Integrating systemic and molecular levels to infer key drivers sustaining metabolic adaptations.

Metabolic adaptations to complex perturbations, like the response to pharmacological treatments in multifactorial diseases such as cancer, can be described through measurements of part of the fluxes and concentrations at the systemic level and individual transporter and enzyme activities at the molecular level. In the framework of Metabolic Control Analysis (MCA), ensembles of linear constraints can be built integrating these measurements at both systemic and molecular levels, which are expressed as relative differences or changes produced in the metabolic adaptation. Here, combining MCA with Linear Programming, an efficient computational strategy is developed to infer additional non-measured changes at the molecular level that are required to satisfy these constraints. An application of this strategy is illustrated by using a set of fluxes, concentrations, and differentially expressed genes that characterize the response to cyclin-dependent kinases 4 and 6 inhibition in colon cancer cells. Decreases and increases in transporter and enzyme individual activities required to reprogram the measured changes in fluxes and concentrations are compared with down-regulated and up-regulated metabolic genes to unveil those that are key molecular drivers of the metabolic response.

MIDcor, an R-program for deciphering mass interferences in mass spectra of metabolites enriched in stable isotopes.

BACKGROUND: Tracing stable isotopes, such as 13C using various mass spectrometry (MS) methods provides a valuable information necessary for the study of biochemical processes in cells. However, extracting such information requires special care, such as a correction for naturally occurring isotopes, or overlapping mass spectra of various components of the cell culture medium. Developing a method for a correction of overlapping peaks is the primary objective of this study. RESULTS: Our computer program-MIDcor (free at https://github.com/seliv55/mid_correct) written in the R programming language, corrects the raw MS spectra both for the naturally occurring isotopes and for the overlapping of peaks corresponding to various substances. To this end, the mass spectra of unlabeled metabolites measured in two media are necessary: in a minimal medium containing only derivatized metabolites and chemicals for derivatization, and in a complete cell incubated medium. The MIDcor program calculates the difference (D) between the theoretical and experimentally measured spectra of metabolites containing only the naturally occurring isotopes. The result of comparison of D in the two media determines a way of deciphering the true spectra. (1) If D in the complete medium is greater than that in the minimal medium in at least one peak, then unchanged D is subtracted from the raw spectra of the labeled metabolite. (2) If D does not depend on the medium, then the spectrum probably overlaps with a derivatized fragment of the same metabolite, and D is modified proportionally to the metabolite labeling. The program automatically reaches a decision regarding the way of correction. For some metabolites/fragments in the case (2) D was found to decrease when the tested substance was 13C labeled, and this isotopic effect also can be corrected automatically, if the user provides a measured spectrum of the substance in which the 13C labeling is known a priori. CONCLUSION: Using the developed program improves the reliability of stable isotope tracer data analysis.

Metabolic Reprogramming and Dependencies Associated with Epithelial Cancer Stem Cells Independent of the Epithelial-Mesenchymal Transition Program.

In solid tumors, cancer stem cells (CSCs) can arise independently of epithelial-mesenchymal transition (EMT). In spite of recent efforts, the metabolic reprogramming associated with CSC phenotypes uncoupled from EMT is poorly understood. Here, by using metabolomic and fluxomic approaches, we identify major metabolic profiles that differentiate metastatic prostate epithelial CSCs (e-CSCs) from non-CSCs expressing a stable EMT. We have found that the e-CSC program in our cellular model is characterized by a high plasticity in energy substrate metabolism, including an enhanced Warburg effect, a greater carbon and energy source flexibility driven by fatty acids and amino acid metabolism and an essential reliance on the proton buffering capacity conferred by glutamine metabolism. An analysis of transcriptomic data yielded a metabolic gene signature for our e-CSCs consistent with the metabolomics and fluxomics analyses that correlated with tumor progression and metastasis in prostate cancer and in 11 additional cancer types. Interestingly, an integrated metabolomics, fluxomics, and transcriptomics analysis allowed us to identify key metabolic players regulated at the post-transcriptional level, suggesting potential biomarkers and therapeutic targets to effectively forestall metastasis. Stem Cells 2016;34:1163-1176.

