Nonoxidative pentose phosphate pathways and their direct role in ribose synthesis in tumors: is cancer a disease of cellular glucose metabolism?

Pentose phosphate pathways (PPP) are considered important in tumor proliferation processes because of their role in supplying tumor cells with reduced NADP and carbons for intracellular anabolic processes. Direct involvement of PPP in tumor DNA/RNA synthesis is not considered as significant as in lipid and protein syntheses. Currently, PPP activity in tumor cells is measured by lactate production, which shows a moderate activity: about 4% to 7% compared with glycolysis. Recent data generated in our laboratory indicate that PPP are directly involved in ribose synthesis in pancreatic adenocarcinoma cells, through oxidative steps (< 31%) and transketolase reactions (69%). These findings raise serious questions about the adequacy of lactate in measuring PPP activity in tumors. We hypothesize that ribose, not lactate, is the major product of PPP in tumor cells. Control of both oxidative and nonoxidative PPP may be critical in the treatment of cancer. PPP are substantially involved in the proliferation of human tumors, which raises the prospect of new treatment strategies targeting specific biochemical reactions of PPP by hormones related to glucose metabolism, controlling thiamine intake, the cofactor of the nonoxidative transketolase PPP reaction, or treating cancer patients with antithiamine analogues.

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

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

Oxythiamine and dehydroepiandrosterone inhibit the nonoxidative synthesis of ribose and tumor cell proliferation

This study investigates the significance of the glucose-6-phosphate dehydrogenase (G6PD) catalyzed oxidative and the transketolase (TK) catalyzed nonoxidative pentose cycle (PC) reactions in the tumor proliferation process by characterizing tumor growth patterns and synthesis of the RNA ribose moiety in the presence of respective inhibitors of G6PD and TK. Mass spectra analysis of 13C-labeled carbons revealed that these PC reactions contribute to over 85% of de novo ribose synthesis in RNA from [1,2-(13)C]glucose in cultured Mia pancreatic adenocarcinoma cells, with the fraction synthesized through the TK pathway predominating (85%). Five days of treatment with the TK inhibitor oxythiamine (OT) and the G6PD inhibitor dehydroepiandrosterone-sulfate (0.5 microM each) exerted a 39 and a 23% maximum inhibitory effect on cell proliferation in culture, which was increased to 60% when the two drugs were administered in combination. In vivo testing of 400 mg/kg OT or dehydroepiandrosterone-sulfate in C57BL/6 mice hosting Ehrlich's ascitic tumor cells revealed a 90.4 and a 46% decrease in the final tumor mass after 3 days of treatment. RNA ribose fractional synthesis through the TK reaction using metabolites directly from glycolysis declined by 9.1 and 23.9% after OT or the combined treatment, respectively. Nonoxidative PC reactions play a central regulating role in the carbon-recruiting process toward de novo nucleic acid ribose synthesis and cell proliferation in vitro and in vivo. Therefore, enzymes or substrates regulating the nonoxidative synthesis of ribose could also be the sites to preferentially target tumor cell proliferation by new anticancer drugs.

How did glycogen structure evolve to satisfy the requirement for rapid mobilization of glucose? A problem of physical constraints in structure building

Optimization of molecular design in cellular metabolism is a necessary condition for guaranteeing a good structure-function relationship. We have studied this feature in the design of glycogen by means of the mathematical model previously presented that describes glycogen structure and its optimization function [Meléndez-Hevia et al. (1993), Biochem J 295: 477-483]. Our results demonstrate that the structure of cellular glycogen is in good agreement with these principles. Because the stored glucose in glycogen must be ready to be used at any phase of its synthesis or degradation, the full optimization of glycogen structure must also imply the optimization of every intermediate stage in its formation. This case can be viewed as a molecular instance of the eye problem, a classical paradigm of natural selection which states that every step in the evolutionary formation of a functional structure must be functional. The glycogen molecule has a highly optimized structure for its metabolic function, but the optimization of the full molecule has meaning and can be understood only by taking into account the optimization of each intermediate stage in its formation.

