FlySilico: Flux balance modeling of Drosophila larval growth and resource allocation.

Organisms depend on a highly connected and regulated network of biochemical reactions fueling life sustaining and growth promoting functions. While details of this metabolic network are well established, knowledge of the superordinate regulatory design principles is limited. Here, we investigated by iterative wet lab and modeling experiments the resource allocation process during the larval development of Drosophila melanogaster. We chose this system, as survival of the animals depends on the successful allocation of their available resources to the conflicting processes of growth and storage metabolite deposition. First, we generated "FlySilico", a curated metabolic network of Drosophila, and performed time-resolved growth and metabolite measurements with larvae raised on a holidic diet. Subsequently, we performed flux balance analysis simulations and tested the predictive power of our model by simulating the impact of diet alterations on growth and metabolism. Our predictions correctly identified the essential amino acids as growth limiting factor, and metabolic flux differences in agreement with our experimental data. Thus, we present a framework to study important questions of resource allocation in a multicellular organism including process priorization and optimality principles.

A yield-cost tradeoff governs Escherichia coli's decision between fermentation and respiration in carbon-limited growth.

Living cells react to changes in growth conditions by re-shaping their proteome. This accounts for different stress-response strategies, both specific (i.e., aimed at increasing the availability of stress-mitigating proteins) and systemic (such as large-scale changes in the use of metabolic pathways aimed at a more efficient exploitation of resources). Proteome re-allocation can, however, imply significant biosynthetic costs. Whether and how such costs impact the growth performance are largely open problems. Focusing on carbon-limited E. coli growth, we integrate genome-scale modeling and proteomic data to address these questions at quantitative level. After deriving a simple formula linking growth rate, carbon intake, and biosynthetic costs, we show that optimal growth results from the tradeoff between yield maximization and protein burden minimization. Empirical data confirm that E. coli growth is indeed close to Pareto-optimal over a broad range of growth rates. Moreover, we establish that, while most of the intaken carbon is diverted into biomass precursors, the efficiency of ATP synthesis is the key driver of the yield-cost tradeoff. These findings provide a quantitative perspective on carbon overflow, the origin of growth laws and the multidimensional optimality of E. coli metabolism.

Neural control of body-plan axis in regenerating planaria.

Control of axial polarity during regeneration is a crucial open question. We developed a quantitative model of regenerating planaria, which elucidates self-assembly mechanisms of morphogen gradients required for robust body-plan control. The computational model has been developed to predict the fraction of heteromorphoses expected in a population of regenerating planaria fragments subjected to different treatments, and for fragments originating from different regions along the anterior-posterior and medio-lateral axis. This allows for a direct comparison between computational and experimental regeneration outcomes. Vector transport of morphogens was identified as a fundamental requirement to account for virtually scale-free self-assembly of the morphogen gradients observed in planarian homeostasis and regeneration. The model correctly describes altered body-plans following many known experimental manipulations, and accurately predicts outcomes of novel cutting scenarios, which we tested. We show that the vector transport field coincides with the alignment of nerve axons distributed throughout the planarian tissue, and demonstrate that the head-tail axis is controlled by the net polarity of neurons in a regenerating fragment. This model provides a comprehensive framework for mechanistically understanding fundamental aspects of body-plan regulation, and sheds new light on the role of the nervous system in directing growth and form.

Assessment of the Biotransformation of Low-Turnover Drugs in the HµREL Human Hepatocyte Coculture Model.

Metabolic profiles of four drugs possessing diverse metabolic pathways (timolol, meloxicam, linezolid, and XK469) were compared following incubations in both suspended cryopreserved human hepatocytes and the HµREL hepatocyte coculture model. In general, minimal metabolism was observed following 4-hour incubations in both suspended hepatocytes and the HµREL model, whereas incubations conducted up to 7 days in the HµREL coculture model resulted in more robust metabolic turnover. In the case of timolol, in vivo human data suggest that 22% of the dose is transformed via multistep oxidative opening of the morpholine moiety. Only the first-step oxidation was detected in suspended hepatocytes, whereas the relevant downstream metabolites were produced in the HµREL model. For meloxicam, both the hydroxymethyl and subsequent carboxylic acid metabolites were abundant following incubation in the HµREL model, while only a trace amount of the hydroxymethyl metabolite was observed in suspension. Similar to timolol, linezolid generated substantially higher levels of morpholine ring-opened carboxylic acid metabolites in the HµREL model. Finally, while the major aldehyde oxidase-mediated mono-oxidative metabolite of XK469 was minimally produced in hepatocyte suspension, the HµREL model robustly produced this metabolite, consistent with a pathway reported to account for 54% of the total urinary excretion in human. In addition, low-level taurine and glycine conjugates were identified in the HµREL model. In summary, continuous metabolite production was observed for up to 7 days of incubation in the HµREL model, covering cytochrome P450, aldehyde oxidase, and numerous conjugative pathways, while predominant metabolites correlated with relevant metabolites reported in human in vivo studies.