Workforce preparation: the Biohealth computing model for Master and PhD students.

The article addresses the strategic role of workforce preparation in the process of adoption of Systems Medicine as a driver of biomedical research in the new health paradigm. It reports on relevant initiatives, like CASyM, fostering Systems Medicine at EU level. The chapter focuses on the BioHealth Computing Program as a reference for multidisciplinary training of future systems-oriented researchers describing the productive interactions with the Synergy-COPD project.

Glutamine Modulates Expression and Function of Glucose 6-Phosphate Dehydrogenase via NRF2 in Colon Cancer Cells.

Nucleotide pools need to be constantly replenished in cancer cells to support cell proliferation. The synthesis of nucleotides requires glutamine and 5-phosphoribosyl-1-pyrophosphate produced from ribose-5-phosphate via the oxidative branch of the pentose phosphate pathway (ox-PPP). Both PPP and glutamine also play a key role in maintaining the redox status of cancer cells. Enhanced glutamine metabolism and increased glucose 6-phosphate dehydrogenase (G6PD) expression have been related to a malignant phenotype in tumors. However, the association between G6PD overexpression and glutamine consumption in cancer cell proliferation is still incompletely understood. In this study, we demonstrated that both inhibition of G6PD and glutamine deprivation decrease the proliferation of colon cancer cells and induce cell cycle arrest and apoptosis. Moreover, we unveiled that glutamine deprivation induce an increase of G6PD expression that is mediated through the activation of the nuclear factor (erythroid-derived 2)-like 2 (NRF2). This crosstalk between G6PD and glutamine points out the potential of combined therapies targeting oxidative PPP enzymes and glutamine catabolism to combat colon cancer.

Antitumoral effect of phenazine N5,N10-dioxide derivatives on Caco-2 cells.

We studied the in vitro antitumoral effect of a series of phenazine di- N-oxide derivatives, named 2-chloroacetylamino-7(8)-nitrophenazine N(5), N(10)-dioxide (1), 2-amino-7(8)-(1,3-dioxol-2-yl)phenazine N(5), N(10)-dioxide (2), 2-chloroacetylamino-7(8)-(1,3-dioxol-2-yl)phenazine N(5), N(10)-dioxide (3), and 2-amino-7(8)-methoxyphenazine N(5), N(10)-dioxide (4), on Caco-2 cells. These phenazine N(5), N(10)-dioxide derivatives belong to our in-house chemical library. The products were selected according to their stereoelectronic characteristics and taking into account their differential cytotoxicity against V79 cells. Human colorectal adenocarcinoma cell line Caco-2 was used to study the cell growth inhibition capacity of these compounds, their capacity of altering the cell cycle and possible induction of apoptosis, DNA fragmentation, and genotoxic damage. The IC 50 after 24 h of incubation was lower for 1, 2, and 3 (4.8, 46.8, and 8.2 microM, respectively) than for 4 (474.7 microM). Compound 1 induced arrest in the G2/M phase at 24 and 48 h of treatment and apoptosis at the highest doses at 24 h of treatment. These facts were corroborated with caspase 3, caspase 9, and cytochrome c activation and DNA fragmentation at 24 h of treatment. The derivatives studied induced neither significant single strand breaks nor oxidative damage at the different studied times. We concluded that among the series of N(5), N(10)-dioxide phenazine derivatives analyzed, 1, which contains a nitro moiety and a chloroacetamide group, is the most promising as an antitumoral compound.

Untargeted metabolomics reveals distinct metabolic reprogramming in endothelial cells co-cultured with CSC and non-CSC prostate cancer cell subpopulations.

