Control of the flux in the arginine pathway of Neurospora crassa. Modulations of enzyme activity and concentration

The metabolic control theory: Its development and its application to mitochondrial oxidative phosphorylation

Metabolic Control Theory (MCT) and Metabolic Control Analysis (MCA) are the two sides, theoretical and experimental, of the measurement of the sensitivity of metabolic networks in the vicinity of a steady state. We will describe the birth and the development of this theory from the first analyses of linear pathways up to a global mathematical theory applicable to any metabolic network. We will describe how the theory, given the global nature of mitochondrial oxidative phosphorylation, solved the problem of what controls mitochondrial ATP synthesis and then how it led to a better understanding of the differential tissue expression of human mitochondrial pathologies and of the heteroplasmy of mitochondrial DNA, leading to the concept of the threshold effect.

On paradoxes between optimal growth, metabolic control analysis, and flux balance analysis

In Microbiology it is often assumed that growth rate is maximal. This may be taken to suggest that the dependence of the growth rate on every enzyme activity is at the top of an inverse-parabolic function, i.e. that all flux control coefficients should equal zero. This might seem to imply that the sum of these flux control coefficients equals zero. According to the summation law of Metabolic Control Analysis (MCA) the sum of flux control coefficients should equal 1 however. And in Flux Balance Analysis (FBA) catabolism is often limited by a hard bound, causing catabolism to fully control the fluxes, again in apparent contrast with a flux control coefficient of zero. Here we resolve these paradoxes (apparent contradictions) in an analysis that uses the 'Edinburgh pathway', the 'Amsterdam pathway', as well as a generic metabolic network providing the building blocks or Gibbs energy for microbial growth. We review and show that (i) optimization depends on so-called enzyme control coefficients rather than the 'catalytic control coefficients' of MCA's summation law, (ii) when optimization occurs at fixed total protein, the former differ from the latter to the extent that they may all become equal to zero in the optimum state, (iii) in more realistic scenarios of optimization where catalytically inert biomass is compensating or maintenance metabolism is taken into consideration, the optimum enzyme concentrations should not be expected to equal those that maximize the specific growth rate, (iv) optimization may be in terms of yield rather than specific growth rate, which resolves the paradox because the sum of catalytic control coefficients on yield equals 0, (v) FBA effectively maximizes growth yield, and for yield the summation law states 0 rather than 1, thereby removing the paradox, (vi) furthermore, FBA then comes more often to a 'hard optimum' defined by a maximum catabolic flux and a catabolic-enzyme control coefficient of 1. The trade-off between maintenance metabolism and growth is highlighted as worthy of further analysis.

Whole-cell metabolic control analysis

Since its conception some fifty years ago, metabolic control analysis (MCA) aims to understand how cells control their metabolism by adjusting the activity of their enzymes. Here we extend its scope to a whole-cell context. We consider metabolism in the evolutionary context of growth-rate maximisation by optimisation of protein concentrations. This framework allows for the prediction of flux control coefficients from proteomics data or stoichiometric modelling. Since genes compete for finite biosynthetic resources, we treat all protein concentrations as interdependent. We show that elementary flux modes (EFMs) emerge naturally as the optimal metabolic networks in the whole-cell context and we derive their control properties. In the evolutionary optimum, the number of expressed EFMs is determined by the number of protein-concentration constraints that limit growth rate. We use published glucose-limited chemostat data of S. cerevisiae to illustrate that it uses only two EFMs prior to the onset of fermentation and that it uses four EFMs during fermentation. We discuss published enzyme-titration data to show that S. cerevisiae and E. coli indeed can express proteins at growth-rate maximising concentrations. Accordingly, we extend MCA to elementary flux modes operating at an optimal state. We find that the expression of growth-unassociated proteins changes results from classical metabolic control analysis. Finally, we show how flux control coefficients can be estimated from proteomics and ribosome-profiling data. We analyse published proteomics data of E. coli to provide a whole-cell perspective of the control of metabolic enzymes on growth rate. We hope that this paper stimulates a renewed interest in metabolic control analysis, so that it can serve again the purpose it once had: to identify general principles that emerge from the biochemistry of the cell and are conserved across biological species.

Evolution of Henrik Kacser's thought: Early publications on the organization of the whole system

Although the papers of Kacser and Burns (1973) and Heinrich and Rapoport (1974a,b) are commonly taken as the birth of metabolic control analysis, many of the ideas in them are foreshadowed in earlier papers, from 1956 onwards, when Kacser first argued for taking a systemic view of genetics and biochemistry.

Plants are intelligent, here's how

HYPOTHESES

The drive to survive is a biological universal. Intelligent behaviour is usually recognized when individual organisms including plants, in the face of fiercely competitive or adverse, real-world circumstances, change their behaviour to improve their probability of survival.