Validation and steady-state analysis of a power-law model of purine metabolism in man

The paper introduces a model of human purine metabolism in situ. Chosen from among several alternative system descriptions, the model is formulated as a Generalized Mass Action system within Biochemical Systems Theory and validated with analyses of steady-state and dynamic characteristics. Eigenvalue and sensitivity analyses indicate that the model has a stable and robust steady-state. The model quite accurately reproduces numerous biochemical and clinical observations in healthy subjects as well as in patients with disorders of purine metabolism. These results suggest that the model can be used to assess biochemical and clinical aspects of human purine metabolism. It provides a means of exploring effects of enzyme deficiencies and is a potential tool for identifying steps of the pathway that could be the target of therapeutical intervention. Numerous quantitative comparisons with data are given. The model can be used for biomathematical exploration of relationships between enzymic deficiencies and clinically manifested diseases.

The metabolic productivity of the cell factory

It is widely accepted that some performance function has been optimized during the evolution of metabolic pathways. One can study the nature of such a function by analogy with the industrial manufacturing world, in which there have been efforts over recent decades to optimize production chains, and in which it is now accepted that fluxes are not the only important system variables that determine process efficiency, because inventory turnover must also be considered. Inspired by the parallels between living cells and manufacturing factories, we propose that fluxes and transit time may have simultaneously been major targets of natural selection in the optimization of the design, structure and kinetic parameters of metabolic pathways. Accordingly we define the ratio of flux to transit time as a performance index of productivity in metabolic systems: it measures the efficiency with which stocks are administered, and facilitates comparison of a pathway in different steady states or in different tissues or organisms. For a linear chain of two enzymes, at a fixed total equilibrium constant, we have analysed the variation of flux, transit time and productivity index as functions of the equilibrium constants of the two steps. The results show that only the productivity index has a maximum, which represents a good compromise in optimizing flux and transit time. We have extended control analysis to the productivity index and derived the summation theorem that applies to it. For linear chains of different length with maximum productivity index values, the distribution of control coefficients with regard to the three parameters has a characteristic profile independent of the length of the chain. Finally, this control profile changes when other variables are optimized, and we compare the theoretical results with the control profile of the first steps of glycolysis in rat liver.

Molecular bureaucracy: who controls the delays? Transient times in branched pathways and their control

Analysis of metabolic control has until now been mainly confined to systems at steady state. This includes studies of the control of "transition time", which is actually a steady-state transit time that does not refer to the transient state. In this paper we examine the control of the transition state of a metabolic pathway in the approach to a stable steady state, showing that the time needed to attain it can be decreased or increased in different branches. Our analysis only applies to branched pathways, and we discuss why similar deviations cannot occur in unbranched pathways. In systems with several branches the acceleration of some branches during the transient phase, so that they reach their steady states more quickly, occurs at the expense of others, which are thus delayed. We present theorems that describe properties of the transient variables and their control.

The puzzle of the Krebs citric acid cycle: assembling the pieces of chemically feasible reactions, and opportunism in the design of metabolic pathways during evolution

The evolutionary origin of the Krebs citric acid cycle has been for a long time a model case in the understanding of the origin and evolution of metabolic pathways: How can the emergence of such a complex pathway be explained? A number of speculative studies have been carried out that have reached the conclusion that the Krebs cycle evolved from pathways for amino acid biosynthesis, but many important questions remain open: Why and how did the full pathway emerge from there? Are other alternative routes for the same purpose possible? Are they better or worse? Have they had any opportunity to be developed in cellular metabolism evolution? We have analyzed the Krebs cycle as a problem of chemical design to oxidize acetate yielding reduction equivalents to the respiratory chain to make ATP. Our analysis demonstrates that although there are several different chemical solutions to this problem, the design of this metabolic pathway as it occurs in living cells is the best chemical solution: It has the least possible number of steps and it also has the greatest ATP yielding. Study of the evolutionary possibilities of each one-taking the available material to build new pathways-demonstrates that the emergence of the Krebs cycle has been a typical case of opportunism in molecular evolution. Our analysis proves, therefore, that the role of opportunism in evolution has converted a problem of several possible chemical solutions into a single-solution problem, with the actual Krebs cycle demonstrated to be the best possible chemical design. Our results also allow us to derive the rules under which metabolic pathways emerged during the origin of life.

