Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

Background: Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results: Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions: Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Identifying the preferred subset of enzymatic profiles in nonlinear kinetic metabolic models via multiobjective global optimization and pareto filters

Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA) representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study that optimizes the ethanol production in the fermentation of Saccharomyces cerevisiae.

Effects of a post-weaning cafeteria diet in young rats: metabolic syndrome, reduced activity and low anxiety-like behaviour.

Among adolescents, overweight, obesity and metabolic syndrome are rapidly increasing in recent years as a consequence of unhealthy palatable diets. Animal models of diet-induced obesity have been developed, but little is known about the behavioural patterns produced by the consumption of such diets. The aim of the present study was to determine the behavioural and biochemical effects of a cafeteria diet fed to juvenile male and female rats, as well as to evaluate the possible recovery from these effects by administering standard feeding during the last week of the study. Two groups of male and female rats were fed with either a standard chow diet (ST) or a cafeteria (CAF) diet from weaning and for 8 weeks. A third group of males (CAF withdrawal) was fed with the CAF diet for 7 weeks and the ST in the 8th week. Both males and females developed metabolic syndrome as a consequence of the CAF feeding, showing overweight, higher adiposity and liver weight, increased plasma levels of glucose, insulin and triglycerides, as well as insulin resistance, in comparison with their respective controls. The CAF diet reduced motor activity in all behavioural tests, enhanced exploration, reduced anxiety-like behaviour and increased social interaction; this last effect was more pronounced in females than in males. When compared to animals only fed with a CAF diet, CAF withdrawal increased anxiety in the open field, slightly decreased body weight, and completely recovered the liver weight, insulin sensitivity and the standard levels of glucose, insulin and triglycerides in plasma. In conclusion, a CAF diet fed to young animals for 8 weeks induced obesity and metabolic syndrome, and produced robust behavioural changes in young adult rats, whereas CAF withdrawal in the last week modestly increased anxiety, reversed the metabolic alterations and partially reduced overweight.

Assessment of metabolic fluxes in the mouse brain in vivo using 1H-[13C] NMR spectroscopy at 14.1 Tesla.

(13)C magnetic resonance spectroscopy (MRS) combined with the administration of (13)C labeled substrates uniquely allows to measure metabolic fluxes in vivo in the brain of humans and rats. The extension to mouse models may provide exclusive prospect for the investigation of models of human diseases. In the present study, the short-echo-time (TE) full-sensitivity (1)H-[(13)C] MRS sequence combined with high magnetic field (14.1 T) and infusion of [U-(13)C6] glucose was used to enhance the experimental sensitivity in vivo in the mouse brain and the (13)C turnover curves of glutamate C4, glutamine C4, glutamate+glutamine C3, aspartate C2, lactate C3, alanine C3, γ-aminobutyric acid C2, C3 and C4 were obtained. A one-compartment model was used to fit (13)C turnover curves and resulted in values of metabolic fluxes including the tricarboxylic acid (TCA) cycle flux VTCA (1.05 ± 0.04 μmol/g per minute), the exchange flux between 2-oxoglutarate and glutamate Vx (0.48 ± 0.02 μmol/g per minute), the glutamate-glutamine exchange rate V(gln) (0.20 ± 0.02 μmol/g per minute), the pyruvate dilution factor K(dil) (0.82 ± 0.01), and the ratio for the lactate conversion rate and the alanine conversion rate V(Lac)/V(Ala) (10 ± 2). This study opens the prospect of studying transgenic mouse models of brain pathologies.