Determination of control coefficients in intact metabolic systems

On the relevance of precision autophagy flux control in vivo - Points of departure for clinical translation

Macroautophagy (which we will call autophagy hereafter) is a critical intracellular bulk degradation system that is active at basal rates in eukaryotic cells. This process is embedded in the homeostasis of nutrient availability and cellular metabolic demands, degrading primarily long-lived proteins and specific organelles.. Autophagy is perturbed in many pathologies, and its manipulation to enhance or inhibit this pathway therapeutically has received considerable attention. Although better probes are being developed for a more precise readout of autophagic activity in vitro and increasingly in vivo, many questions remain. These center in particular around the accurate measurement of autophagic flux and its translation from the in vitro to the in vivo environment as well as its clinical application. In this review, we highlight key aspects that appear to contribute to stumbling blocks on the road toward clinical translation and discuss points of departure for reaching some of the desired goals. We discuss techniques that are well aligned with achieving desirable spatiotemporal resolution to gather data on autophagic flux in a multi-scale fashion, to better apply the existing tools that are based on single-cell analysis and to use them in the living organism. We assess how current techniques may be used for the establishment of autophagic flux standards or reference points and consider strategies for a conceptual approach on titrating autophagy inducers based on their effect on autophagic flux . Finally, we discuss potential solutions for inherent controls for autophagy analysis, so as to better discern systemic and tissue-specific autophagic flux in future clinical applications.Abbreviations: GFP: Green fluorescent protein; J: Flux; MAP1LC3/LC3: Microtubule-associated protein 1 light chain 3; nA: Number of autophagosomes; TEM: Transmission electron microscopy; τ: Transition time.

Kinetic modelling of the Zymomonas mobilis Entner-Doudoroff pathway: insights into control and functionality

Zymomonas mobilis, an ethanol-producing bacterium, possesses the Entner-Doudoroff (E-D) pathway, pyruvate decarboxylase and two alcohol dehydrogenase isoenzymes for the fermentative production of ethanol and carbon dioxide from glucose. Using available kinetic parameters, we have developed a kinetic model that incorporates the enzymic reactions of the E-D pathway, both alcohol dehydrogenases, transport reactions and reactions related to ATP metabolism. After optimizing the reaction parameters within likely physiological limits, the resulting kinetic model was capable of simulating glycolysis in vivo and in cell-free extracts with good agreement with the fluxes and steady-state intermediate concentrations reported in previous experimental studies. In addition, the model is shown to be consistent with experimental results for the coupled response of ATP concentration and glycolytic flux to ATPase inhibition. Metabolic control analysis of the model revealed that the majority of flux control resides not inside, but outside the E-D pathway itself, predominantly in ATP consumption, demonstrating why past attempts to increase the glycolytic flux through overexpression of glycolytic enzymes have been unsuccessful. Co-response analysis indicates how homeostasis of ATP concentrations starts to deteriorate markedly at the highest glycolytic rates. This kinetic model has potential for application in Z. mobilis metabolic engineering and, since there are currently no E-D pathway models available in public databases, it can serve as a basis for the development of models for other micro-organisms possessing this type of glycolytic pathway.

Modular kinetic analysis

Modularization is an important strategy to tackle the study of complex biological systems. Modular kinetic analysis (MKA) is a quantitative method to extract kinetic information from such a modularized system that can be used to determine the control and regulatory structure of the system, and to pinpoint and quantify the interaction of effectors with the system. The principles of the method are described, and the relation with metabolic control analysis is discussed. Examples of application of MKA are given.

Models of the human metabolic network: aiming to reconcile metabolomics and genomics

The metabolic syndrome, inborn errors of metabolism, and drug-induced changes to metabolic states all bring about a seemingly bewildering array of alterations in metabolite concentrations; these often occur in tissues and cells that are distant from those containing the primary biochemical lesion. How is it possible to collect sufficient biochemical information from a patient to enable us to work backwards and pinpoint the primary lesion, and possibly treat it in this whole human metabolic network? Potential analyses have benefited from modern methods such as ultra-high-pressure liquid chromatography, mass spectrometry, nuclear magnetic resonance spectroscopy, and more. A yet greater challenge is the prediction of outcomes of possible modern therapies using drugs and genetic engineering. This exposes the notion of viewing metabolism from a completely different perspective, with focus on the enzymes, regulators, and structural elements that are encoded by genes that specify the amino acid sequences, and hence encode the various interactions, be they regulatory or catalytic. The mainstream view of metabolism is being challenged, so we discuss here the reconciling of traditionally quantitative chemocentric metabolism with the seemingly 'parameter-free' genomic description, and vice versa.

