Use of Mathematical Models for Predicting the Metabolic Effect of Large-Scale Enzyme Activity Alterations. Application to Enzyme Deficiencies of Red Blood Cells

Metabolite interactions in the bacterial Calvin cycle and implications for flux regulation

Metabolite-level regulation of enzyme activity is important for microbes to cope with environmental shifts. Knowledge of such regulations can also guide strain engineering for biotechnology. Here we apply limited proteolysis-small molecule mapping (LiP-SMap) to identify and compare metabolite-protein interactions in the proteomes of two cyanobacteria and two lithoautotrophic bacteria that fix CO2 using the Calvin cycle. Clustering analysis of the hundreds of detected interactions shows that some metabolites interact in a species-specific manner. We estimate that approximately 35% of interacting metabolites affect enzyme activity in vitro, and the effect is often minor. Using LiP-SMap data as a guide, we find that the Calvin cycle intermediate glyceraldehyde-3-phosphate enhances activity of fructose-1,6/sedoheptulose-1,7-bisphosphatase (F/SBPase) from Synechocystis sp. PCC 6803 and Cupriavidus necator in reducing conditions, suggesting a convergent feed-forward activation of the cycle. In oxidizing conditions, glyceraldehyde-3-phosphate inhibits Synechocystis F/SBPase by promoting enzyme aggregation. In contrast, the glycolytic intermediate glucose-6-phosphate activates F/SBPase from Cupriavidus necator but not F/SBPase from Synechocystis. Thus, metabolite-level regulation of the Calvin cycle is more prevalent than previously appreciated.

Quantitative modeling of pentose phosphate pathway response to oxidative stress reveals a cooperative regulatory strategy

Living cells use signaling and regulatory mechanisms to adapt to environmental stresses. Adaptation to oxidative stress involves the regulation of many enzymes in both glycolysis and pentose phosphate pathways (PPP), so as to support PPP-driven NADPH recycling for antioxidant defense. The underlying regulatory logic is investigated by developing a kinetic modeling approach fueled with metabolomics and 13C-fluxomics datasets from human fibroblast cells. Bayesian parameter estimation and phenotypic analysis of models highlight complementary roles for several metabolite-enzyme regulations. Specifically, carbon flux rerouting into PPP involves a tight coordination between the upregulation of G6PD activity concomitant to a decreased NADPH/NADP+ ratio and the differential control of downward and upward glycolytic fluxes through the joint inhibition of PGI and GAPD enzymes. Such functional interplay between distinct regulatory feedbacks promotes efficient detoxification and homeostasis response over a broad range of stress level, but can also explain paradoxical pertubation phenotypes for instance reported for 6PGD modulation in mammalian cells.

Strong Emergence in Biological Systems: Is It Open to Mathematical Reasoning?

Complex, multigenic biological traits are shaped by the emergent interaction of proteins being the main functional units at the molecular scale. Based on a phenomenological approach, algorithms for quantifying two different aspects of emergence were introduced (Wegner and Hao in Progr Biophys Mol Biol 161:54-61, 2021) describing: (i) pairwise reciprocal interactions of proteins mutually modifying their contribution to a complex trait (denoted as weak emergence), and (ii) formation of a new, complex trait by a set of n 'constitutive' proteins at concentrations exceeding individual threshold values (strong emergence). The latter algorithm is modified here to take account of protein redundancy with respect to a complex trait ('full redundancy'). Irreducibility is considered a necessary and sufficient criterion for strong biological emergence; if one constitutive protein is missing, or its concentration drops below the threshold the trait is lost. A definition based on 'unpredictability' is dismissed, because this criterion is irrelevant for the evolution of a complex trait, and apparent unpredictability may rather reflect our basic deficits in understanding unless we can provide an unequivocal proof for it. The phenomenological approach advocated here allows to identify hidden rules according to which strongly emergent traits may be organized. This is of high value for understanding the evolution of complex traits which seems to require the saltational advent of all constitutive proteins 'in one turn' to arrive at a functional trait providing for an improved fitness of the organism. Rather than being a purely random process, it may be guided by fundamental structural principles.

Assessment of in vitro kinetics and biological impact of nebulized trehalose on human bronchial epithelium

Trehalose is added in drug formulations to act as fillers or improve aerosolization performance. Its characteristics as a carrier molecule have been explored; however, the fate of trehalose in human airway tissues has not been thoroughly investigated. Here, we investigated the fate of nebulized trehalose using in vitro human air-liquid bronchial epithelial cultures. First, a tracing experiment was conducted using ¹³C₁₂-trehalose; we measured trehalose distribution in different culture compartments (apical surface liquid, epithelial culture, and basal side medium) at various time points following acute exposure to ¹³C₁₂-labeled trehalose. We found that ¹³C₁₂-trehalose was metabolized into ¹³C₆-glucose. The data was then used to model the kinetics of trehalose disappearance from the apical surface of bronchial cultures. Secondly, we evaluated the potential adverse effects of nebulized trehalose on the bronchial cultures after they were acutely exposed to nebulized trehalose up to a level just below its solubility limit (50 g/100 g water). We assessed the ciliary beating frequency and histological characteristics. We found that nebulized trehalose did not lead to marked alteration in ciliary beating frequency and morphology of the epithelial cultures. The in vitro testing approach used here may enable the early selection of excipients for future development of inhalation products.

Carbohydrate metabolism in trypanosomatids: New insights revealing novel complexity, diversity and species-unique features

The human pathogenic trypanosomatid species collectively called the "TriTryp parasites" - Trypanosoma brucei, Trypanosoma cruzi and Leishmania spp. - have complex life cycles, with each of these parasitic protists residing in a different niche during their successive developmental stages where they encounter diverse nutrients. Consequently, they adapt their metabolic network accordingly. Yet, throughout the life cycles, carbohydrate metabolism - involving the glycolytic, gluconeogenic and pentose-phosphate pathways - always plays a central role in the biology of these parasites, whether the available carbon and free energy sources are saccharides, amino acids or lipids. In this paper, we provide an updated review of the carbohydrate metabolism of the TriTryps, highlighting new data about this metabolic network, the interconnection of its pathways and the compartmentalisation of its enzymes within glycosomes, cytosol and mitochondrion. Differences in the expression of the branches of the metabolic network between the successive life-cycle stages of each of these parasitic trypanosomatids are discussed, as well as differences between them. Recent structural and kinetic studies have revealed unique regulatory mechanisms for some of the network's key enzymes with important species-specific variations. Furthermore, reports of multiple post-translational modifications of trypanosomal glycolytic enzymes suggest that additional mechanisms for stage- and/or environmental cues that regulate activity are operational in the parasites. The detailed comparison of the carbohydrate metabolism of the TriTryps has thus revealed multiple differences and a greater complexity, including for the reduced metabolic network in bloodstream-form T. brucei, than previously appreciated. Although these parasites are related, share many cytological and metabolic features and are grouped within a single taxonomic family, the differences highlighted in this review reflect their separate evolutionary tracks from a common ancestor to the extant organisms. These differences are indicative of their adaptation to the different insect vectors and niches occupied in their mammalian hosts.

