metabolic models and flux balance analysis (FBA) have been extensively used in the last years to investigate the behavior of cells and also as basis for different industrial applications. In this context, this work provides a validation of a small-sized FBA model of the yeast Pichia pastoris. Our main objective is testing how accurate is the hypothesis of maximum growth to predict the behavior of P. pastoris in a range of experimental environments. Results: A constraint-based model of P. pastoris was previously validated using metabolic flux analysis (MFA). In this paper we have verified the model ability to predict the cells behavior in different conditions without introducing measurements, experimental parameters, or any additional constraint, just by assuming that cells will make the best use of the available resources to maximize its growth. In particular, we have tested FBA model ability to: (a) predict growth yields over single substrates (glucose, glycerol, and methanol); (b) predict growth rate, substrate uptakes, respiration rates, and by-product formation in scenarios where different substrates are available (glucose, glycerol, methanol, or mixes of methanol and glycerol); (c) predict the different behaviors of P. pastoris cultures in aerobic and hypoxic conditions for each single substrate. In every case, experimental data from literature are used as validation. Conclusions: We conclude that our predictions based on growth maximisation are reasonably accurate, but still far from perfect. The deviations are significant in scenarios where P. pastoris grows on methanol, suggesting that the hypothesis of maximum growth could be not dominating in these situations. However, predictions are much better when glycerol or glucose are used as substrates. In these scenarios, even if our FBA model is small and imposes a strong assumption regarding how cells will regulate their metabolic fluxes, it provides reasonably good predictions in terms of growth, substrate preference, product formation, and respiration ratesThis research has been partially supported by the Spanish Government (cicyt: DPI 2011-28112-C04-01, DPI 2013-46982-C2-2-R) and Biopolis S.L. (R.C.055/12). Yeimy Morales is grateful for the BR Grant of the University of Girona (BR2012/26). The authors are grateful to the company Biopolis S.L. for his support to this research.Morales, Y.; Tortajada, M.; Picó Marco, JA.; Vehi, J.; Llaneras, F. (2014). Validation of a FBA model for Pichia pastoris in chemostat cultures. BMC Systems Biology. 8:1-17. https://doi.org/10.1186/s12918-014-0142-yS1178Macauley-Patrick S, Fazenda ML, McNeil B, Harvey LM: Heterologous protein production using the Pichia pastoris expression system. 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