Optimization of bioreactor using metabolic control analysis approach

A new methodology based on a metabolic control analysis (MCA) approach is developed for the optimization of continuous cascade bioreactor system. A general framework for representation of a cascade bioreactor system consisting of a large number of reactors as a single network is proposed. The kinetic and transport processes occurring in the system are represented as a reaction network with appropriate stoichiometry. Such representation of the bioreactor systems makes it amenable to the direct application of the MCA approach. The process sensitivity information is extracted using MCA methodology in the form of flux and concentration control coefficients. The process sensitivity information is shown to be a useful guide for determining the choice of decision variables for the purpose of optimization. A generalized problem of optimization of the bioreactor is formulated in which the decision variables are the operating conditions and kinetic parameters. The gradient of the objective function to be maximized with respect to all decision variables is obtained in the form of response coefficients. This gradient information can be used in any gradient-based optimization algorithm. The efficiency of the proposed technique is demonstrated with two examples taken from literature: biotransformation of crotonobetaine and alcohol fermentation in cascade bioreactor system.     

Optimization-based metabolic control analysis

In this work, a novel optimization-based metabolic control analysis (OMCA) method is introduced for reducing data requirement for metabolic control analysis (MCA). It is postulated that using the optimal control approach, the fluxes in a metabolic network are correlated to metabolite concentrations and enzyme activities as a state-feedback control system that is optimal with respect to a homeostasis objective. It is then shown that the optimal feedback gains are directly related to the elasticity coefficients (ECs) of MCA. This approach requires determination of the relative "importance" of metabolites and fluxes for the system, which is possible with significantly reduced experimental data, as compared with typical MCA requirements. The OMCA approach is applied to a top-down control model of glycolysis in hepatocytes. It is statistically demonstrated that the OMCA model is capable of predicting the ECs observed experimentally with few exceptions. Further, an OMCA-based model reconciliation study shows that the modification of four assumed stoichiometric coefficients in the model can explain most of the discrepancies, with the exception of elasticities with respect to the NADH/NAD ratio.     

Topological analysis of metabolic control

A topological approach is presented for the analysis of control and regulation in metabolic pathways. In this approach, the control structure of a metabolic pathway is represented by a weighted directed graph. From an inspection of the topology of the graph, the control coefficients of the enzymes are evaluated in a heuristic manner in terms of the enzyme elasticities. The major advantage of the topological approach is that it provides a visual framework for (1) calculating the control coefficients of the enzymes, (2) analyzing the cause-effect relationships of the individual enzymes, (3) assessing the relative importance of the enzymes in metabolic regulation, and (4) simplifying the structure of a given pathway, from a regulatory viewpoint. Results are obtained for (a) an unbranched pathway in the absence of feedback the feedforward regulation and (b) an unbranched pathway with feedback inhibition. Our formulation is based on the metabolic control theory of Kacser and Burns (1973) and Heinrich and Rapoport (1974).     

Heterotrimeric G protein signaling: Getting inside the cell

Heterotrimeric G proteins have traditionally been thought to transduce signals at the plasma membrane. In this issue, Slessareva et al. (2006) now show that a G protein alpha subunit acts at the endosome to stimulate a phosphatidylinositol 3-kinase to help yeast respond to mating pheromones.     

Characterisation of the control of respiration in potato tuber mitochondria using the top-down approach of metabolic control analysis.

Control over oxidative phosphorylation by purified potato mitochondria was determined using the top-down approach of metabolic control analysis. The control over the respiration rate, phosphorylation rate, proton-leak rate and proton motive force exerted by the respiratory chain, phosphorylation reactions and the proton leak were measured over a range of phosphorylation rates from resting (state 4) to maximal (state 3). These rates were obtained by adding different amounts of hexokinase in the presence of glucose, or different amounts of oligomycin in the presence of ADP. The respiratory substrate was NADH or succinate, both of which feed electrons directly to ubiquinone. The rate of oxygen consumption by the alternative oxidase pathway was negligible with NADH as substrate but was measurable with succinate and was subtracted. Control over the respiration rate in potato mitochondria was predominantly exerted by the respiratory chain at all rates except close to state 4, where control by the proton leak was equally or more important. For oxidation of NADH, the flux control coefficient over the respiration rate exerted by the respiratory chain in state 3 was between 0.8 and 1.0, while in state 4, control over the respiration rate was shared about equally between the chain and the proton leak. The control over the phosphorylation rate was predominantly exerted by the respiratory chain, although at low rates control by the phosphorylation system was also important. For oxidation of NADH, the flux control coefficient over the phosphorylation rate exerted by the respiratory chain in state 3 was 0.8-1.0, while near state 4 the flux control coefficients over the phosphorylation rate were about 0.8 for the phosphorylation system and 0.25 for the chain. Control over the proton leak rate was shared between the respiratory chain and the proton leak; the phosphorylation system had negative control. For oxidation of NADH, the flux control coefficients over the leak rate in state 3 were 1.0 for the leak, 0.4 for the chain and -0.4 for the phosphorylation system, while in state 4 the flux control coefficients over leak rate were about 0.5 for the leak and 0.5 for the chain. Control over the magnitude of the protonmotive force was small, between -0.2 and +0.2, reflecting the way the system operates to keep the protonmotive force fairly constant; the respiratory chain and the phosphorylation system had equal and opposite control and there was very little control by the proton leak except near state 4.     

