Computer model of the metabolism of phenylalanine in normal subjects and in patients with phenylketonuria

The techniques of systems analysis have been applied to the metabolism of phenylalanine in healthy subjects and in phenylketonuria to derive a computer model. The model consists of seven compartments and four biological functions. Enzyme reactions are assumed to obey Michaelis-Menten kinetics. The computer program is written in FORTRAN. A biological validation of the model has been performed. The computer model has potential value for estimating concentrations of key metabolites in human organs which are not accessible to direct analysis from measurement of metabolites in blood and urine and phenylalanine intake. Such estimates would be helpful in clinical decisions concerning modification or termination of dietary treatment in phenylketonuria.     

Pervasive gene conversion in chromosomal inversion heterozygotes

Chromosomal inversions shape recombination landscapes, and species differing by inversions may exhibit reduced gene flow in these regions of the genome. Though single crossovers within inversions are not usually recovered from inversion heterozygotes, the recombination barrier imposed by inversions is nuanced by noncrossover gene conversion. Here, we provide a genomewide empirical analysis of gene conversion rates both within species and in species hybrids. We estimate that gene conversion occurs at a rate of 1 × 10^–5 to 2.5 × 10^–5 converted sites per bp per generation in experimental crosses within Drosophila pseudoobscura and between D. pseudoobscura and its naturally hybridizing sister species D. persimilis. This analysis is the first direct empirical assessment of gene conversion rates within inversions of a species hybrid. Our data show that gene conversion rates in interspecies hybrids are at least as high as within‐species estimates of gene conversion rates, and gene conversion occurs regularly within and around inverted regions of species hybrids, even near inversion breakpoints. We also found that several gene conversion events appeared to be mitotic rather than meiotic in origin. Finally, we observed that gene conversion rates are higher in regions of lower local sequence divergence, yet our observed gene conversion rates in more divergent inverted regions were at least as high as in less divergent collinear regions. Given our observed high rates of gene conversion despite the sequence differentiation between species, especially in inverted regions, gene conversion has the potential to reduce the efficacy of inversions as barriers to recombination over evolutionary time.     

Multivesicular bodies: a mechanism to package lytic and storage functions in one organelle?

Multivesicular bodies (MVBs) are endosomes or prevacuolar compartments. The lumens of their internal vesicles are thought to be topologically equivalent to cytoplasm and their membranes direct proteins and lipids for degradation. Here, we describe a new MVB function; in certain plant MVBs, the internal vesicles contain lytic enzymes and the surrounding 'soup' is a storage compartment. Separate vesicular pathways deliver proteins to the storage and lytic compartments. Recent data indicate that mammalian secretory lysosomes also have two compartments served by separate vesicular pathways. The formation of separate storage and lytic compartments within MVBs poses problems for membrane organization and topology that have not previously been considered in the literature. We offer a hypothetical model to address these problems.     

Transient changes in four GLUT4 compartments in rat adipocytes during the transition,insulin-stimulated to basal: implications for the GLUT4 trafficking pathway

In rat adipocytes, insulin-induced GLUT4 recruitment to the plasma membrane (PM) is associated with characteristic changes in the GLUT4 contents of three distinct endosomal fractions, T, H, and L. The organelle-specific marker distribution pattern suggests that these endosomal GLUT4 compartments are sorting endosomes (SR), GLUT4-storage endosomes (ST), and GLUT4 exocytotic vesicules (EV), respectively, prompting us to analyze GLUT4 recycling based upon a four-compartment kinetic model. Our analysis revealed that insulin modulates GLUT4 trafficking at multiple steps, including not only the endocytotic and exocytotic rates, but also the two rate coefficients coupling the three intracellular compartments. This analysis assumes that GLUT4 cycles through PM T, H,L, and back to PM, in that order, with transitions characterized by four first-order coefficients. Values assigned to these coefficients are based upon the four steady-state GLUT4 pool sizes assessed under both basal and insulin stimulated states and the transition time courses observed in the plasma membrane GLUT4 pool. Here we present the first reported experimental measurements of transient changes in each of the four GLUT4 compartments during the insulin-stimulated to basal transition in rat adipocytes and compare these experimental results with the corresponding model simulations. The close correlation of these results offers clear support for the general validity of the assumed model structure and the assignment of the T compartment to the sorting endosome GLUT4 pool. Variations in the recycling pathway from that of an unbranched cyclic topography are also considered in the light of these experimental observations. The possibility that H is a coupled GLUT4 storage compartment lying outside the direct cyclic pathway is contraindicated by the data. Okadaic acid-induced GLUT4 recruitment is accompanied by modulation of the rate coefficients linking individual endosomal GLUT4 compartments, further demonstrating a significant role of the endosomal pathways in GLUT4 exocytosis.     