Comparison of multiple gene assembly methods for metabolic engineering

A universal, rapid DNA assembly method for efficient multigene plasmid construction is important for biological research and for optimizing gene expression in industrial microbes. Three different approaches to achieve this goal were evaluated. These included creating long complementary extensions using a uracil-DNA glycosylase technique, overlap extension polymerase chain reaction, and a SfiI-based ligation method. SfiI ligation was the only successful approach for assembling large DNA fragments that contained repeated homologous regions. In addition, the SfiI method has been improved over a similar, previous published technique so that it is more flexible and does not require polymerase chain reaction to incorporate adaptors. In the present study, Saccharomyces cerevisiae genes TAL1, TKL1, and PYK1 under control of the 6-phosphogluconate dehydrogenase promoter were successfully ligated together using multiple unique SfiI restriction sites. The desired construct was obtained 65% of the time during vector construction using four-piece ligations. The SfiI method consists of three steps: first a SfiI linker vector is constructed, whose multiple cloning site is flanked by two three-base linkers matching the neighboring SfiI linkers on SfiI digestion; second, the linkers are attached to the desired genes by cloning them into SfiI linker vectors; third, the genes flanked by the three-base linkers, are released by SfiI digestion. In the final step, genes of interest are joined together in a simple one-step ligation.

Shuffling of promoters for multiple genes to optimize xylose fermentation in an engineered Saccharomyces cerevisiae strain

We describe here a useful metabolic engineering tool, multiple-gene-promoter shuffling (MGPS), to optimize expression levels for multiple genes. This method approaches an optimized gene overexpression level by fusing promoters of various strengths to genes of interest for a particular pathway. Selection of these promoters is based on the expression levels of the native genes under the same physiological conditions intended for the application. MGPS was implemented in a yeast xylose fermentation mixture by shuffling the promoters for GND2 and HXK2 with the genes for transaldolase (TAL1), transketolase (TKL1), and pyruvate kinase (PYK1) in the Saccharomyces cerevisiae strain FPL-YSX3. This host strain has integrated xylose-metabolizing genes, including xylose reductase, xylitol dehydrogenase, and xylulose kinase. The optimal expression levels for TAL1, TKL1, and PYK1 were identified by analysis of volumetric ethanol production by transformed cells. We found the optimal combination for ethanol production to be GND2-TAL1-HXK2-TKL1-HXK2-PYK1. The MGPS method could easily be adapted for other eukaryotic and prokaryotic organisms to optimize expression of genes for industrial fermentation.

Measuring in vivo elasticities of Calvin cycle enzymes: network structure and patterns of modulations

To measure the kinetics of enzymes, the proteins are usually assayed in vitro after isolation from their parent organisms. We make an attempt to show how one might determine enzyme elasticities in an intact system by a multiple modulation approach. Certain target enzymes are modulated in their activities and the changes in metabolite concentrations and flux rates upon the modulations are used to calculate the enzyme elasticities. Central to this approach is that the modulations must be independent of each other, and an algorithm is developed for finding all independent modulations that allow determining the elasticities of a given enzyme. This approach is applied to a mass-action model of the Calvin cycle. The goal is to determine the elasticities of as many enzymes as possible by modulating the activities of as few of them as possible. It is shown that the elasticities of 20 (out of 22) Calvin cycle enzymes can be determined by modulating just five reactions. Moreover, visualization of independence of modulations may be used to decompose the Calvin cycle into several sections that are independent of each other regarding flow of matter and information.

