Explicit consideration of topological and parameter uncertainty gives new insights into a well-established model of glycolysis

An adaptable in silico ensemble model of the arachidonic acid cascade

Eicosanoids are a family of bioactive lipids, including derivatives of the ubiquitous fatty acid arachidonic acid (AA). The intimate involvement of eicosanoids in inflammation motivates the development of predictive in silico models for a systems-level exploration of disease mechanisms, drug development and replacement of animal models. Using an ensemble modelling strategy, we developed a computational model of the AA cascade. This approach allows the visualisation of plausible and thermodynamically feasible predictions, overcoming the limitations of fixed-parameter modelling. A quality scoring method was developed to quantify the accuracy of ensemble predictions relative to experimental data, measuring the overall uncertainty of the process. Monte Carlo ensemble modelling was used to quantify the prediction confidence levels. Model applicability was demonstrated using mass spectrometry mediator lipidomics to measure eicosanoids produced by HaCaT epidermal keratinocytes and 46BR.1N dermal fibroblasts, treated with stimuli (calcium ionophore A23187), (ultraviolet radiation, adenosine triphosphate) and a cyclooxygenase inhibitor (indomethacin). Experimentation and predictions were in good qualitative agreement, demonstrating the ability of the model to be adapted to cell types exhibiting differences in AA release and enzyme concentration profiles. The quantitative agreement between experimental and predicted outputs could be improved by expanding network topology to include additional reactions. Overall, our approach generated an adaptable, tuneable ensemble model of the AA cascade that can be tailored to represent different cell types and demonstrated that the integration of in silico and in vitro methods can facilitate a greater understanding of complex biological networks such as the AA cascade.

The unusual kinetics of lactate dehydrogenase of Schistosoma mansoni and their role in the rapid metabolic switch after penetration of the mammalian host

Lactate dehydrogenase (LDH) from Schistosoma mansoni has peculiar properties for a eukaryotic LDH. Schistosomal LDH (SmLDH) isolated from schistosomes, and the recombinantly expressed protein, are strongly inhibited by ATP, which is neutralized by fructose-1,6-bisphosphate (FBP). In the conserved FBP/anion binding site we identified two residues in SmLDH (Val187 and Tyr190) that differ from the conserved residues in LDHs of other eukaryotes, but are identical to conserved residues in FBP-sensitive prokaryotic LDHs. Three-dimensional (3D) models were generated to compare the structure of SmLDH with other LDHs. These models indicated that residues Val187, and especially Tyr190, play a crucial role in the interaction of FBP with the anion pocket of SmLDH. These 3D models of SmLDH are also consistent with a competitive model of SmLDH inhibition in which ATP (inhibitor) and FBP (activator) compete for binding in a well-defined anion pocket. The model of bound ATP predicts a distortion of the nearby key catalytic residue His195, resulting in enzyme inhibition. To investigate a possible physiological role of this allosteric regulation of LDH in schistosomes we made a kinetic model in which the allosteric regulation of the glycolytic enzymes can be varied. The model showed that inhibition of LDH by ATP prevents fermentation to lactate in the free-living stages in water and ensures complete oxidation via the Krebs cycle of the endogenous glycogen reserves. This mechanism of allosteric inhibition by ATP prevents the untimely depletion of these glycogen reserves, the only fuel of the free-living cercariae. Neutralization by FBP of this ATP inhibition of LDH prevents accumulation of glycolytic intermediates when S. mansoni schistosomula are confronted with the sudden large increase in glucose availability upon penetration of the final host. It appears that the LDH of S. mansoni is special and well suited to deal with the variations in glucose availability the parasite encounters during its life cycle.

The bloodstream form of Trypanosoma brucei displays non-canonical gluconeogenesis

Trypanosoma brucei is a causative agent of the Human and Animal African Trypanosomiases. The mammalian stage parasites infect various tissues and organs including the bloodstream, central nervous system, skin, adipose tissue and lungs. They rely on ATP produced in glycolysis, consuming large amounts of glucose, which is readily available in the mammalian host. In addition to glucose, glycerol can also be used as a source of carbon and ATP and as a substrate for gluconeogenesis. However, the physiological relevance of glycerol-fed gluconeogenesis for the mammalian-infective life cycle forms remains elusive. To demonstrate its (in)dispensability, first we must identify the enzyme(s) of the pathway. Loss of the canonical gluconeogenic enzyme, fructose-1,6-bisphosphatase, does not abolish the process hence at least one other enzyme must participate in gluconeogenesis in trypanosomes. Using a combination of CRISPR/Cas9 gene editing and RNA interference, we generated mutants for four enzymes potentially capable of contributing to gluconeogenesis: fructose-1,6-bisphoshatase, sedoheptulose-1,7-bisphosphatase, phosphofructokinase and transaldolase, alone or in various combinations. Metabolomic analyses revealed that flux through gluconeogenesis was maintained irrespective of which of these genes were lost. Our data render unlikely a previously hypothesised role of a reverse phosphofructokinase reaction in gluconeogenesis and preclude the participation of a novel biochemical pathway involving transaldolase in the process. The sustained metabolic flux in gluconeogenesis in our mutants, including a triple-null strain, indicates the presence of a unique enzyme participating in gluconeogenesis. Additionally, the data provide new insights into gluconeogenesis and the pentose phosphate pathway, and improve the current understanding of carbon metabolism of the mammalian-infective stages of T. brucei.