Getting the right cells to the array: Gene expression microarray analysis of cell mixtures and sorted cells.

BACKGROUND: Most biological samples are cell mixtures. Some basic questions are still unanswered about analyzing these heterogeneous samples using gene expression microarray technology (MAT). How meaningful is a cell mixture's overall gene expression profile (GEP)? Is it necessary to purify the cells of interest before microarray analysis, and how much purity is needed? How much does the purification itself distort the GEP, and how well can the GEP of a small cell subset be recovered? METHODS: Model cell mixtures with different cell ratios were analyzed by both spotted and Affymetrix MAT. GEP distortion during cell purification and GEPs of purified cells were studied. CD34+ cord blood cells were purified and analyzed by MAT. RESULTS: GEPs for mixed cell populations were found to mirror the cell ratios in the mixture. Over 75% pure samples were indistinguishable from pure cells by their overall GEP. Cell purification preserved the GEP. The GEPs of small cell subsets could be accurately recovered by cell sorting both from model cell mixtures and from cord blood. CONCLUSIONS: Purification of small cell subsets from a mixture prior to MAT is necessary for meaningful results. Even completely hidden GEPs of small cell subpopulations can be recovered by cell sorting.     

Increasing the flux in metabolic pathways: A metabolic control analysis perspective

The problems of engineering increased flux in metabolic pathways are analyzed in terms of the understanding provided by metabolic control analysis. Over-expression of a single enzyme is unlikely to be effective unless it is known to have a high flux control coefficient, which can be used as an approximate predictive tool. This is likely to rule out enzymes subject to feedback inhibition, because it transfers control downstream from the inhibited enzyme to the enzymes utilizing the feedback metabolite. Although abolishing feedback inhibition can restore flux control to an enzyme, it is also likely to cause large increases in the concentrations of metabolic intermediates. Simultaneous and coordinated over-expression of most of the enzymes in a pathway can, in principle, produce substantial flux increases without changes in metabolite levels, though technically it may be difficult to achieve. It is, however, closer to the method used by cells to change flux levels, where coordinated changes in the level of activity of pathway enzymes are the norm. Another option is to increase the demand for the pathway product, perhaps by increasing its rate of excretion or removal. Copyright 1998 John Wiley & Sons, Inc.     

Synergizing metabolic flux analysis and nucleotide sugar metabolism to understand the control of glycosylation of recombinant protein in CHO cells

Background

The photorespiratory nitrogen cycle in C₃ plants involves an extensive diversion of carbon and nitrogen away from the direct pathways of assimilation. The liberated ammonia is re-assimilated, but up to 25% of the carbon may be released into the atmosphere as CO₂. Because of the loss of CO₂ and high energy costs, there has been considerable interest in attempts to decrease the flux through the cycle in C₃ plants. Transgenic tobacco plants were generated that contained the genes gcl and hyi from E. coli encoding glyoxylate carboligase (EC 4.1.1.47) and hydroxypyruvate isomerase (EC 5.3.1.22) respectively, targeted to the peroxisomes. It was presumed that the two enzymes could work together and compete with the aminotransferases that convert glyoxylate to glycine, thus avoiding ammonia production in the photorespiratory nitrogen cycle.

Results

When grown in ambient air, but not in elevated CO₂, the transgenic tobacco lines had a distinctive phenotype of necrotic lesions on the leaves. Three of the six lines chosen for a detailed study contained single copies of the gcl gene, two contained single copies of both the gcl and hyi genes and one line contained multiple copies of both gcl and hyi genes. The gcl protein was detected in the five transgenic lines containing single copies of the gcl gene but hyi protein was not detected in any of the transgenic lines. The content of soluble amino acids including glycine and serine, was generally increased in the transgenic lines growing in air, when compared to the wild type. The content of soluble sugars, glucose, fructose and sucrose in the shoot was decreased in transgenic lines growing in air, consistent with decreased carbon assimilation.

Conclusions

Tobacco plants have been generated that produce bacterial glyoxylate carboligase but not hydroxypyruvate isomerase. The transgenic plants exhibit a stress response when exposed to air, suggesting that some glyoxylate is diverted away from conversion to glycine in a deleterious short-circuit of the photorespiratory nitrogen cycle. This diversion in metabolism gave rise to increased concentrations of amino acids, in particular glutamine and asparagine in the leaves and a decrease of soluble sugars.     