Modulation of metabolite concentrations with no net effect on fluxes

The concentration of a metabolite in a metabolic system can be varied without affecting any other concentrations or any fluxes by varying the concentrations of two inhibitors, one a competitive inhibitor of the enzyme that produces the metabolite, the other a competitive inhibitor of the enzyme that consumes it. The two concentrations need to be varied in opposite directions in such a way that the they add up to 100% when each is expressed as a percentage of the concentration that gives the desired flux in the absence of the other. The general approach can be extended to systems in which the inhibited enzymes do not catalyse consecutive reactions.

Metabolomics--the link between genotypes and phenotypes

Metabolites are the end products of cellular regulatory processes, and their levels can be regarded as the ultimate response of biological systems to genetic or environmental changes. In parallel to the terms 'transcriptome' and proteome', the set of metabolites synthesized by a biological system constitute its 'metabolome'. Yet, unlike other functional genomics approaches, the unbiased simultaneous identification and quantification of plant metabolomes has been largely neglected. Until recently, most analyses were restricted to profiling selected classes of compounds, or to fingerprinting metabolic changes without sufficient analytical resolution to determine metabolite levels and identities individually. As a prerequisite for metabolomic analysis, careful consideration of the methods employed for tissue extraction, sample preparation, data acquisition, and data mining must be taken. In this review, the differences among metabolite target analysis, metabolite profiling, and metabolic fingerprinting are clarified, and terms are defined. Current approaches are examined, and potential applications are summarized with a special emphasis on data mining and mathematical modelling of metabolism.

Metabolomics--the link between genotypes and phenotypes

Metabolites are the end products of cellular regulatory processes, and their levels can be regarded as the ultimate response of biological systems to genetic or environmental changes. In parallel to the terms 'transcriptome' and proteome', the set of metabolites synthesized by a biological system constitute its 'metabolome'. Yet, unlike other functional genomics approaches, the unbiased simultaneous identification and quantification of plant metabolomes has been largely neglected. Until recently, most analyses were restricted to profiling selected classes of compounds, or to fingerprinting metabolic changes without sufficient analytical resolution to determine metabolite levels and identities individually. As a prerequisite for metabolomic analysis, careful consideration of the methods employed for tissue extraction, sample preparation, data acquisition, and data mining must be taken. In this review, the differences among metabolite target analysis, metabolite profiling, and metabolic fingerprinting are clarified, and terms are defined. Current approaches are examined, and potential applications are summarized with a special emphasis on data mining and mathematical modelling of metabolism.

Building the cellular puzzle: control in multi-level reaction networks

Quantitative conceptual tools dealing with control and regulation of cellular processes have been mostly developed for and applied to the pathways of intermediary metabolism. Yet, cellular processes are organized in different levels, metabolism forming the lowest level in a cascade of processes. Well-known examples are the DNA-mRNA-enzyme-metabolism cascade and the signal transduction cascades consisting of covalent modification cycles. The reaction network that constitutes each level can be viewed as a "module" in which reactions are linked by mass transfer. Although in principle all of these cellular modules are ultimately linked by mass transfer, in practice they can often be regarded as "isolated" from each other in terms of mass transfer. Here modules can interact with each other only by means of regulatory or catalytic effects-a chemical species in one module may affect the rate of a reaction in another module by binding to an enzyme or transport system or by acting as a catalyst. This paper seeks to answer two questions about the control and regulation of such multi-level reaction networks: (i) How can the control properties of the system as a whole be expressed in terms of the control properties of individual modules and the effects between modules? (ii) How do the control properties of a module in its isolated state change when it is embedded in the whole system through its connections with the other modules? In order to answer these questions a quantitative theoretical framework is developed and applied to systems containing two, three or four fully interacting modules; it is shown how it can be extended in principle to n modules. This newly developed theory therefore makes it possible to quantitatively dissect intermodular, internal and external regulation in multi-level systems.

