Total cell protein concentration as an evolutionary constraint on the metabolic control distribution in cells.

Cell protein occupies 15-35% of cell volume. This level is argued to be the maximum compatible with cell function. Because of this constraint, selection pressure during evolution is likely to have maximized pathway fluxes for minimum total protein level. Pathways optimized in this way are shown to have the following characteristics: (1) the "simple" flux control coefficients of all enzymes are equal, (2) the normal flux control coefficients depend on the relative kinetic constants of the enzymes, such that enzymes with low specific activity are present at relatively high levels and have high flux control, (3) the normal flux control coefficients are proportional to enzyme levels. A single rate limiting step located at the first step in a pathway is likely to be inefficient in terms of protein levels, and the major metabolic pathways are therefore expected to have control distributed throughout the pathway. This has important implications for metabolic control.     

Modeling cancer glycolysis

Most cancer cells exhibit an accelerated glycolysis rate compared to normal cells. This metabolic change is associated with the over-expression of all the pathway enzymes and transporters (as induced by HIF-1α and other oncogenes), and with the expression of hexokinase (HK) and phosphofructokinase type 1 (PFK-1) isoenzymes with different regulatory properties. Hence, a control distribution of tumor glycolysis, modified from that observed in normal cells, can be expected. To define the control distribution and to understand the underlying control mechanisms, kinetic models of glycolysis of rodent AS-30D hepatoma and human cervix HeLa cells were constructed with experimental data obtained here for each pathway step (enzyme kinetics; steady-state pathway metabolite concentrations and fluxes). The models predicted with high accuracy the fluxes and metabolite concentrations found in living cancer cells under physiological O(2) and glucose concentrations as well as under hypoxic and hypoglycemic conditions prevailing during tumor progression. The results indicated that HK≥HPI>GLUT in AS-30D whereas glycogen degradation≥GLUT>HK in HeLa were the main flux- and ATP concentration-control steps. Modeling also revealed that, in order to diminish the glycolytic flux or the ATP concentration by 50%, it was required to decrease GLUT or HK or HPI by 76% (AS-30D), and GLUT or glycogen degradation by 87-99% (HeLa), or decreasing simultaneously the mentioned steps by 47%. Thus, these proteins are proposed to be the foremost therapeutic targets because their simultaneous inhibition will have greater antagonistic effects on tumor energy metabolism than inhibition of all other glycolytic, non-controlling, enzymes.     

Sensitivity of pathway rate to activities of substrate-cycle enzymes: application to gluconeogenesis and glycolysis

In a study of metabolic regulation, it is frequently useful to consider the degree to which an enzyme can influence the rate of its pathway. The most productive expression of rate-controlling influence is the fractional change in pathway rate per fractional change in enzyme activity (called control strength or sensitivity coefficient). We have developed a system for considering how a substrate-cycle enzyme's control strength depends on its flux and reaction order and on related features of other enzymes of its pathway. We have applied this system to the gluconeogenic pathway of rat liver and the glycolytic pathway of bovine sperm, where enough fluxes and reaction orders have been published to allow valid estimates of several control strengths. In normal fed animals where gluconeogenesis is slow and unidirectional substrate-to-product and product-to-substrate fluxes are comparable, all substrate-cycle limbs have very high and similar control strengths regardless of their flux rates and positions in the pathway. The activity of a step affects all substrate-cycle control strengths similarly as it affects unidirectional end-to-end fluxes relative to net rate. Control strengths of non-substrate-cycle enzymes are negligible compared to those of substrate cycles. In fasting animals, on the other hand, where unidirectional Pyr----Glc flux is much greater than Glc----Pyr flux, upstream enzymes (near Pyr) have a regulatory advantage over downstream enzymes (near Glc). In this circumstance, control strength of each substrate-cycle enzyme is inversely related to rate limitingness between its substrate and the pathway substrate. Because the Pyr/PEP cycle is significantly rate limiting, the control strength of the Pyr----PEP limb is much greater than that of pyruvate kinase and all downstream enzymes. In the glycolytic pathway of bovine sperm, strong product inhibition of hexokinase detracts greatly from its rate limitingness and control strength, which are very small despite its position at the beginning of the pathway and its large free energy. Because the glucose-transport-hexokinase segment is not rate limiting, phosphofructo 1-kinase has almost as much control strength as it would have as the first enzyme of the pathway, and because the F6P/FDP cycle is only moderately rate limiting, Fru-1,6-P2ase and enzymes further downstream have substantial control strengths. When glycolysis is accelerated by stimulation of phosphofructo 1-kinase, control strength shifts from phosphofructo-1-kinase and all downstream enzymes to the transporthesokinase segment.(ABSTRACT TRUNCATED AT 400 WORDS)     

