Professor David Fell

Clostridium autoethanogenum is an industrial microbe used for the commercial-scale production of ethanol from carbon monoxide. While significant progress has been made in the attempted diversification of this bioprocess, further improvements are desirable, particularly in the formation of the high-value platform chemicals, such as 2,3-butanediol. A new, experimentally parameterised genome scale model of C. autoethanogenum predicts dramatically increased 2,3-butanediol production under non-carbon-limited conditions when thermodynamic constraints on hydrogen production are considered.

Analysis of the impact of photorespiration on plant metabolism is usually based on manual inspection of small network diagrams. Here we create a structural metabolic model that contains the reactions that participate in photorespiration in the plastid, peroxisome, mitochondrion and cytosol and the metabolite exchanges between them. This model was subjected to elementary flux modes analysis, a technique that enumerates all the component, minimal pathways of a network. Any feasible photorespiratory metabolism in the plant will be some combination of the elementary flux modes (EFMs) that contain the Rubisco oxygenase reaction. Amongst the EFMs we obtained was the classic photorespiratory cycle, but there were also modes that involve photorespiration coupled with mitochondrial metabolism and ATP production, the glutathione‐ascorbate (GSH‐ASC) cycle and nitrate reduction to ammonia. The modes analysis demonstrated the underlying basis of the metabolic linkages with photorespiration that have been inferred experimentally. The set of reactions common to all the elementary modes showed good agreement with the gene products of mutants that have been reported to have a defective phenotype in photorespiratory conditions. Finally, the set of modes provided a formal demonstration that photorespiration itself does not impact on the CO2:O2 ratio (assimilation quotient, AQ), except in those modes associated with concomitant nitrate reduction.

Produce rich in phytochemicals may alter postprandial glucose and insulin responses by interacting with the pathways that regulate glucose uptake and insulin secretion in humans. The aims of the present study were to assess the phytochemical constituents of red beetroot juice and to measure the postprandial glucose and insulin responses elicited by either 225 ml beetroot juice (BEET), a control beverage matched for macronutrient content (MCON) or a glucose beverage in healthy adults. Beetroot juice was a particularly rich source of betalain degradation compounds. The orange/yellow pigment neobetanin was measured in particularly high quantities (providing 1·3 g in the 225 ml). A total of sixteen healthy individuals were recruited, and consumed the test meals in a controlled single-blind cross-over design. Results revealed a significant lowering of the postprandial insulin response in the early phase (0–60 min) (P

Previously we have used a genome scale model of rice metabolism to describe how metabolism reconfigures at different light intensities in an expanding leaf of rice. Although this established that the metabolism of the leaf was adequately represented, in the model, the scenario was not that of the typical function of the leaf—to provide material for the rest of the plant. Here we extend our analysis to explore the transition to a source leaf as export of photosynthate increases at the expense of making leaf biomass precursors, again as a function of light intensity. In particular we investigate whether, when the leaf is making a smaller range of compounds for export to the phloem, the same changes occur in the interactions between mitochondrial and chloroplast metabolism as seen in biomass synthesis for growth when light intensity increases. Our results show that the same changes occur qualitatively, though there are slight quantitative differences reflecting differences in the energy and redox requirements for the different metabolic outputs.

Mathematical modeling of metabolism is essential for rational metabolic engineering. The present work focuses on several types of modeling approach to quantitative understanding of central metabolic network and energetics in the bioethanol-producing bacterium Zymomonas mobilis. Combined use of Flux Balance, Elementary Flux Mode, and thermodynamic analysis of its central metabolism, together with dynamic modeling of the core catabolic pathways, can help to design novel substrate and product pathways by systematically analyzing the solution space for metabolic engineering, and yields insights into the function of metabolic network, hardly achievable without applying modeling tools.

Flux balance models of metabolism generally utilize synthesis of biomass as the main determinant of intracellular fluxes. However, the biomass constraint alone is not sufficient to predict realistic fluxes in central heterotrophic metabolism of plant cells because of the major demand on the energy budget due to transport costs and cell maintenance. This major limitation can be addressed by incorporating transport steps into the metabolic model and by implementing a procedure that uses Pareto optimality analysis to explore the trade-off between ATP and NADPH production for maintenance. This leads to a method for predicting cell maintenance costs on the basis of the measured flux ratio between the oxidative steps of the oxidative pentose phosphate pathway and glycolysis. We show that accounting for transport and maintenance costs substantially improves the accuracy of fluxes predicted from a flux balance model of heterotrophic Arabidopsis cells in culture, irrespective of the objective function used in the analysis. Moreover, when the new method was applied to cells under control, elevated temperature and hyper-osmotic conditions, only elevated temperature led to a substantial increase in cell maintenance costs. It is concluded that the hyper-osmotic conditions tested did not impose a metabolic stress, in as much as the metabolic network is not forced to devote more resources to cell maintenance.