A flux model of glycolysis and the oxidative pentosephosphate pathway in developing Brassica napus embryos

Developing oilseeds synthesize large quantities of triacylglycerol from sucrose and hexose. To understand the fluxes involved in this conversion, a quantitative metabolic flux model was developed and tested for the reaction network of glycolysis and the oxidative pentose phosphate pathway (OPPP). Developing Brassica napus embryos were cultured with [U-13C6]glucose, [1-13C]glucose, [6-13C]glucose, [U-13C12]sucrose, and/or [1,2-13C2]glucose and the labeling patterns in amino acids, lipids, sucrose, and starch were measured by gas chromatography/mass spectrometry and NMR. Data were used to verify a reaction network of central carbon metabolism distributed between the cytosol and plastid. Computer simulation of the steady state distribution of isotopomers in intermediates of the glycolysis/OPPP network was used to fit metabolic flux parameters to the experimental data. The observed distribution of label in cytosolic and plastidic metabolites indicated that key intermediates of glycolysis and OPPP have similar labeling in these two compartments, suggesting rapid exchange of metabolites between these compartments compared with net fluxes into end products. Cycling between hexose phosphate and triose phosphate and reversible transketolase velocity were similar to net glycolytic flux, whereas reversible transaldolase velocity was minimal. Flux parameters were overdetermined by analyzing labeling in different metabolites and by using data from different labeling experiments, which increased the reliability of the findings. Net flux of glucose through the OPPP accounts for close to 10% of the total hexose influx into the embryo. Therefore, the reductant produced by the OPPP accounts for at most 44% of the NADPH and 22% of total reductant needed for fatty acid synthesis.     

Estimation of secretory rates of hormones from the specific activities of metabolites which have multiple secreted precursors

The calculation of rates of entry of material into an open system of multiple pools in the steady state from the specific activities of end products, which may be derived from several pools, is described. This analysis may be applied to estimate the rates of secretion of steroid hormones from the specific activities of urinary metabolites which may have various hormones as common precursors. In a previous publication (Gurpideet al., 1963) formulae have been presented by which secretory rates could be calculated after a single injection of the tracers assuming that each of the urinary metabolites was uniquely derived from one of the pools in the system. In the present article similar formulae were derived without this assumption. Consequently, it is shown that, under certain circumstances, non-uniquely derived metabolites can be used to estimate secretory rates, and that it may be unnecessary to consider the pathways of conversion of the hormones to the metabolites or the sites where these conversion occur.     

Estimation of secretory rates of hormones from the specific activities of metabolites which have multiple secreted precursors

The calculation of rates of entry of material into an open system of multiple pools in the steady state from the specific activities of end products, which may be derived from several pools, is described. This analysis may be applied to estimate the rates of secretion of steroid hormones from the specific activities of urinary metabolites which may have various hormones as common precursors. In a previous publication (Gurpideet al., 1963) formulae have been presented by which secretory rates could be calculated after a single injection of the tracers assuming that each of the urinary metabolites was uniquely derived from one of the pools in the system. In the present article similar formulae were derived without this assumption. Consequently, it is shown that, under certain circumstances, non-uniquely derived metabolites can be used to estimate secretory rates, and that it may be unnecessary to consider the pathways of conversion of the hormones to the metabolites or the sites where these conversion occur. This work was supported in part by Grant AM-00110 of the National Institutes of Health of the United States Public Health Service.     

Bridging the gap: linking molecular simulations and systemic descriptions of cellular compartments

Metabolic processes in biological cells are commonly either characterized at the level of individual enzymes and metabolites or at the network level. Often these two paradigms are considered as mutually exclusive because concepts from neither side are suited to describe the complete range of scales. Additionally, when modeling metabolic or regulatory cellular systems, often a large fraction of the required kinetic parameters are unknown. This even applies to such simple and extensively studied systems like the photosynthetic apparatus of purple bacteria. Using the chromatophore vesicles of Rhodobacter sphaeroides as a model system, we show that a consistent kinetic model emerges when fitting the dynamics of a molecular stochastic simulation to a set of time dependent experiments even though about two thirds of the kinetic parameters in this system are not known from experiment. Those kinetic parameters that were previously known all came out in the expected range. The simulation model was built from independent protein units composed of elementary reactions processing single metabolites. This pools-and-proteins approach naturally compiles the wealth of available molecular biological data into a systemic model and can easily be extended to describe other systems by adding new protein or nucleic acid types. The automated parameter optimization, performed with an evolutionary algorithm, reveals the sensitivity of the model to the value of each parameter and the relative importances of the experiments used. Such an analysis identifies the crucial system parameters and guides the setup of new experiments that would add most knowledge for a systemic understanding of cellular compartments. The successful combination of the molecular model and the systemic parametrization presented here on the example of the simple machinery for bacterial photosynthesis shows that it is actually possible to combine molecular and systemic modeling. This framework can now straightforwardly be applied to other currently less well characterized but biologically more relevant systems.     

