Modeling Protein Destiny in Developing Fruit.

Protein synthesis and degradation are essential processes that regulate cell status. Because labeling in bulky organs, such as fruits, is difficult, we developed a modeling approach to study protein turnover at the global scale in developing tomato (Solanum lycopersicum) fruit. Quantitative data were collected for transcripts and proteins during fruit development. Clustering analysis showed smaller changes in protein abundance compared to mRNA abundance. Furthermore, protein and transcript abundance were poorly correlated, and the coefficient of correlation decreased during fruit development and ripening, with transcript levels decreasing more than protein levels. A mathematical model with one ordinary differential equation was used to estimate translation (kt ) and degradation (kd ) rate constants for almost 2,400 detected transcript-protein pairs and was satisfactorily fitted for >1,000 pairs. The model predicted median values of ∼2 min for the translation of a protein, and a protein lifetime of ∼11 d. The constants were validated and inspected for biological relevance. Proteins involved in protein synthesis had higher kt and kd values, indicating that the protein machinery is particularly flexible. Our model also predicts that protein concentration is more strongly affected by the rate of translation than that of degradation.

Respiration climacteric in tomato fruits elucidated by constraint-based modelling.

Tomato is a model organism to study the development of fleshy fruit including ripening initiation. Unfortunately, few studies deal with the brief phase of accelerated ripening associated with the respiration climacteric because of practical problems involved in measuring fruit respiration. Because constraint-based modelling allows predicting accurate metabolic fluxes, we investigated the respiration and energy dissipation of fruit pericarp at the breaker stage using a detailed stoichiometric model of the respiratory pathway, including alternative oxidase and uncoupling proteins. Assuming steady-state, a metabolic dataset was transformed into constraints to solve the model on a daily basis throughout tomato fruit development. We detected a peak of CO2 released and an excess of energy dissipated at 40 d post anthesis (DPA) just before the onset of ripening coinciding with the respiration climacteric. We demonstrated the unbalanced carbon allocation with the sharp slowdown of accumulation (for syntheses and storage) and the beginning of the degradation of starch and cell wall polysaccharides. Experiments with fruits harvested from plants cultivated under stress conditions confirmed the concept. We conclude that modelling with an accurate metabolic dataset is an efficient tool to bypass the difficulty of measuring fruit respiration and to elucidate the underlying mechanisms of ripening.

Modelling central metabolic fluxes by constraint-based optimization reveals metabolic reprogramming of developing Solanum lycopersicum (tomato) fruit.

Modelling of metabolic networks is a powerful tool to analyse the behaviour of developing plant organs, including fruits. Guided by our current understanding of heterotrophic metabolism of plant cells, a medium-scale stoichiometric model, including the balance of co-factors and energy, was constructed in order to describe metabolic shifts that occur through the nine sequential stages of Solanum lycopersicum (tomato) fruit development. The measured concentrations of the main biomass components and the accumulated metabolites in the pericarp, determined at each stage, were fitted in order to calculate, by derivation, the corresponding external fluxes. They were used as constraints to solve the model by minimizing the internal fluxes. The distribution of the calculated fluxes of central metabolism were then analysed and compared with known metabolic behaviours. For instance, the partition of the main metabolic pathways (glycolysis, pentose phosphate pathway, etc.) was relevant throughout fruit development. We also predicted a valid import of carbon and nitrogen by the fruit, as well as a consistent CO2 release. Interestingly, the energetic balance indicates that excess ATP is dissipated just before the onset of ripening, supporting the concept of the climacteric crisis. Finally, the apparent contradiction between calculated fluxes with low values compared with measured enzyme capacities suggest a complex reprogramming of the metabolic machinery during fruit development. With a powerful set of experimental data and an accurate definition of the metabolic system, this work provides important insight into the metabolic and physiological requirements of the developing tomato fruits.

Model-assisted analysis of sugar metabolism throughout tomato fruit development reveals enzyme and carrier properties in relation to vacuole expansion.