The active, yet energetically inefficient electron transport chain of the ethanologenic bacterium Zymomonas mobilis could be used in metabolic engineering for redox-balancing purposes during synthesis of certain products. Although several reconstructions of Z. mobilis metabolism have been published, important aspects of redox balance and aerobic catabolism have not previously been considered. Here, annotated genome sequences and metabolic reconstructions have been combined with existing biochemical evidence to yield a medium-scale model of Z. mobilis central metabolism in the form of COBRA Toolbox model files for flux balance analysis (FBA). The stoichiometric analysis presented here suggests the feasibility of several metabolic engineering strategies for obtaining high-value products, such as glycerate, succinate, and glutamate that would use the electron transport chain to oxidize the excess NAD(P)H, generated during synthesis of these metabolites. Oxidation of the excess NAD(P)H would also be needed for synthesis of ethanol from glycerol. Maximum product yields and the byproduct spectra have been estimated for each product, with glucose, xylose, or glycerol as the carbon substrates. These novel pathways represent targets for future metabolic engineering, as they would exploit both the rapid Entner–Doudoroff glycolysis, and the energetically uncoupled electron transport of Z. mobilis.

We describe the construction and analysis of a genome-scale metabolic model representing a developing leaf cell of rice (Oryza sativa) primarily derived from the annotations in the RiceCyc database. We used flux balance analysis to determine that the model represents a network capable of producing biomass precursors (amino acids, nucleotides, lipid, starch, cellulose, and lignin) in experimentally reported proportions, using carbon dioxide as the sole carbon source. We then repeated the analysis over a range of photon flux values to examine responses in the solutions. The resulting flux distributions show that (1) redox shuttles between the chloroplast, cytosol, and mitochondrion may play a significant role at low light levels, (2) photorespiration can act to dissipate excess energy at high light levels, and (3) the role of mitochondrial metabolism is likely to vary considerably according to the balance between energy demand and availability. It is notable that these organelle interactions, consistent with many experimental observations, arise solely as a result of the need for mass and energy balancing without any explicit assumptions concerning kinetic or other regulatory mechanisms.

We describe the construction and analysis of a genome-scale metabolic model representing a developing leaf cell of rice (Oryza sativa) primarily derived from the annotations in the RiceCyc database. We used flux balance analysis to determine that the model represents a network capable of producing biomass precursors (amino acids, nucleotides, lipid, starch, cellulose, and lignin) in experimentally reported proportions, using carbon dioxide as the sole carbon source. We then repeated the analysis over a range of photon flux values to examine responses in the solutions. The resulting flux distributions show that (1) redox shuttles between the chloroplast, cytosol, and mitochondrion may play a significant role at low light levels, (2) photorespiration can act to dissipate excess energy at high light levels, and (3) the role of mitochondrial metabolism is likely to vary considerably according to the balance between energy demand and availability. It is notable that these organelle interactions, consistent with many experimental observations, arise solely as a result of the need for mass and energy balancing without any explicit assumptions concerning kinetic or other regulatory mechanisms.

Flux is a key measure of the metabolic phenotype. Recently, complete (genome-scale) metabolic network models have been established for Arabidopsis (Arabidopsis thaliana), and flux distributions have been predicted using constraints-based modeling and optimization algorithms such as linear programming. While these models are useful for investigating possible flux states under different metabolic scenarios, it is not clear how close the predicted flux distributions are to those occurring in vivo. To address this, fluxes were predicted for heterotrophic Arabidopsis cells and compared with fluxes estimated in parallel by 13C-metabolic flux analysis (MFA). Reactions of the central carbon metabolic network (glycolysis, the oxidative pentose phosphate pathway, and the tricarboxylic acid [TCA] cycle) were independently analyzed by the two approaches. Net fluxes in glycolysis and the TCA cycle were predicted accurately from the genome-scale model, whereas the oxidative pentose phosphate pathway was poorly predicted. MFA showed that increased temperature and hyperosmotic stress, which altered cell growth, also affected the intracellular flux distribution. Under both conditions, the genome-scale model was able to predict both the direction and magnitude of the changes in flux: namely, increased TCA cycle and decreased phosphoenolpyruvate carboxylase flux at high temperature and a general decrease in fluxes under hyperosmotic stress. MFA also revealed a 3-fold reduction in carbon-use efficiency at the higher temperature. It is concluded that constraints-based genome-scale modeling can be used to predict flux changes in central carbon metabolism under stress conditions.