Applications of the Pharmacophore Concept in Natural Product inspired Drug Design

Pharmacophore-based techniques are nowadays an important part of many computer-aided drug design workflows and have been successfully applied for tasks such as virtual screening, lead optimization and de novo design. Natural products, on the other hand, can serve as a valuable source for unconventional molecular scaffolds that stimulate ideas for novel lead compounds in a more diverse chemical space that does not follow the rules of traditional medicinal chemistry. The first part of this review provides a brief introduction to the pharmacophore concept, the methods for pharmacophore model generation, and their applications. The second, concluding part, presents examples for recent, pharmacophore method related research in the field of natural product chemistry. The selected examples show, that pharmacophore-based methods which get mainly applied on synthetic drug-like molecules work equally well in the realm of natural products and thus can serve as a valuable tool for researchers in the field of natural product inspired drug design.

The Pharmacophore Concept and Its Applications in Computer-Aided Drug Design

Pharmacophore-based techniques currently are an integral part of many computer-aided drug design workflows and have been successfully and extensively applied for tasks such as virtual screening, de novo design, and lead optimization. Pharmacophore models can be derived both in a receptor-based and in a ligand-based manner, and provide an abstract description of essential non-bonded interactions that typically occur between small-molecule ligands and macromolecular targets. Due to their simplistic and abstract nature, pharmacophores are both perfectly suited for efficient computer processing and easy to comprehend by life and physical scientists. As a consequence, they have also proven to be a valuable tool for communicating between computational and medicinal chemists.This chapter aims to provide a short overview of the pharmacophore concept and its applications in modern computer-aided drug design. The chapter is divided into three distinct parts. The first section contains a brief introduction to the pharmacophore concept. The second section provides a description of the most common nonbonded interaction types and their representation as pharmacophoric features. Furthermore, it gives an overview of the various methods for pharmacophore generation and important pharmacophore-based techniques in drug design. This part concludes with examples for recent pharmacophore concept-related research and development. The last section is dedicated to a review of research in the field of natural product chemistry as carried out by employing pharmacophore-based drug design methods.

Targeting pathogen metabolism without collateral damage to the host

The development of drugs that can inactivate disease-causing cells (e.g. cancer cells or parasites) without causing collateral damage to healthy or to host cells is complicated by the fact that many proteins are very similar between organisms. Nevertheless, due to subtle, quantitative differences between the biochemical reaction networks of target cell and host, a drug can limit the flux of the same essential process in one organism more than in another. We identified precise criteria for this ‘network-based’ drug selectivity, which can serve as an alternative or additive to structural differences. We combined computational and experimental approaches to compare energy metabolism in the causative agent of sleeping sickness, Trypanosoma brucei, with that of human erythrocytes, and identified glucose transport and glyceraldehyde-3-phosphate dehydrogenase as the most selective antiparasitic targets. Computational predictions were validated experimentally in a novel parasite-erythrocytes co-culture system. Glucose-transport inhibitors killed trypanosomes without killing erythrocytes, neurons or liver cells.

In Silico Identification and in Vitro Activity of Novel Natural Inhibitors of Trypanosoma brucei Glyceraldehyde-3-phosphate-dehydrogenase

As part of our ongoing efforts to identify natural products with activity against pathogens causing neglected tropical diseases, we are currently performing an extensive screening of natural product (NP) databases against a multitude of protozoan parasite proteins. Within this project, we screened a database of NPs from a commercial supplier, AnalytiCon Discovery (Potsdam, Germany), against Trypanosoma brucei glyceraldehyde-3-phosphate dehydrogenase (TbGAPDH), a glycolytic enzyme whose inhibition deprives the parasite of energy supply. NPs acting as potential inhibitors of the mentioned enzyme were identified using a pharmacophore-based virtual screening and subsequent docking of the identified hits into the active site of interest. In a set of 700 structures chosen for the screening, 13 (1.9%) were predicted to possess significant affinity towards the enzyme and were therefore tested in an in vitro enzyme assay using recombinant TbGAPDH. Nine of these in silico hits (69%) showed significant inhibitory activity at 50 µM, of which two geranylated benzophenone derivatives proved to be particularly active with IC50 values below 10 µM. These compounds also showed moderate in vitro activity against T. brucei rhodesiense and may thus represent interesting starting points for further optimization.

Sequential metabolic phases as a means to optimize cellular output in a constant environment

Temporal changes of gene expression are a well-known regulatory feature of all cells, which is commonly perceived as a strategy to adapt the proteome to varying external conditions. However, temporal (rhythmic and non-rhythmic) changes of gene expression are also observed under virtually constant external conditions. Here we hypothesize that such changes are a means to render the synthesis of the metabolic output more efficient than under conditions of constant gene activities. In order to substantiate this hypothesis, we used a flux-balance model of the cellular metabolism. The total time span spent on the production of a given set of target metabolites was split into a series of shorter time intervals (metabolic phases) during which only selected groups of metabolic genes are active. The related flux distributions were calculated under the constraint that genes can be either active or inactive whereby the amount of protein related to an active gene is only controlled by the number of active genes: the lower the number of active genes the more protein can be allocated to the enzymes carrying non-zero fluxes. This concept of a predominantly protein-limited efficiency of gene expression clearly differs from other concepts resting on the assumption of an optimal gene regulation capable of allocating to all enzymes and transporters just that fraction of protein necessary to prevent rate limitation. Applying this concept to a simplified metabolic network of the central carbon metabolism with glucose or lactate as alternative substrates, we demonstrate that switching between optimally chosen stationary flux modes comprising different sets of active genes allows producing a demanded amount of target metabolites in a significantly shorter time than by a single optimal flux mode at fixed gene activities. Our model-based findings suggest that temporal expression of metabolic genes can be advantageous even under conditions of constant external substrate supply.