SCOPE

This article explains the potential relationship of intelligence to adaptability and emphasizes the need to recognize individual variation in intelligence showing it to be goal directed and thus being purposeful. Intelligent behaviour in single cells and microbes is frequently reported. Individual variation might be underpinned by a novel learning mechanism, described here in detail. The requirements for real-world circumstances are outlined, and the relationship to organic selection is indicated together with niche construction as a good example of intentional behaviour that should improve survival. Adaptability is important in crop development but the term may be complex incorporating numerous behavioural traits some of which are indicated.

CONCLUSION

There is real biological benefit to regarding plants as intelligent both from the fundamental issue of understanding plant life but also from providing a direction for fundamental future research and in crop breeding.

Evolution on the Biophysical Fitness Landscape of an RNA Virus

Viral evolutionary pathways are determined by the fitness landscape, which maps viral genotype to fitness. However, a quantitative description of the landscape and the evolutionary forces on it remain elusive. Here, we apply a biophysical fitness model based on capsid folding stability and antibody binding affinity to predict the evolutionary pathway of norovirus escaping a neutralizing antibody. The model is validated by experimental evolution in bulk culture and in a drop-based microfluidics that propagates millions of independent small viral subpopulations. We demonstrate that along the axis of binding affinity, selection for escape variants and drift due to random mutations have the same direction, an atypical case in evolution. However, along folding stability, selection and drift are opposing forces whose balance is tuned by viral population size. Our results demonstrate that predictable epistatic tradeoffs between molecular traits of viral proteins shape viral evolution.

Systems, variation, individuality and plant hormones

Inter-individual variation in plants and particularly in hormone content, figures strongly in evolution and behaviour. Homo sapiens and Arabidopsis exhibit similar and substantial phenotypic and molecular variation. Whereas there is a very substantial degree of hormone variation in mankind, reports of inter-individual variation in plant hormone content are virtually absent but are likely to be as large if not larger than that in mankind. Reasons for this absence are discussed. Using an example of inter-individual variation in ethylene content in ripening, the article shows how biological time is compressed by hormones. It further resolves an old issue of very wide hormone dose response that result directly from negative regulation in hormone (and light) transduction. Negative regulation is used because of inter-individual variability in hormone synthesis, receptors and ancillary proteins, a consequence of substantial genomic and environmental variation. Somatic mosaics have been reported for several plant tissues and these too contribute to tissue variation and wide variation in hormone response. The article concludes by examining what variation exists in gravitropic responses. There are multiple sensing systems of gravity vectors and multiple routes towards curvature. These are an aspect of the need for reliability in both inter-individual variation and unpredictable environments. Plant hormone inter-individuality is a new area for research and is likely to change appreciation of the mechanisms that underpin individual behaviour.

Plant metabolic modeling: achieving new insight into metabolism and metabolic engineering

Models are used to represent aspects of the real world for specific purposes, and mathematical models have opened up new approaches in studying the behavior and complexity of biological systems. However, modeling is often time-consuming and requires significant computational resources for data development, data analysis, and simulation. Computational modeling has been successfully applied as an aid for metabolic engineering in microorganisms. But such model-based approaches have only recently been extended to plant metabolic engineering, mainly due to greater pathway complexity in plants and their highly compartmentalized cellular structure. Recent progress in plant systems biology and bioinformatics has begun to disentangle this complexity and facilitate the creation of efficient plant metabolic models. This review highlights several aspects of plant metabolic modeling in the context of understanding, predicting and modifying complex plant metabolism. We discuss opportunities for engineering photosynthetic carbon metabolism, sucrose synthesis, and the tricarboxylic acid cycle in leaves and oil synthesis in seeds and the application of metabolic modeling to the study of plant acclimation to the environment. The aim of the review is to offer a current perspective for plant biologists without requiring specialized knowledge of bioinformatics or systems biology.

1,4-naphthoquinones and other NADPH-dependent glutathione reductase-catalyzed redox cyclers as antimalarial agents

The homodimeric flavoenzyme glutathione reductase catalyzes NADPH-dependent glutathione disulfide reduction. This reaction is important for keeping the redox homeostasis in human cells and in the human pathogen Plasmodium falciparum. Different types of NADPH-dependent disulfide reductase inhibitors were designed in various chemical series to evaluate the impact of each inhibition mode on the propagation of the parasites. Against malaria parasites in cultures the most potent and specific effects were observed for redox-active agents acting as subversive substrates for both glutathione reductases of the Plasmodium-infected red blood cells. In their oxidized form, these redox-active compounds are reduced by NADPH-dependent flavoenzyme-catalyzed reactions in the cytosol of infected erythrocytes. In their reduced forms, these compounds can reduce molecular oxygen to reactive oxygen species, or reduce oxidants like methemoglobin, the major nutrient of the parasite, to indigestible hemoglobin. Furthermore, studies on a fluorinated suicide-substrate of the human glutathione reductase indicate that the glutathione reductase-catalyzed bioactivation of 3-benzylnaphthoquinones to the corresponding reduced 3-benzoyl metabolites is essential for the observed antimalarial activity. In conclusion, the antimalarial lead naphthoquinones are suggested to perturb the major redox equilibria of the targeted cells. These effects result in developmental arrest of the parasite and contribute to the removal of the parasitized erythrocytes by macrophages.

