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.     

Metabolic control analysis of the Trypanosoma cruzi peroxide detoxification pathway identifies tryparedoxin as a suitable drug target

Background

The principal oxidative-stress defense in the human parasite Trypanosoma cruzi is the tryparedoxin-dependent peroxide detoxification pathway, constituted by trypanothione reductase (TryR), tryparedoxin (TXN), tryparedoxin peroxidase (TXNPx) and tryparedoxin-dependent glutathione peroxidase A (GPxA). Here, Metabolic Control Analysis (MCA) was applied to quantitatively prioritize drug target(s) within the pathway by identifying its flux-controlling enzymes.

Methods

The recombinant enzymes were kinetically characterized at physiological pH/temperature. Further, the pathway was in vitro reconstituted using enzyme activity ratios and fluxes similar to those observed in the parasites; then, enzyme and substrate titrations were performed to determine their degree of control on flux. Also, kinetic characterization of the whole pathway was performed.

Results

Analyses of the kinetic properties indicated that TXN is the less efficient pathway enzyme derived from its high Km_app for trypanothione and low Vmax values within the cell. MCA established that the TXN–TXNPx and TXN–GPxA redox pairs controlled by 90–100% the pathway flux, whereas 10% control was attained by TryR. The Km_app values of the complete pathway for substrates suggested that the pathway flux was determined by the peroxide availability, whereas at high peroxide concentrations, flux may be limited by NADPH.

Conclusion

These quantitative kinetic and metabolic analyses pointed out to TXN as a convenient drug target due to its low catalytic efficiency, high control on the flux of peroxide detoxification and role as provider of reducing equivalents to the two main peroxidases in the parasite.

General Significance

MCA studies provide rational and quantitative criteria to select enzymes for drug-target development.     

Metabolic control analysis indicates a change of strategy in the treatment of cancer

Much of the search for the “magic cancer bullet” or “block buster” has followed the expectation of a single gene or protein as “the rate-limiting step” for tumor persistence. Examples continue to abound: EGFR, VEGFR, Akt/PI3K, HIF-1α, PHD, PDK, or FAS continue to be targeted individually. However, many such attempts to block a metabolic or signal transduction pathway by targeting, specifically, a single rate-limiting molecule have proven to be unsuccessful. Metabolic control analysis (MCA) of cancer cells has generated a generic explanation for this phenomenon: several steps share the control of energy metabolism (for glycolysis: glucose transporter, hexokinase, glycogen synthesis and ATP demand; for oxidative phosphorylation: respiratory complex I and ATP demand), i.e., there is no single “rate-limiting step”. Targeting a type of step that does not exist is unlikely to be a successful paradigm for continued research into drug targeting of cancer.MCA establishes how to determine, quantitatively, the degrees of control that the various enzymes in the intracellular network exert on vital flux (or function) and on the concentration of important metabolites, substituting for the intuitive, qualitative and most often erroneous concept of single rate-limiting step. Moreover, MCA helps to understand (i) the underlying mechanisms by which a given enzyme exerts high or low control, (ii) why the control of the pathway is shared by several pathway enzymes and transporters and (iii) what are the better sets of drug targets. Indeed, by applying MCA it should now be possible to identify the group of proteins (and genes) that should be modified to achieve a successful modulation of the intracellular networks of biotechnological or clinical relevance. The challenge is to move away from the design of drugs that specifically inhibit a single controlling step, towards unspecific drugs or towards drug mixtures, which may have multiple target sites in the most exacerbated, unique and controlling pathways in cancer cells. Successful nonspecific drugs should still be specific for the networks of cancer cells over those of normal cells and to establish such cell-type specificity within molecular non-specificity will continue to require sophisticated analyses. Clinical practice has anticipated the latter strategy of mixtures of drugs: combinations of anti-neoplastic drugs are already administered with encouraging results. Therefore, the most promising strategy for cancer treatment seems to be that of a multi-targeted, MCA-advised, therapy.     

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.     