Strong control on the transit time in metabolic channelling

A suite of different characteristic times is used to describe the temporal behavior of a metabolic pathway. Here we focus on the 'transit' time, that is the average time it takes for a molecule, entering the steady-state pathway as a substrate, to exit the pathway as a product. We show that metabolic channelling results in dramatic changes in control exerted by pathway enzymes on the transit time. In an 'ideal' pathway a doubling of the enzyme concentrations halves the transit time. In a dynamic channel such an increase can reduce the transit time by a factor of four or more.

Effect of channelling on the concentration of bulk-phase intermediates as cytosolic proteins become more concentrated

This paper shows that metabolic channelling can provide a mechanism for decreasing the concentration of metabolites in the cytoplasm when cytosolic proteins become more concentrated. A dynamic complex catalysing the direct transfer of an intermediate is compared with the analogous pathway lacking a channel (an "ideal" pathway). In an ideal pathway a proportional increase in protein content does not result in a change in the steady-state concentration of the bulk-phase intermediate, whereas in a channelling pathway the bulk-phase intermediate either decreases or increases depending on the elemental rate constants within the enzyme mechanisms. When the concentration of the enzymes are equal, the pool size decreases with increasing protein concentration if the elemental step depleting the bulk-phase intermediate exerts more control on its concentration than the step supplying the intermediate. Results are illustrated numerically, and a simplified dynamic channel is analysed in which the concentration of the enzyme-enzyme forms. For such a "hit-and-run" channel it is shown that, when the product-releasing step of the enzyme located upstream is close to equilibrium, the pool size decreases as the concentrations of the enzymes increase in proportion, regardless of the rate, equilibrium constants and concentration ratios of the two sequential enzymes.

Comparative characterization of the fermentation pathway of Saccharomyces cerevisiae using biochemical systems theory and metabolic control analysis: model definition and nomenclature

Mathematical tools that involve the determination of systemic responses to small changes in metabolites or enzymes have demonstrated their utility for analyzing metabolic pathways. The different methodologies based on these ideas allow for modeling and analyzing biochemical pathways focusing on the coordinate behavior of the whole system. However, one must become familiar with the difference in nomenclature and methodology to relate the models and results obtained by applying these techniques and to appreciate their potential for answering fundamental questions about biochemical systems. In the following three papers we show how this can be facilitated by comparing the nomenclature, methodology, and results of the two leading techniques in this area, metabolic control analysis and biochemical systems theory, using a model of the fermentation pathway in Saccharomyces cerevisiae as a reference system. In the present paper we review the nomenclature, technical concepts, and related experimental measurements while creating a practical dictionary for the reference system that makes the relatedness of the two approaches more apparent. In the second paper, subtitled Steady-State Analysis, we show that both approaches give the same picture for many systemic responses of the reference system. In the third paper of this series, subtitled Model Validation and Dynamic Behavior, we show that the quality of the model can be assessed by studying the sensitivity to changes in the system parameters. We hope to illustrate the usefulness of these tools in providing an interpretation of the experimental measurements in a specific metabolic pathway.

Comparative characterization of the fermentation pathway of Saccharomyces cerevisiae using biochemical systems theory and metabolic control analysis: steady-state analysis

In the preceding paper in this issue, we have shown that metabolic control analysis and biochemical systems theory use the same experimental information to describe a metabolic system. In this paper, we analyze the steady-state properties of this pathway by applying both methods. Our results show the correspondence of the steady-state characterizations and illustrate the relationships between the different nomenclatures used. With both approaches, we identify metabolite pools that are strongly influenced by changes in enzyme concentration when cells are immobilized at pH 5.5. In the final paper of this series, which follows, we discuss the need to assess the quality of a model and the potential difficulties that may arise if the steady-state characterization is accepted without testing its quality. We then validate the different models using parameter sensitivity concepts.