The 2-oxoglutarate supply exerts significant control on the lysine synthesis flux in Saccharomyces cerevisiae

To determine the extent to which the supply of the precursor 2-oxoglutarate (2-OG) controls the synthesis of lysine in Saccharomyces cerevisiae growing exponentially in high glucose, top-down elasticity analysis was used. Three groups of reactions linked by 2-OG were defined. The 2-OG supply group comprised all metabolic steps leading to its formation, and the two 2-OG consumer groups comprised the enzymes and transporters involved in 2-OG transformation into lysine and glutamate and their further utilization for protein synthesis and storage. Various 2-OG steady-state concentrations that produced different fluxes to lysine and glutamate were attained using yeast mutants with increasing activities of Krebs cycle enzymes and decreased activities of Lys synthesis enzymes. The elasticity coefficients of the three enzyme groups were determined from the dependence of the amino acid fluxes on the 2-OG concentration. The respective degrees of control on the flux towards lysine (flux control coefficients) were determined from their elasticities, and were 1.1, 0.41 and -0.52 for the 2-OG producer group and the Lys and Glu branches, respectively. Thus, the predominant control exerted by the 2-OG supply on the rate of lysine synthesis suggests that over-expression of 2-OG producer enzymes may be a highly effective strategy to enhance Lys production.

The Lys20 homocitrate synthase isoform exerts most of the flux control over the lysine synthesis pathway in Saccharomyces cerevisiae

In Saccharomyces cerevisiae, the first committed step in the lysine (Lys) biosynthetic pathway is catalysed by the Lys20 and Lys21 homocitrate synthase (HCS) isoforms. Overexpression of Lys20 resulted in eightfold increased Lys, as well as 2-oxoglutarate pools, which were not attained by overexpressing Lys21 or other pathway enzymes (Lys1, Lys9 or Lys12). A metabolic control analysis-based strategy, by gradually and individually manipulating the Lys20 and Lys21 activities demonstrated that the cooperative and strongly feedback-inhibited Lys21 isoform exerted low control of the pathway flux whereas most of the control resided on the non-cooperative and weakly feedback-inhibited Lys20 isoform. Therefore, the higher control of Lys20 over the Lys flux represents an exception to the dogma of higher pathway control by the strongest feedback-inhibited enzyme and points out to multi-site engineering (HCS isoforms and supply of precursors) to increase Lys synthesis.

Towards a quantitative prediction of the fluxome from the proteome

The promise of proteomics and fluxomics is limited by our current inability to integrate these two levels of cellular organization. Here we present the derivation, experimental parameterization, and appraisal of flux functions that enable the quantitative prediction of changes in metabolic fluxes from changes in enzyme levels. We based our derivation on the hypothesis that, in the determination of steady-state flux changes, the direct proportionality between enzyme concentrations and reaction rates is principal, whereas the complexity of enzyme-metabolite interactions is secondary and can be described using an approximate kinetic format. The quality of the agreement between predicted and experimental fluxes in Lactococcus lactis, supports our hypothesis and demonstrates the need and usefulness of approximative descriptions in the study of complex biological systems. Importantly, these flux functions are scalable to genome-wide networks, and thus drastically expand the capabilities of flux prediction for metabolic engineering efforts beyond those conferred by the currently used constraints-based models.

Systems biochemistry in practice: experimenting with modelling and understanding, with regulation and control

Biology and medicine have become ‘big science’, even though we may not always like this: genomics and the subsequent analysis of what the genomes encode has shown that interesting living organisms require many more than 300 gene products to interact. We once thought that somewhere in this jungle of interacting macromolecules was hidden the molecule that constitutes the secret of Life, and therewith of health and disease. Now we know that, somehow, the secret of Life is the jungle of interactions. Consequently, we need to find the Rosetta Stones, i.e. interpretations of this jungle of systems biology. We need to find, perhaps convoluted, paths of understanding and intervention. Systems biochemistry is a good place to start, as it has the foothold that what goes in must come out. In the present paper, we review two strategies, which look at control and regulation. We discuss the difference between control and regulation and prove a relationship between them.