A novel method for measuring the ATP-related compounds in human erythrocytes

The ATP-related compounds in whole blood or red blood cells have been used to evaluate the energy status of erythrocytes and the degradation level of the phosphorylated compounds under various conditions, such as chronic renal failure, drug monitoring, cancer, exposure to environmental toxics, and organ preservation. The complete interpretation of the energetic homeostasis of erythrocytes is only performed using the compounds involved in the degradation pathway for adenine nucleotides alongside the uric acid value. For the first time, we report a liquid chromatographic method using a diode array detector that measures all of these compounds in a small human whole blood sample (125 μL) within an acceptable time of 20 min. The stability was evaluated for all of the compounds and ranged from 96.3 to 105.1% versus the day zero values. The measurement had an adequate sensitivity for the ATP-related compounds (detection limits from 0.001 to 0.097 μmol/L and quantification limits from 0.004 to 0.294 μmol/L). This method is particularly useful for measuring inosine monophosphate, inosine, hypoxanthine, and uric acid. Moreover, this assay had acceptable linearity (r > 0.990), precision (coefficients of variation ranged from 0.1 to 2.0%), specificity (similar retention times and spectra in all samples) and recoveries (ranged from 89.2 to 104.9%). The newly developed method is invaluable for assessing the energetic homeostasis of red blood cells under diverse conditions, such as in vitro experiments and clinical settings.

Integration of methods in cheminformatics and biocalorimetry for the design of trypanosomatid enzyme inhibitors

Background: The enzyme GAPDH, which acts in the glycolytic pathway, is seen as a potential target for pharmaceutical intervention of Chagas disease. Results: Herein, we report the discovery of new Trypanosoma cruzi GAPDH (TcGAPDH) inhibitors from target- and ligand-based virtual screening protocols using isothermal titration calorimetry (ITC) and molecular dynamics. Molecular dynamics simulations were used to gain insight on the binding poses of newly identified inhibitors acting at the TcGAPDH substrate (G3P) site. Conclusion: Nequimed125, the most potent inhibitor to act upon TcGAPDH so far, which sits on the G3P site without any contact with the co-factor (NAD+) site, underpins the result obtained by ITC that it is a G3P-competitive inhibitor. Molecular dynamics simulation provides biding poses of TcGAPDH inhibitors that correlate with mechanisms of inhibition observed by ITC. Overall, a new class of dihydroindole compounds that act upon TcGAPDH through a competitive mechanism of inhibition as proven by ITC measurements also kills T. cruzi.

Metabolic flux is a determinant of the evolutionary rates of enzyme-encoding genes

Relationships between evolutionary rates and gene properties on a genomic, functional, pathway, or system level are being explored to unravel the principles of the evolutionary process. In particular, functional network properties have been analyzed to recognize the constraints they may impose on the evolutionary fate of genes. Here we took as a case study the core metabolic network in human erythrocytes and we analyzed the relationship between the evolutionary rates of its genes and the metabolic flux distribution throughout it. We found that metabolic flux correlates with the ratio of nonsynonymous to synonymous substitution rates. Genes encoding enzymes that carry high fluxes have been more constrained in their evolution, while purifying selection is more relaxed in genes encoding enzymes carrying low metabolic fluxes. These results demonstrate the importance of considering the dynamical functioning of gene networks when assessing the action of selection on system-level properties.

KINETIC MODEL OF PHOSPHOFRUCTOKINASE-1 FROMESCHERICHIA COLI

This paper presents a kinetic model of phosphofructokinase-1 from Escherichia coli. A complete catalytic cycle has been reconstructed based on available information on the oligomeric structure of the enzyme and kinetic mechanism of its monomer. Applying the generalization of the Monod–Wyman–Changeux approach proposed by Popova and Sel'kov35–37to the reconstructed catalytic cycle rate equation has been derived. Dependence of the reaction rate on pH , magnesium, and effectors has been taken into account. Kinetic parameters have been estimated via fitting the rate equation against experimentally measured dependencies of initial rate on substrates, products, effectors, and pH available from the literature. The model of phosphofructokinase-1 predicts (1) cooperativity of binding both fructose-6-phosphate and ATPMg2-, (2) significant inhibition of the enzyme resulting from an increase in total concentration of ATP under the condition of fixed concentration of Mg2+ions, and (3) dual effect of ADP consisting of allosteric activation and product inhibition of the enzyme. Moreover, the model developed can be used in the kinetic modeling of biochemical pathways containing phosphofructokinase-1.

Enzymatic features of the glucose metabolism in tumor cells

Many tumor types exhibit an impaired Pasteur effect, i.e. despite the presence of oxygen, glucose is consumed at an extraordinarily high rate compared with the tissue from which they originate - the so-called 'Warburg effect'. Glucose has to serve as the source for a diverse array of cellular functions, including energy production, synthesis of nucleotides and lipids, membrane synthesis and generation of redox equivalents for antioxidative defense. Tumor cells acquire specific enzyme-regulatory mechanisms to direct the main flux of glucose carbons to those pathways most urgently required under challenging external conditions such as varying substrate availability, presence of anti-cancer drugs or different phases of the cell cycle. In this review we summarize the currently available information on tumor-specific expression, activity and kinetic properties of enzymes involved in the main pathways of glucose metabolism with due regard to the explanation of the regulatory basis and physiological significance of the Warburg effect. We conclude that, besides the expression level of the metabolic enzymes involved in the glucose metabolism of tumor cells, the unique tumor-specific pattern of isozymes and accompanying changes in the metabolic regulation below the translation level enable tumor cells to drain selfishly the blood glucose pool that non-transformed cells use as sparingly as possible.