Flux control analysis for biphenyl metabolism by Rhodococcus pyridinovorans R04

The flux control coefficients of the four enzymes involved in the upper pathway of biphenyl degradation were determined from transient metabolite concentrations. The first enzyme was indicated as the major rate-limiting step of the pathway with a control coefficient of 0.48. The flux control coefficients of the other three enzymes were 0.03, 0.23 and 0.27, respectively. This is the first experimental evidence of the control step in the pathway of biphenyl degradation using metabolic control analysis.     

Strategies for Manipulating Metabolic Fluxes in Biotechnology

Strategies for biotechnologically manipulating metabolic fluxes are critically examined in relation to a model system. The common idea of first identifying the rate-limiting enzyme in the biosynthetic pathway to a desired end-product, and then increasing its activity, is shown to be completely ineffective; such manipulation typically produces only trivial changes in flux. Manipulating the activities of all of the enzymes in a biosynthetic pathway by amounts calculated to increase a desired flux while leaving all other fluxes and all concentrations unchanged is potentially effective, and can be applied to any system without regard to its regulatory design. however, it requires accurate knowledge of the initial state of the system and the ability to make precise changes to numerous activities. The classical information about the regulatory mechanisms that exist in living organisms suggests that one can make much simpler manipulations, involving only the steps that remove the desired end-product, with almost equally satisfactory results.     

Control of gluconeogenesis in rat liver cells. Flux control coefficients of the enzymes in the gluconeogenic pathway in the absence and presence of glucagon.

We have used control analysis to quantify the distribution of control in the gluconeogenic pathway in liver cells from starved rats. Lactate and pyruvate were used as gluconeogenic substrates. The flux control coefficients of the various enzymes in the gluconeogenic pathway were calculated from the elasticity coefficients of the enzymes towards their substrates and products and the fluxes through the different branches in the pathway. The elasticity coefficients were either calculated from gamma/Keq. ratios (where gamma is the mass-action ratio and Keq. is the equilibrium constant) and enzyme-kinetic data or measured experimentally. It is concluded that the gluconeogenic enzyme pyruvate carboxylase and the glycolytic enzyme pyruvate kinase play a central role in control of gluconeogenesis. If pyruvate kinase is inactive, gluconeogenic flux from lactate is largely controlled by pyruvate carboxylase. The low elasticity coefficient of pyruvate carboxylase towards its product oxaloacetate minimizes control by steps in the gluconeogenic pathway located after pyruvate carboxylase. This situation occurs when maximal gluconeogenic flux is required, i.e. in the presence of glucagon. In the absence of the hormone, when pyruvate kinase is active, control of gluconeogenesis is distributed among many steps, including pyruvate carboxylase, pyruvate kinase, fructose-1,6-bisphosphatase and also steps outside the classic gluconeogenic pathway such as the adenine-nucleotide translocator.     

Systems analysis of the tricarboxylic acid cycle in Dictyostelium discoideum. II. Control analysis.