Summation theorems for flux and concentration control coefficients of dynamic systems

Metabolic control analysis (MCA) was developed to quantify how system variables are affected by parameter variations in a system. In addition, MCA can express the global properties of a system in terms of the individual catalytic steps, using connectivity and summation theorems to link the control coefficients to the elasticity coefficients. MCA was originally developed for steady-state analysis and not all summation theorems have been derived for dynamic systems. A method to determine time-dependent flux and concentration control coefficients for dynamic systems by expressing the time domain as a function of percentage progression through any arbitrary fixed interval of time is reported. Time-dependent flux and concentration control coefficients of dynamic systems, provided that they are evaluated in this novel way, obey the same summation theorems as steady-state flux and concentration control coefficients, respectively.     

Flux modules in metabolic networks

The huge number of elementary flux modes in genome-scale metabolic networks makes analysis based on elementary flux modes intrinsically difficult. However, it has been shown that the elementary flux modes with optimal yield often contain highly redundant information. The set of optimal-yield elementary flux modes can be compressed using modules. Up to now, this compression was only possible by first enumerating the whole set of all optimal-yield elementary flux modes. We present a direct method for computing modules of the thermodynamically constrained optimal flux space of a metabolic network. This method can be used to decompose the set of optimal-yield elementary flux modes in a modular way and to speed up their computation. In addition, it provides a new form of coupling information that is not obtained by classical flux coupling analysis. We illustrate our approach on a set of model organisms.     

The Evolution of Control and Distribution of Adaptive Mutations in a Metabolic Pathway