The metabolic theory of ecology and the cost of parasitism.

With over 1 million species on earth, each biologically unique, do we have any hope of understanding whether species will persist in a warming world? We might, because it turns out that there is surprising regularity in how warming accelerates the major metabolic processes that power life. A persistent challenge has been to understand ecological effects of temperature in the context of species interactions, especially when individuals not only experience temperature but also mortality due to parasitism or predation. Kirk et al. have shown how the effects of parasites vary with warming in a manner entirely consistent with general temperature dependence of host and parasite metabolism.

Formulation, construction and analysis of kinetic models of metabolism: A review of modelling frameworks.

Kinetic models are critical to predict the dynamic behaviour of metabolic networks. Mechanistic kinetic models for large networks remain uncommon due to the difficulty of fitting their parameters. Recent modelling frameworks promise new ways to overcome this obstacle while retaining predictive capabilities. In this review, we present an overview of the relevant mathematical frameworks for kinetic formulation, construction and analysis. Starting with kinetic formalisms, we next review statistical methods for parameter inference, as well as recent computational frameworks applied to the construction and analysis of kinetic models. Finally, we discuss opportunities and limitations hindering the development of larger kinetic reconstructions.

Engineering E. coli for large-scale production - Strategies considering ATP expenses and transcriptional responses.

Microbial producers such as Escherichia coli are evolutionarily trained to adapt to changing substrate availabilities. Being exposed to large-scale production conditions, their complex, multilayered regulatory programs are frequently activated because they face changing substrate supply due to limited mixing. Here, we show that E. coli can adopt both short- and long-term strategies to withstand these stress conditions. Experiments in which glucose availability was changed over a short time scale were performed in a two-compartment bioreactor system. Quick metabolic responses were observed during the first 30s of glucose shortage, and after 70s, fundamental transcriptional programs were initiated. Since cells are fluctuating under simulated large-scale conditions, this scenario represents a continuous on/off switching of about 600 genes. Furthermore, the resulting ATP maintenance demands were increased by about 40-50%, allowing us to conclude that hyper-producing strains could become ATP-limited under large-scale production conditions. Based on the observed transcriptional patterns, we identified a number of candidate gene deletions that may reduce unwanted ATP losses. In summary, we present a theoretical framework that provides biological targets that could be used to engineer novel E. coli strains such that large-scale performance equals laboratory-scale expectations.

Functional characterization of the oxidative capacity of mitochondria and glycolytic assessment in benthic aquatic organisms.

The metabolism of benthic aquatic invertebrates, populating transitional water ecosystems, is influenced by both physiological and environmental factors, thus involving an adjustment of physiological processes which has a metabolic cost. In order to discover changes in metabolic pathways in response to specific factors, it's firstly necessary characterizing the principal cellular metabolic activities of the small benthic aquatic organisms. We approach here the bioenergetic state issue of two benthic organisms, i.e. Lekanesphaera monodi and Gammarus insensibilis, evidencing that no apparent and statistically significative differences between them in aerobic as well in glycolytic capacities are detected, except for COX activity.

Phenotypic constraints promote latent versatility and carbon efficiency in metabolic networks.

System-level properties of metabolic networks may be the direct product of natural selection or arise as a by-product of selection on other properties. Here we study the effect of direct selective pressure for growth or viability in particular environments on two properties of metabolic networks: latent versatility to function in additional environments and carbon usage efficiency. Using a Markov chain Monte Carlo (MCMC) sampling based on flux balance analysis (FBA), we sample from a known biochemical universe random viable metabolic networks that differ in the number of directly constrained environments. We find that the latent versatility of sampled metabolic networks increases with the number of directly constrained environments and with the size of the networks. We then show that the average carbon wastage of sampled metabolic networks across the constrained environments decreases with the number of directly constrained environments and with the size of the networks. Our work expands the growing body of evidence about nonadaptive origins of key functional properties of biological networks.

Comprehensive Assessment of Transcriptional Regulation Facilitates Metabolic Engineering of Isoprenoid Accumulation in Arabidopsis.