A kinetic model combining enzyme activity measurements and subcellular compartmentation was parameterized to fit the sucrose, hexose, and glucose-6-P contents of pericarp throughout tomato (Solanum lycopersicum) fruit development. The model was further validated using independent data obtained from domesticated and wild tomato species and on transgenic lines. A hierarchical clustering analysis of the calculated fluxes and enzyme capacities together revealed stage-dependent features. Cell division was characterized by a high sucrolytic activity of the vacuole, whereas sucrose cleavage during expansion was sustained by both sucrose synthase and neutral invertase, associated with minimal futile cycling. Most importantly, a tight correlation between flux rate and enzyme capacity was found for fructokinase and PPi-dependent phosphofructokinase during cell division and for sucrose synthase, UDP-glucopyrophosphorylase, and phosphoglucomutase during expansion, thus suggesting an adaptation of enzyme abundance to metabolic needs. In contrast, for most enzymes, flux rates varied irrespectively of enzyme capacities, and most enzymes functioned at <5% of their maximal catalytic capacity. One of the major findings with the model was the high accumulation of soluble sugars within the vacuole together with organic acids, thus enabling the osmotic-driven vacuole expansion that was found during cell division.

Modeling the respiratory chain complexes with biothermokinetic equations - the case of complex I.

The mitochondrial respiratory chain plays a crucial role in energy metabolism and its dysfunction is implicated in a wide range of human diseases. In order to understand the global expression of local mutations in the rate of oxygen consumption or in the production of adenosine triphosphate (ATP) it is useful to have a mathematical model in which the changes in a given respiratory complex are properly modeled. Our aim in this paper is to provide thermodynamics respecting and structurally simple equations to represent the kinetics of each isolated complexes which can, assembled in a dynamical system, also simulate the behavior of the respiratory chain, as a whole, under a large set of different physiological and pathological conditions. On the example of the reduced nicotinamide adenine dinucleotide (NADH)-ubiquinol-oxidoreductase (complex I) we analyze the suitability of different types of rate equations. Based on our kinetic experiments we show that very simple rate laws, as those often used in many respiratory chain models, fail to describe the kinetic behavior when applied to a wide concentration range. This led us to adapt rate equations containing the essential parameters of enzyme kinetic, maximal velocities and Henri-Michaelis-Menten like-constants (KM and KI) to satisfactorily simulate these data.

Virtual mitochondrion: towards an integrated model of oxidative phosphorylation complexes and beyond.

The modelling of OXPHOS (oxidative phosphorylation) in order to integrate all kinetic and thermodynamic aspects of chemiosmotic theory has a long history. We briefly review this history and show how new ways of modelling are required to integrate a local model of the individual respiratory complexes into a global model of OXPHOS and, beyond that, into a reliable overall model of central metabolism.

Mitochondrial energetic metabolism: a simplified model of TCA cycle with ATP production.

Mitochondria play a central role in cellular energetic metabolism. The essential parts of this metabolism are the tricarboxylic acid (TCA) cycle, the respiratory chain and the adenosine triphosphate (ATP) synthesis machinery. Here a simplified model of these three metabolic components with a limited set of differential equations is presented. The existence of a steady state is demonstrated and results of numerical simulations are presented. The relevance of a simple model to represent actual in vivo behavior is discussed.

An old paper revisited: "a mathematical model of carbohydrate energy metabolism. Interaction between glycolysis, the Krebs cycle and the H-transporting shuttles at varying ATPases load" by V.V. Dynnik, R. Heinrich and E.E. Sel'kov.

We revisit an old Russian paper by V.V. Dynnik, R. Heinrich and E.E. Sel'kov (1980a,b) describing: "A mathematical model of carbohydrate energy metabolism. Interaction between glycolysis, the Krebs cycle and the H-transporting shuttles at varying ATPases load". We analyse the model mathematically and calculate the control coefficients as a function of ATPase loads. We also evaluate the structure of the metabolic network in terms of elementary flux modes. We show how this model can respond to an ATPase load as well as to the glucose supply. We also show how this simple model can help in understanding the articulation between the major blocks of energetic metabolism, i.e. glycolysis, the Krebs cycle and the H-transporting shuttles.

Virtual mitochondria: metabolic modelling and control.

Inside the eukaryotic cell, mitochondria are internal organelles of prokaryotic origin, responsible for energy supply in the cell. The control of the mitochondrial ATP production is a complex problem with different patterns according to different tissues and organs. Our aim is to continue to develop the modelling of oxidative phosphorylation in different tissues, to model other parts of mitochondrial metabolism and to include this virtual mitochondria in a virtual cell. In constructing the complete metabolic map of mitochondria, we will take advantage of the sequenced genomes of eukaryotic organism (10-15% of the yeast genome concerns mitochondria).