Model discrimination in time-course kinetics : the glyoxalase pathway in S. cerevisiae

Tese de doutoramento, Bioquímica (Bioquímica Teórica), Universidade de Lisboa, Faculdade de Ciências, 2010.The present work addresses the problem of model discrimination in enzyme kinetics. Frequently, more than one kinetic model is considered during the characterization of an enzymatic reaction or a metabolic pathway. The statistical selection of a model may be difficult if the candidate models fit the experimental data with very similar fitting scores. Since each model corresponds to a different possible mechanism of the studied process, model selection also reflects the choice of a particular mechanism. In addition, predictions given by models with equal fitting scores may be different. The glyoxalase system is a metabolic pathway that has been studied using two alternative kinetic models. These models could not be discriminated despite extensive kinetic experiments and an alternative branched mechanism combining the two models has been proposed. This pathway is therefore ideal for model discrimination research in Biochemistry. The glyoxalase pathway comprises the enzymes glyoxalase I and glyoxalase II. Glyoxalase I catalyzes the isomerization of the hemithioacetal that forms from the condensation of methylglyoxal (a by-­product of glycolysis) and glutathione to S-­D-­lactoylglutathione. Glyoxalase II catalyzes the hydrolysis of S-­D-­glutathione to D-­ lactate and glutathione. The methylglyoxal-­glutathione hemithioacetal forms spontaneously without the presence of enzymes. Therefore the glyoxalase I reaction can be described either as irreversible single-­substrate or as irreversible two-­substrate, considering that the hemithioacetal forms before binding the enzyme or that it forms in the active centre of the enzyme after sequential binding of glutathione and methylglyoxal, respectively. The glyoxalase system is the most important catabolic pathway for methylglyoxal. Methylglyoxal is a toxic agent due to its ability to react with proteins and nucleic acid amine groups that leads to formation of advanced glycation end-­products. Therefore the glyoxalase pathway was suggested to be a potential dug target for its cellular defensive role against methylglyoxal. An introduction to the subjects developed through this dissertation is given in chapter 1, covering the state of art of research on the glyoxalase pathway and methylglyoxal metabolism and on relevant mathematical and computational methods for model analysis and discrimination. In chapter 2 the glyoxalase system is investigated by analyzing the algebraic solutions of the rate equations describing the pathway at steady state. The two mentioned glyoxalase I kinetic models were used in this approach. It is observed that for the existence of a steady state a minimum amount of glutathione must be available;; in addition, glyoxalase I and II activities must exceed thresholds higher than the flux of the pathway. It is shown that methylglyoxal steady-­state concentration is not sensitive to variations of glyoxalase II activity but varies significantly with total glutathione concentration and methylglyoxal formation rate. Sensitivity to glyoxalase I activity depends on the kinetic model describing the enzyme: highly sensitivity if the two-­ substrate model is used but not so for the one-­substrate model. The pathway seems to operate very far from the conditions of disruption of the physiological steady state to assure a very low methylglyoxal concentration and a fast regeneration and high concentration of free glutathione. Time-­course kinetic studies with purified yeast enzyme and yeast permeabilized cells are described in chapter 3. Akaike’s information criterion and residual analysis are used to discuss the selection of the most appropriate kinetic model for glyoxalase I. Parameter least-­square estimates for this study are obtained with a combination of the stochastic Differential Evolution with the deterministic downhill-­simplex optimization algorithms. Although the two-­substrate model performs slightly better for the purified enzyme data, the Akaike score differences for both data sets and the residual analysis for the permeabilized cell data are not conclusive. A method developed to design optimized experimental conditions for model discrimination is explained in chapter 4. The method employs a multiobjective optimization algorithm (the Generalized Differential Evolution, generation 3) to search for the experimental conditions that maximize the divergence between the reaction time courses predicted by the models. The Kullback-­Leibler distance is the measure of divergence employed. The combination of the chosen algorithm and divergence criterion is successful in finding solutions that result in very different predictions from the two models for glyoxalase I in the presence of glyoxalase II, proving to be useful for planning model discrimination experiments. The importance of keeping a high free glutathione concentration seems to establish the properties of the glyoxalase pathway identified in chapter 2. Glutathione is also a key antioxidant and its oxidized form is reduced through the glutathione reductase system at the expense of NADPH. Indeed, the pyridine nucleotides NADPH and NADH have crucial metabolic roles. NADH, formed mainly in catabolic reactions, is the substrate of the respiratory chain and therefore it ultimately supplies the synthesis of ATP. NADPH is the main reducing agent in biosynthetic pathways. In addition, the pyridine nucleotides are among the metabolites that participate in a larger number of reactions in the cell. Therefore it is important to understand the effects of concentration changes of these metabolites. In chapter 5 perturbations to pyridine nucleotide concentrations are studied in living yeast cells cultured in bioreactors. The results for five recombinant S. cerevisiae strains overexpressing a cytosolic NADH oxidase, a mitochondrial NADH oxidase, a cytosolic NADH kinase, a mitochondrial NADH kinase and a cytosolic soluble pyridine nucleotide transhydrogenase are discussed. Extracellular and intracellular metabolite measurements and a stoichiometric model are used to assess the consequences of such perturbations, unveiling how metabolism in intact cells adapts to different redox conditions. Strains with enhanced NADH oxidation in the cytosol show a lower glycerol production. On the other hand enhanced NADH consumption in the mitochondrion lowers ethanol production and enhances ATP synthesis efficiency. The results presented here show that different kinetic models may fit experimental data equally well, making the selection of one model extremely. An original contribution is established to aid planning experiments for model discrimination. In addition, a broad characterization of the effects of perturbations to pyridine nucleotide metabolism is given, which is valuable to understand the complex response of yeast’s metabolic network, with direct biotechnological application.Fundação para a Ciência e Tecnologia – Ministério da Ciência, Tecnologia e Ensino Superior, Portugal (SFRH/BD/21947/2005