In plants, two spatially separated pathways provide the precursors for isoprenoid biosynthesis. We generated transgenic Arabidopsis (Arabidopsis thaliana) lines with modulated levels of expression of each individual gene involved in the cytosolic/peroxisomal mevalonate and plastidial methylerythritol phosphate pathways. By assessing the correlation of transgene expression levels with isoprenoid marker metabolites (gene-to-metabolite correlation), we determined the relative importance of transcriptional control at each individual step of isoprenoid precursor biosynthesis. The accumulation patterns of metabolic intermediates (metabolite-to-gene correlation) were then used to infer flux bottlenecks in the sterol pathway. The extent of metabolic cross talk, the exchange of isoprenoid intermediates between compartmentalized pathways, was assessed by a combination of gene-to-metabolite and metabolite-to-metabolite correlation analyses. This strategy allowed the selection of genes to be modulated by metabolic engineering, and we demonstrate that the overexpression of predictable combinations of genes can be used to significantly enhance flux toward specific end products of the sterol pathway. Transgenic plants accumulating increased amounts of sterols are characterized by significantly elevated biomass, which can be a desirable trait in crop and biofuel plants.

Evaluation of the interindividual human variation in bioactivation of methyleugenol using physiologically based kinetic modeling and Monte Carlo simulations.

The present study aims at predicting the level of formation of the ultimate carcinogenic metabolite of methyleugenol, 1'-sulfooxymethyleugenol, in the human population by taking variability in key bioactivation and detoxification reactions into account using Monte Carlo simulations. Depending on the metabolic route, variation was simulated based on kinetic constants obtained from incubations with a range of individual human liver fractions or by combining kinetic constants obtained for specific isoenzymes with literature reported human variation in the activity of these enzymes. The results of the study indicate that formation of 1'-sulfooxymethyleugenol is predominantly affected by variation in i) P450 1A2-catalyzed bioactivation of methyleugenol to 1'-hydroxymethyleugenol, ii) P450 2B6-catalyzed epoxidation of methyleugenol, iii) the apparent kinetic constants for oxidation of 1'-hydroxymethyleugenol, and iv) the apparent kinetic constants for sulfation of 1'-hydroxymethyleugenol. Based on the Monte Carlo simulations a so-called chemical-specific adjustment factor (CSAF) for intraspecies variation could be derived by dividing different percentiles by the 50th percentile of the predicted population distribution for 1'-sulfooxymethyleugenol formation. The obtained CSAF value at the 90th percentile was 3.2, indicating that the default uncertainty factor of 3.16 for human variability in kinetics may adequately cover the variation within 90% of the population. Covering 99% of the population requires a larger uncertainty factor of 6.4. In conclusion, the results showed that adequate predictions on interindividual human variation can be made with Monte Carlo-based PBK modeling. For methyleugenol this variation was observed to be in line with the default variation generally assumed in risk assessment.

Direct assessment of hepatic mitochondrial oxidative and anaplerotic fluxes in humans using dynamic 13C magnetic resonance spectroscopy.

Despite the central role of the liver in the regulation of glucose and lipid metabolism, there are currently no methods to directly assess hepatic oxidative metabolism in humans in vivo. By using a new (13)C-labeling strategy in combination with (13)C magnetic resonance spectroscopy, we show that rates of mitochondrial oxidation and anaplerosis in human liver can be directly determined noninvasively. Using this approach, we found the mean rates of hepatic tricarboxylic acid (TCA) cycle flux (VTCA) and anaplerotic flux (VANA) to be 0.43 ± 0.04 µmol g(-1) min(-1) and 0.60 ± 0.11 µmol g(-1) min(-1), respectively, in twelve healthy, lean individuals. We also found the VANA/VTCA ratio to be 1.39 ± 0.22, which is severalfold lower than recently published estimates using an indirect approach. This method will be useful for understanding the pathogenesis of nonalcoholic fatty liver disease and type 2 diabetes, as well as for assessing the effectiveness of new therapies targeting these pathways in humans.

Metabolic impact assessment for heterologous protein production in Streptomyces lividans based on genome-scale metabolic network modeling.

The metabolic impact exerted on a microorganism due to heterologous protein production is still poorly understood in Streptomyces lividans. In this present paper, based on exometabolomic data, a proposed genome-scale metabolic network model is used to assess this metabolic impact in S. lividans. Constraint-based modeling results obtained in this work revealed that the metabolic impact due to heterologous protein production is widely distributed in the genome of S. lividans, causing both slow substrate assimilation and a shift in active pathways. Exchange fluxes that are critical for model performance have been identified for metabolites of mouse tumor necrosis factor, histidine, valine and lysine, as well as biomass. Our results unravel the interaction of heterologous protein production with intracellular metabolism of S. lividans, thus, a possible basis for further studies in relieving the metabolic burden via metabolic or bioprocess engineering.