Super life--how and why 'cell selection' leads to the fastest-growing eukaryote

What is the highest possible replication rate for living organisms? The cellular growth rate is controlled by a variety of processes. Therefore, it is unclear which metabolic process or group of processes should be activated to increase growth rate. An organism that is already growing fast may already have optimized through evolution all processes that could be optimized readily, but may be confronted with a more generic limitation. Here we introduce a method called 'cell selection' to select for highest growth rate, and show how such a cellular site of 'growth control' was identified. By applying pH-auxostat cultivation to the already fast-growing yeast Kluyveromyces marxianus for a sufficiently long time, we selected a strain with a 30% increased growth rate; its cell-cycle time decreased to 52 min, much below that reported to date for any eukaryote. The increase in growth rate was accompanied by a 40% increase in cell surface at a fairly constant cell volume. We show how the increase in growth rate can be explained by a dominant (80%) limitation of growth by the group of membrane processes (a 0.7% increase of specific growth rate to a 1% increase in membrane surface area). Simultaneous activation of membrane processes may be what is required to accelerate growth of the fastest-growing form of eukaryotic life to growth rates that are even faster, and may be of potential interest for single-cell protein production in industrial 'White' biotechnology processes.

Metabolic control analysis: a tool for designing strategies to manipulate metabolic pathways

The traditional experimental approaches used for changing the flux or the concentration of a particular metabolite of a metabolic pathway have been mostly based on the inhibition or over-expression of the presumed rate-limiting step. However, the attempts to manipulate a metabolic pathway by following such approach have proved to be unsuccessful. Metabolic Control Analysis (MCA) establishes how to determine, quantitatively, the degree of control that a given enzyme exerts on flux and on the concentration of metabolites, thus substituting the intuitive, qualitative concept of rate limiting step. Moreover, MCA helps to understand (i) the underlying mechanisms by which a given enzyme exerts high or low control and (ii) why the control of the pathway is shared by several pathway enzymes and transporters. By applying MCA it is possible to identify the steps that should be modified to achieve a successful alteration of flux or metabolite concentration in pathways of biotechnological (e.g., large scale metabolite production) or clinical relevance (e.g., drug therapy). The different MCA experimental approaches developed for the determination of the flux-control distribution in several pathways are described. Full understanding of the pathway properties when is working under a variety of conditions can help to attain a successful manipulation of flux and metabolite concentration.

Extreme nuclear disproportion and constancy of enzyme activity in a heterokaryon of Neurospora crassa

Heterokaryons of Neurospora crassa were generated by transformation of multinucleate conidia of a histidine-3 auxotroph with his-3(+) plasmid. In one of the transformants, propagated on a medium with histidine supplementation, a gradual but drastic reduction occurred in the proportion of prototrophic nuclei that contained an ectopically integrated his-3(+) allele. This response was specific to histidine. The reduction in prototrophic nuclei was confirmed by several criteria: inoculum size test, hyphal tip analysis, genomic Southern analysis, and by visual change in colour of the transformant incorporating genetic colour markers. Construction and analyses of three-component heterokaryons revealed that the change in nuclear ratio resulted from interaction of auxotrophic nucleus with prototrophic nucleus that contained an ectopically integrated his-3(+) gene, but not with prototrophic nucleus that contained his-3(+) gene at the normal chromosomal location. The growth rate of heterokaryons and the activity of histidinol dehydrogenase - the protein encoded by the his-3(+) gene - remained unchanged despite prototrophic nuclei becoming very scarce. The results suggest that not all nuclei in the coenocytic fungal mycelium may be active simultaneously, the rare active nuclei being sufficient to confer the wild-type phenotype.

Biochemical pathways and mechanisms nitrogen, amino acid, and carbon metabolism

For both nitrogen and carbon metabolism there exist specific regulatory mechanisms to enable cells to assimilate a wide variety of nitrogen and carbon sources. Superimposed are regulatory circuits, the so called nitrogen and carbon catabolite regulation, to allow for selective use of "rich" sources first and "poor" sources later. Evidence points to the importance of specific regulatory mechanisms for short term adaptations, while generalized control circuits are used for long term modulation of nitrogen and carbon metabolism. Similarly a variety of regulatory mechanisms operate in amino acid metabolism. Modulation of enzyme activity and modulation of enzyme levels are the outstanding regulatory mechanisms. In prokaryotes, attenuation and repressor/operator control are predominant, besides a so called "metabolic control" which integrates amino acid metabolism into the overall nutritional status of the cells. In eukaryotic cells compartmentation of amino acid metabolites as well as of part of the pathways becomes an additional regulatory factor; pathway specific controls seem to be rare, but a complex regulatory network, the "general control of amino acid biosynthesis", coordinates the synthesis of enzymes of a number of amino acid biosynthetic pathways.

