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PI3K (phosphoinositide 3-kinase) signalling pathways regulate a large array of cell biological functions in normal and cancer cells. In the present study we investigated the involvement of PI3K in modulating small molecule metabolism. A LC (liquid chromatography)-MS screen in colorectal cancer cell lines isogenic for oncogenic PIK3CA mutations revealed an association between PI3K activation and the levels of polyamine pathway metabolites, including 5-methylthioadenosine, putrescine and spermidine. Pharmacological inhibition confirmed that the PI3K pathway controls polyamine production. Despite inducing a decrease in PKB (protein kinase B)/Akt phosphorylation, spermidine promoted cell survival and opposed the anti-proliferative effects of PI3K inhibitors. Conversely, polyamine depletion by an ornithine decarboxylase inhibitor enhanced PKB/Akt phosphorylation, but suppressed cell survival. These results suggest that spermidine mediates cell proliferation and survival downstream of PI3K/Akt and indicate that these two biochemical pathways control each other's activities, highlighting a mechanism by which small molecule metabolism feeds back to regulate kinase signalling. Consistent with this feedback loop having a functional role in these cell models, pharmacological inhibitors of PI3K and ornithine decarboxylase potentiated each other in inhibiting tumour growth in a xenograft model. The results of the present study support the notion that the modulation of spermidine concentrations may be a previously unrecognized mechanism by which PI3K sustains chronic proliferation of cancer cells.

Recent studies in metabolic profiling have underscored the importance of the concept of a metabolic network of pathways with special functional characteristics that differ from those of simple reaction sequences. The characterization of metabolic functions requires the simultaneous measurement of substrate fluxes of interconnecting pathways. Here we present a novel stable isotope method by which the forward and reverse fluxes of the futile cycles of the hepatic glucose metabolic network are simultaneously determined. Unlike previous radio-isotope methods, a single tracer [1,2-13C2]D-glucose and mass isotopomer analysis is used. Changes in fluxes of substrate cycles, in response to several gluconeogenic substrates, in isolated fasted hepatocytes from male Wistar rats were measured simultaneously. Incubation with these substrates resulted in a change in glucose-6-phosphatase/glucokinase and glycolytic/gluconeogenic flux ratios. Different net redistributions of intermediates in the glucose network were observed, resulting in distinct metabolic phenotypes of the fasted hepatocytes in response to each substrate condition. Our experimental observations show that the constraints of concentrations of shared intermediates, and enzyme kinetics of intersecting pathways of the metabolic network determine substrate redistribution throughout the network when it is perturbed. These results support the systems-biology notion that network analysis provides an integrated view of the physiological state. Interaction between metabolic intermediates and glycolytic/gluconeogenic pathways is a basic element of cross-talk in hepatocytes, and may explain some of the difficulties in genotype and phenotype correlation.

The concentration of an inhibitor that decreases the rate of an enzyme-catalysed reaction by 50%, symbolized i(0.5), is often used in pharmacological studies to characterize inhibitors. It can be estimated from the common inhibition plots used in biochemistry by means of the fact that the extrapolated inhibitor concentration at which the rate becomes infinite is equal to -i(0.5). This method is, in principle, more accurate than comparing the rates at various different inhibitor concentrations, and inferring the value of i(0.5) by interpolation. Its reciprocal, 1/i(0.5), is linearly dependent on v(0)/V, the uninhibited rate divided by the limiting rate, and the extrapolated value of v(0)/V at which 1/i(0.5) is zero allows the type of inhibition to be characterized: this value is 1 if the inhibition is strictly competitive; greater than 1 if the inhibition is mixed with a predominantly competitive component; infinite (i.e. 1/i(0.5) does not vary with v(0)/V) if the inhibition is pure non-competitive (i.e. mixed with competitive and uncompetitive components equal); negative if the inhibition is mixed with a predominantly uncompetitive component; and zero if it is strictly uncompetitive. The type of analysis proposed has been tested experimentally by examining inhibition of lactate dehydrogenase by oxalate (an uncompetitive inhibitor with respect to pyruvate) and oxamate (a competitive inhibitor with respect to pyruvate), and of cytosolic malate dehydrogenase by hydroxymalonate (a mixed inhibitor with respect to oxaloacetate). In all cases there is excellent agreement between theory and experiment.