Spatial modeling of cell signaling networks.

The shape of a cell, the sizes of subcellular compartments, and the spatial distribution of molecules within the cytoplasm can all control how molecules interact to produce a cellular behavior. This chapter describes how these spatial features can be included in mechanistic mathematical models of cell signaling. The Virtual Cell computational modeling and simulation software is used to illustrate the considerations required to build a spatial model. An explanation of how to appropriately choose between physical formulations that implicitly or explicitly account for cell geometry and between deterministic versus stochastic formulations for molecular dynamics is provided, along with a discussion of their respective strengths and weaknesses. As a first step toward constructing a spatial model, the geometry needs to be specified and associated with the molecules, reactions, and membrane flux processes of the network. Initial conditions, diffusion coefficients, velocities, and boundary conditions complete the specifications required to define the mathematics of the model. The numerical methods used to solve reaction-diffusion problems both deterministically and stochastically are then described and some guidance is provided in how to set up and run simulations. A study of cAMP signaling in neurons ends the chapter, providing an example of the insights that can be gained in interpreting experimental results through the application of spatial modeling.

Predicting outcomes of steady-state ¹³C isotope tracing experiments using Monte Carlo sampling.

BACKGROUND: Carbon-13 (13C) analysis is a commonly used method for estimating reaction rates in biochemical networks. The choice of carbon labeling pattern is an important consideration when designing these experiments. We present a novel Monte Carlo algorithm for finding the optimal substrate input label for a particular experimental objective (flux or flux ratio). Unlike previous work, this method does not require assumption of the flux distribution beforehand. RESULTS: Using a large E. coli isotopomer model, different commercially available substrate labeling patterns were tested computationally for their ability to determine reaction fluxes. The choice of optimal labeled substrate was found to be dependent upon the desired experimental objective. Many commercially available labels are predicted to be outperformed by complex labeling patterns. Based on Monte Carlo Sampling, the dimensionality of experimental data was found to be considerably less than anticipated, suggesting that effectiveness of 13C experiments for determining reaction fluxes across a large-scale metabolic network is less than previously believed. CONCLUSIONS: While 13C analysis is a useful tool in systems biology, high redundancy in measurements limits the information that can be obtained from each experiment. It is however possible to compute potential limitations before an experiment is run and predict whether, and to what degree, the rate of each reaction can be resolved.

From chemical graphs in computer-aided drug design to general Markov-Galvez indices of drug-target, proteome, drug-parasitic disease, technological, and social-legal networks.

Complex Networks are useful in solving problems in drug research and industry, developing mathematical representations of different systems. These systems move in a wide range from relatively simple graph representations of drug molecular structures to large systems. We can cite for instance, drug-target protein interaction networks, drug policy legislation networks, or drug treatment in large geographical disease spreading networks. In any case, all these networks have essentially the same components: nodes (atoms, drugs, proteins, microorganisms and/or parasites, geographical areas, drug policy legislations, etc.) and edges (chemical bonds, drug-target interactions, drug-parasite treatment, drug use, etc.). Consequently, we can use the same type of numeric parameters called Topological Indices (TIs) to describe the connectivity patterns in all these kinds of Complex Networks despite the nature of the object they represent. The main reason for this success of TIs is the high flexibility of this theory to solve in a fast but rigorous way many apparently unrelated problems in all these disciplines. Another important reason for the success of TIs is that using these parameters as inputs we can find Quantitative Structure-Property Relationships (QSPR) models for different kind of problems in Computer-Aided Drug Design (CADD). Taking into account all the above-mentioned aspects, the present work is aimed at offering a common background to all the manuscripts presented in this special issue. In so doing, we make a review of the most common types of complex networks involving drugs or their targets. In addition, we review both classic TIs that have been used to describe the molecular structure of drugs and/or larger complex networks. Next, we use for the first time a Markov chain model to generalize Galvez TIs to higher order analogues coined here as the Markov-Galvez TIs of order k (MGk). Lastly, we illustrate the calculation of MGk values for different classes of networks found in drug research, nature, technology, and social-legal sciences.

A mechanistic modeling framework for predicting metabolic interactions in complex mixtures.