A functional genomics strategy that uses metabolome data to reveal the phenotype of silent mutations

A large proportion of the 6,000 genes present in the genome of Saccharomyces cerevisiae, and of those sequenced in other organisms, encode proteins of unknown function. Many of these genes are "silent, " that is, they show no overt phenotype, in terms of growth rate or other fluxes, when they are deleted from the genome. We demonstrate how the intracellular concentrations of metabolites can reveal phenotypes for proteins active in metabolic regulation. Quantification of the change of several metabolite concentrations relative to the concentration change of one selected metabolite can reveal the site of action, in the metabolic network, of a silent gene. In the same way, comprehensive analyses of metabolite concentrations in mutants, providing "metabolic snapshots," can reveal functions when snapshots from strains deleted for unstudied genes are compared to those deleted for known genes. This approach to functional analysis, using comparative metabolomics, we call FANCY-an abbreviation for functional analysis by co-responses in yeast.

Redirection of the respiro-fermentative flux distribution in Saccharomyces cerevisiae by overexpression of the transcription factor Hap4p

Reduction of aerobic fermentation on sugars by altering the fermentative/oxidative balance is of significant interest for optimization of industrial production of Saccharomyces cerevisiae. Glucose control of oxidative metabolism in baker's yeast is partly mediated through transcriptional regulation of the Hap4p subunit of the Hap2/3/4/5p transcriptional activator complex. To alleviate glucose repression of oxidative metabolism, we constructed a yeast strain with constitutively elevated levels of Hap4p. Genetic analysis of expression levels of glucose-repressed genes and analysis of respiratory capacity showed that Hap4p overexpression (partly) relieves glucose repression of respiration. Analysis of the physiological properties of the Hap4p overproducer in batch cultures in fermentors (aerobic, glucose excess) has shown that the metabolism of this strain is more oxidative than in the wild-type strain, resulting in a significant reduced ethanol production and improvement of growth rate and a 40% gain in biomass yield. Our results show that modification of one or more transcriptional regulators can be a powerful and a widely applicable tool for redirection of metabolic fluxes in microorganisms.

'Slave' metabolites and enzymes. A rapid way of delineating metabolic control

Although control of fluxes and concentrations tends to be distributed rather than confined to a single rate-limiting enzyme, the extent of control can differ widely between enzymes in a metabolic network. In some cases, there are enzymes that lack control completely. This paper identifies one surprising origin of such lack of control: If, in a metabolic system, there is a metabolite that affects the catalytic rate of only one enzyme, the corresponding enzyme cannot control any metabolic variable other than the concentration of that metabolite. We call such enzymes 'slave enzymes', and the corresponding metabolites 'slave metabolites'. Implications of the existence of slave enzymes for the control properties of enzymes further down the metabolic pathway are discussed and examined for the glycolytic pathway of yeast. Inadvertent assumptions in metabolic models may cause the latter incorrectly to calculate absence of metabolic control. The phenomenon of slave enzymes may well be important in enhancing metabolic signal transduction.

Internal regulation of ATP turnover, glycolysis and oxidative phosphorylation in rat hepatocytes

Previously [Ainscow, E.K. & Brand, M.D. (1999) Eur. J. Biochem. 263, 671-685], top-down control analysis was used to describe the control pattern of energy metabolism in rat hepatocytes. The system was divided into nine reaction blocks (glycogen breakdown, glucose release, glycolysis, lactate production, NADH oxidation, pyruvate oxidation, mitochondrial proton leak, mitochondrial phosphorylation and ATP consumption) linked by five intermediates (intracellular glucose 6-phosphate, pyruvate and ATP levels, cytoplasmic NADH/NAD ratio and mitochondrial membrane potential). The kinetic responses (elasticities) of reaction blocks to intermediates were determined and used to calculate control coefficients. In the present paper, these elasticities and control coefficients are used to quantify the internal regulatory pathways within the cell. Flux control coefficients were partitioned to give partial flux control coefficients. These describe how strongly one block of reactions controls the flux through another via its effects on the concentration of a particular intermediate. Most flux control coefficients were the sum of positive and negative partial effects acting through different intermediates; these partial effects could be large compared to the final control strength. An important result was the breakdown of the way ATP consumption controlled respiration: changes in ATP level were more important than changes in mitochondrial membrane potential in stimulating oxygen consumption when ATP consumption increased. The partial internal response coefficients to changes in each intermediate were also calculated; they describe how steady state concentrations of intermediates are maintained. Increases in mitochondrial membrane potential were opposed mostly by decreased supply, whereas increases in glucose-6-phosphate, NADH/NAD and pyruvate were opposed mostly by increased consumption. Increases in ATP were opposed significantly by both decreased supply and increased consumption.