In an attempt to understand whether it should be expected that some genes tend to be used disproportionately often by natural selection, we investigated two related phenomena: the evolution of flux control among enzymes in a metabolic pathway and properties of adaptive substitutions in pathway enzymes. These two phenomena are related by the principle that adaptive substitutions should occur more frequently in enzymes with greater flux control. Predicting which enzymes will be preferentially involved in adaptive evolution thus requires an evolutionary theory of flux control. We investigated the evolution of enzyme control in metabolic pathways with two models of enzyme kinetics: metabolic control theory (MCT) and Michaelis–Menten saturation kinetics (SK). Our models generate two main predictions for pathways in which reactions are moderately to highly irreversible: (1) flux control will evolve to be highly unequal among enzymes in a pathway and (2) upstream enzymes evolve a greater control coefficient then those downstream. This results in upstream enzymes fixing the majority of beneficial mutations during adaptive evolution. Once the population has reached high fitness, the trend is reversed, with the majority of neutral/slightly deleterious mutations occurring in downstream enzymes. These patterns are the result of three factors (the first of these is unique to the MCT simulations while the other two seem to be general properties of the metabolic pathways): (1) the majority of randomly selected, starting combinations of enzyme kinetic rates generate pathways that possess greater control for the upstream enzymes compared to downstream enzymes; (2) selection against large pools of intermediate substrates tends to prevent majority control by downstream enzymes; and (3) equivalent mutations in enzyme kinetic rates have the greatest effect on flux for enzymes with high levels of flux control, and these enzymes will accumulate adaptive substitutions, strengthening their control. Prediction 1 is well supported by available data on control coefficients. Data for evaluating prediction 2 are sparse but not inconsistent with this prediction.THEORETICAL research on the process of adaptation has focused primarily on describing the size and number of genetic changes underlying phenotypic change (Fisher 1930; Kimura 1983; Orr 1998, 2002, 2003). By contrast, comparatively little theoretical attention has been given to the question of whether certain genes or types of genes are preferentially involved in the process of adaptation. Yet the current debate over the relative importance of regulatory vs. structural genes in morphological evolution (Hoekstra and Coyne 2007; Stern and Orgogozo 2008) clearly indicates that this question is of interest to evolutionary biologists.One situation in which this question is pertinent is the evolution of characters that are influenced by the concentration of end products of metabolic pathways. Often change in end-product concentration can be achieved by substitutions in any one of several genes in the pathway. One example is the intensity of floral pigmentation. To a first approximation, final pigment concentration, and hence color intensity, can be viewed as being determined by the flux rate down the pigment biosynthetic pathway for a fixed time corresponding to the duration of floral development. More generally, any situation in which flux rate determines phenotype is likely to fall in this category. In such situations, metabolic control theory (MCT) (Kacser and Burns 1973) and similar approaches (Heinrich and Rapoport 1974; Savageau 1976) indicate that changes in flux can be achieved by changing the activity of any enzyme in the pathway. We seek to determine whether and, if so, why enzymes differ in the probability that they contribute to evolutionary change in pathway flux.It has been suggested as a general principle that enzymes with the greatest control over flux will be disproportionately involved in such evolutionary change (Hartl et al. 1985; Eanes 1999; Watt and Dean 2000). This argument is based on the theoretical expectation that the probability of fixation of an advantageous allele is roughly proportional to its selection coefficient (Hedrick 2000). Since mutations equivalent in terms of enzyme kinetic properties will have greater effects on flux, and hence on fitness, in enzymes with greater metabolic control, mutations in those enzymes will be substituted preferentially.While this argument is likely sound, it simply pushes back the question of which genes evolve preferentially to the question of which enzymes are expected to have greatest control over flux. Although we are unaware of any theoretical attempts to model the evolution of flux control, many authors have speculated about where in pathways control is expected to be highest.Kacser and Burns (1973) hypothesized that the magnitudes of flux control exerted by different enzymes may be very similar. This hypothesis was based on the result from MCT that in linear pathways, overall flux control can be shared by all enzymes. Since metabolic pathways often consist of many enzymes, each would be expected to have only a limited potential to influence flux. Subsequent theoretical analysis of this hypothesis demonstrated that a given flux is consistent with many different flux-control distributions, including, at one extreme, equal flux control by all enzymes and, at the other extreme, major control by one or a few enzymes and little control for all others (Mazat et al. 1996). However, the question of which of these possibilities, if any, are likely to be favored by selection has not been addressed.Another hypothesis, the epistatic or synergistic principle, predicts that control will be vested in a single enzyme at any given time, but will shift over time among enzymes (Dykhuizen et al. 1987; Keightley 1989; Bost et al. 2001) According to this hypothesis, starting from equal control among enzymes in the pathway, selection to increase (or decrease) flux will cause the activity of one enzyme to increase (decrease). This change results in a decrease (increase) in flux control for the enzyme that changes and an increase (decrease) in control for the other pathway enzymes, causing control to be unequally shared. While this argument seems plausible, there has been no analysis of whether over time all enzymes have an equal chance of having elevated control.Finally, Eanes'' (1999) review of enzyme polymorphisms found that control is often centered in enzymes at pathway branch points, which constitute the most upstream enzymes of their specific branch. Flowers et al. (2007) also demonstrated that branching enzymes tend to exhibit more adaptive substitutions than downstream enzymes as would be expected under the principle that evolutionary change will be concentrated in enzymes with the largest control coefficients. In addition, evolutionary changes in these enzymes may be favored because they allow organisms to modify flux allocation to alternate functions and track environmental fluctuations. This suggestion is supported by the “branch point effect,” a theoretical demonstration that control coefficients can dramatically shift between enzymes depending on the kinetic rates of the two competing enzymes (LaPorte et al. 1984). However, this study does not address the question of how the distribution of control is likely to evolve, but describes only which distributions of control are mathematically possible. Thus, Eanes (1999, p. 318) concludes his review, stating “all enzymes in [a] contributing pathway may not be equal; determining the rule[s] for these inequalities should be a major goal in studies of enzyme polymorphism.”A control coefficient (CC) indicates the degree to which flux through a pathway is altered by a small change in the activity of an enzyme (see appendix; this is equivalent to the sensitivity coefficient of Kacser and Burns 1973). The “rules” governing the distribution of control coefficients are determined by the biological evolution of metabolic systems. While research demonstrates that there are many possible distributions of control coefficients, none has examined which of these is most likely to evolve. The optimization of metabolic systems has been explored in detail (Heinrich et al. 1991, 1997; Heinrich and Schuster 1998). In these studies, however, the investigators employ as optimization criteria maximizing flux, maximizing transient times, or minimizing metabolic intermediates, criteria whose biological and evolutionary relevance is unclear.In an effort to understand how control is expected to be shared among enzymes and predict which enzymes are most likely to contribute to adaptive genetic changes, we present two models of the evolution of flux control in a simple linear pathway. The first model employs the framework of MCT. Although there have been many challenges to the MCT framework (Savageau 1976, 1992; Cornish-Bowden 1989; Savageau and Sorribas 1989), it should be made clear that our aim is not to construct a precisely parameterized model of a particular biological system, but to use this generalized framework to address a single, critically ignored question: What are the rules governing how control will evolve to be distributed among enzymes? The use of the MCT framework to address questions in evolutionary genetics is firmly established, with investigation focused on the molecular basis of dominance (Kacser and Burns 1981; Keightley 1996a; Phadnis and Fry 2005; but see Bagheri and Wagner 2004), the relationship between metabolic flux and fitness (Dykhuizen et al. 1987; Szathmary 1993), the amount of additive and nonadditive genetic variance in metabolic systems (Keightley 1989), whether this variation can be explained by mutation–selection balance (Clark 1991), and patterns of response of quantitative traits to selection (Keightley 1996b). The second model we examine, saturation kinetics (SK), is based on Michealis–Menten kinetics and enables us to relax one major assumption of MCT: that enzymes are far from saturation.Here we limit our analysis to linear pathways as an initial attempt to examine these issues. We find that for such pathways control coefficients will generally evolve to be unequal; that the magnitude of this inequality depends on the thermodynamic properties, rather than the kinetic properties, of each reaction step; that upstream enzymes tend to evolve higher control coefficients than downstream enzymes; and that upstream enzymes fix advantageous mutations in greater numbers, and those mutations have larger effects than in downstream enzymes.     