TNT phytotransformation pathway characteristics in Arabidopsis: role of aromatic hydroxylamines

Basic knowledge of the plant transformation pathways of TNT will aid phytoremediation design and assessment. While TNT transformation by plant metabolism has been demonstrated in previous studies, the presence and role of hydroxylamines in the transformation pathway has not been sufficiently understood. Hydroxylamines are unequivocally shown to be formed by plant transformation of TNT by two axenic plant systems (Arabidopsis thaliana and Catharanthusroseus). In addition, confirmation was obtained for conversion of these hydroxylamines to previously identified conjugates. Further characteristics of TNT transformation in Arabidopsis, an increasingly popular model system for genetic and biochemical studies of TNT transformation, were elucidated by [U-14C]TNT mass balance studies and metabolite feeding studies. These studies showed the rapid conversion of TNT to unextractable bound compounds by Arabidopsis seedlings in agreement with the green-liver model. Arabidopsis seedlings formed and transformed 4-substituted metabolites more efficiently than the 2-substituted metabolites. A qualitative kinetic rate analysis of the pathway was performed to propose rate-limiting steps in the pathway and theoretical schemes for improved rates are suggested.     

Phospholipid capture combined with non-linear chromatographic correction for improved serum metabolite profiling

Serum analysis with LC/MS can yield thousands of potential metabolites. However, in metabolomics, biomarkers of interest will often be of low abundance, and ionization suppression from high abundance endogenous metabolites such as phospholipids may prevent the detection of these metabolites. Here a cerium-modified column and methyl-tert-butyl-ether (MTBE) liquid–liquid extraction were employed to remove phospholipids from serum in order to obtain a more comprehensive metabolite profile. XCMS, an in-house developed data analysis software platform, showed that the intensity of existing endogenous metabolites increased, and that new metabolites were observed. This application of phospholipid capture in combination with XCMS non-linear data processing has enormous potential in metabolite profiling, for biomarker detection and quantitation.     

A metabolic system-wide characterisation of the pig: a model for human physiology

The pig is a single-stomached omnivorous mammal and is an important model of human disease and nutrition. As such, it is necessary to establish a metabolic framework from which pathology-based variation can be compared. Here, a combination of one and two-dimensional (1)H and (13)C nuclear magnetic resonance spectroscopy (NMR) and high-resolution magic angle spinning (HR-MAS) NMR was used to provide a systems overview of porcine metabolism via characterisation of the urine, serum, liver and kidney metabolomes. The metabolites observed in each of these biological compartments were found to be qualitatively comparable to the metabolic signature of the same biological matrices in humans and rodents. The data were modelled using a combination of principal components analysis and Venn diagram mapping. Urine represented the most metabolically distinct biological compartment studied, with a relatively greater number of NMR detectable metabolites present, many of which are implicated in gut-microbial co-metabolic processes. The major inter-species differences observed were in the phase II conjugation of extra-genomic metabolites; the pig was observed to conjugate p-cresol, a gut microbial metabolite of tyrosine, with glucuronide rather than sulfate as seen in man. These observations are important to note when considering the translatability of experimental data derived from porcine models.     

Viral infection in internally structured hosts. I. Conditions for persistent infection

For a virus population within its host, two important levels of structure can be considered: multiple cell types which can be infected, and tissue types or body compartments which may be coupled via movement. We develop a model with both types of structure. Migration between compartments can create "sources" and "sinks" within the virus population, where realized viral growth rate and abundance is lowered in some compartments compared to what would be observed in isolation. Using both analytical and numerical methods, we investigate how this within-host spatial structure affects the conditions for persistent viral infection. We find that migration between compartments makes the establishment of infection more difficult than it would be in the absence of migration, implying that within-host spatial structure combined with viral movement decreases the likelihood of viral establishment. If migration is symmetrical and compartments are heterogeneous, an increase in migration rates between compartments generally makes establishment less likely. This may help to explain the tissue specificity observed for many viruses. There are, however, important exceptions to this result. These include circumstances where the virus initially invades a compartment that is unfavorable to population growth and migration is necessary to infect other parts of the host body. Stochastic aspects of viral establishment may also favor increased migration as it tends to dampen the amplitude of fluctuations in population size during the initial transient phase of establishment.     