Systems biology from micro-organisms to human metabolic diseases: the role of detailed kinetic models

Human metabolic diseases are typically network diseases. This holds not only for multifactorial diseases, such as metabolic syndrome or Type 2 diabetes, but even when a single gene defect is the primary cause, where the adaptive response of the entire network determines the severity of disease. The latter may differ between individuals carrying the same mutation. Understanding the adaptive responses of human metabolism naturally requires a systems biology approach. Modelling of metabolic pathways in micro-organisms and some mammalian tissues has yielded many insights, qualitative as well as quantitative, into their control and regulation. Yet, even for a well-known pathway such as glycolysis, precise predictions of metabolite dynamics from experimentally determined enzyme kinetics have been only moderately successful. In the present review, we compare kinetic models of glycolysis in three cell types (African trypanosomes, yeast and skeletal muscle), evaluate their predictive power and identify limitations in our understanding. Although each of these models has its own merits and shortcomings, they also share common features. For example, in each case independently measured enzyme kinetic parameters were used as input. Based on these 'lessons from glycolysis', we will discuss how to make best use of kinetic computer models to advance our understanding of human metabolic diseases.

IGERS: inferring Gibbs energy changes of biochemical reactions from reaction similarities

Mathematical analysis and modeling of biochemical reaction networks requires knowledge of the permitted directionality of reactions and membrane transport processes. This information can be gathered from the standard Gibbs energy changes (DeltaG(0)) of reactions and the concentration ranges of their reactants. Currently, experimental DeltaG(0) values are not available for the vast majority of cellular biochemical processes. We propose what we believe to be a novel computational method to infer the unknown DeltaG(0) value of a reaction from the known DeltaG(0) value of the chemically most similar reaction. The chemical similarity of two arbitrary reactions is measured by the relative number (T) of co-occurring changes in the chemical attributes of their reactants. Testing our method across a validated reference set of 173 biochemical reactions with experimentally determined DeltaG(0) values, we found that a minimum reaction similarity of T = 0.6 is required to infer DeltaG(0) values with an error of <10 kJ/mol. Applying this criterion, our method allows us to assign DeltaG(0) values to 458 additional reactions of the BioPath database. We believe our approach permits us to minimize the number of DeltaG(0) measurements required for a full coverage of a given reaction network with reliable DeltaG(0) values.

STOCHASTIC KINETIC MODELS: DYNAMIC INDEPENDENCE, MODULARITY AND GRAPHS

The dynamic properties and independence structure of stochastic kinetic models (SKMs) are analyzed. An SKM is a highly multivariate jump process used to model chemical reaction networks, particularly those in biochemical and cellular systems. We identify SKM subprocesses with the corresponding counting processes and propose a directed, cyclic graph (the kinetic independence graph or KIG) that encodes the local independence structure of their conditional intensities. Given a partition [A, D, B] of the vertices, the graphical separation A ⊥ B|D in the undirected KIG has an intuitive chemical interpretation and implies that A is locally independent of B given A ∪ D. It is proved that this separation also results in global independence of the internal histories of A and B conditional on a history of the jumps in D which, under conditions we derive, corresponds to the internal history of D. The results enable mathematical definition of a modularization of an SKM using its implied dynamics. Graphical decomposition methods are developed for the identification and efficient computation of nested modularizations. Application to an SKM of the red blood cell advances understanding of this biochemical system.

The silicon trypanosome

African trypanosomes have emerged as promising unicellular model organisms for the next generation of systems biology. They offer unique advantages, due to their relative simplicity, the availability of all standard genomics techniques and a long history of quantitative research. Reproducible cultivation methods exist for morphologically and physiologically distinct life-cycle stages. The genome has been sequenced, and microarrays, RNA-interference and high-accuracy metabolomics are available. Furthermore, the availability of extensive kinetic data on all glycolytic enzymes has led to the early development of a complete, experiment-based dynamic model of an important biochemical pathway. Here we describe the achievements of trypanosome systems biology so far and outline the necessary steps towards the ambitious aim of creating a 'Silicon Trypanosome', a comprehensive, experiment-based, multi-scale mathematical model of trypanosome physiology. We expect that, in the long run, the quantitative modelling enabled by the Silicon Trypanosome will play a key role in selecting the most suitable targets for developing new anti-parasite drugs.

Rewiring and regulation of cross-compartmentalized metabolism in protists

Plastid acquisition, endosymbiotic associations, lateral gene transfer, organelle degeneracy or even organelle loss influence metabolic capabilities in many different protists. Thus, metabolic diversity is sculpted through the gain of new metabolic functions and moderation or loss of pathways that are often essential in the majority of eukaryotes. What is perhaps less apparent to the casual observer is that the sub-compartmentalization of ubiquitous pathways has been repeatedly remodelled during eukaryotic evolution, and the textbook pictures of intermediary metabolism established for animals, yeast and plants are not conserved in many protists. Moreover, metabolic remodelling can strongly influence the regulatory mechanisms that control carbon flux through the major metabolic pathways. Here, we provide an overview of how core metabolism has been reorganized in various unicellular eukaryotes, focusing in particular on one near universal catabolic pathway (glycolysis) and one ancient anabolic pathway (isoprenoid biosynthesis). For the example of isoprenoid biosynthesis, the compartmentalization of this process in protists often appears to have been influenced by plastid acquisition and loss, whereas for glycolysis several unexpected modes of compartmentalization have emerged. Significantly, the example of trypanosomatid glycolysis illustrates nicely how mathematical modelling and systems biology can be used to uncover or understand novel modes of pathway regulation.

Triosephosphate isomerase deficiency: new insights into an enigmatic disease

The triosephosphate isomerase (TPI) functions at a metabolic cross-road ensuring the rapid equilibration of the triosephosphates produced by aldolase in glycolysis, which is interconnected to lipid metabolism, to glycerol-3-phosphate shuttle and to the pentose phosphate pathway. The enzyme is a stable homodimer, which is catalytically active only in its dimeric form. TPI deficiency is an autosomal recessive multisystem genetic disease coupled with hemolytic anemia and neurological disorder frequently leading to death in early childhood. Various genetic mutations of this enzyme have been identified; the mutations result in decrease in the catalytic activity and/or the dissociation of the dimers into inactive monomers. The impairment of TPI activity apparently does not affect the energy metabolism at system level; however, it results in accumulation of dihydroxyacetone phosphate followed by its chemical conversion into the toxic methylglyoxal, leading to the formation of advanced glycation end products. By now, the research on this disease seems to enter a progressive stage by adapting new model systems such as Drosophila, yeast strains and TPI-deficient mouse, which have complemented the results obtained by prediction and experiments with recombinant proteins or erythrocytes, and added novel data concerning the complexity of the intracellular behavior of mutant TPIs. This paper reviews the recent studies on the structural and catalytic changes caused by mutation and/or nitrotyrosination of the isomerase leading to the formation of an aggregation-prone protein, a characteristic of conformational disorders.