Reconstructing a model of the metabolic network of an organism from its annotated genome sequence would seem, at first sight, to be one of the most straightforward tasks in functional genomics, even if the various data sources required were never designed with this application in mind. The number of genome-scale metabolic models is, however, lagging far behind the number of sequenced genomes and is likely to continue to do so unless the model-building process can be accelerated. Two aspects that could usefully be improved are the ability to find the sources of error in a nascent model rapidly, and the generation of tenable hypotheses concerning solutions that would improve a model. We will illustrate these issues with approaches we have developed in the course of building metabolic models of Streptococcus agalactiae and Arabidopsis thaliana.

Organisms share a common core to their metabolic networks. But what determined this: chance, chemical necessity, or evolutionary optimization? In this issue of Molecular Cell, Noor et al. (2010) provide new evidence for selection of a network with optimal features from a broader set of possibilities.

We describe the construction and analysis of a genome-scale metabolic model of Arabidopsis (Arabidopsis thaliana) primarily derived from the annotations in the Aracyc database. We used techniques based on linear programming to demonstrate the following: (1) that the model is capable of producing biomass components (amino acids, nucleotides, lipid, starch, and cellulose) in the proportions observed experimentally in a heterotrophic suspension culture; (2) that approximately only 15% of the available reactions are needed for this purpose and that the size of this network is comparable to estimates of minimal network size for other organisms; (3) that reactions may be grouped according to the changes in flux resulting from a hypothetical stimulus (in this case demand for ATP) and that this allows the identification of potential metabolic modules; and (4) that total ATP demand for growth and maintenance can be inferred and that this is consistent with previous estimates in prokaryotes and yeast.

Motivation: In recent years, several methods have been proposed for determining metabolic pathways in an automated way based on network topology. The aim of this work is to analyse these methods by tackling a concrete example relevant in biochemistry. It concerns the question whether even-chain fatty acids, being the most important constituents of lipids, can be converted into sugars at steady state. It was proved five decades ago that this conversion using the Krebs cycle is impossible unless the enzymes of the glyoxylate shunt (or alternative bypasses) are present in the system. Using this example, we can compare the various methods in pathway analysis. Results: Elementary modes analysis (EMA) of a set of enzymes corresponding to the Krebs cycle, glycolysis and gluconeogenesis supports the scientific evidence showing that there is no pathway capable of converting acetyl-CoA to glucose at steady state. This conversion is possible after the addition of isocitrate lyase and malate synthase (forming the glyoxylate shunt) to the system. Dealing with the same example, we compare EMA with two tools based on graph theory available online, PathFinding and Pathway Hunter Tool. These automated network generating tools do not succeed in predicting the conversions known from experiment. They sometimes generate unbalanced paths and reveal problems identifying side metabolites that are not responsible for the carbon net flux. This shows that, for metabolic pathway analysis, it is important to consider the topology (including bimolecular reactions) and stoichiometry of metabolic systems, as is done in EMA.

Motivation: In recent years, several methods have been proposed for determining metabolic pathways in an automated way based on network topology. The aim of this work is to analyse these methods by tackling a concrete example relevant in biochemistry. It concerns the question whether even-chain fatty acids, being the most important constituents of lipids, can be converted into sugars at steady state. It was proved five decades ago that this conversion using the Krebs cycle is impossible unless the enzymes of the glyoxylate shunt (or alternative bypasses) are present in the system. Using this example, we can compare the various methods in pathway analysis. Results: Elementary modes analysis (EMA) of a set of enzymes corresponding to the Krebs cycle, glycolysis and gluconeogenesis supports the scientific evidence showing that there is no pathway capable of converting acetyl-CoA to glucose at steady state. This conversion is possible after the addition of isocitrate lyase and malate synthase (forming the glyoxylate shunt) to the system. Dealing with the same example, we compare EMA with two tools based on graph theory available online, PathFinding and Pathway Hunter Tool. These automated network generating tools do not succeed in predicting the conversions known from experiment. They sometimes generate unbalanced paths and reveal problems identifying side metabolites that are not responsible for the carbon net flux. This shows that, for metabolic pathway analysis, it is important to consider the topology (including bimolecular reactions) and stoichiometry of metabolic systems, as is done in EMA.