Comparative characterization of the fermentation pathway of Saccharomyces cerevisiae using biochemical systems theory and metabolic control analysis: model validation and dynamic behavior

In the first two papers of this series (immediately preceding, this issue), we characterized the steady-state properties of a model of a fermentation pathway in Saccharomyces cerevisiae in four experimental conditions. In each of these conditions, the pictures obtained by metabolic control analysis and biochemical systems theory were coincident, which illustrates the relatedness of the two approaches. In this paper we analyze the quality of this description by means of the tools available within biochemical systems theory, and we show that in some of the experimental conditions studied the system is poorly characterized. The most critical condition corresponds to the immobilization of the cells at pH 5.5, in which the kinetic characterization appears to be inaccurate. Furthermore, sensitivity analysis and the study of the local steady-state stability identify the most critical parameters. The results of these analyses are confirmed by the predictions of the dynamic response of the model using its S-system representation. This illustrates the utility of these tools and warns against using the steady-state characterization without testing its validity.

Elusive control

The concept of a single rate-limiting step was proven to be too simplistic for understanding control and regulation of metabolism. Consequently, searches have identified relatively few steps with high control. Here we review a number of such searches and indicate what mechanisms may be responsible for this elusiveness of control. It turns out that this elusiveness of control has itself led to increased understanding of the roles played in metabolic control and regulation of such diverse factors as distributiveness of control, condition dependence, enzyme elasticity, homeostasis, control hierarchies, the input into a pathway, coenzyme sequestration, and redundancy and diversity of control function.

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

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

Control analysis of transit time for free and enzyme-bound metabolites: physiological and evolutionary significance of metabolic response times

Control analysis of transit time, defined as tau = delta/J, has previously been considered with the constraint of low enzyme concentrations compared with free pools of metabolites [Meléndez-Hevia, Torres, Sicilia and Kacser (1990) Biochem. J. 265, 195-202]. One of the conclusions was that the sum of the control coefficients of the transition time with respect to enzyme concentration was -1. Here we demonstrate that, if the enzyme-bound pools are taken into consideration (which would be important at high enzyme concentrations and high affinities), the sum lies between 0 and -1. The transition time between two steady states, which are frequent physiological events, is mainly governed by time constants involved in changing the enzyme concentrations. Some physiological and evolutionary aspects are discussed.

Coenzyme cycles and metabolic control analysis: the determination of the elasticity coefficients from the generalised connectivity theorem

Metabolic control analysis allows one to express the elasticity coefficients (which describe the "local" kinetic features of enzymes) in terms of the control coefficients (quantitative indicators of the "global" control properties). However, when coenzymes (or metabolites linked by conservation constraints) are present in the pathway this procedure yields the "apparent" values of elasticity coefficients that correspond to the kinetic responses of the enzymes to such a simultaneous change of the coenzyme forms which leaves the total concentration of these forms unchanged (e.g., NAD+ + NADH in the glycolysis). We show that a generalised connectivity theorem (Kholodenko et al, Eur. J. Biochem. (1994) 225, 179-186) makes it possible to express the elasticity coefficients with respect to every coenzyme form separately. Such expressions include (i) the control coefficients and (ii) the responses to changes in the total concentrations of the coenzymes.

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 model of the pentose phosphate pathway in rat liver cells

A mathematical model based on kinetic data taken from the literature is presented for the pentose phosphate pathway in fasted rat liver steady-state. Since the oxidative and non oxidative pentose phosphate pathway can act independently, the complete (oxidative+non oxidative) and the non oxidative pentose pathway were stimulated. Sensitivity analyses are reported which show that the fluxes are mainly regulated by D-glucose-6-phosphate dehydrogenase (for the oxidative pathway) and by transketolase (for the non oxidative pathway). The most influent metabolites were the group ATP, ADP, P1 and the group NADPH, NADP+ (for the non oxidative pathway).

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.

Structure identifiability in metabolic pathways: parameter estimation in models based on the power-law formalism

An important step in understanding a metabolic pathway is to identify its structure, in terms of the flow of material and information. In pursuing this goal, the available information for a given system is usually obtained from experiments in vitro and comes from different sources. Frequently, the final set of regulatory signals acting in the system in vivo is unclear, and some kind of test is needed on the intact system. Besides defining an appropriate experimental approach, identification of the regulatory pattern needs a theoretical framework in which the different experimental measurements can be evaluated and a final picture can be agreed on. Mathematical approaches based on sensitivity coefficients provide a useful tool for addressing this problem. Within this framework, the appropriate parameters are related to both the structure of the reaction network and the signals that regulate the target system. Thus the identification of the regulatory structure can be related to the estimation of the appropriate set of parameters. In pursuing this goal, we will show the limitations of using steady-state measurements and the usefulness of using dynamic data. We suggest a way to test the regulatory pattern in a given metabolic pathway by combining both kinds of data, and we show, by using a reference system, the potential of the method suggested.