Defining informative priors for ensemble modeling in systems biology

Ensemble modeling in molecular systems biology requires the reproducible translation of kinetic parameter data into informative probability distributions (priors), as well as approaches that sample parameters from these distributions without violating the thermodynamic consistency of the overall model. Although a number of pioneering frameworks for ensemble modeling have been published, the issue of generating informative priors has not yet been addressed. Here, we present a protocol that aims to fill this gap. This protocol discusses the collection of parameter values from a diverse range of sources (literature, databases and experiments), assessment of their plausibility, and creation of log-normal probability distributions that can be used as informative priors in ensemble modeling. Furthermore, the protocol enables sampling from the generated distributions while maintaining thermodynamic consistency. Once all parameter values have been retrieved from literature and databases, the protocol can be implemented within ~5-10 min per parameter. The aim of this protocol is to facilitate the design and use of informative distributions for ensemble modeling, especially in fields such as synthetic biology and systems medicine.

Gluconeogenesis using glycerol as a substrate in bloodstream-form Trypanosoma brucei

Bloodstream form African trypanosomes are thought to rely exclusively upon glycolysis, using glucose as a substrate, for ATP production. Indeed, the pathway has long been considered a potential therapeutic target to tackle the devastating and neglected tropical diseases caused by these parasites. However, plasma membrane glucose and glycerol transporters are both expressed by trypanosomes and these parasites can infiltrate tissues that contain glycerol. Here, we show that bloodstream form trypanosomes can use glycerol for gluconeogenesis and for ATP production, particularly when deprived of glucose following hexose transporter depletion. We demonstrate that Trypanosoma brucei hexose transporters 1 and 2 (THT1 and THT2) are localized to the plasma membrane and that knockdown of THT1 expression leads to a growth defect that is more severe when THT2 is also knocked down. These data are consistent with THT1 and THT2 being the primary routes of glucose supply for the production of ATP by glycolysis. However, supplementation of the growth medium with glycerol substantially rescued the growth defect caused by THT1 and THT2 knockdown. Metabolomic analyses with heavy-isotope labelled glycerol demonstrated that trypanosomes take up glycerol and use it to synthesize intermediates of gluconeogenesis, including fructose 1,6-bisphosphate and hexose 6-phosphates, which feed the pentose phosphate pathway and variant surface glycoprotein biosynthesis. We used Cas9-mediated gene knockout to demonstrate a gluconeogenesis-specific, but fructose-1,6-bisphosphatase (Tb927.9.8720)-independent activity, converting fructose 1,6-bisphosphate into fructose 6-phosphate. In addition, we observed increased flux through the tricarboxylic acid cycle and the succinate shunt. Thus, contrary to prior thinking, gluconeogenesis can operate in bloodstream form T. brucei. This pathway, using glycerol as a physiological substrate, may be required in mammalian host tissues.

PASI: A novel pathway method to identify delicate group effects

Pathway analysis is a common approach in diverse biomedical studies, yet the currently-available pathway tools do not typically support the increasingly popular personalized analyses. Another weakness of the currently-available pathway methods is their inability to handle challenging data with only modest group-based effects compared to natural individual variation. In an effort to address these issues, this study presents a novel pathway method PASI (Pathway Analysis for Sample-level Information) and demonstrates its performance on complex diseases with different levels of group-based differences in gene expression. PASI is freely available as an R package.

Deletion of transketolase triggers a stringent metabolic response in promastigotes and loss of virulence in amastigotes of Leishmania mexicana

Transketolase (TKT) is part of the non-oxidative branch of the pentose phosphate pathway (PPP). Here we describe the impact of removing this enzyme from the pathogenic protozoan Leishmania mexicana. Whereas the deletion had no obvious effect on cultured promastigote forms of the parasite, the Δtkt cells were not virulent in mice. Δtkt promastigotes were more susceptible to oxidative stress and various leishmanicidal drugs than wild-type, and metabolomics analysis revealed profound changes to metabolism in these cells. In addition to changes consistent with those directly related to the role of TKT in the PPP, central carbon metabolism was substantially decreased, the cells consumed significantly less glucose, flux through glycolysis diminished, and production of the main end products of metabolism was decreased. Only minor changes in RNA abundance from genes encoding enzymes in central carbon metabolism, however, were detected although fructose-1,6-bisphosphate aldolase activity was decreased two-fold in the knock-out cell line. We also showed that the dual localisation of TKT between cytosol and glycosomes is determined by the C-terminus of the enzyme and by engineering different variants of the enzyme we could alter its sub-cellular localisation. However, no effect on the overall flux of glucose was noted irrespective of whether the enzyme was found uniquely in either compartment, or in both.