Tumour angiogenesis is an important hallmark of cancer and the study of its metabolic adaptations, downstream to any cellular change, can reveal attractive targets for inhibiting cancer growth. In the tumour microenvironment, endothelial cells (ECs) interact with heterogeneous tumour cell types that drive angiogenesis and metastasis. In this study we aim to characterize the metabolic alterations in ECs influenced by the presence of tumour cells with extreme metastatic abilities. Human umbilical vein endothelial cells (HUVECs) were subjected to different microenvironmental conditions, such as the presence of highly metastatic PC-3M and highly invasive PC-3S prostate cancer cell lines, in addition to the angiogenic activator vascular endothelial growth factor (VEGF), under normoxia. Untargeted high resolution liquid chromatography-mass spectrometry (LC-MS) based metabolomics revealed significant metabolite differences among the various conditions and a total of 25 significantly altered metabolites were identified including acetyl L-carnitine, NAD+, hypoxanthine, guanine and oleamide, with profile changes unique to each of the experimental conditions. Biochemical pathway analysis revealed the importance of fatty acid oxidation and nucleotide salvage pathways. These results provide a global metabolic preview that could help in selectively targeting the ECs aiding in either cancer cell invasion or metastasis in the heterogeneous tumour microenvironment.

Metabolic control analysis in drug discovery and disease.

Metabolic control analysis (MCA) provides a quantitative description of substrate flux in response to changes in system parameters of complex enzyme systems. Medical applications of the approach include the following: understanding the threshold effect in the manifestation of metabolic diseases; investigating the gene dose effect of aneuploidy in inducing phenotypic transformation in cancer; correlating the contributions of individual genes and phenotypic characteristics in metabolic disease (e.g., diabetes); identifying candidate enzymes in pathways suitable as targets for cancer therapy; and elucidating the function of "silent" genes by identifying metabolic features shared with genes of known pathways. MCA complements current studies of genomics and proteomics, providing a link between biochemistry and functional genomics that relates the expression of genes and gene products to cellular biochemical and physiological events. Thus, it is an important tool for the study of genotype-phenotype correlations. It allows genes to be ranked according to their importance in controlling and regulating cellular metabolic networks. We can expect that MCA will have an increasing impact on the choice of targets for intervention in drug discovery.

Unveiling the Metabolic Changes on Muscle Cell Metabolism Underlying p-Phenylenediamine Toxicity.

Rhabdomyolysis is a disorder characterized by acute damage of the sarcolemma of the skeletal muscle leading to release of potentially toxic muscle cell components into the circulation, most notably creatine phosphokinase (CK) and myoglobulin, and is frequently accompanied by myoglobinuria. In the present work, we evaluated the toxicity of p-phenylenediamine (PPD), a main component of hair dyes which is reported to induce rhabdomyolysis. We studied the metabolic effect of this compound in vivo with Wistar rats and in vitro with C2C12 muscle cells. To this aim we have combined multi-omic experimental measurements with computational approaches using model-driven methods. The integrative study presented here has unveiled the metabolic disorders associated to PPD exposure that may underlay the aberrant metabolism observed in rhabdomyolys disease. Animals treated with lower doses of PPD (10 and 20 mg/kg) showed depressed activity and myoglobinuria after 10 h of treatment. We measured the serum levels of aspartate aminotransferase (AST), alanine aminotransferase (ALT), and creatine kinase (CK) in rats after 24, 48, and 72 h of PPD exposure. At all times, treatment with PPD at higher doses (40 and 60 mg/kg) showed an increase of AST and ALT, and also an increase of lactate dehydrogenase (LDH) and CK after 24 h. Blood packed cell volume and hemoglobin levels, as well as organs weight at 48 and 72 h, were also measured. No significant differences were observed in these parameters under any condition. PPD induce cell cycle arrest in S phase and apoptosis (40% or early apoptotic cells) on mus musculus mouse C2C12 cells after 24 h of treatment. Incubation of mus musculus mouse C2C12 cells with [1,2-13C2]-glucose during 24 h, subsequent quantification of 13C isotopologues distribution in key metabolites of glucose metabolic network and a computational fluxomic analysis using in-house developed software (Isodyn) showed that PPD is inhibiting glycolysis, non-oxidative pentose phosphate pathway, glycogen turnover, and ATPAse reaction leading to a reduction in ATP synthesis. These findings unveil the glucose metabolism collapse, which is consistent with a decrease in cell viability observed in PPD-treated C2C12 cells and with the myoglubinuria and other effects observed in Wistar Rats treated with PPD. These findings shed new light on muscle dysfunction associated to PPD exposure, opening new avenues for cost-effective therapies in Rhabdomyolysis disease.