Enzyme-enzyme interactions and metabolite channelling: alternative mechanisms and their evolutionary significance

Metabolite channelling may result from different kinetic mechanisms in which enzyme-enzyme interactions occur, so that intermediates are not released into the bulk solution and cannot be used by enzymes outside the channel. From an evolutionary point of view, the emergence of such mechanisms may provide new functional possibilities for the system, which would result in a selective advantage. Hence, it would be useful to evaluate the objective advantages provided by the various options by considering different criteria for functional effectiveness. Following this strategy, the goal of this paper is to compare a model for a free-diffusion two-enzyme system with two different models with inclusion of enzyme-enzyme interactions. In addition, models with simultaneous free and interacting branches are also analysed, and their advantages or disadvantages are presented. Basic guidelines are suggested that help in predicting the occurrence of specific mechanisms in different circumstances, and provide theoretical evidence in support of the hypothesis that no single solution simultaneously optimizes all the possible desired properties of the system.

Dramatic changes in control properties that accompany channelling and metabolite sequestration

A simple summation theorem describes the control of fluxes in 'ideal' metabolic pathways. This paper shows how this theorem and the control properties of a pathway change when direct transfer of intermediates and/or sequestration of metabolites involved in moiety conservations (by enzymes present at high concentrations) take place. The derived generalized summation theorem quantifies the extent to which metabolite sequestration decreases and direct metabolite transfer can increase the control exerted by enzymes on the flux. The implications of metabolite channelling for the control of fluxes are discussed quantitatively.

Metabolic pathway characterization from transient response data obtained in situ: parameter estimation in S-system models

The actual values of internal metabolites and fluxes can be measured by a number of experimental techniques and they provide important information for evaluating the properties of a metabolic pathway in situ. In this paper we propose a strategy to properly exploit this information. The suggested approach permits estimation of a set of parameters on the whole system so that a useful model can be constructed and used to describe its components and systemic properties and to predict its behavior under new conditions. A simulated reference pathway is provided to validate this method and to show its utility in metabolic studies.

Experimental strategy to study the pH dependence of the kinetic behavior of enzymes: practical application to chicken liver xanthine dehydrogenase

An experimental strategy has been developed to analyze the pH dependence of kinetic parameters in two-substrate enzyme kinetics based upon model discrimination, parameter refinement, and optimal discrete design. The experimental protocol proposed includes obtaining reproducible experimental results in different sessions, replicates of each experimental determination, and rejection of outliers. This strategy leads to an empirical kinetic equation that fits the experimental results. As a practical application of this strategy we studied the pH dependence of kinetic parameters of chicken liver xanthine dehydrogenase. We obtained an empirical rate law from the determination of the initial rates at different substrate concentrations and pH. Finally, we have proposed a plausible kinetic mechanism that may explain the experimental findings. This model is not the only one leading to the empirical equation, but it is based on previous experimental findings (Bruguera, P., López-Cabrera, A., and Canela, E. I., 1988, Biochem. J. 249, 171-178).