A decrease in retinoic acid levels due to alcohol consumption has been proposed as a contributor to such conditions as fetal alcohol spectrum diseases and ethanol-induced cancers. One molecular mechanism, competitive inhibition by ethanol of the catalytic activity of human alcohol dehydrogenase (EC 1.1.1.1) (ADH) on all-trans-retinol oxidation has been shown for the ADH7 isoform. Ethanol metabolism also causes an increase in the free reduced nicotinamide adenine dinucleotide (NADH) in cells, which might reasonably be expected to decrease the retinol oxidation rate by product inhibition of ADH isoforms. To understand the relative importance of these two mechanisms by which ethanol decreases the retinol oxidation in vivo we need to assess them quantitatively. We have built a model system of 4 reactions: (1) ADH oxidation of ethanol and NAD(+), (2) ADH oxidation of retinol and NAD(+), (3) oxidation of ethanol by a generalized Ethanol(oxidase) that uses NAD(+), (4) NADH(oxidase) which carries out NADH turnover. Using the metabolic modeling package ScrumPy, we have shown that the ethanol-induced increase in NADH contributes from 0% to 90% of the inhibition by ethanol, depending on (ethanol) and ADH isoform. Furthermore, while the majority of flux control of retinaldehyde production is exerted by ADH, Ethanol(oxidase) and the NADH(oxidase) contribute as well. Our results show that the ethanol-induced increase in NADH makes a contribution of comparable importance to the ethanol competitive inhibition throughout the range of conditions likely to occur in vivo, and must be considered in the assessment of the in vivo mechanism of ethanol interference with fetal development and other diseases.

Motivation: In recent years, several methods have been proposed for determining metabolic pathways in an automated way based on network topology. The aim of this work is to analyse these methods by tackling a concrete example relevant in biochemistry. It concerns the question whether even-chain fatty acids, being the most important constituents of lipids, can be converted into sugars at steady state. It was proved five decades ago that this conversion using the Krebs cycle is impossible unless the enzymes of the glyoxylate shunt (or alternative bypasses) are present in the system. Using this example, we can compare the various methods in pathway analysis.

Motivation: Metabolic modelling provides a mathematically rigorous basis for system-level analysis of biochemical networks. However, the growing sizes of metabolic models can lead to serious problems in their construction and validation. In this work, we describe a relatively poorly investigated type of modelling error, called stoichiometric inconsistencies. These errors are caused by incorrect definitions of reaction stoichiometries and result in conflicts between two fundamental physical constraints to be satisfied by any valid metabolic model: positivity of molecular masses of all metabolites and mass conservation in all interconversions. Results: We introduce formal definitions of stoichiometric inconsistencies, inconsistent net stoichiometries, elementary leakage modes and other important fundamental properties of incorrectly defined biomolecular networks. Algorithms are described for the verification of stoichiometric consistency of a model, detection of unconserved metabolites and inconsistent minimal net stoichiometries. The usefulness of these algorithms for effective resolving of inconsistencies and for detection of input errors is demonstrated on a published genome-scale metabolic model of Saccharomyces cerevisiae and one of Streptococcus agalactiae constructed using the KEGG database.

Stoichiometric analysis of metabolic networks allows the calculation of possible metabolic flux distributions in the absence of kinetic data. In order to predict which of the possible fluxes are present under certain conditions, additional constraints and optimization principles can be applied. One approach of calculating unknown fluxes (frequently called flux balance analysis) is based on the optimality principle of maximizing the molar yield of biotransformations. Here, the relevance and applicability of that approach are examined, and it is compared with the principle of maximizing pathway flux. We discuss diverse experimental evidence showing that, often, those biochemical pathways are operative that allow fast but low-yield synthesis of important products, such as fermentation in Saccharomyces cerevisiae and several other yeast species. Together with arguments based on evolutionary game theory, this leads us to the conclusion that maximization of molar yield is by no means a universal principle.

We describe a method by which the reactions in a metabolic system may be grouped hierarchically into sets of modules to form a metabolic reaction tree. In contrast to previous approaches, the method described here takes into account the fact that, in a viable network, reactions must be capable of sustaining a steady-state flux. In order to achieve this decomposition we introduce a new concept-”the reaction correlation coefficient, φ, and show that this is a logical extension of the concept of enzyme (or reaction) subsets. In addition to their application to modular decomposition, reaction correlation coefficients have a number of other interesting properties, including a convenient means for identifying disconnected subnetworks in a system and potential applications to metabolic engineering. The method computes reaction correlation coefficients from an orthonormal basis of the null-space of the stoichiometry matrix. We show that reaction correlation coefficients are uniquely defined, even though the basis of the null-space is not. Once a complete set of reaction correlation coefficients is calculated, a metabolic reaction tree can be determined through the application of standard programming techniques. Computation of the reaction correlation coefficients, and the subsequent construction of the metabolic reaction tree is readily achievable for genome-scale models using a commodity desk-top PC.

In the post-genomic era, the biochemical information for individual compounds, enzymes, reactions to be found within named organisms has become readily available. The well-known KEGG and BioCyc databases provide a comprehensive catalogue for this information and have thereby substantially aided the scientific community. Using these databases, the complement of enzymes present in a given organism can be determined and, in principle, used to reconstruct the metabolic network. However, such reconstructed networks contain numerous properties contradicting biological expectation. The metabolic networks for a number of organisms are reconstructed from KEGG and BioCyc databases, and features of these networks are related to properties of their originating database.