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.     

Metabolic control analysis of an enzymatic biofuel cell

Metabolic control analysis (MCA) is an analytical technique that aims to quantify the distribution of control that enzymes exhibit over the steady‐state fluxes through a metabolic network. In an enzymatic biofuel cell, the flux of interest is the electrical current generated by the system. Regardless of transport limitations and other constraints, kinetic limitations can become potential bottlenecks in the operation of a biofuel cell. We have used an indirect approach to MCA to investigate a common osmium‐mediated glucose oxidase/laccase enzymatic biofuel cell. The results of the analysis show that the control of the electron flux strongly depends on the total mediator concentrations and the extent of polarization of the individual electrodes. The effect of varying oxygen concentrations is also examined, as oxygen is required for the cathode, but it participates in a non‐productive reaction at the anode. Under normal operating conditions the electrodes will be highly polarized and will both contain high mediator concentrations. This configuration will result in a dominant FCC at the anode, and the conditions that are needed for balanced flux control between the anode and cathode are explored. As increasingly complex bioelectrocatalytic systems and architectures are envisioned, MCA will be a valuable framework to facilitate their design and subsequent operation. Biotechnol. Bioeng. 2009;102: 1624–1635. © 2008 Wiley Periodicals, Inc.     

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.     

The X6 "thermostabilizing" domains of xylanases are carbohydrate-binding modules: structure and biochemistry of the Clostridium thermocellum X6b domain

Many polysaccharide-degrading enzymes display a modular structure in which a catalytic module is attached to one or more noncatalytic modules. Several xylanases contain a module of previously unknown function (termed "X6" modules) that had been implicated in thermostability. We have investigated the properties of two such "thermostabilizing" modules, X6a and X6b from the Clostridium thermocellumxylanase Xyn10B. These modules, expressed either as discrete entities or as their natural fusions with the catalytic module, were assayed, and their capacity to bind various carbohydrates and potentiate hydrolytic activity was determined. The data showed that X6b, but not X6a, increased the activity of the enzyme against insoluble xylan and bound specifically to xylooligosaccharides and various xylans. In contrast, X6a exhibited no affinity for soluble or insoluble forms of xylan. Isothermal titration calorimetry revealed that the ligand-binding site of X6b accommodates approximately four xylose residues. The protein exhibited K(d) values in the low micromolar range for xylotetraose, xylopentaose, and xylohexaose; 24 microM for xylotriose; and 50 microM for xylobiose. Negative DeltaH and DeltaS values indicate that the interaction of X6b with xylooligosaccharides and xylan is driven by enthalpic forces. The three-dimensional structure of X6b has been solved by X-ray crystallography to a resolution of 2.1 A. The protein is a beta-sandwich that presents a tryptophan and two tyrosine residues on the walls of a shallow cleft that is likely to be the xylan-binding site. In view of the structural and carbohydrate-binding properties of X6b, it is proposed that this and related modules be re-assigned as family 22 carbohydrate-binding modules.     