(2Alpha,3beta)-2,3-dihydroxyolean-12-en-28-oic acid, a new natural triterpene from Olea europea, induces caspase dependent apoptosis selectively in colon adenocarcinoma cells.

Triterpenoids are known to induce apoptosis and to be anti-tumoural. Maslinic acid, a pentacyclic triterpene, is present in high concentrations in olive pomace. This study examines the response of HT29 and Caco-2 colon-cancer cell lines to maslinic-acid treatment. At concentrations inhibiting cell growth by 50-80% (IC50HT29=61+/-1 microM, IC80HT29=76+/-1 microM and IC50Caco-2=85+/-5 microM, IC80Caco-2=116+/-5 microM), maslinic acid induced strong G0/G1 cell-cycle arrest and DNA fragmentation, and increased caspase-3 activity. However, maslinic acid did not alter the cell cycle or induce apoptosis in the non-tumoural intestine cell lines IEC-6 and IEC-18. Moreover, maslinic acid induced cell differentiation in colon adenocarcinoma cells. These findings support a role for maslinic acid as a tumour suppressant and as a possible new therapeutic tool for aberrant cell proliferation in the colon. In this report, we demonstrate for the first time that, in tumoural cancer cells, maslinic acid exerts a significant anti-proliferation effect by inducing an apoptotic process characterized by caspase-3 activation by a p53-independent mechanism, which occurs via mitochondrial disturbances and cytochrome c release.

Electron-transfer capacity of catechin derivatives and influence on the cell cycle and apoptosis in HT29 cells.

Galloylated and nongalloylated catechin conjugates with cysteine derivatives have been synthesized and evaluated for their capacity to scavenge free radicals and to influence crucial functions (cell cycle, apoptosis) in HT29 colon carcinoma cells. We show that the nonphenolic part of the molecule modified the capacity of catechins to donate hydrogen atoms and to transfer electrons to free radicals. Nongalloylated derivatives did not significantly influence either the cell cycle or apoptosis. Among the galloylated species, 4beta-[S-(O-ethyl-cysteinyl)]epicatechin 3-O-gallate, which showed a high electron-transfer capacity (5 e- per molecule), arrested the cell cycle and induced apoptosis as expected for galloylated catechins such as tea (-)-epigallocatechin 3-O-gallate. 4beta-[S-(N-Acetyl-O-methyl-cysteinyl)]epicatechin 3-O-gallate, which showed the highest hydrogen-donating capacity (10 H per molecule) while keeping the electron-transfer capacity low (2.9 e- per molecule), did not trigger any significant apoptosis. The gallate moiety did not appear to be sufficient for the pro-apoptotic effect of the catechin derivatives in HT29 cells. Instead, a high electron-transfer capacity is more likely to be behind this effect. The use of stable radicals sensitive exclusively to electron transfer may help to design molecules with either preventive scavenging action (high hydrogen donation, low electron transfer) or therapeutic pro-apoptotic activity (high electron transfer).

In situ localization of transketolase activity in epithelial cells of different rat tissues and subcellularly in liver parenchymal cells.

Metabolic mapping of enzyme activities (enzyme histochemistry) is an important tool to understand (patho)physiological functions of enzymes. A new enzyme histochemical method has been developed to detect transketolase activity in situ in various rat tissues and its ultrastructural localization in individual cells. In situ detection of transketolase is important because this multifunctional enzyme has been related with diseases such as cancer, diabetes, Alzheimer's disease, and Wernicke-Korsakoff's syndrome. The proposed method is based on the tetrazolium salt method applied to unfixed cryostat sections in the presence of polyvinyl alcohol. The method appeared to be specific for transketolase activity when the proper control reaction is performed and showed a linear increase of the amount of final reaction product with incubation time. Transketolase activity was studied in liver, small intestine, trachea, tongue, kidney, adrenal gland, and eye. Activity was found in liver parenchyma, epithelium of small intestine, trachea, tongue, proximal tubules of kidney and cornea, and ganglion cells in medulla of adrenal gland. To demonstrate transketolase activity ultrastructurally in liver parenchymal cells, the cupper iron method was used. It was shown that transketolase activity was present in peroxisomes and at membranes of granular endoplasmic reticulum. This ultrastructural localization is similar to that of glucose-6-phosphate dehydrogenase activity, suggesting activity of the pentose phosphate pathway at these sites. It is concluded that the method developed for in situ localization of transketolase activity for light and electron microscopy is specific and allows further investigation of the role of transketolase in (proliferation of) cancer cells and other pathophysiological processes.