Comparison of control analysis data using different approaches: modelling and experiments with muscle extract

Experimental and model studies have been performed to characterize the control properties of hexokinase and phosphofructokinase in muscle glycolysis and to examine the nature of error associated with experimental flux control coefficient determinations. Different approaches of metabolic control analysis, classical titration, co-response analysis and kinetic modelling indicated that flux control coefficients could be reliably estimated experimentally for the upper part of glycolysis. The kinetic parameters applied to construct the mathematical model were determined in muscle extract under similar conditions used for flux studies. If the kinetic parameters of commercial enzymes are introduced into the model the control analysis data cannot be trusted. Co-response analysis can also be successfully applied to determination of the flux control coefficients of the system. However, the involvement of a rapid-equilibrium enzyme, such as glucose 6-phosphate isomerase, could result in estimation errors for the relevant co-response coefficients that are propagated into the elasticity matrix. If the co-response coefficients related to isomerase activity are replaced by the values obtained by kinetic modelling, the values of elasticities are correct. Our data also suggest that in the upper part of glycolysis hexokinase mainly controls the pathway flux whereas phosphofructokinase exerts dominant control on the turnover of internal metabolite stocks inside the system.

Generalization of the double-modulation method for in situ determination of elasticities

The double-modulation method [Kacser and Burns (1979) Biochem. Soc. Trans. 7, 1149-1160] was the first method proposed for determining elasticities in situ. It is based on measuring changes in steady-state metabolite concentrations and fluxes induced by parameter modulations. It has the important advantage that it is not necessary to know the values of the changes in the parameters. Here we develop a matrix formulation of the double-modulation method that allows it to be applied to metabolic systems of any structure and size. It also shows which parameters need to be modulated and which variables need to be measured in order to calculate the elasticities that correspond to particular rates. Some suggestions for the practical implementation of the method are given, including various ways of testing the reliability of the results.

Metabolic regulation: a control analytic perspective

A possible basis for a quantitative theory of metabolic regulation is outlined. Regulation is defined here as the alteration of reaction properties to augment or counteract the mass-action trend in a network reactions. In living systems the enzymes that catalyze these reactions are the "handles" through which such alteration is effected. It is shown how the elasticity coefficients of an enzyme-catalyzed reaction with respect to substrates and products are the sum of a mass-action term and a regulatory kinetic term; these coefficients therefore distinguish between mass-action effects and regulatory effects and are recognized as the key to quantifying regulation. As elasticity coefficients are also basic ingredients of metabolic control analysis, it is possible to relate regulation to such concepts as control, signalling, stability, and homeostasis. The need for care in the choice of relative or absolute changes when considering questions of metabolic regulation is stressed. Although the concepts are illustrated in terms of a simple coupled reaction system, they apply equally to more complex systems. When such systems are divided into reaction blocks, co-response coefficients can be used to measure the elasticities of these blocks.

Composite control of cell function: metabolic pathways behaving as single control units

This paper shows that under some conditions the control exerted by a part of a metabolic network (a pathway) on a flux or concentration in any other part can be described through a single (overall) control coefficient. This has the following implications: (i) the relative contributions of a pathway enzyme to the regulation of the pathway (output) flux and of any flux or concentration outside are identical; therefore, the control analysis of the pathway 'in isolation' allows one to determine the control exerted by any pathway enzyme on the rest of the cell by estimation of the control efficient of just one, arbitrarily chosen enzyme; (ii) the relative control of any two metabolic variables outside the pathway (measured as the ratio of the control coefficients over these two variables outside) is the same for all pathway enzymes. These properties allow one to substitute effectively a pathway by a single (super)reaction and make it possible to consider such a pathway as a metabolic unit within the cellular enzyme network.