A steady-state computer model of the tricarboxylic cycle in Dictyostelium discoideum was analyzed using metabolic control theory. The steady state had variations of less than 0.04% over the last half of the simulation for both metabolite concentrations and fluxes. Metabolite and flux control coefficients were determined by varying enzymatic activities within 2% of their initial values and simulating the responses of metabolite concentrations and fluxes to these changes. Under these conditions, summation properties were met for most metabolite and all flux control coefficients. Maximum flux control coefficients were found for succinate dehydrogenase (0.35), malic enzyme (0.24), and malate dehydrogenase (-0.18). Comparable control was found for the reaction supplying pyruvate (0.14) and for the sum of the input amino acids (0.43), which serve as an energy source for D. discoideum. The time-dependent processes by which a new steady state was established were examined after increasing malic enzyme or malate dehydrogenase activities. This provided a method for an analysis of the mechanisms by which the observed control coefficients were generated. In addition, the effects of increasing the stimuli within 5-20% of the original enzyme activity were examined. Under these conditions, more typical of experimental stimuli and measurable responses, the metabolic model failed to return to steady state, and thus summation properties were not met. Whether "true" steady states ever occur or whether metabolic control theory can be applied in vivo is discussed.     

The matrix method of metabolic control analysis: its validity for complex pathway structures

The sensitivities of the variables of a metabolic system (such as fluxes and concentrations) to variations in enzyme concentration are expressed in metabolic control analysis as control coefficients. The matrix method is a system of writing matrix equations that generate expressions for the control coefficients in terms of the characteristics of the components (principally the enzymes). Previously, the matrix method has been considered in terms of simple pathway structures; here we justify its applicability to complex pathways, such as those with multiple branches. It is shown that this requires modification of the branch point relationship to take account of changes of flux along the limbs of the branch and of stoichiometric factors. The method of deriving the flux control coefficients with respect to different fluxes in the system is extended to cope with these circumstances.     

Regulatory role of acetylation on enzyme activity and fluxes of energy metabolism pathways

BackgroundMost of the enzymes involved in the central carbon metabolism are acetylated in Lys residues. It has been claimed that this covalent modification represents a novel regulatory mechanism by which both enzyme/transporter activities and pathway fluxes can be modulated.MethodsTo establish which enzymes are regulated by acetylation, a systematic experimental analysis of activities and acetylation profile for several energy metabolism enzymes and pathway fluxes was undertaken in cells and mitochondria.ResultsThe majority of the glycolytic and neighbor enzymes as well as mitochondrial enzymes indeed showed Lys-acetylation, with GLUT1, HPI, CS, ATP synthase displaying comparatively lower acetylation patterns. The incubation of cytosolic and mitochondrial fractions with recombinant Sirt-3 produced lower acetylation signals, whereas incubation with acetyl-CoA promoted protein acetylation. Significant changes in acetylation levels of MDH and IDH-2 from rat liver mitochondria revealed no change in their activities. Similar observations were attained for the cytosolic enzymes from AS-30D and HeLa cells. A minor but significant (23%) increase in the AAT-MDH complex activity induced by acetylation was observed. To examine this question further, AS-30D and HeLa cells were treated with nicotinamide and valproic acid. These compounds promoted changes in the acetylation patterns of glycolytic proteins, although their activities and the glycolytic flux (as well as the OxPhos flux) revealed no clear correlation with acetylation.ConclusionAcetylation seems to play no predominant role in the control of energy metabolism enzyme activities and pathway fluxes.General significanceThe physiological function of protein acetylation on energy metabolism pathways remains to be elucidated.     

Metabolic design: how to engineer a living cell to desired metabolite concentrations and fluxes

A biotechnological aim of genetic engineering is to increase the intracellular concentration or secretion of valuable compounds, while making the other concentrations and fluxes optimal for viability and productivity. Efforts to accomplish this based on over-expression of the enzyme, catalyzing the so-called "rate-limiting step," have not been successful. Here we develop a method to determine the enzyme concentrations that are required to achieve such an aim. This method is called Metabolic Design Analysis and is based on the perturbation method and the modular ("top-down") approach-formalisms that were first developed for the analysis of biochemical regulation such as, Metabolic Control Analysis. Contrary to earlier methods, the desired alterations of cellular metabolism need not be small or confined to a single metabolite or flux. The limits to the alterations of fluxes and metabolite concentrations are identified. To employ Metabolic Design Analysis, only limited kinetic information concerning the pathway enzymes is needed.     