Use of sensitivity analysis to assess reliability of metabolic and physiological models

Because ethical considerations often preclude directly determining the human health effects of treatments or interventions by experimentation, such effects are estimated by extrapolating reactions predicted from animal experiments. Under such conditions, it must be demonstrated that the reliability of the extrapolated predictions is not excessively affected by inherent data limitations and other components of model specification. This is especially true of high-level models composed of ad hoc algebraic equations whose parameters do not correspond to specific physical properties or processes. Models based on independent experimental data restricting the numerical space of parameters that do represent actual physical properties can be represented at a more detailed level. Sensitivities of the computed trajectories to parameter variations permit more detailed attribution of uncertainties in the predictions to these low-level properties. S-systems, in which parameters are estimated empirically, and physiological models, whose parameters can be estimated accurately from independent data, are used to illustrate the applicability of trajectory sensitivity analysis to lower-level models.

Variation of enzyme activities at a branched pathway involved in the utilization of gluconate in Escherichia coli

Twenty-four strains of Escherichia coli from the ECOR collection were characterized for growth rate in gluconate minimal salts medium and for Vmax and Km of the three enzymes (gluconokinase, 6-phosphogluconate dehydrogenase, and 6-phosphogluconate dehydratase) that form a branch point for the utilization of gluconate. A total of 11 characters--growth rate, three Vmax values, four Km values, and three Vmax/Km values--were determined for these 24 ECOR strains. Most of the characters were normally distributed. Statistical tests showed that growth rate is significantly less variable than enzyme activities. Also, analyses of variance showed significant differences among strains and among the extant five genetic groups of E. coli for the characters measured. A Mantel test showed that, for some characters, closely related strains shared similar character values. Two hypotheses regarding the relationships between growth rate and enzyme activity and between various enzyme activities were tested. None of the expected correlations between growth rate and enzyme activity or between enzyme activities was detected. The results were discussed in terms of metabolic control analysis and neutral theory.

Regulation in metabolic systems under homeostatic flux control

The general properties of metabolic systems under homeostatic flux control are analyzed. It is shown that the main characteristic point for an enzyme in such a system is a sharp transition from limitation outside the system to limitation by some enzyme inside the system. A method for the quantitative treatment of the experimental dependence of metabolic flux on enzyme content is presented. The conception of "nonlimiting," "near-limiting," and "limiting" enzymes is developed for these systems. It is pointed out that reactions close to a thermodynamic equilibrium under normal conditions can considerably limit the homeostatic fluxes. The rules for regulation of fluxes in such systems are illustrated by the data obtained for transgenic plants with reduced activities of some Calvin-cycle enzymes and further examples. A comparison is made between the developed quantitative description of metabolic fluxes under homeostatic flux control and the methods of metabolic control analysis.

Engineering a living cell to desired metabolite concentrations and fluxes: pathways with multifunctional enzymes

With molecular genetics enabling modulation of the concentrations of cellular enzymes, metabolic engineering becomes limited by the question of which modulations of the enzyme concentrations are required to bring about a desired pattern of cellular metabolism. In an earlier paper (Kholodenko et al. (1998). Biotechnol. Bioeng. 59, 239-247) we derived a method to determine the required modulations. This method, however, cannot be immediately applied to cellular pathways with enzymes catalyzing more than one step in metabolism (multifunctional enzymes). In the present paper we show to which extent the presence of multifunctional enzymes limits biotechological ambitions, which one might otherwise pursue in vain. In particular, it is impossible to change the concentration of a single intermediate and leave the rest of metabolism unperturbed if that intermediate interacts directly with a multifunctional enzyme. The analytical machinery of Metabolic Control Analysis is used to relate the desired and ensuing changes in the metabolic pattern. An explicit solution to this problem of engineering metabolism is then given in the form of a single matrix equation.

Metabolic control analysis of biochemical pathways based on a thermokinetic description of reaction rates

Metabolic control analysis is a powerful technique for the evaluation of flux control within biochemical pathways. Its foundation is the elasticity coefficients and the flux control coefficients (FCCs). On the basis of a thermokinetic description of reaction rates it is here shown that the elasticity coefficients can be calculated directly from the pool levels of metabolites at steady state. The only requirement is that one thermodynamic parameter be known, namely the reaction affinity at the intercept of the tangent in the inflection point of the curve of reaction rate against reaction affinity. This parameter can often be determined from experiments in vitro. The methodology is applicable only to the analysis of simple two-step pathways, but in many cases larger pathways can be lumped into two overall conversions. In cases where this cannot be done it is necessary to apply an extension of the thermokinetic description of reaction rates to include the influence of effectors. Here the reaction rate is written as a linear function of the logarithm of the metabolite concentrations. With this type of rate function it is shown that the approach of Delgado and Liao [Biochem. J. (1992) 282, 919-927] can be much more widely applied, although it was originally based on linearized kinetics. The methodology of determining elasticity coefficients directly from pool levels is illustrated with an analysis of the first two steps of the biosynthetic pathway of penicillin. The results compare well with previous findings based on a kinetic analysis.