In this paper some of the general concepts underpinning the computer modelling of metabolic systems are introduced. The difference between kinetic and structural modelling is emphasized, and the more important techniques from both, along with the physiological implications, are described. These approaches are then illustrated by descriptions of other work, in which they have been applied to models of the Calvin cycle, sucrose metabolism in sugar cane, and starch metabolism in potatoes.

Despite dramatic increases in glucose influx during the transition from fasting to fed states, plasma glucose concentration remains tightly controlled. This constancy is in large part due to the capacity of skeletal muscle to absorb excess glucose and store it as glycogen. The magnitude of this capacity is controlled by insulin by way of regulated insertion of glucose transporters into the muscle cell membrane. Here, we examine the mechanism by which muscle cells are able to tolerate large flux increases across their transporters without significantly changing their own metabolite pools. MCA was used to probe data sets that measured the effects of changing plasma glucose and/or insulin concentrations on the rates of glycogen synthesis and the concentrations of metabolites, particularly glucose-6-phosphate. We find that homeostasis is achieved by insulin-dependent phosphorylation changes in GSase sensitivity to the upstream metabolite glucose-6-phosphate. The centrality of GSase to homeostasis resolves the paradox of its sensitivity to allosteric and covalent regulation despite its minimal role in flux control. The importance of this role for enzymatic phosphorylation to diabetes pathology is discussed, and its general applicability is suggested.

Myocardial hibernation represents an adaptation to sustained ischemia to maintain tissue vitality during severe supply–demand imbalance which is characterized by an increased glucose uptake. To elucidate this adaptive protective mechanism, the regulation of anaerobic glycolysis was investigated using human biopsies. In hibernating myocardium showing an increase in anaerobic glycolytic flux metabolizing exogenous glucose, the adjustment of flux through this pathway was analyzed by flux:metabolite co-responses. By this means, a previously unknown pattern of regulation using multisite modulation was found which largely differs from traditional concepts of metabolic control of the Embden–Meyerhof pathway in normal and diseased myocardium.

Exact adjustment of the Embden-Meyerhof pathway (EMP) is an important issue in ischemic preconditioning (IP) because an attenuated ischemic lactate accumulation contributes to myocardial protection. However, precise mechanisms of glycolytic flux and its regulation in IP remain to be elucidated. In open chest pigs, IP was achieved by two cycles of 10-min coronary artery occlusion and 30-min reperfusion prior to a 45-min index ischemia and 120-min reperfusion. Myocardial contents in glycolytic intermediates were assessed by high performance liquid chromatographic analysis of serial myocardial biopsies under control conditions and IP. Detailed time courses of metabolite contents allow an in-depth description of EMP regulation during index ischemia using metabolic control analysis. IP reduced myocardial infarct size (control, 90.0 ± 3.1 versus 5.05 ± 2.1%;p < 0.001) and attenuated myocardial lactate accumulation (end-ischemic contents, 31.9 ± 4.47versus 10.3 ± 1.26 μmol/wet weight,p < 0.0001), whereby a decrease in anaerobic glycolytic flux by at least 70% could constantly be observed throughout index ischemia. By calculation of flux:metabolite co-responses, the mechanisms of glycolytic regulation were investigated. The continuous deceleration of EMP flux in control myocadium could neither be explained on the basis of substrate availability nor be attributed to regulatory “key enzymes,” as multisite regulation was employed for flux adjustment. In myocardium subjected to IP, an even pronounced deceleration of EMP flux during index ischemia was observed. Again, the adjustment of EMP flux was because of multisite modulation without any evidence for flux limitation by substrate availability or a key enzyme. However, IP changed the regulatory properties of most EMP enzymes, and some of these patterns could not be explained on the basis of substrate kinetics. Instead, other regulatory mechanisms, which have previously not yet been described for EMP enzymes, must be considered. These altered biochemical properties of the EMP enzymes have not yet been described.

We have determined the kinetic parameters of the individual steps of the threonine pathway from aspartate inEscherichia coli under a single set of experimental conditions chosen to be physiologically relevant. Our aim was to summarize the kinetic behaviour of each enzyme in a single tractable equation that takes into account the effect of the products as competitive inhibitors of the substrates in the forward reaction and also, when appropriate (e.g. near-equilibrium reactions), as substrates of the reverse reactions. Co-operative feedback inhibition by threonine and lysine was also included as necessary. We derived the simplest rate equations that describe the salient features of the enzymes in the physiological range of metabolite concentrations in order to incorporate them ultimately into a complete model of the threonine pathway, able to predict quantitatively the behaviour of the pathway under natural or engineered conditions.