Uncovering metabolic objectives pursued by changes of enzyme levels

Expression profiling and proteomic techniques reveal significant variations in the levels of thousands of mRNAs and proteins in response to environmental changes such as substrate depletion, oxidative stress, and hormonal stimulation. However, in most cases the functional implications of these variations remain elusive. One crucial problem complicating the functional interpretation of high-throughput data is that changes of protein levels do not simply translate into equivalent changes in the rate of the associated chemical processes due to various modes of enzyme regulation and the instantaneous effect of changed metabolite concentrations on adjacent flux rates. Here, we outline a theoretical concept to exploit information on (relative) changes in the level of metabolic enzymes for the prediction of (relative) flux changes in the underlying metabolic network. Our approach rests on the assumption that size and direction of fluxes (flux distribution) in the network are determined by an optimization principle in that the production of the physiologically relevant output metabolites is accomplished with minimal total flux. The prediction method comprises two main steps. First, we approximate (unknown) flux changes by a linear combination of so-called minimal flux modes, each representing a specific flux distribution minimally required to accomplish the production of only one of the numerous functionally relevant output metabolites. Second, the unknown coefficients of this decomposition are chosen such that a maximal correlation with observed differential expression data is obtained. Based on simulated enzyme expression scenarios in a metabolic model of the human red blood cell, we demonstrate the predictive capacity of our method.

Kinetic hybrid models composed of mechanistic and simplified enzymatic rate laws--a promising method for speeding up the kinetic modelling of complex metabolic networks

Kinetic modelling of complex metabolic networks - a central goal of computational systems biology - is currently hampered by the lack of reliable rate equations for the majority of the underlying biochemical reactions and membrane transporters. On the basis of biochemically substantiated evidence that metabolic control is exerted by a narrow set of key regulatory enzymes, we propose here a hybrid modelling approach in which only the central regulatory enzymes are described by detailed mechanistic rate equations, and the majority of enzymes are approximated by simplified(non mechanistic) rate equations (e.g. mass action, LinLog, Michaelis-Menten and power law) capturing only a few basic kinetic features and hence containing only a small number of parameters to be experimentally determined. To check the reliability of this approach, we have applied it to two different metabolic networks, the energy and redox metabolism of red blood cells, and the purine metabolism of hepatocytes, using in both cases available comprehensive mechanistic models as reference standards. Identification of the central regulatory enzymes was performed by employing only information on network topology and the metabolic data for a single reference state of the network [Grimbs S, Selbig J, Bulik S, Holzhutter HG & Steuer R (2007) Mol Syst Biol 3, 146, doi:10.1038/msb4100186].Calculations of stationary and temporary states under various physiological challenges demonstrate the good performance of the hybrid models. We propose the hybrid modelling approach as a means to speed up the development of reliable kinetic models for complex metabolic networks.

The stability and robustness of metabolic states: identifying stabilizing sites in metabolic networks

The dynamic behavior of metabolic networks is governed by numerous regulatory mechanisms, such as reversible phosphorylation, binding of allosteric effectors or temporal gene expression, by which the activity of the participating enzymes can be adjusted to the functional requirements of the cell. For most of the cellular enzymes, such regulatory mechanisms are at best qualitatively known, whereas detailed enzyme-kinetic models are lacking. To explore the possible dynamic behavior of metabolic networks in cases of lacking or incomplete enzyme-kinetic information, we present a computational approach based on structural kinetic modeling. We derive statistical measures for the relative impact of enzyme-kinetic parameters on dynamic properties (such as local stability) and apply our approach to the metabolism of human erythrocytes. Our findings show that allosteric enzyme regulation significantly enhances the stability of the network and extends its potential dynamic behavior. Moreover, our approach allows to differentiate quantitatively between metabolic states related to senescence and metabolic collapse of the human erythrocyte. We think that the proposed method represents an important intermediate step on the long way from topological network analysis to detailed kinetic modeling of complex metabolic networks.

A comparative analysis of kinetic models of erythrocyte glycolysis

Since the 1970s, with Heinrich as a pioneer in the field, numerous kinetic models of erythrocyte glycolysis have been constructed. A functional comparison of eight of these models indicates that the production of ATP and GSH in the red blood cell is largely controlled by the demand reactions. The rate characteristics for the supply and demand blocks indicate a good homeostatic control of ATP and GSH concentrations at different work loads for the pathway, while the production rates of ATP and GSH can be adjusted as needed by the demand reactions.

Structural robustness of metabolic networks with respect to multiple knockouts

We present a generalised framework for analysing structural robustness of metabolic networks, based on the concept of elementary flux modes (EFMs). Extending our earlier study on single knockouts [Wilhelm, T., Behre, J., Schuster, S., 2004. Analysis of structural robustness of metabolic networks. IEE Proc. Syst. Biol. 1(1), 114-120], we are now considering the general case of double and multiple knockouts. The robustness measures are based on the ratio of the number of remaining EFMs after knockout vs. the number of EFMs in the unperturbed situation, averaged over all combinations of knockouts. With the help of simple examples we demonstrate that consideration of multiple knockouts yields additional information going beyond single-knockout results. It is proven that the robustness score decreases as the knockout depth increases. We apply our extended framework to metabolic networks representing amino acid anabolism in Escherichia coli and human hepatocytes, and the central metabolism in human erythrocytes. Moreover, in the E. coli model the two subnetworks synthesising amino acids that are essential and those that are non-essential for humans are studied separately. The results are discussed from an evolutionary viewpoint. We find that E. coli has the most robust metabolism of all the cell types studied here. Considering only the subnetwork of the synthesis of non-essential amino acids, E. coli and the human hepatocyte show about the same robustness.

Dynamic modeling of the central carbon metabolism of Escherichia coli

Application of metabolic engineering principles to the rational design of microbial production processes crucially depends on the ability to describe quantitatively the systemic behavior of the central carbon metabolism to redirect carbon fluxes to the product-forming pathways. Despite the importance for several production processes, development of an essential dynamic model for central carbon metabolism of Escherichia coli has been severely hampered by the current lack of kinetic information on the dynamics of the metabolic reactions. Here we present the design and experimental validation of such a dynamic model, which, for the first time, links the sugar transport system (i.e., phosphotransferase system [PTS]) with the reactions of glycolysis and the pentose-phosphate pathway. Experimental observations of intracellular concentrations of metabolites and cometabolites at transient conditions are used to validate the structure of the model and to estimate the kinetic parameters. Further analysis of the detailed characteristics of the system offers the possibility of studying important questions regarding the stability and control of metabolic fluxes.