Defining control coefficients in non-ideal metabolic pathways

The extent to which an enzyme controls a flux has been defined as the effect on that flux of a small modulation of the activity of that enzyme divided by the magnitude of the modulation. We here show that in pathways with metabolic channelling or high enzyme concentrations and conserved moieties involving both enzymic and non-enzymic species, this definition is ambiguous; the magnitude of the corresponding flux control coefficient depends on how the enzyme activity is modulated. This is illustrated with two models of biochemically relevant pathways, one in which dynamic metabolite channelling plays a role, and one with a moiety-conserved cycle. To avoid such ambiguity, we view biochemical pathways in a more detailed manner, i.e., as a network of elemental steps. We define 'elemental control coefficients' in terms of the effect on a flux of an equal modulation of the forward and reverse rate constant of any such elemental step (which may correspond to transitions between enzyme states). This elemental control coefficient is independent of the method of modulation. We show how metabolic control analysis can proceed when formulated in terms of the elemental control coefficients and how the traditional control coefficients are related to these elemental control coefficients. An 'impact' control coefficient is defined which quantifies the effect of an activation of all elemental processes in which an enzyme is involved. It equals the sum of the corresponding elemental control coefficients. In ideal metabolic pathways this impact control coefficient reduces to the traditional flux control coefficient. Differences between the traditional control coefficients are indicative of non-ideality of a metabolic pathway, i.e. of channelling or high enzyme concentrations.

Energy, control and DNA structure in the living cell

Maintenance (let alone growth) of the highly ordered living cell is only possible through the continuous input of free energy. Coupling of energetically downhill processes (such as catabolic reactions) to uphill processes is essential to provide this free energy and is catalyzed by enzymes either directly or via "storage" in an intermediate high energy form, i.e., high ATP/ADP ratio or H+ ion gradient. Although maintenance of a sufficiently high ATP/ADP ratio is essential to overcome the thermodynamic burden of uphill processes, it is not clear to what degree enzymes that control this ratio also control cell physiology. Indeed, in the living cell homeostatic control mechanisms might exist for the free-energy transduction pathways so as to prevent perturbation of cellular function when the Gibbs energy supply is compromised. This presentation addresses the extent to which the intracellular ATP level is involved in the control of cell physiology, how the elaborate control of cell function may be analyzed theoretically and quantitatively, and if this can be utilized selectively to affect certain cell types.

Control theory of metabolic channelling

Various factors appear to control muscle energetics, often in conjunction. This calls for a quantitative approach of the type provided by Metabolic Control Analysis for intermediary metabolism and mitochondrial oxidative phosphorylation. To the extent that direct transfer of high energy phosphates and spatial organization plays a role in muscle energetics however, the standard Metabolic Control Theory does not apply, neither do its theorems regarding control. This paper develops the Control Theory that does apply to the muscle system. It shows that direct transfer of high energy phosphates bestows a system with enhanced control: the sum of the control exerted by the participating enzymes on the flux of free energy from the mitochondrial matrix to the actinomyosin may well exceed the 100% mandatory for ideal metabolic pathways. It is also shown how sequestration of high energy phosphates may allow for negative control on pathway flux. The new control theory gives method functionally to diagnose the extent to which channelling and metabolite sequestration occur.

Control in channelled pathways. A matrix method calculating the enzyme control coefficients

The usual equations expressing the enzyme control coefficients (quantitative indicators of 'global' control properties of a pathway) via the elasticity coefficients (reflecting local kinetic properties of an enzyme reaction), cannot be applied to a variety of 'non-ideal' pathways, in particular to pathways with metabolic channelling. Here we show that the relationship between the control and elasticity coefficients can be obtained by considering such a metabolic pathway as a network of elemental chemical conversions (steps). To calculate the control coefficients of enzymes one should first determine the elasticity coefficients of such elemental steps and then take their appropriate combinations. Although the method is illustrated for a channelled pathway it can be used for any non-ideal pathway including those with high enzyme concentrations where the sequestration of metabolites by enzymes cannot be neglected.

A molecular investigation of genotype by environment interactions

The fitnesses conferred by seven lactose operons, which had been transduced into a common genetic background from natural isolates of Escherichia coli, were determined during competition for growth rate-limiting quantities of galactosyl-glycerol, a naturally occurring galactoside. The fitnesses of these same operons have been previously determined on lactose and three artificial galactosides, lactulose, methyl-galactoside and galactosyl-arabinose. Analysis suggests that although marked genotype by environment interactions occur, changes in the fitness rankings are rare. The relative activities of the beta-galactosidases and the permeases were determined on galactosyl-glycerol, lactose, lactulose and methyl-galactoside. Both enzymes display considerable kinetic variation. The beta-galactosidase alleles provide no evidence for genotype by environment interactions at the level of enzyme activity. The permease alleles display genotype by environment interactions with a few causing changes in activity rankings. The contributions to fitness made by the permeases and the beta-galactosidases were partitioned using metabolic control analysis. Most of the genotype by environment interaction at the level of fitness is generated by changes in the distribution of control among steps in the pathway, particularly at the permease where large control coefficients ensure that its kinetic variation has marked fitness effects. Indeed, changes in activity rankings at the permease account for the few changes in fitness rankings. In contrast, the control coefficients of the beta-galactosidase are sufficiently small that its kinetic variation is in, or close to, the neutral limit. The selection coefficients are larger on the artificial galactosides because the control coefficients of the permease and beta-galactosidase are larger. The flux summation theorem requires that control coefficients associated with other steps in the pathway must be reduced, implying that the selection at these steps will be less intense on the artificial galactosides. This suggests that selection intensities need not be greater in novel environments.