A computer simulation of the threonine-synthesis pathway in Escherichia coli Tir-8 has been developed based on our previous measurements of the kinetics of the pathway enzymes under near-physiological conditions. The model successfully simulates the main features of the time courses of threonine synthesis previously observed in a cell-free extract without alteration of the experimentally determined parameters, although improved quantitative fits can be obtained with small parameter adjustments. At the concentrations of enzymes, precursors and products present in cells, the model predicts a threonine-synthesis flux close to that required to support cell growth. Furthermore, the first two enzymes operate close to equilibrium, providing an example of a near-equilibrium feedback-inhibited enzyme. The predicted flux control coefficients of the pathway enzymes under physiological conditions show that the control of flux is shared between the first three enzymes: aspartate kinase, aspartate semialdehyde dehydrogenase and homoserine dehydrogenase, with no single activity dominating the control. The response of the model to the external metabolites shows that the sharing of control between the three enzymes holds across a wide range of conditions, but that the pathway flux is sensitive to the aspartate concentration. When the model was embedded in a larger model to simulate the variable demands for threonine at different growth rates, it showed the accumulation of free threonine that is typical of the Tir-8 strain at low growth rates. At low growth rates, the control of threonine flux remains largely with the pathway enzymes. As an example of the predictive power of the model, we studied the consequences of over-expressing different enzymes in the pathway.

Although epidermal growth factor (EGF) induces transient activation of Ras and the mitogen-activated protein kinase (MAPK) cascade in PC12 cells, whereas nerve growth factor (NGF) stimulates sustained activation, the basis for these contrasting responses is not known. We have developed a computer simulation of EGF-induced MAPK cascade activation, which provides quantitative evidence that feedback inhibition of the MAPK cascade is the most important factor in determining the duration of cascade activation. Hence, we propose that the observed quantitative differences in EGF and NGF signalling can be accounted for by differential feedback regulation of the MAPK cascade.

The dynamic and steady‐state behaviour of a computer simulation of the Calvin cycle reactions of the chloroplast, including starch synthesis and degradation, and triose phosphate export have been investigated. A major difference compared with previous models is that none of the reversible reactions are assumed to be at equilibrium. The model can exhibit alternate steady states of low or high carbon assimilation flux, with hysteresis in the transitions between the steady states induced by environmental factors such as phosphate and light intensity. The enzymes which have the greatest influence on the flux have been investigated by calculation of their flux control coefficients. Different patterns of control are exhibited over the assimilation flux, the flux to starch and the flux to cytosolic triose phosphate. The assimilation flux is mostly sensitive to sedoheptulose bisphosphatase and Rubisco, with the exact distribution depending on their relative activities. Other enzymes, particularly the triose phosphate translocator, become more influential when other fluxes are considered. These results are shown to be broadly consistent with observations on transgenic plants.

A theoretical metabolic-control-analysis approach has been used to study aspects of glycolytic-flux control and carbon-metabolite regulation, particularly the role of ATP demand (ATPase), in order to determine what general features of the regulation of energy metabolism would be consistent with good carbon-metabolite homeostasis in the face of large changes in carbon flux. On the basis of a semi-quantitative control-analysis model, incorporating estimates of substrate, product and effector actions on the enzymes, the experimentally observed characteristics of glycolytic-flux changes prove to impose constraints on the feasible ranges of these estimates. This leads to the identification of several features of energy metabolism, each of which is necessary but not sufficient to explain the observations; although most of these have been advocated previously (such as AMP activation of phosphofructokinase (PFK), ADP inhibition of ATPase and the role of energy charge or ATP/ADP ratio), our analysis allows their relative importance to be assessed. In the model, the distribution of flux control depends primarily on ADP inhibition of ATPase, and on the activation of PFK by AMP; increase in ADP inhibition of ATPase increases the control on PFK; increase in AMP activation of PFK increases control on ATPase. PFK exerts greater flux control than does ATPase over approximately 50 % of the ranges (parameter space) studied, but its control is sufficiently high to achieve sizeable flux increases over less than 20 % of the space. Furthermore, control by alteration in PFK activity is shown to result in poor glycolytic metabolite homeostasis over the entire parameter space studied. However, over a large proportion of the parameter space, control by activation of ATPase can lead to large flux changes, i.e. high flux control, coupled with excellent glycolytic-metabolite homeostasis, similar to that observed in working muscle. As well as altering the relative degrees of flux control invested in PFK and ATPase, ADP inhibition of ATPase and AMP activation of PFK have pronounced effects on the homeostatic properties of the system. Stronger ADP inhibition of ATPase results in improved homeostasis of glycolytic metabolites, ATP and ADP in response to PFK activation, whereas stronger activation of PFK by AMP improves the homeostasis of these three quantities in response to ATPase activation. The results are further evidence of the potential for physiological ATP demand to exert control over glycolytic flux, but additionally show that the known effector interactions, in addition to their previously known role in ATP regulation, could contribute to the remarkable homeostasis of glycolytic-metabolite levels observed in vivo. They further indicate that quantitative characterisation of likely domains of behaviour of metabolic systems can be achieved by an algebraic analysis that is not highly dependent on a full and precise knowledge of the molecular details of the kinetic/regulatory properties of the enzymes, but that still allows an assessment of whether hypotheses regarding the system are feasible and sufficient to account for the observations.