Experimental determination of control of glycolysis in Lactococcus lactis

The understanding of control of metabolic processes requires quantitative studies of the importance of the different enzymatic steps for the magnitude of metabolic fluxes and metabolite concentrations. An important element in such studies is the modulation of enzyme activities in small steps above and below the wild-type level. We review a genetic approach that is well suited for both Metabolic Optimization and Metabolic Control Analysis and studies on the importance of a number of glycolytic enzymes for metabolic fluxes in Lactococcus lactis. The glycolytic enzymes phosphofructokinase (PFK), glyceraldehyde-3-phosphate dehydrogenase (GAPDH), pyruvate kinase (PYK) and lactate dehydrogenase (LDH) are shown to have no significant control on the glycolytic flux in exponentially growing cells of L. lactis MG1363. Introduction of an uncoupled ATPase activity results in uncoupling of glycolysis from biomass production. With MG1363 growing in defined medium supplemented with glucose, the ATP demanding processes do not have a significant control on the glycolytic flux; it appears that glycolysis is running at maximal rate. It is likely that the flux control is distributed over many enzymes in L. lactis, but it cannot yet be excluded that one of the remaining glycolytic steps is a rate-limiting step for the glycolytic flux.     

Experimental and in silico analyses of glycolytic flux control in bloodstream form Trypanosoma brucei

A mathematical model of glycolysis in bloodstream form Trypanosoma brucei was developed previously on the basis of all available enzyme kinetic data (Bakker, B. M., Michels, P. A. M., Opperdoes, F. R., and Westerhoff, H. V. (1997) J. Biol. Chem. 272, 3207-3215). The model predicted correctly the fluxes and cellular metabolite concentrations as measured in non-growing trypanosomes and the major contribution to the flux control exerted by the plasma membrane glucose transporter. Surprisingly, a large overcapacity was predicted for hexokinase (HXK), phosphofructokinase (PFK), and pyruvate kinase (PYK). Here, we present our further analysis of the control of glycolytic flux in bloodstream form T. brucei. First, the model was optimized and extended with recent information about the kinetics of enzymes and their activities as measured in lysates of in vitro cultured growing trypanosomes. Second, the concentrations of five glycolytic enzymes (HXK, PFK, phosphoglycerate mutase, enolase, and PYK) in trypanosomes were changed by RNA interference. The effects of the knockdown of these enzymes on the growth, activities, and levels of various enzymes and glycolytic flux were studied and compared with model predictions. Data thus obtained support the conclusion from the in silico analysis that HXK, PFK, and PYK are in excess, albeit less than predicted. Interestingly, depletion of PFK and enolase had an effect on the activity (but not, or to a lesser extent, expression) of some other glycolytic enzymes. Enzymes located both in the glycosomes (the peroxisome-like organelles harboring the first seven enzymes of the glycolytic pathway of trypanosomes) and in the cytosol were affected. These data suggest the existence of novel regulatory mechanisms operating in trypanosome glycolysis.     

Theory of metabolism regulation: a complete system of equations for regulation coefficients

Basic quantitative parameters of control in a metabolic system are considered: control coefficients of enzymes with respect to metabolic fluxes and concentrations, and in the case when there are conservation laws, the response coefficients of metabolic fluxes and concentrations to changes in the conserved sums of metabolite concentrations (e. g. conserved moieties). Relationships are obtained which generalize the well known connectivity relations for the case of metabolites binding by conservation laws. Additional relationships are obtained which complement the set of connectivity relations up to the complete system of equations for determining all the control coefficients. The control coefficients are expressed through the enzyme elasticity coefficients, steady state metabolic fluxes and concentrations. Formulas are derived which express response coefficients of flux and concentrations through the enzyme control and elasticity coefficients and metabolite concentrations.     