BACKGROUND: Computational modeling of the absorption, distribution, metabolism, and excretion of chemicals is now theoretically able to describe metabolic interactions in realistic mixtures of tens to hundreds of substances. That framework awaits validation. OBJECTIVES: Our objectives were to a) evaluate the conditions of application of such a framework, b) confront the predictions of a physiologically integrated model of benzene, toluene, ethylbenzene, and m-xylene (BTEX) interactions with observed kinetics data on these substances in mixtures and, c) assess whether improving the mechanistic description has the potential to lead to better predictions of interactions. METHODS: We developed three joint models of BTEX toxicokinetics and metabolism and calibrated them using Markov chain Monte Carlo simulations and single-substance exposure data. We then checked their predictive capabilities for metabolic interactions by comparison with mixture kinetic data. RESULTS: The simplest joint model (BTEX interacting competitively for cytochrome P450 2E1 access) gives qualitatively correct and quantitatively acceptable predictions (with at most 50% deviations from the data). More complex models with two pathways or back-competition with metabolites have the potential to further improve predictions for BTEX mixtures. CONCLUSIONS: A systems biology approach to large-scale prediction of metabolic interactions is advantageous on several counts and technically feasible. However, ways to obtain the required parameters need to be further explored.

Proteomic assessment of the acute phase of dystrophin deficiency in mdx mice.

Duchenne muscular dystrophy (DMD) is caused by the absence of a functional dystrophin protein and is modeled by the mdx mouse. The mdx mouse suffers an early necrotic bout in the hind limb muscles lasting from approximately 4 to 7 weeks. The purpose of this investigation was to determine the extent to which dystrophin deficiency changed the proteome very early in the disease process. In order to accomplish this, proteins from gastrocnemius from 6-week-old C57 (n = 6) and mdx (n = 6) mice were labeled with fluorescent dye and subjected to two-dimensional differential in-gel electrophoresis (2D-DIGE). Resulting differentially expressed spots were excised and protein identity determined via MALDI-TOF followed by database searching using MASCOT. Proteins of the immediate energy system and glycolysis were generally down-regulated in mdx mice compared to C57 mice. Conversely, expression of proteins involved in the Kreb's cycle and electron transport chain were increased in dystrophin-deficient muscle compared to control. Expression of cytoskeletal components, including tubulins, vimentin, and collagen, were increased in mdx mice compared to C57 mice. Importantly, these changes are occurring at only 6 weeks of age and are caused by acute dystrophin deficiency rather than more chronic injury. These data may provide insight regarding early pathologic changes occurring in dystrophin-deficient skeletal muscle.

Pyruvate kinase type M2: a key regulator of the metabolic budget system in tumor cells.

Cell proliferation only proceeds when metabolism is capable of providing a budget of metabolic intermediates that is adequate to ensure both energy regeneration and the synthesis of cell building blocks in sufficient amounts. In tumor cells, the glycolytic pyruvate kinase isoenzyme M2 (PKM2, M2-PK) determines whether glucose is converted to lactate for regeneration of energy (active tetrameric form, Warburg effect) or used for the synthesis of cell building blocks (nearly inactive dimeric form). This review discusses the regulation mechanisms of pyruvate kinase M2 expression by different transcription factors as well as the regulation of pyruvate kinase M2 activity by direct interaction with certain oncoproteins, tyrosine and serine phosphorylation, binding of phosphotyrosine peptides, association with other glycolytic and non glycolytic enzymes, the promyelocytic leukemia tumor suppressor protein, as well as metabolic intermediates. An intervention in the regulation mechanisms of the expression, activity and tetramer to dimer ratio of pyruvate kinase M2 has severe consequences for metabolism as well as proliferation and tumorigenic capacity of the cells which makes this enzyme a promising target for potential therapeutic approaches. The quantification of the dimeric form of pyruvate kinase M2 (Tumor M2-PK) in plasma and stool allows early detection of tumors and therapy control. Several different mechanisms may induce a translocation of pyruvate kinase M2 into the nucleus. The role of pyruvate kinase M2 in the nucleus is complex as witnessed by evidence of its effect both as pro-proliferative as well as pro-apoptotic stimuli.

Single-variable reaction systems: deterministic and stochastic models.

Biochemical reaction networks are often described by deterministic models based on macroscopic rate equations. However, for small numbers of molecules, intrinsic noise can play a significant role and stochastic methods may thus be required. In this work, we analyze the differences and similarities between a class of macroscopic deterministic models and corresponding mesoscopic stochastic models. We derive expressions that provide a clear and intuitive view upon the behavior of the stochastic model. In particular, these expressions show the dependence of both the dynamics and the stationary distribution of the stochastic model on the number of molecules in the system. As expected, most properties of the stochastic model correspond well with those in the deterministic model if the number of molecules is large enough. However, for some properties, both models are inconsistent, even if the number of molecules in the stochastic model tends to infinity. Throughout this paper, we use a bistable autophosphorylation cycle as a running example. For such a bistable system, we give an explicit proof that the rate of convergence to the stationary distribution (or the second eigenvalue of the transition matrix) depends exponentially on the number of molecules.