Over recent years, the concept that flux through a metabolic pathway is controlled by a single rate-limiting enzyme has been challenged from a number of quarters. We have presented three lines of evidence that the control of pathway flux by activation of multiple several steps, including steps responsible for consumption of pathway products, is an important feature of physiological flux control in response to external stimmuli. Theoretical tools exist that can be used to analyze the distribution of flux control between the steps involved in signal transduction and enzyme activation.

Genetically engineered organisms overexpressing phosphofructokinase (PFK), a supposed 'regulatory' step of glycolysis, often show little or no measurable change in glycolytic or respiratory flux, although the concentrations of glycolytic intermediates may change. We have used the finite change theory of Metabolic Control Analysis (MCA) to analyse the concentrations of glycolytic metabolites in aged disks of tuber tissue from four lines of transgenic potatoes expressing different amounts of PFK that, under aerobic conditions, showed statistically indistinguishable rates of respiration. The constancy of the metabolites' concentration deviation indices for different increases in PFK expression indicated that the metabolite changes from a graded series, excluding the possibility of anomalous behaviour that might be observed in a single transgenic line. Consequently we were able to use the finite change method to validate the results of an MCA model of tuber glycolysis [Thomas, Mooney, Burrell and Fell (1997) Biochem. J. 322, 119-127]. Furthermore the metabolite changes with PFK activity are evidence that near-equilibrium steps do not transmit increased substrate concentrations down the pathway without attenuation. Our results support the view that flux increase by activation of a single enzyme early in the pathway will, contrary to expectations, be of limited effectiveness in achieving flux increases.

We have applied Metabolic Control Analysis (MCA) in an attempt to determine the distribution of glycolytic flux control between the steps of glycolysis in aged disks of potato tuber under aerobic conditions, using concentrations of glycolytic metabolites in tuber tissue from a range of transgenic potato plants and published enzyme kinetic data. We modelled the substrate and effector kinetics of potato tuber phosphofructokinase (PFK) by reanalysing published results. Despite the scarcity of reliable kinetic data, our results are in agreement with experimental findings namely that, under the conditions described, PFK has little control over glycolytic flux. Furthermore our analysis predicts that under these conditions far more control lies in the dephosphorylation of phosphoenolpyruvate and/or in the steps beyond. We have validated the results of our analysis in two ways. First, predictions based on calculated concentration control coefficients from the analysis show generally good agreement with observed metabolite deviation indices discussed in the preceding paper [Thomas, Mooney, Burrell, and Fell (1997) Biochem. J. 322, 111-117]. Second, sensitivity analysis of our results shows that the calculated control coefficients are robust to errors in the elasticities used in the analysis, of which relatively few need to be known accurately. Experimental and control analysis results agree with previous predictions of MCA that strong co-operative feedback inhibition of enzymes serves to move flux control downstream of the inhibiting metabolite. We conclude that MCA can successfully model the outcome of experiments in the genetic manipulation of enzyme amounts.

Metabolic Control Analysis has invalidated many traditional biochemical concepts of control, in particular the rate-limiting step. However, it has not been used to question the mechanisms by which pathway flux is thought to be controlled, such as the action of allosteric effectors or of covalent modification mechanisms. Here we use Control Analysis and computer simulation to examine the response of pathway segments to change in flux imposed by action on an enzyme outside the segment. Whether these segments contain near-equilibrium enzyme-catalysed reactions, cooperative enzymes, feedforward activation loops or feedback inhibition loops, their responses are significantly different from those observedin vivo. In particular, they do not exhibit the remarkable degrees of metabolite homoeostasis during large flux changes that have frequently been observed experimentally. On the other hand, near-constant levels of metabolites in spite of large changes of flux are consistent with our recent proposal thatmulti-site modulation—simultaneous activation of many pathway steps—is the normal method by which metabolism is controlled.

Letter

Since Blackman [1] proposed the concept of the 'rate-limiting

step' in 1905, it has dominated the approach to understanding

the control of metabolic pathways. For example, it was endorsed

in Krebs' concept of 'pacemaker' enzymes [2], which he saw as

the target sites for hormone and drug action on metabolism.