Including metabolite concentrations into flux balance analysis: thermodynamic realizability as a constraint on flux distributions in metabolic networks

BACKGROUND

In recent years, constrained optimization - usually referred to as flux balance analysis (FBA) - has become a widely applied method for the computation of stationary fluxes in large-scale metabolic networks. The striking advantage of FBA as compared to kinetic modeling is that it basically requires only knowledge of the stoichiometry of the network. On the other hand, results of FBA are to a large degree hypothetical because the method relies on plausible but hardly provable optimality principles that are thought to govern metabolic flux distributions.

RESULTS

To augment the reliability of FBA-based flux calculations we propose an additional side constraint which assures thermodynamic realizability, i.e. that the flux directions are consistent with the corresponding changes of Gibb's free energies. The latter depend on metabolite levels for which plausible ranges can be inferred from experimental data. Computationally, our method results in the solution of a mixed integer linear optimization problem with quadratic scoring function. An optimal flux distribution together with a metabolite profile is determined which assures thermodynamic realizability with minimal deviations of metabolite levels from their expected values. We applied our novel approach to two exemplary metabolic networks of different complexity, the metabolic core network of erythrocytes (30 reactions) and the metabolic network iJR904 of Escherichia coli (931 reactions). Our calculations show that increasing network complexity entails increasing sensitivity of predicted flux distributions to variations of standard Gibb's free energy changes and metabolite concentration ranges. We demonstrate the usefulness of our method for assessing critical concentrations of external metabolites preventing attainment of a metabolic steady state.

CONCLUSION

Our method incorporates the thermodynamic link between flux directions and metabolite concentrations into a practical computational algorithm. The weakness of conventional FBA to rely on intuitive assumptions about the reversibility of biochemical reactions is overcome. This enables the computation of reliable flux distributions even under extreme conditions of the network (e.g. enzyme inhibition, depletion of substrates or accumulation of end products) where metabolite concentrations may be drastically altered.

Metabolic control analysis to identify optimal drug targets

This chapter describes the basic principles of Metabolic Control Analysis (MCA) which is a quantitative methodology to evaluate the importance and relative contribution of individual metabolic steps in the overall functioning of a particular system. The control on the flux through a metabolic pathway or subsystem can be quantified by the control coefficients of the individual enzymes or components which reflects the extent to which the component is rate-limiting. The perturbation of an individual step is measured by its elasticity coefficient. The effect of perturbation of a single step on the entire pathway or subsystem is, in turn, measured by the response coefficient. Differential control analysis can be used to compare flux through a single metabolic pathway in a pathogen with the same pathway in its host to identify uniquely vulnerable steps with the greatest potential for specifically inhibiting flux through the pathogen metabolic pathway. The utility of this methodology is illustrated with the glycolysis in Trypanosomes and with oncogenic signaling.

Analysis of enzymopathies in the human red blood cells by constraint-based stoichiometric modeling approaches

The human red blood cell (RBC) metabolism is investigated by calculating steady state fluxes using constraint-based stoichiometric modeling approaches. For the normal RBC metabolism, flux balance analysis (FBA) is performed via optimization of various alternative objective functions, and the maximization of production of ATP and NADPH is found to be the primary objective of the RBC metabolism. FBA and two novel approaches, minimization of metabolic adjustment (MOMA) and regulatory on-off minimization (ROOM), which can describe the behavior of the metabolic networks in case of enzymopathies, are applied to observe the relative changes in the flux distribution of the deficient network. The deficiencies in several enzymes in RBC metabolism are investigated and the flux distributions are compared with the non-deficient FBA distribution to elucidate the metabolic changes in response to enzymopathies. It is found that the metabolism is mostly affected by the glucose-6-phosphate dehydrogenase (G6PDH) and phosphoglycerate kinase (PGK) enzymopathies, whereas the effects of the deficiency in DPGM on the metabolism are negligible. These stoichiometric modeling results are found to be in accordance with the experimental findings in the literature related to metabolic behavior of the human red blood cells, showing that human RBC metabolism can be modeled stoichiometrically.

Triosephosphate isomerase deficiency: consequences of an inherited mutation at mRNA, protein and metabolic levels

Triosephosphate isomerase (TPI) deficiency is a unique glycolytic enzymopathy coupled with neurodegeneration. Two Hungarian compound heterozygote brothers inherited the same TPI mutations (F240L and E145Stop), but only the younger one suffers from neurodegeneration. In the present study, we determined the kinetic parameters of key glycolytic enzymes including the mutant TPI for rational modelling of erythrocyte glycolysis. We found that a low TPI activity in the mutant cells (lower than predicted from the protein level and specific activity of the purified recombinant enzyme) is coupled with an increase in the activities of glycolytic kinases. The modelling rendered it possible to establish the steady-state flux of the glycolysis and metabolite concentrations, which was not possible experimentally due to the inactivation of the mutant TPI and other enzymes during the pre-steady state. Our results showed that the flux was 2.5-fold higher and the concentration of DHAP (dihydroxyacetone phosphate) and fructose 1,6-bisphosphate increased 40- and 5-fold respectively in the erythrocytes of the patient compared with the control. Although the rapid equilibration of triosephosphates is not achieved, the energy state of the cells is not 'sick' due to the activation of key regulatory enzymes. In lymphocytes of the two brothers, the TPI activity was also lower (20%) than that of controls; however, the remaining activity was high enough to maintain the rapid equilibration of triosephosphates; consequently, no accumulation of DHAP occurs, as judged by our experimental and computational data. Interestingly, we found significant differences in the mRNA levels of the brothers for TPI and some other, apparently unrelated, proteins. One of them is the prolyl oligopeptidase, the activity decrease of which has been reported in well-characterized neurodegenerative diseases. We found that the peptidase activity of the affected brother was reduced by 30% compared with that of his neurologically intact brother.