Developments in cell biology for quantitative immunoelectron microscopy based on thin sections: a review

Quantitative immunoelectron microscopy uses ultrathin sections and gold particle labelling to determine distributions of molecules across cell compartments. Here, we review a portfolio of new methods for comparing labelling distributions between different compartments in one study group (method 1) and between the same compartments in two or more groups (method 2). Specimen samples are selected unbiasedly and then observed and expected distributions of gold particles are estimated and compared by appropriate statistical procedures. The methods can be used to analyse gold label distributed between volume-occupying (organelle) and surface-occupying (membrane) compartments, but in method 1, membranes must be treated as organelles. With method 1, gold counts are combined with stereological estimators of compartment size to determine labelling density (LD). For volume-occupiers, LD can be expressed simply as golds per test point and, for surface-occupiers, as golds per test line intersection. Expected distributions are generated by randomly assigning gold particles to compartments and expressing observed/expected counts as a relative labelling index (RLI). Preferentially-labelled compartments are identified from their RLI values and by Chi-squared analysis of observed and expected distributions. For method 2, the raw gold particle counts distributed between compartments are simply compared across groups by contingency table and Chi-squared analysis. This identifies the main compartments responsible for the differences between group distributions. Finally, we discuss labelling efficiency (the number of gold particles per target molecule) and describe how it can be estimated for volume- or surface-occupiers by combining stereological data with biochemical determinations.     

Zea mays iRS1563: a comprehensive genome-scale metabolic reconstruction of maize metabolism

The scope and breadth of genome-scale metabolic reconstructions have continued to expand over the last decade. Herein, we introduce a genome-scale model for a plant with direct applications to food and bioenergy production (i.e., maize). Maize annotation is still underway, which introduces significant challenges in the association of metabolic functions to genes. The developed model is designed to meet rigorous standards on gene-protein-reaction (GPR) associations, elementally and charged balanced reactions and a biomass reaction abstracting the relative contribution of all biomass constituents. The metabolic network contains 1,563 genes and 1,825 metabolites involved in 1,985 reactions from primary and secondary maize metabolism. For approximately 42% of the reactions direct literature evidence for the participation of the reaction in maize was found. As many as 445 reactions and 369 metabolites are unique to the maize model compared to the AraGEM model for A. thaliana. 674 metabolites and 893 reactions are present in Zea mays iRS1563 that are not accounted for in maize C4GEM. All reactions are elementally and charged balanced and localized into six different compartments (i.e., cytoplasm, mitochondrion, plastid, peroxisome, vacuole and extracellular). GPR associations are also established based on the functional annotation information and homology prediction accounting for monofunctional, multifunctional and multimeric proteins, isozymes and protein complexes. We describe results from performing flux balance analysis under different physiological conditions, (i.e., photosynthesis, photorespiration and respiration) of a C4 plant and also explore model predictions against experimental observations for two naturally occurring mutants (i.e., bm1 and bm3). The developed model corresponds to the largest and more complete to-date effort at cataloguing metabolism for a plant species.     

Developing a multiscale, multi-resolution agent-based brain tumor model by graphics processing units

Background

Arsenic in drinking water, a major health hazard to millions of people in South and East Asia and in other parts of the world, is ingested primarily as trivalent inorganic arsenic (iAs), which then undergoes hepatic methylation to methylarsonic acid (MMAs) and a second methylation to dimethylarsinic acid (DMAs). Although MMAs and DMAs are also known to be toxic, DMAs is more easily excreted in the urine and therefore methylation has generally been considered a detoxification pathway. A collaborative modeling project between epidemiologists, biologists, and mathematicians has the purpose of explaining existing data on methylation in human studies in Bangladesh and also testing, by mathematical modeling, effects of nutritional supplements that could increase As methylation.

Methods

We develop a whole body mathematical model of arsenic metabolism including arsenic absorption, storage, methylation, and excretion. The parameters for arsenic methylation in the liver were taken from the biochemical literature. The transport parameters between compartments are largely unknown, so we adjust them so that the model accurately predicts the urine excretion rates of time for the iAs, MMAs, and DMAs in single dose experiments on human subjects.

Results

We test the model by showing that, with no changes in parameters, it predicts accurately the time courses of urinary excretion in mutiple dose experiments conducted on human subjects. Our main purpose is to use the model to study and interpret the data on the effects of folate supplementation on arsenic methylation and excretion in clinical trials in Bangladesh. Folate supplementation of folate-deficient individuals resulted in a 14% decrease in arsenicals in the blood. This is confirmed by the model and the model predicts that arsenicals in the liver will decrease by 19% and arsenicals in other body stores by 26% in these same individuals. In addition, the model predicts that arsenic methyltransferase has been upregulated by a factor of two in this population. Finally, we also show that a modification of the model gives excellent fits to the data on arsenic metabolism in human cultured hepatocytes.