A model for adenosine transport and metabolism

1. A model is presented for adenosine transport and metabolism in different steady states. The model considers steady-state equations for metabolic enzymes based on information from the literature on their kinetic behaviour. 2. Assuming that extracellular adenosine and inosine are translocated by three transporters, we have devised rate equations for these nucleoside transporters which are valid when both nucleosides are present. Since the Na(+)-independent transporter can either incorporate nucleosides into the cell or release them, various conditions have been simulated in which inosine was either incorporated or released. 3. Control analyses are reported which show that the fluxes towards intracellular adenine nucleosides are controlled by ecto-5'-nucleotidase in some circumstances and by the nucleoside transporters in others. The nucleoside transporter is responsible for five fluxes (two Na+ dependent adenosine transport mechanisms, a Na(+)-dependent inosine transport, a Na(+)-independent adenosine transport and a Na(+)-independent inosine influx or efflux) but the control is not always positive for all these fluxes. The control patterns of these five fluxes indicate that, in the presence of extracellular adenosine and inosine, the intracellular metabolism of adenine derivatives would be highly dependent on the extracellular and intracellular concentrations of both nucleosides, on the ectoenzymes (5'-nucleotidase and adenosine deaminase) and on the transporter. 4. Predictions of the model were examined. The results indicate that a change in one independent variable (extracellular AMP concentration) makes the system evolve towards a new steady state which is far from the initial one and has a different control pattern. In contrast, simulation of inhibition of the carriers produces only slight modification of the fluxes since the concentrations of the metabolites change to counteract the effect. Thus, for instance, a 50% inhibition of the three carriers does not affect the flux towards intracellular adenine nucleotides. Finally, our model has confirmed that the evolution of the concentration of extracellular adenosine, when an increase in extracellular AMP is produced, agrees with the behaviour expected for a neurohormone.

The molybdoenzymes xanthine oxidase and aldehyde oxidase contain fast- and slow-DTNB reacting sulphydryl groups

The reactivities with an excess of 5-5'-dithiobis (2-nitrobenzoic) acid (DTNB) of sulphydryl residues present in xanthine oxidase and aldehyde oxidase were studied and compared. The results show that two classes of sulphydryl groups with quite different reactivities exist in both enzymes either native or denatured. Some of the available sulphydryl residues thus react instantaneously with the DTNB, whereas the others react very slowly following pseudo-first-order kinetics. The number of sulphydryl residues of each class and the rate constant of slowly reacting groups are, respectively, 1.7 and 0.8 in native xanthine oxidase and 1.6 and 1.7 in native aldehyde oxidase. In denatured enzymes, the number of fast- and slow-reacting sulphydryl residues obtained are, respectively, 13.9 and 7.9 in xanthine oxidase and 5.7 and 5.4 in aldehyde oxidase. Analogously, the rate constant for the slowly reacting groups is similar for the two native enzymes, but in denatured aldehyde oxidase it is double that of denatured xanthine oxidase.

Biochemical systems theory: increasing predictive power by using second-order derivatives measurements

Models based on the power-law formalism provide a useful tool for analyzing metabolic systems. Within this methodology, the S-system variant furnishes the best strategy. In this paper we explore an extension of this formalism by considering second-order derivative terms of the Taylor series which the power-law is based upon. Results show that the S-system equations which include second-order Taylor coefficients give better accuracy in predicting the response of the system to a perturbation. Hence, models based on this new approach could provide a useful tool for quantitative purposes if one is able to measure the required derivatives experimentally. In particular we show the utility of this approach when it comes to discriminating between two mechanisms that are equivalent in the S-system a representation based on first-order coefficients. However, the loss of analytical tractability is a serious disadvantage for using this approach as a general tool for studying metabolic systems.

An improved purification procedure for sulfite oxidase from bovine liver

Sulfite oxidase (Sulfite:O2 oxidoreductase, EC 1.8.3.1) has been purified 2,440-fold from bovine liver. The procedure developed was used to isolate the enzyme from 1,000 g of liver and permitted the rapid isolation of enzyme with a very high specific activity (40,405 mU/mg). The enzyme preparations obtained have been characterized by electrophoretic and spectrophotometric analysis and the molecular mass and the Stokes radius of the enzyme have been determined.

Control analysis of transition times. Extension of analysis and matrix method

The present theoretical basis of Control Analysis is extended with the definition of Transition Time Response Coefficients. Some new relationships between local and global coefficients defined in Control Analysis are presented. These relationships are in the form of matrix products constructed in a priori form. The use of these straightforward relationships is shown in an exemplary application corresponding to an experimental system consisting of the glycolytic degradation from glucose to glyceraldehyde-3-phosphate.