Energy metabolism and its compartmentation in Trypanosoma brucei

African trypanosomes are parasitic protozoa of the order of Kinetoplastida, which cause sleeping sickness and nagana. Trypanosomes are not only of scientific interest because of their clinical importance, but also because these protozoa contain several very unusual biological features, such as their special energy metabolism. The energy metabolism of Trypanosoma brucei differs significantly from that of its host, not only because it comprises distinct enzymes and metabolic pathways, but also because some of the glycolytic enzymes are localized in organelles called glycosomes. Furthermore, the energy metabolism changes drastically during the complex life cycle of this parasite. This review will focus on the recent advances made in understanding the process of ATP production in T. brucei during its life cycle and the consequences of the special subcellular compartmentation.

Cancer: a Systems Biology disease

Cancer research has focused on the identification of molecular differences between cancerous and healthy cells. The emerging picture is overwhelmingly complex. Molecules out of many parallel signal transduction pathways are involved. Their activities appear to be controlled by multiple factors. The action of regulatory circuits, cross-talk between pathways and the non-linear reaction kinetics of biochemical processes complicate the understanding and prediction of the outcome of intracellular signaling. In addition, interactions between tumor and other cell types give rise to a complex supra-cellular communication network. If cancer is such a complex system, how can one ever predict the effect of a mutation in a particular gene on a functionality of the entire system? And, how should one go about identifying drug targets? Here, we argue that one aspect is to recognize, where the essence resides, i.e. recognize cancer as a Systems Biology disease. Then, more cancer biologists could become systems biologists aiming to provide answers to some of the above systemic questions. To this aim, they should integrate the available knowledge stemming from quantitative experimental results through mathematical models. Models that have contributed to the understanding of complex biological systems are discussed. We show that the architecture of a signaling network is important for determining the site at which an oncologist should intervene. Finally, we discuss the possibility of applying network-based drug design to cancer treatment and how rationalized therapies, such as the application of kinase inhibitors, may benefit from Systems Biology.

Adenine and adenosine salvage pathways in erythrocytes and the role of S-adenosylhomocysteine hydrolase. A theoretical study using elementary flux modes

This article is devoted to the study of redundancy and yield of salvage pathways in human erythrocytes. These cells are not able to synthesize ATP de novo. However, the salvage (recycling) of certain nucleosides or bases to give nucleotide triphosphates is operative. As the salvage pathways use enzymes consuming ATP as well as enzymes producing ATP, it is not easy to see whether a net synthesis of ATP is possible. As for pathways using adenosine, a straightforward assumption is that these pathways start with adenosine kinase. However, a pathway bypassing this enzyme and using S-adenosylhomocysteine hydrolase instead was reported. So far, this route has not been analysed in detail. Using the concept of elementary flux modes, we investigate theoretically which salvage pathways exist in erythrocytes, which enzymes belong to each of these and what relative fluxes these enzymes carry. Here, we compute the net overall stoichiometry of ATP build-up from the recycled substrates and show that the network has considerable redundancy. For example, four different pathways of adenine salvage and 12 different pathways of adenosine salvage are obtained. They give different ATP/glucose yields, the highest being 3:10 for adenine salvage and 2:3 for adenosine salvage provided that adenosine is not used as an energy source. Implications for enzyme deficiencies are discussed.

Glycolysis and Flux Control

Central metabolism of carbohydrates uses the Embden-Meyerhof-Parnas (EMP), pentose phosphate (PP), and Entner-Doudoroff (ED) pathways. This review reviews the biological roles of the enzymes and genes of these three pathways of E. coli. Glucose, pentoses, and gluconate are primarily discussed as the initial substrates of the three pathways, respectively. The genetic and allosteric regulatory mechanisms of glycolysis and the factors that affect metabolic flux through the pathways are considered here. Despite the fact that a lot of information on each of the reaction steps has been accumulated over the years for E. coli, surprisingly little quantitative information has been integrated to analyze glycolysis as a system. Therefore, the review presents a detailed description of each of the catalytic steps by a systemic approach. It considers both structural and kinetic aspects. Models that include kinetic information of the reaction steps will always contain the reaction stoichiometry and therefore follow the structural constraints, but in addition to these also kinetic rate laws must be fulfilled. The kinetic information obtained on isolated enzymes can be integrated using computer models to simulate behavior of the reaction network formed by these enzymes. Successful examples of such approaches are the modeling of glycolysis in S. cerevisiae, the parasite Trypanosoma brucei, and the red blood cell. With the rapid developments in the field of Systems Biology many new methods have been and will be developed, for experimental and theoretical approaches, and the authors expect that these will be applied to E. coli glycolysis in the near future.

Metabolic homeostasis in the human erythrocyte: in silico analysis

A detailed computer model of human erythrocyte metabolism was shown to predict three steady states, two stable and one unstable. The most extreme steady state is characterized by almost zero concentrations of all the phosphorylated intermediates. The "normal" steady state is remarkably robust in the face of large changes in the activity of most of the enzymes of glycolysis and the pentose phosphate pathway: this steady state can be viewed as an attractor towards which the system returns following a metabolic perturbation. Focus is given to three responses of the system: (1) the 'energy charge' that pertains to the concentration of ATP relative to all purine nucleotides; (2) redox power expressed as the ratio of reduced-to-total glutathione and (3) the concentration of 2,3-bisphosphoglycerate, that directly affects the oxygen affinity of haemoglobin thus affecting the main physiological function of the cell. The collapse of the normal steady state in what can be viewed topologically as a catastrophe is posited as one key element of erythrocyte senescence and it is particularly important for erythrocyte destruction in patients with an inborn enzyme deficiency.

The generalized flux-minimization method and its application to metabolic networks affected by enzyme deficiencies

The flux-minimization method [Holzhütter, H.G., 2004. The principle of flux-minimization and its application to calculate stationary fluxes in metabolic networks. Eur. J. Biochem. 271, 2905-2922] has been proposed as an alternative to kinetic modeling to calculate stationary fluxes in metabolic networks. Here a generalization of this method is proposed that takes into account possible limitations of internal fluxes, e.g. due to enzyme defects or partial inhibition of enzyme activities by drugs. The generalized method consists in the minimization of an objective function which expresses the compromise that has to be made between minimization of internal fluxes on one hand and maintenance of the metabolic output required for various cellular functions on the other. Fulfillment of the latter condition is measured through a fitness function, which evaluates the relative deviation of the output fluxes from demanded target values. The method is applied to assess the metabolic consequences caused by a deficiency of enzymes involved in the metabolism of erythrocytes. The obtained results are in good agreement with those obtained on the basis of a comprehensive kinetic model.