Control of metabolic pathways by time-scale separation

The bases underlying the distribution of metabolic control have been elusive, even though many intuitive arguments exist. To analyze this problem, we have applied the structural properties of the control coefficients to systems in which the eigenvalues of the Jacobian of the system are widely separated, that is, systems with time-scale separation. We show that time-scale separation is an effective way to localize metabolic control to only a few enzymes. To achieve time-scale separation, the cell can overproduce most of the enzymes relative to the required activity for the steady state, and control the expression level of only a few enzymes, provided that the overexpressed enzymes do not cause adverse effects. The overexpressed enzymes are responsible for the small response times of the system, and the reactions catalyzed by them are termed 'fast' reactions. The metabolite concentration control coefficients of the 'fast' reactions are always small compared with the 'slow' reactions. Furthermore, the 'fast' reactions do not have effective control on the overall flux. However, the 'fast' reactions may compete with each other at a branch point, leading to significant control coefficients for fluxes to the branches. These results are useful in justifying lumping of 'fast' reactions in mathematical modelling or in the experimental determination of control coefficients. The theoretical results are derived under the assumption that the system possesses a unique, asymptotically stable steady-state and that the reaction steps of the system under analysis are well represented by linear kinetics around the steady state. The application of the results presented in this article are demonstrated with three illustrative examples.

The sum of flux control coefficients in the electron-transport chain of mitochondria

The sum of the flux control coefficients for group-transfer reactions such as electron transport has been proposed to be two when the coefficients are calculated from experiments in which the concentrations of the electron carriers are changed (CE) but one when they are calculated from changes in the rates of the electron-transfer processes (Cv). We tested this proposal using electron transport in uncoupled beef heart, potato tuber and rat liver mitochondria. First, with ascorbate plus N,N,N',N"-tetramethyl-p-phenylenediamine as substrate, the CE flux control coefficients of ascorbate, N,N,N',N"-tetramethyl-p-phenylenediamine, mitochondria and oxygen over electron-transport rate were measured by direct titration of the concentrations of these electron carriers. CE values were close to zero, one, one and zero, respectively, giving a sum of CE flux control coefficients of approximately two. At higher concentrations of N,N,N',N'-tetramethyl-p-phenylenediamine, its CE control decreased and the sum decreased towards one as predicted. Secondly, the Cv control coefficients of groups of electron-transfer processes with succinate or ascorbate plus N,N,N',N'-tetramethyl-p-phenylenediamine as substrate were measured. This was achieved by measuring the effects of KCN (or malonate or N,N,N',N'-tetramethyl-p-phenylenediamine) on system flux when intermediates were allowed to relax and on local flux when intermediates were held constant. The Cv flux control coefficients were calculated as the ratio of the effects on system flux and on local flux. The sum of the Cv flux control coefficients was approximately one. Whether a sum of one or a sum of two was obtained depended entirely on the definition of control coefficients that was used, since either sum was obtained from the same set of data depending on the method of calculation. Both definitions are valid, but they give different information. It is important to be aware of which definition is being used when analysing control coefficients in electron-transport chains and other group-transfer systems.

Effects of cadmium on the control and internal regulation of oxidative phosphorylation in potato tuber mitochondria

The effect of cadmium on the distribution of control over oxidative phosphorylation in potato tuber mitochondria was quantified by measuring control coefficients using top-down metabolic control analysis. Oxidative phosphorylation was divided into three subsystems, namely substrate oxidation, the phosphorylation reactions and the proton leak. The control exerted by each of these subsystems over the system fluxes, the value of the protonmotive force and the effective P/O ratio was quantified in the presence of different concentrations of free cadmium (up to 21 microM). Cadmium is known to stimulate the proton leak and inhibit the substrate oxidation reactions, but it had little effect on the distribution of control over the system variables except to shift the pattern to lower rates. Control exerted by particular subsystems appeared to change or to stay the same as cadmium was varied, depending on whether the control coefficients were presented as a function of respiration rate or protonmotive force. The regulatory strength of protonmotive force on the system variables was also calculated, as partial internal response coefficients. These coefficients changed with ATP turnover rate and with cadmium concentration, showing how the internal regulation of oxidative phosphorylation shifts under different conditions. The values of control coefficients and partial internal response coefficients show where control lies and how intermediates regulate the system variables under different conditions of ATP demand and external effector (i.e. cadmium) concentration. However, they are not useful for identifying the sites of action of external effectors, for which elasticity and regulation analysis must be used.