Leishmania parasites endanger over 1 billion people worldwide, infecting 300,000 people and causing 20,000 deaths annually. In this study, we scrutinized metabolism in Leishmania mexicana after deletion of the gene encoding transketolase (TKT), an enzyme involved in sugar metabolism via the pentose phosphate pathway which plays key roles in creating ribose 5-phosphate for nucleotide synthesis and also defence against oxidative stress. The insect stage of the parasite, grown in culture medium, did not suffer from any obvious growth defect after the gene was deleted. However, its metabolism changed dramatically, with metabolomics indicating profound changes to flux through the pentose phosphate pathway: decreased glucose consumption, and generally enhanced efficiency in using metabolic substrates with reduced secretion of partially oxidised end products of metabolism. This ‘stringent’ metabolism is reminiscent of the mammalian stage parasites. The cells were also more sensitive to oxidative stress inducing agents and leishmanicidal drugs. Crucially, mice inoculated with the TKT knock-out parasites did not develop an infection pointing to the enzyme playing a key role in allowing the parasites to remain viable in the host, indicating that TKT may be considered a useful target for development of new drugs against leishmaniasis.

Respectful Modeling: Addressing Uncertainty in Dynamic System Models for Molecular Biology

Although there is still some skepticism in the biological community regarding the value and significance of quantitative computational modeling, important steps are continually being taken to enhance its accessibility and predictive power. We view these developments as essential components of an emerging 'respectful modeling' framework which has two key aims: (i) respecting the models themselves and facilitating the reproduction and update of modeling results by other scientists, and (ii) respecting the predictions of the models and rigorously quantifying the confidence associated with the modeling results. This respectful attitude will guide the design of higher-quality models and facilitate the use of models in modern applications such as engineering and manipulating microbial metabolism by synthetic biology.

Probing the metabolic network in bloodstream-form Trypanosoma brucei using untargeted metabolomics with stable isotope labelled glucose

Metabolomics coupled with heavy-atom isotope-labelled glucose has been used to probe the metabolic pathways active in cultured bloodstream form trypomastigotes of Trypanosoma brucei, a parasite responsible for human African trypanosomiasis. Glucose enters many branches of metabolism beyond glycolysis, which has been widely held to be the sole route of glucose metabolism. Whilst pyruvate is the major end-product of glucose catabolism, its transamination product, alanine, is also produced in significant quantities. The oxidative branch of the pentose phosphate pathway is operative, although the non-oxidative branch is not. Ribose 5-phosphate generated through this pathway distributes widely into nucleotide synthesis and other branches of metabolism. Acetate, derived from glucose, is found associated with a range of acetylated amino acids and, to a lesser extent, fatty acids; while labelled glycerol is found in many glycerophospholipids. Glucose also enters inositol and several sugar nucleotides that serve as precursors to macromolecule biosynthesis. Although a Krebs cycle is not operative, malate, fumarate and succinate, primarily labelled in three carbons, were present, indicating an origin from phosphoenolpyruvate via oxaloacetate. Interestingly, the enzyme responsible for conversion of phosphoenolpyruvate to oxaloacetate, phosphoenolpyruvate carboxykinase, was shown to be essential to the bloodstream form trypanosomes, as demonstrated by the lethal phenotype induced by RNAi-mediated downregulation of its expression. In addition, glucose derivatives enter pyrimidine biosynthesis via oxaloacetate as a precursor to aspartate and orotate.

In this work we have followed the distribution of carbon derived from glucose in bloodstream form trypanosomes, the causative agent of African trypanosomiasis, revealing it to enter a diverse range of metabolites. The work involved using ¹³C-labelled glucose and following the fate of the labelled carbon with an LC-MS based metabolomics platform. Beyond glycolysis and the oxidative branch of the pentose phosphate pathway the label entered lipid biosynthesis both through glycerol 3-phosphate and also acetate. Glucose derived carbon also entered nucleotide synthesis through ribose and pyrimidine synthesis through oxaloacetate-derived aspartate. Appreciable quantities of the carboxylic acids succinate and malate were identified, although labelling patterns indicate they are not TCA cycle derived. Amino sugars and sugar nucleotides were also labelled as was inositol used in protein modification but not in inositol phospholipid headgroup production. We confirm active and essential oxaloacetate production in bloodstream form trypanosomes and show that phosphoenolpyruvate carboxykinase is essential to these parasites using RNA interference. The amount of glucose entering these metabolites is minor compared to the quantity that enters pyruvate excreted from the cell, but the observation that enzymes contributing to the metabolism of glucose beyond glycolysis can be essential offers potential new targets for chemotherapy against trypanosomiasis.