Control of MAPK signalling: from complexity to what really matters

Oncogenesis results from changes in kinetics or in abundance of proteins in signal transduction networks. Recently, it was shown that control of signalling cannot reside in a single gene product, and might well be dispersed over many components. Which of the reactions in these complex networks are most important, and how can the existing molecular information be used to understand why particular genes are oncogenes whereas others are not? We implement a new method to help address such questions. We apply control analysis to a detailed kinetic model of the epidermal growth factor-induced mitogen-activated protein kinase network. We determine the control of each reaction with respect to three biologically relevant characteristics of the output of this network: the amplitude, duration and integrated output of the transient phosphorylation of extracellular signal-regulated kinase (ERK). We confirm that control is distributed, but far from randomly: a small proportion of reactions substantially control signalling. In particular, the activity of Raf is in control of all characteristics of the transient profile of ERK phosphorylation, which may clarify why Raf is an oncogene. Most reactions that really matter for one signalling characteristic are also important for the other characteristics. Our analysis also predicts the effects of mutations and changes in gene expression.

The Silicon Cell initiative: working towards a detailed kinetic description at the cellular level

The Silicon Cell initiative aims to understand cellular systems on the basis of the characteristics of their components. As a tool to achieve this, detailed kinetic models at the network reaction level are being constructed. Such detailed kinetic models are extremely useful for medical and biotechnological applications and form strong tools for fundamental studies. Several recently constructed detailed kinetic models on metabolism (glycolysis), signal transduction (EGF receptor), and the eukaryotic cell cycle (Saccharomyces cerevisiae) have been used to exemplify the Silicon Cell project. These models are stored and made accessible via the JWS Online Cellular Systems Modeling project, a web-based repository of kinetic models. Using a web-browser the models can be interrogated via a user-friendly graphical interface. The goal of the two projects is to combine models on parts of cellular systems and ultimately to construct detailed kinetic models at the cellular level.

Functional ingredient production: application of global metabolic models

The biotechnology industry continuously explores new ways to improve the performance of microbial strains in fermentation processes. Recent focus has been on new genome-wide modelling approaches in functional genomics, which aim to take full advantage of genome sequence data, transcription profiling, proteomics and metabolite profiling for strain improvement. The integration of global metabolic models with genetic and regulatory models will be essential for the practice of metabolic engineering for strain improvement to move forward, simply because we cannot rely on our intuition to grasp the complexity of the biological systems involved.

Uniform sampling of steady-state flux spaces: means to design experiments and to interpret enzymopathies

Reconstruction of genome-scale metabolic networks is now possible using multiple different data types. Constraint-based modeling is an approach to interrogate capabilities of reconstructed networks by constraining possible cellular behavior through the imposition of physicochemical laws. As a result, a steady-state flux space is defined that contains all possible functional states of the network. Uniform random sampling of the steady-state flux space allows for the unbiased appraisal of its contents. Monte Carlo sampling of the steady-state flux space of the reconstructed human red blood cell metabolic network under simulated physiologic conditions yielded the following key results: 1), probability distributions for the values of individual metabolic fluxes showed a wide variety of shapes that could not have been inferred without computation; 2), pairwise correlation coefficients were calculated between all fluxes, determining the level of independence between the measurement of any two fluxes, and identifying highly correlated reaction sets; and 3), the network-wide effects of the change in one (or a few) variables (i.e., a simulated enzymopathy or fixing a flux range based on measurements) were computed. Mathematical models provide the most compact and informative representation of a hypothesis of how a cell works. Thus, understanding model predictions clearly is vital to driving forward the iterative model-building procedure that is at the heart of systems biology. Taken together, the Monte Carlo sampling procedure provides a broadening of the constraint-based approach by allowing for the unbiased and detailed assessment of the impact of the applied physicochemical constraints on a reconstructed network.

New 3-piperonylcoumarins as inhibitors of glycosomal glyceraldehyde-3-phosphate dehydrogenase (gGAPDH) from Trypanosoma cruzi

This article describes the synthesis and inhibitory activities of a series of new 3-piperonylcoumarins, designed as inhibitors of glycosomal glyceraldehyde-3-phosphate dehydrogenase (gGAPDH) from Trypanosoma cruzi. The design was based on the structures of previously identified natural products hits. The most active synthesized derivatives contain heterocyclic rings at position 6. SAR studies, performed by electronic indices methodology (EIM), clustered the molecules in different groups due to the chemical substitutions regarding the biological activity. Molecular modeling studies by docking suggested a different binding mode for the most active derivatives, when compared to natural hit chalepin. Moreover, the coumarin ring seems to act only as a spacer group.

Computational design of reduced metabolic networks

Cellular functions are based on thousands of chemical reactions and transport processes, most of them being catalysed and regulated by specific proteins. Systematic gene knockouts have provided evidence that this complex reaction network possesses considerable redundancy, that is, alternative routes exist along which signals and metabolic fluxes may be directed to accomplish an identical output behaviour. This property is of particular importance in cases where parts of the reaction network are transiently or permanently impaired, for example, due to an infection or genetic alterations. Here we present a computational concept to determine enzyme-reduced metabolic networks that are still sufficient to accomplish a given set of cellular functions. Our approach consists of defining an objective function that expresses the compromise that has to be made between successive reduction of the network by omission of enzymes and its decreasing thermodynamic and kinetic feasibility. Optimisation of this objective function results in a linear mixed-integer program. With increasing weight given to the reduction of the number of enzymes, the total flux in the network increases and some of the reactions have to proceed in thermodynamically unfavourable directions. The approach was applied to two metabolic schemes: the energy and redox metabolism of red blood cells and the carbon metabolism of Methylobacterium extorquens. For these two example networks, we determined various variants of reduced networks differing in the number and types of disabled enzymes and disconnected reactions. Using a comprehensive kinetic model of the erythrocyte metabolism, we assess the kinetic feasibility of enzyme-reduced subnetworks. The number of enzymes predicted to be indispensable amounts to 14 (out of 28) for the erythrocyte scheme and 13 (out of 77) for the bacterium scheme, the largest group of enzymes predicted to be simultaneously dispensable amounts to 3 and 37 for these two systems. Our approach might contribute to identifying potential target enzymes for rational drug design, to rationalising gene-expression profiles of metabolic enzymes and to designing synthetic networks with highly specialised metabolic functions.