Even though the theory of Metabolic Control Analysis [3,4] has

since shown that control can be distributed over many steps in a

pathway, and that the degree of control of any given step can be

quantified by its flux control coefficient, qualitative explanations

of how a pathway can be controlled have not been greatly

affected. Indeed, although Metabolic Control Analysis has been

increasingly adopted in metabolic biochemistry, and experiments

have confirmed both that control is generally distributed [5] and

that genuinely rate-limiting enzymes are rare, it has also

legitimized the concept that an enzyme that responds to some

external controlling factor can be an agent of metabolic control

provided the enzyme has a finite flux control coefficient. However,

we shall cite arguments that such mechanisms cannot be responsible

for large changes in metabolic flux. On the other hand,

recent theoretical developments arising from Metabolic Control

Analysis do allow us to characterize how large changes in

metabolic flux could be implemented; they can only be achieved

with minimal disturbance ofmetabolite concentrations and fluxes

in other pathways by co-ordinated changes in the activities of

many of the enzymes in the pathway, and this can be shown to

be a common mechanism of control.

Related experimental and theoretical evidence also contradicts

the view that regulatory enzymes exhibiting allosteric properties

are effective agents for control of metabolic flux. Our conclusion

is that their more significant role is in homoeostasis. In consequence,

different approaches are needed to both the study and

explanation of metabolic control.

Metabolic control analyses of glucose utilization were performed for four groups of working rat hearts perfused with Krebs-Henseleit buffer containing 10 mM glucose only, or with the addition of 4 mM D-beta-hydroxybutyrate/1 mM acetoacetate, 100 nM insulin (0.05 unit/ml), or both. Net glycogen breakdown occurred in the glucose group only and was converted to net glycogen synthesis in the presence of all additions. The flux of [2-3H]glucose through P-glucoisomerase (EC 5.3.1.9) was reduced with ketones, elevated with insulin, and unchanged with the combination. Net glycolytic flux was reduced in the presence of ketones and the combination. The flux control coefficients were determined for the portion of the pathway involving glucose transport to the branches of glycogen synthesis and glycolysis. Major control was divided between the glucose transporter and hexokinase (EC 2.7.1.1) in the glucose group. The distribution of the control was slightly shifted to hexokinase with ketones, and control at the glucose transport step was abolished in the presence of insulin. Analysis of the pathway from 3-P-glycerate to pyruvate determined that the major control was shared by enolase (EC 4.2.1.1) and pyruvate kinase (EC 2.7.1.40) in the glucose group. Addition of ketones, insulin, or the combination shifted the control to P-glycerate mutase (EC 5.4.2.1) and pyruvate kinase. These results illustrate that the control of the metabolic flux in glucose metabolism of rat heart is not exerted by a single enzyme but variably distributed among enzymes depending upon substrate availability, hormonal stimulation, or other changes of conditions.

Metabolic Control Analysis has provided tools for understanding and quantifying the regulation of biochemical systems, but the values of control coefficients in non-trivial systems can depend on the values of a large number of quantities: metabolite concentrations, fluxes and elasticity coefficients. This poses two related questions. One concerns the accuracy and precision of the values obtained for the control coefficients, depending as they do on a large number of experimentally determined values. The second concerns the importance of the variables in determining the values of the control coefficients: as these variables represent components of the biochemical system under consideration, this corresponds to the question of how do the components determine the regulatory properties of the system? This paper describes an extension to an earlier sensitivity analysis of the control coefficients that can be used to answer both of these questions. The analysis has been incorporated into a computer program (MetaCon), so enabling rapid and automatic determination of the sensitivities of each of the control coefficients to each of the experimental quantities. The program has been used to analyse the control coefficients of two experimental systems taken from the literature. The results of the analysis are presented. Two important points arise: control coefficients in a given biochemical system can show wide variations in their sensitivities to experimental error but, for non-trivial systems, experimental errors of greater than 10-20% may well result in unacceptable errors in calculated control coefficients.

A computer program (MetaCon) is described for the evaluation of flux control, concentration control and branch-point distribution control coefficients of a metabolic pathway. Requiring only the reaction scheme as input, the program produces algebraic expressions for the control coefficients in terms of elasticity coefficients, metabolite concentrations and pathway fluxes. Any of these variables can be substituted by numeric or simple algebraic expressions; the expressions will then be automatically rearranged in terms of the remaining unknown variables. When all variables have been substituted, numeric values will be obtained for the control coefficients. The program is a computerized implementation of the matrix method for the determination of control coefficients. The features of MetaCon are compared with those of other programs available to workers in Metabolic Control Analysis. Potential benefits of, and methods of using, MetaCon are discussed. The mathematical background and validity of the matrix method rules are discussed, and the algorithm used by MetaCon is described. The matrix method is shown to be a specific case of a previously described general formalism for calculating control coefficients.