A method for increasing the concentration of a specific internal metabolite in steady-state systems

An approach is described by which it is possible to increase the concentration of any internal metabolite without affecting the concentrations of other metabolites and fluxes in the organism. This approach requires the manipulation of only a limited number of enzyme activities. The method shows which enzymes to manipulate and the extent of the manipulation required to achieve a given increase in a chosen metabolite. A case study involving tryptophan overproduction in Saccharomyces cerevisae is given as a practical example of how this method could be used.

The kinetic basis of threshold effects observed in mitochondrial diseases: a systemic approach

Threshold effects in the expression of metabolic diseases have often been observed in mitochondrial pathologies, i.e. the clinical demonstration of the disease appears only when the activity of a step has been reduced to a rather low level. We show experimentally that an inhibition of cytochrome c oxidase activity by cyanide, simulating a defect in this step, leads to a decrease in mitochondrial respiration which then exhibits a threshold behaviour similar to that observed in mitochondrial diseases. We discuss this behaviour in terms of metabolic control theory and construct a mathematical model simulating this behaviour.

Control theory of metabolic channelling

Various factors appear to control muscle energetics, often in conjunction. This calls for a quantitative approach of the type provided by Metabolic Control Analysis for intermediary metabolism and mitochondrial oxidative phosphorylation. To the extent that direct transfer of high energy phosphates and spatial organization plays a role in muscle energetics however, the standard Metabolic Control Theory does not apply, neither do its theorems regarding control. This chapter develops the Control Theory that does apply to the muscle system. It shows that direct transfer of high energy phosphates bestows a system with enhanced control: the sum of the control exerted by the participating enzymes on the flux of free energy form the mitochondrial matrix to the actinomyosin may well exceed the 100% mandatory for ideal metabolic pathways. It is also shown how sequestration of high energy phosphates may allow for negative control on pathway flux. The new control theory gives methods functionally to diagnose the extent to which channelling and metabolite sequestration occur.

Fitness, flux and phantoms in temporally variable environments

The evolutionary problem of selection in temporally variable environments is addressed by investigating a metabolic model describing the approach to steady state of a flux emanating from a simple linear pathway of unsaturated enzymes catalyzing reversible monomolecular reactions. Analysis confirms previous claims that steps having no influence on the steady state flux may influence transient behavior, and that enzymes immune to natural selection at steady state may become subject to selection when fitness is a function of individual transient metabolic events. Indeed, calculations show that the beta-galactosidase of Escherichia coli, which exerts a negligible effect on the steady state lactose flux, controls the approach to steady state. However, after 6 sec the lactose flux is within 0.1% of steady state, and so an ever changing environment must be invoked to continually expose beta-galactosidase to selection. Analysis of the metabolic model undergoing multiple transient events reveals that fitness differences remain unaffected if enzyme activities remain constant and become minimized if enzyme activities differ among environments. Until suitable data become available, claims that metabolic behavior away from steady state necessarily exposes a far greater proportion of allozymes to natural selection should be treated with great skepticism.

Determination of control coefficients in intact metabolic systems

The control structure of a metabolic system can in principle be determined without the need for purification of the component enzymes and study of their kinetic properties, provided that their activities can be perturbed by amounts sufficient to produce measurable changes in the steady-state variables, i.e. the fluxes through the system and the concentrations of the intermediates. Each perturbation is characterized in terms of the co-response coefficients of all pairs of variables, i.e. the slopes of the lines produced when the logarithm of one variable is plotted against the logarithm of another, both varying in response to the same perturbation. If all the co-response coefficients are assembled into a matrix, the inverse of this matrix can be transformed into a matrix containing all the component elasticities, which can be inverted to provide the complete matrix of control coefficients. In a simple three-enzyme pathway studied, the analysis proves not to require unrealistically high accuracy in the original co-response measurements: even with errors with standard deviation +/- 5.77 degrees in the angles to the horizontal of the lines in the co-response plots (equivalent at best to errors of +/- 20% in the corresponding co-response coefficients), the final control coefficient matrix may be adequate for assessing the control structure of the system. Examination of literature data from studies of mitochondrial respiration and of gluconeogenesis indicates that considerably higher precision than this is achievable.

