Jesús Picó

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).

Comprehensive pharmacokinetic model of insulin Glargine and other insulin formulations

In this paper, a comprehensive pharmacokinetic model for different insulin formulations including insulin Glargine is developed based on the model proposed by Trajanoski et al. (1993). Current models show limitations for insulin Glargine due to the appearance of an uncharacteristic peak in the concentration-time evolution of plasma insulin that does not coincide with real experimental data. This important limitation has been solved in this paper by introducing a new virtual insulin state called the bound state, in addition to the dimeric and hexameric ones. Trying to describe the retarded action of insulin Glargine, the modeling idea behind this approach is that immediately after the subcutaneous injection all the insulin resides in the bound state, and only then small amounts of insulin in the hexameric form disengage from the bound state. For the model evaluation different simulation results are compared. Using experimental data published by Lepore et al. (2000), the developed model turned out to be capable of at least qualitatively predicting the concentration-time profile of plasma insulin. Both exogenous insulin flow simulations and spatial diffusion simulations show the plausibility and correct implementation of the derived model. Considering all these simulation results, the here presented new pharmacokinetic model demonstrates to be able to reproduce real patient behavior simulating even complete insulin regimes including long-acting, intermediate and short-acting insulin formulations.

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.

Sliding mode scheme for adaptive specific growth rate control in biotechnological fed-batch processes

This paper addresses the control of biomass growth rate in fed-batch bioreactors. The main difficulty when designing controllers for these processes is the lack of accurate on-line knowledge of the controlled variable as well as the strong parameter and model uncertainties. A completely novel approach to the control design is introduced in this paper which allows us to overcome these problems. In fact, the proposed controller, which is applicable to a large class of fermentation processes, requires minimal knowledge of the process parameters and only uses on-line measurement of volume and biomass concentration. First, a reference model is proposed and a goal manifold in the state space is derived where the control objective is satisfied. A partial state feedback law is then proved to be an invariant control for the goal manifold. Then, the feedback gain is dynamically adjusted via a discontinuous action that enforces a sliding regime such that all state trajectories are steered towards the goal manifold. This sliding mode controller presents very attractive robustness properties. The performance of the controller is evaluated through numerical analysis and experimental results.

Stability preserving maps for finite-time convergence: Super-twisting sliding-mode algorithm

The super-twisting algorithm (STA) has become the prototype of second-order sliding mode algorithm. It achieves finite time convergence by means of a continuous action, without using information about derivatives of the sliding constraint. Thus, chattering associated to traditional sliding-mode observers and controllers is reduced. The stability and finite-time convergence analysis have been jointly addressed from different points of view, most of them based on the use of scaling symmetries (homogeneity), or non-smooth Lyapunov functions. Departing from these approaches, in this contribution we decouple the stability analysis problem from that of finite-time convergence. A nonlinear change of coordinates and a time-scaling are used. In the new coordinates and time-space, the transformed system is stabilized using any appropriate standard design method. Conditions under which the combination of the nonlinear coordinates transformation and the time-scaling is a stability preserving map are given. Provided convergence in the transformed space is faster than O(1/@t)-where @t is the transformed time-convergence of the original system takes place in finite-time. The method is illustrated by designing a generalized super-twisting observer able to cope with a broad class of perturbations.

Controller Design Under Fuzzy Pole-Placement Specifications: An Interval Arithmetic Approach

This paper discusses fuzzy specifications for robust controller design, as a way to define different specification levels for different plants in a family and allow the control of performance degradation. Controller synthesis will be understood as mapping a fuzzy plant onto a desired fuzzy set of closed-loop specifications. In this context, a fuzzy plant is considered as a possibility distribution on a given plant space. In particular, pole placement in linear plants with fuzzy parametric uncertainty is discussed, although the basic idea is general and could be applied to other settings. In the case under consideration, the controller coefficients are the solution of a fuzzy linear system of equations with a particular semantics. Modal interval arithmetic is used to solve the system for each alpha-cut. The intersection of the solutions, if not empty, constitutes the solution to the robust control problem

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.

Safety Auxiliary Feedback Element for the Artificial Pancreas in Type 1 Diabetes

The artificial pancreas aims at the automatic delivery of insulin for glycemic control in patients with type 1 diabetes, i.e., closed-loop glucose control. One of the challenges of the artificial pancreas is to avoid controller overreaction leading to hypoglycemia, especially in the late postprandial period. In this study, an original proposal based on sliding mode reference conditioning ideas is presented as a way to reduce hypoglycemia events induced by a closed-loop glucose controller. The method is inspired in the intuitive advantages of two-step constrained control algorithms. It acts on the glucose reference sent to the main controller shaping it so as to avoid violating given constraints on the insulin-on-board. Some distinctive features of the proposed strategy are that 1) it provides a safety layer which can be adjusted according to medical criteria; 2) it can be added to closed-loop controllers of any nature; 3) it is robust against sensor failures and overestimated prandial insulin doses; and 4) it can handle nonlinear models. The method is evaluated in silico with the ten adult patients available in the FDA-accepted UVA simulator.

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.