Integration of enzyme kinetic models and isotopomer distribution analysis for studies of in situ cell operation.

A current trend in neuroscience research is the use of stable isotope tracers in order to address metabolic processes in vivo. The tracers produce a huge number of metabolite forms that differ according to the number and position of labeled isotopes in the carbon skeleton (isotopomers) and such a large variety makes the analysis of isotopomer data highly complex. On the other hand, this multiplicity of forms does provide sufficient information to address cell operation in vivo. By the end of last millennium, a number of tools have been developed for estimation of metabolic flux profile from any possible isotopomer distribution data. However, although well elaborated, these tools were limited to steady state analysis, and the obtained set of fluxes remained disconnected from their biochemical context. In this review we focus on a new numerical analytical approach that integrates kinetic and metabolic flux analysis. The related computational algorithm estimates the dynamic flux based on the time-dependent distribution of all possible isotopomers of metabolic pathway intermediates that are generated from a labeled substrate. The new algorithm connects specific tracer data with enzyme kinetic characteristics, thereby extending the amount of data available for analysis: it uses enzyme kinetic data to estimate the flux profile, and vice versa, for the kinetic analysis it uses in vivo tracer data to reveal the biochemical basis of the estimated metabolic fluxes.

Effect of new antioxidant cysteinyl-flavanol conjugates on skin cancer cells.

Novel catechin derivatives obtained from grape procyanidins and l-cysteine scavenge free radicals by hydrogen atom donation, rather than electron transfer, and reduce cell viability in A375 and M21 melanoma cells. In particular, 4beta-(S-cysteinyl)epicatechin 3-O-gallate has a free radical scavenging capacity as strong as that of tea (-)-epigallocatechin gallate and causes a significant S-phase cell-cycle arrest in both cell lines at doses higher than 100 microM. The other cysteinyl compounds do not affect normal cell cycle distribution. The gallate derivative also induces apoptosis in melanoma cells more strongly than the other derivatives and the parent (-)-epicatechin do. The gallate compound seems to trigger nuclear condensation and fragmentation, which is confirmed by DNA laddering. Interestingly, they do not induce apoptosis in keratinocytes (HaCaT).

Dynamic profiling of the glucose metabolic network in fasted rat hepatocytes using [1,2-13C2]glucose.

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.

Metabolic strategy of boar spermatozoa revealed by a metabolomic characterization.

Metabolomic characteristics in boar spermatozoa were studied using [1,2-(13)C(2)]glucose and mass isotopomer analysis. In boar spermatozoa, glycolysis was the main pathway of glucose utilization producing lactate/pyruvate, whereas no gluconeogenesis was seen. Slight glycogen synthesis through the direct pathway and some incorporation of pyruvate into the Krebs cycle also took place. Neither RNA ribose-5-phosphate nor fatty acid synthesis from glucose occurred despite the detection of pyruvate dehydrogenase activity. In contrast to the known metabolic activities in dog sperm, boar spermatozoa have low levels of energy production and biosynthetic activities suggesting two different metabolic profiles for the two different phenotypes.

Benzodiazepines differently modulate EAAT1/GLAST and EAAT2/GLT1 glutamate transporters expressed in CHO cells.