Control analysis of systems having two steps catalyzed by the same protein molecule in unbranched chains

The analysis of the control of a metabolic pathway having an enzyme catalyzing two different reactions (or a protein displaying two different activities) has been performed. For such systems although the summation theorems are valid, the flux and concentration connectivity theorems of the metabolic control analysis are not valid. Another general relationship of control analysis is shown to be more widely obeyed and holds in these systems. An exemplary case, where the enzyme catalyzes two irreversible reactions, demonstrates that the level of one internal intermediate is constant, i.e. it does not depend upon the independent variables of the system.

Purification of adenosine deaminase from chicken-egg yolk by affinity column chromatography

Adenosine deaminase (adenosine aminohydrolase; E.C. 3.5.4.4) has been purified 4686-fold from egg yolk. The procedure developed was used to isolate the enzyme from eight chicken eggs. An easily prepared affinity column employing purine riboside was used as the final step in the purification. The method developed permits the rapid isolation and a high recovery of the protein. The specific activity of the enzyme preparation obtained is 81.4 mU/mg.

Occurrence and comparison of sulfite oxidase activity in mammalian tissues

Tissue extracts from six mammalian species have been assayed for sulfite oxidase (sulfite: ferricytochrome c oxidoreductase, EC 1.8.3.1) activity with cytochrome c as electron acceptor. Our results show a large distribution of sulfite oxidase activity in mammalian tissues. Liver, kidney, and heart tissues exhibit high activities whereas brain, spleen, and testis show very low activities. No significant species dependence was observed for the activity of this enzyme.

Application of inverse regression for estimating molecular masses and Stokes radii of globular proteins by gel filtration chromatography

The aim of this paper is to apply inverse regression as a method for treating experimental data obtained from gel filtration chromatography in order to obtain estimates of hydrodynamic parameters of globular proteins with true confidence intervals. The method is illustrated with the determination, using inverse regression, of molecular mass and Stokes radius for four test proteins (aldolase, chymotrypsinogen A, aldehyde oxidase and xanthine oxidase), from experimental data obtained with a Sephacryl S-300 column. A simple personal computer (PC) program written in standard basic, that is useful for this purpose, is included.

Use of implicit methods from general sensitivity theory to develop a systematic approach to metabolic control. I. Unbranched pathways

It is shown that metabolic control theory (MCT), is its present form, is a particular case of general sensitivity theory, which studies the effects of parameter variations on the behavior of dynamic systems. It has been shown that metabolic control theory is obtained from this more general theory for the particular case of steady-state and linear relationships between velocities and enzyme concentrations. In such conditions the relationships between elasticities and flux control coefficients are easily obtained. These relationships are in the form of a matrix product constructed in a priori form. Relationships between combined response coefficients and concentration control coefficients are presented. The use of implicit methodology from general sensitivity theory provides a generalization of MCT, which is applied to unbranched pathways. For this particular case, provided the matrices have been properly constructed, the matrix of global properties (flux and concentration control coefficients) can be obtained by inversion of the matrix of local properties (elasticities). The theorems of MCT (concentration summation, flux summation, flux connectivity, and concentration connectivity) applicable for unbranched pathways are directly obtained by inspection of the matrix product. With these results, the present theoretical basis of MCT is extended with a more structured framework that allows a wider range of application. The results make clearer the relatedness of MCT to the more general approach provided by biochemical systems theory (BST).

Use of implicit methods from general sensitivity theory to develop a systematic approach to metabolic control. II. Complex systems

In the accompanying paper (Cascante et al., this issue) we have used general sensitivity theory to develop a matrix algebra that, in the case of sequential reactions, directly relates global and local properties of a given system. In complex biochemical systems this direct relationship is not possible due to the existence of linear dependencies among fluxes and among metabolite concentrations (conserved aggregate concentrations in BST or moiety-conserved concentrations in MCT). In this paper our matrix algebra is applied to conserved cycles and branched pathways, and it is shown that with minor modifications it again relates global properties to the local properties of the enzymes in the system. In the case of conserved cycles, elasticities become modified due to the existence of linear dependencies among the concentration variables in the cycle. In branched pathways, new matrix elements involving ratios of fluxes appear. With these modifications, one can show that the so-called theorems of metabolic control theory specific to these types of pathways are special cases of more general relationships. Rules for the construction of matrices relating global and local properties are given that apply to an arbitrary system of cycles and branches. The implicit approach developed in these papers, which is a generalization of that used in MCT, allows one to make more direct comparisons with the general explicit approach originally developed in BST.

