Francisco Llaneras

Stoichiometric modelling of cell metabolism

There are several methodologies based on representations of cell metabolism that share two characteristics: the use of a metabolic network and the assumption of pseudosteady state. These methodologies have different purposes, employ different mathematical tools and are based on different assumptions; however, they all exploit the properties of a similar mathematical description. In this article we use the term stoichiometric modelling to encompass all these methodologies and to describe them within a common framework. Although the information about reaction stoichiometry embedded in metabolic networks is highly important, the framework encompasses methodologies not limited to the use of stoichiometric information. To highlight this fact, the definition of the framework is approached from a constraint-based perspective. One of the reasons for the success of stoichiometric modelling is that it avoids the difficulties that arise in the development of kinetic models: a consequence of the lack of intracellular experimental measurements. Thus, it makes it possible to exploit the knowledge about the structure of cell metabolism, without considering the still not very well known intracellular kinetic processes. Stoichiometric models have been used to estimate the metabolic flux distribution under given circumstances in the cell at some given moment (metabolic flux analysis), to predict it on the basis of some optimality hypothesis (flux balance analysis), and as tools for the structural analysis of metabolism providing information about systemic characteristics of the cell under investigation (network-based pathway analysis).

A procedure for the estimation over time of metabolic fluxes in scenarios where measurements are uncertain and/or insufficient

BackgroundAn indirect approach is usually used to estimate the metabolic fluxes of an organism: couple the available measurements with known biological constraints (e.g. stoichiometry). Typically this estimation is done under a static point of view. Therefore, the fluxes so obtained are only valid while the environmental conditions and the cell state remain stable. However, estimating the evolution over time of the metabolic fluxes is valuable to investigate the dynamic behaviour of an organism and also to monitor industrial processes. Although Metabolic Flux Analysis can be successively applied with this aim, this approach has two drawbacks: i) sometimes it cannot be used because there is a lack of measurable fluxes, and ii) the uncertainty of experimental measurements cannot be considered. The Flux Balance Analysis could be used instead, but the assumption of optimal behaviour of the organism brings other difficulties.ResultsWe propose a procedure to estimate the evolution of the metabolic fluxes that is structured as follows: 1) measure the concentrations of extracellular species and biomass, 2) convert this data to measured fluxes and 3) estimate the non-measured fluxes using the Flux Spectrum Approach, a variant of Metabolic Flux Analysis that overcomes the difficulties mentioned above without assuming optimal behaviour. We apply the procedure to a real problem taken from the literature: estimate the metabolic fluxes during a cultivation of CHO cells in batch mode. We show that it provides a reliable and rich estimation of the non-measured fluxes, thanks to considering measurements uncertainty and reversibility constraints. We also demonstrate that this procedure can estimate the non-measured fluxes even when there is a lack of measurable species. In addition, it offers a new method to deal with inconsistency.ConclusionThis work introduces a procedure to estimate time-varying metabolic fluxes that copes with the insufficiency of measured species and with its intrinsic uncertainty. The procedure can be used as an off-line analysis of previously collected data, providing an insight into the dynamic behaviour of the organism. It can be also profitable to the on-line monitoring of a running process, mitigating the traditional lack of reliable on-line sensors in industrial environments.

Which Metabolic Pathways Generate and Characterize the Flux Space? A Comparison among Elementary Modes, Extreme Pathways and Minimal Generators

Important efforts are being done to systematically identify the relevant pathways in a metabolic network. Unsurprisingly, there is not a unique set of network-based pathways to be tagged as relevant, and at least four related concepts have been proposed: extreme currents, elementary modes, extreme pathways, and minimal generators. Basically, there are two properties that these sets of pathways can hold: they can generate the flux space—if every feasible flux distribution can be represented as a nonnegative combination of flux through them—or they can comprise all the nondecomposable pathways in the network. The four concepts fulfill the first property, but only the elementary modes fulfill the second one. This subtle difference has been a source of errors and misunderstandings. This paper attempts to clarify the intricate relationship between the network-based pathways performing a comparison among them.

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

BackgroundConstraint-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.ResultsIn this contribution, a simplified constraint-based stoichiometric model of the metabolism of the yeast Pichia pastoris, 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.ConclusionsThis 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.

A possibilistic framework for constraint-based metabolic flux analysis

BackgroundConstraint-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.ResultsHerein 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.ConclusionWe 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.

Validation of an FBA model for Pichia pastoris in chemostat cultures

BackgroundConstraint-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.ResultsA 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.ConclusionsWe 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 rates.

PFA toolbox: a MATLAB tool for Metabolic Flux Analysis

BackgroundMetabolic 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.ResultsHere 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.ConclusionsThe PFA Toolbox for MATLAB is a freely available Toolbox that is able to perform Interval and Possibilistic MFA estimations.

Dynamic Metabolic Flux Analysis for Online Estimation of Recombinant Protein Productivity in Pichia pastoris Cultures

Abstract One approach to model living cells is based on successively imposing the (known) constraints–such as enzyme capacities, mass balances or thermodynamic laws– that limit their behaviour. This process results in a constraint-based model that encloses all the functional states that cells might exhibit. By combining the model with experimental measurements, it is possible to determine the particular cellular state at given conditions, an exercise that is generally referred to as Metabolic Flux Analysis (MFA). In this work we use a previously validated model (Tortajada et al. , 2010) and an MFA-wise method (Llaneras et al. , 2009) for on-line monitoring of industrial cultures of the yeast Pichia pastoris. Given a set of standard measurements –substrates, gases and biomass growth–, Possibilistic dynamic MFA provides estimates for unmeasured, time-varying extracellular metabolites and intracellular fluxes, while accounting for the imprecision and uncertainty common in industrial settings. The production of the recombinant protein of interest can be estimated by means of a relationship among ATP consumption rate and specific growth rate, which is integrated into the model. To test the viability of the approach some preliminary experimental results are shown, using data from a set of batch cultivations performed in microbioreactors. The procedure is of great industrial interest because it can provide not only a way to monitor the metabolic state of P. pastoris cultures during a running process, but also a direct online estimation of the protein production rate.

Applications of possibilistic reasoning to intelligent system monitoring: a case study

This paper discusses the use of a possibilistic framework for system monitoring tasks where a system model jointly with measurements is given as a set of algebraic equations. Uncertainty is handled via the introduction of slack variables and an optimization-based (linear or quadratic programming) approach is proposed to compute the possibility distributions of the internal variables to be monitored. A case study on a bio-engineering problem is presented.

Possibilistic Estimation of Metabolic Fluxes During a Batch Process Accounting for Extracellular Dynamics

Abstract Constraint-based models use the available knowledge about the operating constraints (e.g., mass balances and thermodynamic laws) to define a space of feasible states for cell cultures. Predictions can then be obtained incorporating experimental measurements of metabolite concentrations to perform a metabolic flux analysis. Although these predictions are typically static, aimed to study cells at given state, several works accounting for extracellular dynamics can be found in literature. In this work we formulate these predictions of time-varying fluxes and metabolites as possibilistic constraint satisfaction problems. The benefit of the described approach is that richer estimates are obtained —not only point-wise ones—, while considering uncertainty and even in scenarios of data Scirccity. The method could also be the basis for on-line fault detection in industrial processes.