Conclusions

The analysis of the Bangladesh data using the model suggests that folate supplementation may be more effective at reducing whole body arsenic than previously expected. There is almost no data on the upregulation of arsenic methyltransferase in populations chronically exposed to arsenic. Our model predicts upregulation by a factor of two in the Bangladesh population studied. This prediction should be verified since it could have important public health consequences both for treatment strategies and for setting appropriate limits on arsenic in drinking water. Our model has compartments for the binding of arsenicals to proteins inside of cells and we show that these comparments are necessary to obtain good fits to data. Protein-binding of arsenicals should be explored in future biochemical studies.     

Metabolic compartmentation

Evidence for the association of 'soluble' enzymes in vivo is extensive and compelling. These associations occur in all compartments of the cell of both prokaryotes and eukaryotes. Several factors present in vivo promote these associations among enzymes whose association in vitro is often too weak to detect. Several physiological advantages of the associated enzyme complexes can be identified, most (but not all) of which are the consequence of microcompartmentation of metabolites (substrate channeling). Substrate channeling of intermediates by either a 'direct transfer' process or 'proximity effects' can occur. The latter mechanism does not require the special molecular features needed for the direct transfer mechanism and may, therefore, exist in more general situations in the cell. Criticisms of these views are discussed. We argue that these criticisms have been largely answered by experiment and theory in recent years. Studies on simple systems in vitro, nevertheless, contribute important insights concerning the more complex phenomena in vivo.     

Metabolism of human apolipoproteins A-I and A-II: compartmental models

The metabolism of radioiodinated apolipoproteins (apo) A-I and A-II have been examined using the techniques of compartmental modeling. The model for apoA-I contains two plasma compartments decaying at different rates. One component of apoA-I has a residence time of 3.8 days and the second has a residence time of 6.1 days. In contrast, the apoA-II model has only one plasma component, with a residence time of 5.5 days, which decays through two distinct pathways. Twenty-seven percent of apoA-II decays through a pathway that takes 1.1 days longer to reach the urine than the remaining 73% which decays through the more direct path. These differences in the metabolism exist in both male and female populations. Comparison of fasting and nonfasting concentrations of apoA-I revealed that apoA-I concentration was elevated 0.5 standard deviations in the nonfasting samples while there was no significant difference in the apoA-II concentrations. The fasting apoA-I concentrations were found to be less stable over the study period when compared to fasting apoA-II concentrations. These findings are interpreted as indicating that apoA-I and apoA-II each have a separate metabolism which overlaps when they are present on the same lipoprotein particle. Furthermore, these findings are consistent with the concept that apoA-I metabolism is influenced more by perturbations such as dietary modulation.     

The peroxidase-dependent activation of butylated hydroxyanisole and butylated hydroxytoluene (BHT) to reactive intermediates. Formation of BHT-quinone methide via a chemical-chemical interaction

The food antioxidants butylated hydroxyanisole (BHA) and butylated hydroxytoluene (BHT) are shown to be metabolized to covalent binding intermediates and various other metabolites by prostaglandin H synthase and horseradish peroxidase. BHA was extensively metabolized by horseradish peroxidase (80% conversion of parent BHA into metabolites) resulting in the formation of three dimeric products. Only two of these dimers were observed in prostaglandin H synthase-catalyzed reactions. In contrast to BHA, BHT proved to be a relatively poor substrate for prostaglandin synthase and horseradish peroxidase, resulting in the formation of a small amount of polar and aqueous metabolites (23% conversion of parent BHT into metabolites). With arachidonic acid as the substrate, prostaglandin H synthase catalyzed the covalent binding of [14C]BHA and [14C]BHT to microsomal protein which was significantly inhibited by indomethacin and glutathione. The covalent binding of BHA and its metabolism to dimeric products were also inhibited by BHT. In contrast, the addition of BHA enhanced the covalent binding of BHT by 400%. Moreover, in the presence of BHA, the formation of the polar and aqueous metabolites of BHT was increased and two additional metabolites, BHT-quinone methide and stilbenequinone, were detected. The increased peroxidase-dependent oxidation of BHT in the presence of BHA is proposed to occur via the direct chemical interaction of BHA phenoxyl radical with BHT or BHT phenoxyl radical. These results suggest a potential role for phenoxyl radicals in the activation of xenobiotic chemicals to toxic metabolites.