Kinetic studies of chloride inhibition in aspartate aminotransferase activity

The inhibitive effects of chloride anion on the activity of mitochondrial aspartate aminotransferase (L-aspartate: 2-oxoglutarate-aminotransferase EC. 2.6.1.1.) from chicken (Gallus domesticus) and turkey (Maleagris gallopavo) were studied. Steady-state velocities were obtained from a wide range of chloride concentrations. The data were fitted by rational functions of 0:2 and 1:2 for chloride, using a non-linear regression program which guaranteed the fit. The goodness of fit was improved by the use of a computer program that combined model discrimination, parameter refinement and sequential design. It was concluded that chloride aspartate aminotransferase inhibition requires a minimum velocity equation of 1:2 with regard to chloride, and a plausible kinetic mechanism for this experimental result was proposed.

Interdependence between cooperativity and control coefficients

Influence of the concentration of internal metabolites on the control coefficient (defined as fractional change in flux per fractional change in enzyme activity) and regulatory properties of a given enzyme have been studied theoretically using a cyclic model of three enzymes. This model is useful to investigate the properties of the flux control coefficient for an enzyme following different rate equations. Enzymes can have high or low values of control coefficient irrespective of the type of kinetic equation, but the results obtained show that the sensitivity of these values to substrate variations is strongly dependent on its rate equation. These results help identify which kinetic equation allows the best control of a given metabolic pathway. These results have been applied to the purine nucleotide cycle. It is demonstrated that the best control of the cycle is reached when the irreversible reaction catalyzed by AMP deaminase follows a rate law that corresponds to a rational function of 2:2 degree with respect to AMP concentration.

Kinetic studies of chicken and turkey liver mitochondrial aspartate aminotransferase

The kinetic behaviour of chicken liver and turkey liver aspartate aminotransferases (L-aspartate:2-oxoglutarate aminotransferase, EC 2.6.1.1) was studied. Steady-state data were obtained from a wide range of concentrations of substrates and product L-glutamate. The data were fitted by rational functions of degree 1:1, 1:2 and 2:2 with respect to substrates and 0:1, 1:1, 0:2 and 1:2 with regard to product (L-glutamate), by using a non-linear regression program that guarantees the fit. The goodness of fit was improved by the use of a computer program that combines model discrimination parameter refinement and sequential experimental design. It was concluded that aspartate aminotransferase requires a minimum velocity equation of degree 2:2 for L-aspartate, 2:2 for 2-oxoglutarate and 1:2 for L-glutamate. Finally, a plausible kinetic mechanism that justifies these experimental results is proposed.

Purification and comparative studies of several mitochondrial aspartate aminotransferases from avian liver

A new purification method has been developed which only exploits the chromatographic behaviour of avian liver mitochondrial aspartate aminotransferase enzymes (m-AAT), and permits a rapid isolation of the protein (4 days) in large quantities with high yield and low cost. m-AAT from turkey, chicken and quail livers have been isolated by chromatography on CM-Sepharose, Sephadex G-100 and 5' AMP-Sepharose using TEA-acetate buffer (pH 7.4), and specific activities (A.E.) of 311.6, 318.9, 320.1 I.U./mg respectively were obtained. Preparations were homogeneous as judged by various electrophoretic techniques and by size exclusion HPLC. The amino acid composition, Stokes Radius, subunit molecular weight and pI values have been determined and compared, finding no appreciable differences among them. In contrast, the absorption spectrum of the turkey enzyme differed from those of chicken and quail at both pH 7.4 and pH 5.0.

Intramitochondrial location and some characteristics of chicken liver aspartate aminotransferase

Chicken liver mitochondrial aspartate aminotransferase was found to be located in the intermembrane space and bound to the inner mitochondrial membrane. Purification of two mitochondrial fractions containing aspartate aminotransferase activity was performed. Both fractions showed similar chromatographic behaviour and identical isoelectric point and molecular weight values. There were no significant differences in the general kinetic mechanism, Km values, substrates inhibition and effect of various anions on the activity of mitochondrial aspartate aminotransferase purified from both fractions.