The mathematics of metabolic control analysis revisited

In this minireview, several different approaches to derivation of the theorems and relationships of Metabolic Control Analysis (MCA) are discussed and an alternative approach is presented. This new approach consists of solving the steady-state mass balances for the intracellular metabolites using linearized kinetics. The application of linearized kinetics reflects the fact that MCA is based on linearization of the system equations in a reference steady state. Our derivation is valid for metabolic networks of arbitrary complexity, including those containing conserved moieties and branches. The value of our approach is its simplicity: the derivation is straightforward and therefore easy to follow. It can serve as a compact introduction to the mathematical basis of MCA.     

Modular metabolic control analysis of large responses

Deciphering the laws that govern metabolic responses of complex systems is essential to understand physiological functioning, pathological conditions and the outcome of experimental manipulations of intact cells. To this aim, a theoretical and experimental sensitivity analysis, called modular metabolic control analysis (MMCA), was proposed. This field was previously developed under the assumptions of infinitesimal changes and/or proportionality between parameters and rates, which are usually not fulfilled in vivo. Here we develop a general MMCA for two modules, not relying on those assumptions. Control coefficients and elasticity coefficients for large changes are defined. These are subject to constraints: summation and response theorems, and relationships that allow calculating control from elasticity coefficients. We show how to determine the coefficients from top-down experiments, measuring the rates of the isolated modules as a function of the linking intermediate (there is no need to change parameters inside the modules). The novel formalism is applied to data of two experimental studies from the literature. In one of these, 40% increase in the activity of the supply module results in less than 4% increase in flux, while infinitesimal MMCA predicts more than 30% increase in flux. In addition, it is not possible to increase the flux by manipulating the activity of demand. The impossibility of increasing the flux by changing the activity of a single module is due to an abrupt decrease of the control of the modules when their corresponding activities are increased. In these cases, the infinitesimal approach can give highly erroneous predictions.     

Sugar metabolic analysis of suspensions of plant cells using an FT-IR/ATR method

A simple, rapid and accurate evaluation of the sugar uptake rate of suspended plant cells from culture media was developed with the predicted sugar contents measured by mid-infrared spectroscopy using a Fourier transform infrared (FT-IR) spectrometer equipped with an attenuated total reflectance (ATR) accessory. We performed plant cell cultivation with Nicotiana tabacum cv. Bright Yellow No.2 (TBY-2) in culture media, which had various combinations of glucose, fructose and sucrose concentrations at the initial stage, and measured simultaneously each sugar content in the medium by the FT-IR/ATR method. By applying a logistic function to the predicted sugar contents and cell density in the medium during cultivation, the specific sugar uptake rates by the suspended TBY-2 cells were easily and continuously obtained. Thus the kinetic sugar uptake phenomena by the TBY-2 cells were well confirmed overall using the developed method. Additionally it was found that the fraction of sucrose of the initial total sugar content might kinetically affect the sugar uptake process and cell growth. Also, the relationship between the nondimensional cell density and sucrose content could be classified into three groups on the basis of the initial fraction of sucrose.     

Covalent modification and metabolic control analysis. Modification to the theorems and their application to metabolic systems containing covalently modifiable enzymes

A study of the sensitivity properties of metabolic systems containing covalently modifiable enzymes and cascades has been carried out with the aid of metabolic control analysis. We have considered how the theorems of metabolic control analysis must be modified to take into account covalently modifiable enzymes, and have used these results to investigate the effects of increasing the total amount of modifiable enzyme. The sensitivity of system variables to an effector acting through a covalent-modification cycle has also been investigated.     

Application of fuzzy-logic models for metabolic control analysis

A priori information or valuable qualitative knowledge can be incorporated explicitly to describe enzyme kinetics making use of fuzzy-logic models. Although restricted to linear relationships, it is shown that fuzzy-logic augmented models are not only able to capture non-linear features of enzyme kinetics but also allow the proper mathematical treatment of metabolic control analysis. The explicit incorporation of valuable qualitative knowledge is crucial, particularly when handling data estimated from in vivo kinetics studies, since this experimental information is scarce and usually contains measurement errors. Therefore, data-driven techniques, such as the one presented in this work, form a serious alternative to established kinetics approaches.     

The definitions of metabolic control analysis revisited.

Various definitions of coefficients in metabolic control analysis are examined with respect to their theoretical consistency and practical applicability. We suggest agreement upon a definition for control coefficients which is clearly distinct from that for response coefficients, in such a way that the former describe inherent properties of the metabolic system while the latter refer to the influence of special parameters. Advantages and drawbacks of using normalized or non-normalized control coefficients are studied. It is shown that normalized control coefficients have the advantage of being invariant to a different rescaling of the particular fluxes. We demonstrate that some problems are easier to tackle if the consistency of time-independent control coefficients with their time-dependent counterparts is taken into account. It is shown that the matrix of flux control coefficients is an indempotent matrix. This allows an interpretation in terms of the transduction of the effect of parameter perturbations. Several aspects of the experimental measurement of control coefficients are discussed, with special reference to the different definitions.     

Production of chemicals using dynamic control of metabolic fluxes

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