Hexokinase and not glycogen synthase controls the flux through the glycogen synthesis pathway in frog oocytes

Here we set out to evaluate the role of hexokinase and glycogen synthase in the control of glycogen synthesis in vivo. We used metabolic control analysis (MCA) to determine the flux control coefficient for each of the enzymes involved in the pathway. Acute microinjection experiments in frog oocytes were specifically designed to change the endogenous activities of the enzymes, either by directly injecting increasing amounts of a given enzyme (HK, PGM and UGPase) or by microinjection of a positive allosteric effector (glc-6P for GS). Values of 0.61 ± 0.07, 0.19 ± 0.03, 0.13 ± 0.03, and −0.06 ± 0.08 were obtained for the flux control coefficients of hexokinase EC 2.7.1.1 (HK), phosphoglucomutase EC 5.4.2.1 (PGM), UDPglucose pyrophosphorylase EC 2.7.7.9 (UGPase) and glycogen synthase EC 2.4.1.11 (GS), respectively. These values satisfy the summation theorem since the sum of the control coefficients for all the enzymes of the pathway is 0.87. The results show that, in frog oocytes, glycogen synthesis through the direct pathway is under the control of hexokinase. Phosphoglucomutase and UDPG-pyrophosphorylase have a modest influence, while the control exerted by glycogen synthase is null.     

Effects of the changes in enzyme activities on metabolic flux redistribution around the 2-oxoglutarate branch in glutamate production by<Emphasis Type="Italic"> Corynebacterium glutamicum</Emphasis>

An experimental method for metabolic control analysis (MCA) was applied to the investigation of a metabolic network of glutamate production by Corynebacterium glutamicum. A metabolic reaction (MR) model was constructed and used for flux distribution analysis (MFA). The flux distribution at a key branch point, 2-oxoglutarate, was investigated in detail. Activities of isocitrate dehydrogenase (ICDH), glutamate dehydrogenase (GDH), and 2-oxoglutarate dehydrogenase complex (ODHC) around this the branch point were changed, using two genetically engineered strains (one with enhanced ICDH activity and the other with enhanced GDH activity) and by controlling environmental conditions (i.e. biotin-deficient conditions). The mole flux distribution was determined by an MR model, and the effects of the changes in the enzyme activities on the mole flux distribution were compared. Even though both GDH and ICDH activities were enhanced, the mole flux distribution was not significantly changed. When the ODHC activity was attenuated, the flux through ODHC decreased, and glutamate production was markedly increased. The flux control coefficients of the above three enzymes for glutamate production were determined based on changes in enzyme activities and the mole flux distributions. It was found that the factor with greatest impact on glutamate production in the metabolic network was obtained by attenuation of ODHC activity.     

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.     

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)     

Optimisation of Enzyme Concentrations for Unbranched Reaction Chains: The Concept of Combined Response Coefficient

In the metabolic control theory, the control coefficient is a key parameter in quantifying the sensitivity of the flux towards an infinitesimal variation of enzyme activity. This concept does not apply just as it is for variations of enzyme concentrations whenever there is spatial, energy or resources limitations in the cell. Due to constraint on total enzyme concentration, the variation of concentration of any given enzyme may affect the concentrations of other enzymes. To take into account these correlations between enzyme concentrations, we propose the concept of "combined response coefficient". Its definition is similar to that of the control coefficient, but its mathematical expression is different. Its range of variation is from – + 1, the null value corresponding to optimum enzyme concentration, i.e. to concentrations that maximise the flux, and the negative values to concentrations beyond the optimum value. A summation property could be derived using a simple weighting of the combined response coefficients, the sum of the weighed coefficient being 0.     

Recent advances in the structural biology of modular polyketide synthases and nonribosomal peptide synthetases

Polyketides and nonribosomal peptides are an important class of natural products with useful bioactivities. These compounds are similarly biosynthesized using enzymes with modular structures despite having different physicochemical properties. These enzymes are attractive targets for bioengineering to produce “unnatural” natural products owing to their modular structures. Therefore, their structures have been studied for a long time; however, the main focus was on truncated-single domains. Surprisingly, there is an increasing number of the structures of whole modules reported, most of which have been enabled through the recent advances in cryogenic electron microscopy technology. In this review, we have summarized the recent advances in the structural elucidation of whole modules.