It is widely assumed that the control coefficient of an enzyme on pathway flux decreases as the concentration of enzyme increases. However, it has been shown [Kholodenko and Brown (1996) Biochem. J. 314, 753-760] that enzymes with sigmoidal kinetics can maintain or even gain control with an increase in enzyme activity or concentration. This has been described as 'paradoxical control'. Here we formulate the general requirements for allosteric enzyme kinetics to display this behaviour. We show that a necessary condition is that the Hill coefficient of the enzyme should increase with an increase in substrate concentration or decrease with an increase in product concentration. We also describe the necessary and sufficient requirements for the occurrence of paradoxical control in terms of the flux control coefficients and the derivatives of the elasticities. The derived expression shows that the higher the control coefficient of an allosteric enzyme, the more likely it is that the pathway will display this behaviour. Control of pathway flux is generally shared between a large number of enzymes and therefore the likelihood of observing sustained or increased control is low, even if the kinetic parameters are in the most favourable range to generate the phenomenon. We show that hepatic glucokinase, which has a very high flux control coefficient and displays sigmoidal behaviour within the hepatocyte in situ as a result of interaction with a regulatory protein, displays sustained or increased control over an extended range of enzyme concentrations when the regulatory protein is overexpressed.

We investigated whether hepatocytes permeabilized with alpha-toxin from Staphylococcus aureus are a valid model for studying the channelling of intermediates of glycolysis between glucokinase and triosephosphate isomerase. These cells are permeable to 2-aminoisobutyrate, ATP, glucose 6-phosphate (Glc6P) and fructose 2, 6-bisphosphate [Fru(2,6)P(2)], but maintain cell integrity in the presence of ATP as judged by the retention of cytoplasmic enzymes. During incubation with 25 mM glucose, an ATP-generating system and saturating concentrations of Fru(2,6)P(2), rates of detritiation of [2-(3)H]glucose and [3-(3)H]glucose were similar. Exogenous Glc6P (1 mM) and to a lesser extent fructose 6-phosphate, but not Fru(1, 6)P(2), decreased the rate of detritiation of [3-(3)H]glucose. During incubation with 25 mM glucose and Glc6P (0.2-1 mM), with either [3-(3)H]glucose or [3-(3)H]Glc6P as labelled substrate, there was dilution of metabolism of [3-(3)H]glucose with increasing Glc6P but no overall increase in glycolytic flux from glucose and Glc6P, indicating that glycolysis is apparently saturated with Glc6P despite the permeability of the cells to this metabolite. These findings could be explained by partial channelling of Glc6P between glucokinase and glycolysis in the presence of saturating concentrations of Fru(2,6)P(2). They provide an alternative explanation for the concept that there is more than one Glc6P pool.

A modelling approach is used to analyse diseases associated with purine metabolism in man. The specific focus is on deficiencies in two enzymes, hypoxanthine:guanine phosphoribosyltransferase and adenylosuccinate lyase. These deficiencies can lead to a number of symptoms, including neurological dysfunctions and mental retardation. Although the biochemical mechanisms of dysfunctions associated with adenylosuccinate lyase deficiency are not completely understood, there is at least general agreement in the literature about possible causes. Simulations with our model confirm that accumulation of the two substrates of the enzyme can lead to significant biochemical imbalance. In hypoxanthine:guanine phosphoribosyltransferase deficiency the biochemical mechanisms associated with neurological dysfunctions are less clear. Model analyses support some old hypotheses but also suggest new indicators for possible causes of neurological dysfunctions associated with this deficiency. Hypoxanthine:guanine phosphoribosyltransferase deficiency is known to cause hyperuricaemia and gout. We compare the relative importance of this deficiency with other known causes of gout in humans. The analysis suggests that defects in the excretion of uric acid are more consequential than defects in uric acid synthesis such as hypoxanthine:guanine phosphoribosyltransferase deficiency.

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.

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.

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.

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.

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.

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 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.