It has been described recently that low concentrations of benzodiazepines stimulate the transport activity of the neuronal glutamate transporter EAAT3, whereas high concentrations inhibit it. The present study is aimed to investigate whether benzodiazepines have similar effects on the two glial glutamate transporter, EAAT1 and EAAT2. To this end, the transporters were transiently expressed in CHO cells and transport activity was determined by isotope fluxes using D-aspartate as non-metabolizable homologue of L-glutamate. At low D-aspartate concentrations (1 micromol/l) EAAT1-mediated uptake was reduced significantly by low concentrations of oxazepam (1 micromol/l) and diazepam (1 and 10 micromol/l). At 100 micromol/l D-aspartate oxazepam stimulated EAAT1-mediated uptake up to 150% in a dose dependent manner, whereas the inhibition by low concentrations of diazepam was attenuated. In contrast, a significant effect of diazepam on EAAT2-mediated uptake was only observed at 1000 micromol/l where uptake was inhibited by 60%. A similar inhibition was observed for EAAT1. These studies demonstrate a different modulation of EAAT1 and EAAT2 by benzodiazepines. Furthermore the glial transporters differ from the neuronal glutamate transporter. Thus, a complex in vivo response of the various transporters to benzodiazepines can be expected.

Valorization of grape (Vitis vinifera) byproducts. Antioxidant and biological properties of polyphenolic fractions differing in procyanidin composition and flavonol content.

Many byproducts and wastes generated by agroindustries contain polyphenols with potential application as food antioxidants and preventive agents against skin cancer and other diseases. The performance of polyphenolic fractions from Parellada grape (Vitis vinifera) pomace as antioxidants in different physicochemical environments was tested. Fractions containing oligomers with mean degree of polymerization between 3 and 4 and percentage galloylation ca. 30% were the most potent free radical scavengers and efficient antioxidants in an oil-in-water emulsion. A fraction including glycosylated flavonols was also efficient in the emulsion. All the fractions showed low aquatic toxicity and weak influence on proliferation of human melanoma cells.

A novel cyclometallated Pt(II)-ferrocene complex induces nuclear FOXO3a localization and apoptosis and synergizes with cisplatin to inhibit lung cancer cell proliferation.

Cisplatin is a platinum-based compound that acts as an alkylating agent and is used to treat a variety of malignant tumors including lung cancer. As cisplatin has significant limitations in the clinic, alternative platinum compounds such as cycloplatinated complexes have been considered as attractive anti-tumor agents. Here, we report the antiproliferative activity of a novel diastereomerically pure cycloplatinated complex (Sp,1S,2R)-[Pt{(κ(2)-C,N)[(η(5)-C5H3)-CH[double bond, length as m-dash]N-CH(Me)-CH(OH)-C6H5]Fe(η(5)-C5H5)}Cl(DMSO)] 6a, against A549 non-small cell lung cancer. Mechanistic studies revealed that compound 6a induces nuclear translocation of a FOXO3a reporter protein as well as endogenous FOXO3a in U2OS and A549 cells, respectively. Accordingly, treatment of A549 cells with compound 6a activates the intrinsic caspase pathway and dramatically increases the percentage of apoptotic cells. Furthermore, 6a displays a synergistic antiproliferative effect when applied together with cisplatin. Compound 6a is also active in other cancer cell lines including NCI-H460 large cell lung cancer cells. Importantly, antiproliferative activity of the platinacycle 6a on the non-tumor and non-proliferating 3T3-L1 cell line is weaker than in all cancer cell lines tested.

Effects of cadmium and mercury on the upper part of skeletal muscle glycolysis in mice.

The effects of pre-incubation with mercury (Hg(2+)) and cadmium (Cd(2+)) on the activities of individual glycolytic enzymes, on the flux and on internal metabolite concentrations of the upper part of glycolysis were investigated in mouse muscle extracts. In the range of metal concentrations analysed we found that only hexokinase and phosphofructokinase, the enzymes that shared the control of the flux, were inhibited by Hg(2+) and Cd(2+). The concentrations of the internal metabolites glucose-6-phosphate and fructose-6-phosphate did not change significantly when Hg(2+) and Cd(2+) were added. A mathematical model was constructed to explore the mechanisms of inhibition of Hg(2+) and Cd(2+) on hexokinase and phosphofructokinase. Equations derived from detailed mechanistic models for each inhibition were fitted to the experimental data. In a concentration-dependent manner these equations describe the observed inhibition of enzyme activity. Under the conditions analysed, the integral model showed that the simultaneous inhibition of hexokinase and phosphofructokinase explains the observation that the concentrations of glucose-6-phosphate and fructose-6-phosphate did not change as the heavy metals decreased the glycolytic flux.