LC-MS-based absolute metabolite quantification: application to metabolic flux measurement in trypanosomes

Human African trypanosomiasis is a neglected tropical disease caused by the protozoan parasite, Trypanosoma brucei. In the mammalian bloodstream, the trypanosome's metabolism differs significantly from that of its host. For example, the parasite relies exclusively on glycolysis for energy source. Recently, computational and mathematical models of trypanosome metabolism have been generated to assist in understanding the parasite metabolism with the aim of facilitating drug development. Optimisation of these models requires quantitative information, including metabolite concentrations and/or metabolic fluxes that have been hitherto unavailable on a large scale. Here, we have implemented an LC-MS-based method that allows large scale quantification of metabolite levels by using U-¹³C-labelled E.coli extracts as internal standards. Known amounts of labelled E. coli extract were added into the parasite samples, as well as calibration standards, and used to obtain calibration curves enabling us to convert intensities into concentrations. This method allowed us to reliably quantify the changes of 43 intracellular metabolites and 32 extracellular metabolites in the medium over time. Based on the absolute quantification, we were able to compute consumption and production fluxes. These quantitative data can now be used to optimise computational models of parasite metabolism.

The silicon trypanosome: a test case of iterative model extension in systems biology

The African trypanosome, Trypanosoma brucei, is a unicellular parasite causing African Trypanosomiasis (sleeping sickness in humans and nagana in animals). Due to some of its unique properties, it has emerged as a popular model organism in systems biology. A predictive quantitative model of glycolysis in the bloodstream form of the parasite has been constructed and updated several times. The Silicon Trypanosome is a project that brings together modellers and experimentalists to improve and extend this core model with new pathways and additional levels of regulation. These new extensions and analyses use computational methods that explicitly take different levels of uncertainty into account. During this project, numerous tools and techniques have been developed for this purpose, which can now be used for a wide range of different studies in systems biology.

Handling uncertainty in dynamic models: the pentose phosphate pathway in Trypanosoma brucei

Dynamic models of metabolism can be useful in identifying potential drug targets, especially in unicellular organisms. A model of glycolysis in the causative agent of human African trypanosomiasis, Trypanosoma brucei, has already shown the utility of this approach. Here we add the pentose phosphate pathway (PPP) of T. brucei to the glycolytic model. The PPP is localized to both the cytosol and the glycosome and adding it to the glycolytic model without further adjustments leads to a draining of the essential bound-phosphate moiety within the glycosome. This phosphate “leak” must be resolved for the model to be a reasonable representation of parasite physiology. Two main types of theoretical solution to the problem could be identified: (i) including additional enzymatic reactions in the glycosome, or (ii) adding a mechanism to transfer bound phosphates between cytosol and glycosome. One example of the first type of solution would be the presence of a glycosomal ribokinase to regenerate ATP from ribose 5-phosphate and ADP. Experimental characterization of ribokinase in T. brucei showed that very low enzyme levels are sufficient for parasite survival, indicating that other mechanisms are required in controlling the phosphate leak. Examples of the second type would involve the presence of an ATP:ADP exchanger or recently described permeability pores in the glycosomal membrane, although the current absence of identified genes encoding such molecules impedes experimental testing by genetic manipulation. Confronted with this uncertainty, we present a modeling strategy that identifies robust predictions in the context of incomplete system characterization. We illustrate this strategy by exploring the mechanism underlying the essential function of one of the PPP enzymes, and validate it by confirming the model predictions experimentally.

Mathematical models have been valuable tools for investigating the complex behaviors of metabolism. Due to incomplete knowledge of biological systems, these models contain inevitable uncertainty. This uncertainty is present in the measured or estimated parameter values, but also in the structure of the metabolic network. In this paper we increase the coverage of a particularly well studied model of glucose metabolism in Trypanosoma brucei, a tropical parasite that causes African sleeping sickness, by extending it with an additional pathway in two compartments. During this modeling process we highlighted uncertainties in parameter values and network structure and used these to formulate new hypotheses which were subsequently tested experimentally. The models were improved with the experimentally derived data, but uncertainty remained concerning the exact topology of the system. These models allowed us to investigate the effects of the loss of one enzyme, 6-phosphogluconate dehydrogenase. By taking uncertainty into account, the models demonstrated that the loss of this enzyme is lethal to the parasite by a mechanism different than that in other organisms. Our methodology shows how formally introducing uncertainty into model building provides robust model behavior that is independent of the network structure or parameter values.