Succinate-cytochrome c reductase: assessment of its value in the investigation of defects of the respiratory chain

Defects of the respiratory chain are important causes of human disease and one of the most commonly used assays in the investigation of these patients is the measurement of succinate-cytochrome c reductase. However, this assay measures several components of the respiratory chain and the ability to detect a partial defect in one enzyme complex will depend on the amount of control exerted by that enzyme step on overall electron flux. We show that measurement of succinate-cytochrome c reductase activity may fail to detect partial defects of complex III and therefore is of limited diagnostic value in the identification of complex III defects. However, complex II is a major point of control of flux through succinate-cytochrome reductase and it is likely that measurement of the latter will detect defects of complex II.

Responses of metabolic systems to large changes in enzyme activities and effectors. 1. The linear treatment of unbranched chains

This first paper in a series investigates the problem of predicting and analysing the effects of large changes in enzyme activities or external nutrients/effectors on metabolic fluxes. We introduce the concept of a deviation index, D, which gives a measure of the relative change in a metabolic variable (e.g. flux) due to a large (non-infinitesimal) relative change in a parameter (e.g. enzyme). Using simplifying kinetic assumptions we have found, for an unbranched metabolic chain, a direct relationship between deviation indices and flux control coefficients. This relationship provides a method to estimate flux control coefficients using a single large change in enzyme activity. We also provide a method of predicting the effects of, for example, DNA manipulation or other techniques for enzyme activity/concentration changes on metabolic fluxes. Up-modulations of single enzymes rarely produce significant changes in fluxes. We show that combined changes of activity of a group of enzymes will produce a more than 'additive' response. We provide a method of predicting the effects of these combined changes, given either the flux control coefficients of the group of enzymes or the effects on the flux of changing the enzymes individually. A similar analysis is carried out for large changes in external nutrients or effectors. These amplification factors, f, give experimentally accessible estimates of the expected changes in metabolic variables. We provide three 'case studies' to illustrate our results.

Responses of metabolic systems to large changes in enzyme activities and effectors. 2. The linear treatment of branched pathways and metabolite concentrations. Assessment of the general non-linear case

We extend the analysis of unbranched chains (preceding paper) to large parameter changes in branched systems using linear kinetic assumptions. More complex relationships between flux control coefficients and deviation indices are established. In particular, the deviation index in such systems depends on more than one control coefficient as well as on the magnitude of the enzyme change. Non-additivity of the indices is the general rule. Combined changes of groups of enzymes, whether co-ordinate or not, have also been formulated. Control coefficients can be estimated from a small number of independent large-change experiments. Alternatively, the amplification factors can be calculated given the knowledge of the control coefficients. A 'case study' using published data is presented. The movement of intermediate metabolites as a consequence of large parameter changes can be dealt with in a similar manner. Experimental methods for showing the admissibility of assuming the simplifying assumptions used are summarised. Some simulation studies show possible limits of the application of the approach and some aspects of the general, non-linear, case are discussed. It is concluded that, although metabolic systems are in principle non-linear, many behave, in practice, as quasi-linear systems. The relationships established between deviation indices and control coefficients therefore provide a practical way of predicting the effects of large-scale changes in parameters for many metabolic systems.

The use of lac-type promoters in control analysis

For control analysis, it is necessary to modulate the activity of an enzyme around its normal level and measure the changes in steady-state fluxes or concentrations. We describe an improved method for effecting the modulation, as elaborated for Escherichia coli. The chromosomal gene, encoding the enzyme of interest, is put under the control of a lacUV5 or a tacI promoter. The alternative use of the two promoters leads to an expression range which should make it suitable for the use in control analysis of many enzymes. The lacUV5 promoter should be used when the wild-type expression level is low, the tacI promoter when the latter is high. The endogenous lac operon is placed under the control of a second copy of the lacUV5 promoter and a lacY7am mutation (eliminating lactose permease, the transport system for the inducer isopropyl-thio-beta-D- galactoside) is introduced. The method was demonstrated experimentally by constructing E. coli strains, in which the chromosomal atp operon is transcribed from the lacUV5 and the tacI promoter. We measured the concentration of the c subunit of H(+)-ATPase, and found that the expression of this enzyme could be modulated between non-detectable levels and up to five times the wild-type level. Thus, in the absence of inducer, no expression of atp genes could be detected when the atp operon was controlled by the lacUV5 promoter, and we estimate that the expression was less than 0.0025 times the wild-type level. We show that the introduction of a lacY mutation facilitated the attainment of steady induction levels of partially induced cells. The mutation also reduced positive cooperativity in the dependence of expression on the concentration of isopropyl-thio-beta-D-galactoside (the inducer) and shifted the concentration of inducer needed for half maximum induction to higher values. These properties should facilitate the experimental modulation of the enzyme activity by varying the concentration of the inducer.