Competition for enzymes in metabolic pathways: implications for optimal distributions of enzyme concentrations and for the distribution of flux control

The structures of biochemical pathways are assumed to be determined by evolutionary optimization processes. In the framework of mathematical models, these structures should be explained by the formulation of optimization principles. In the present work, the principle of minimal total enzyme concentration at fixed steady state fluxes is applied to metabolic networks. According to this principle there exists a competition of the reactions for the available amount of enzymes such that all biological functions are maintained. In states which fulfil these optimization criteria the enzyme concentrations are distributed in a non-uniform manner among the reactions. This result has consequences for the distribution of flux control. It is shown that the flux control matrix c, the elasticity matrix epsilon, and the vector e of enzyme concentrations fulfil in optimal states the relations c(T)e = e and epsilon(T)e = 0. Starting from a well-balanced distribution of enzymes the minimization of total enzyme concentration leads to a lowering of the SD of the flux control coefficients.     

Tryptophan biosynthesis in Saccharomyces cerevisiae: control of the flux through the pathway.

Enzyme derepression and feedback inhibition of the first enzyme are the regulatory mechanisms demonstrated for the tryptophan pathway in Saccharomyces cerevisiae. The relative contributions of the two mechanisms to the control of the flux through the pathway in vivo were analyzed by (i) measuring feedback inhibition of anthranilate synthase in vivo, (ii) determining the effect of regulatory mutations on the level of the tryptophan pool and the flux through the pathway, and (iii) varying the gene dose of individual enzymes of the pathway at the tetraploid level. We conclude that the flux through the pathway is adjusted to the rate of protein synthesis by means of feedback inhibition of the first enzyme by the end product, tryptophan. The synthesis of the tryptophan enzymes could not be repressed below a basal level by tryptophan supplementation of the media. The enzymes are present in excess. Increasing or lowering the concentration of individual enzymes had no noticeable influencing on the overall flux to tryptophan. The uninhibited capacity of the pathway could be observed both upon relieving feedback inhibition by tryptophan limitation and in feedback-insensitive mutants. It exceeded the rate of consumption of the amino acid on minimal medium by a factor of three. Tryptophan limitation caused derepression of four of the five tryptophan enzymes and, as a consequence, led to a further increase in the capacity of the pathway. However, because of the large reserve capacity of the "repressed" pathway, tryptophan limitation could not be imposed on wild-type cells without resorting to the use of analogs. Our results, therefore, suggest that derepression does not serve as an instrument for the specific regulation of the flux through the tryptophan pathway.     

Alcohol dehydrogenase controls the flux from ethanol into lipids in Drosophila larvae. A 13C NMR study

The dependence of the flux in the alcohol-degrading pathway on the activity of alcohol dehydrogenase was investigated in Drosophila larvae. Third-instar larvae were supplied with [2-13C]ethanol as a dietary carbon source. Specific carbon enrichments in de novo synthesized fatty acids were determined in vitro by means of 13C nuclear magnetic resonance spectroscopy. Carbon fluxes deduced from these enrichment patterns were correlated with the in vitro alcohol dehydrogenase activities in three different Adh genotypes in seven different strains. The flux control coefficient for alcohol dehydrogenase was shown to be approximately 1.0. This indicates that the alcohol dehydrogenase gene-enzyme system in Drosophila larvae can be a major target of natural selection.     

The influence of starvation and tryptophan administration on the metabolism of phenylalanine, tyrosine and tryptophan in isolated rat liver cells.

Liver cells from fed Sprague-Dawley rats metabolized phenylalanine, tyrosine and tryptophan at rates consistent with the known kinetic properties of the first enzymes of each pathway. Starvation of rats for 48 h did not increase the maximal activities of phenylalanine hydroxylase, tryptophan 2,3-dioxygenase and tyrosine aminotransferase in liver cell extracts, when results were expressed in terms of cellular DNA. Catabolic flux through the first two enzymes was unchanged; that through the aminotransferase was elevated relatively to enzyme activity. This is interpreted in terms of changes in the concentrations of 2-oxoglutarate and glutamate. Cells from tryptophan-treated animals exhibited significant increases in the catabolism of tyrosine and tryptophan, but not of phenylalanine. The activities of tyrosine aminotransferase and tryptophan 2,3-dioxygenase were also increased, although the changes in flux and enzyme activity did not correspond exactly. These results are discussed with reference to the control of aromatic amino acid catabolism in liver; the role of substrate concentration is emphasized.