Incorporating expression data in metabolic modeling: a case study of lactate dehydrogenase

Integrating biological information from different sources to understand cellular processes is an important problem in systems biology. We use data from mRNA expression arrays and chemical kinetics to formulate a metabolic model relevant to K562 erythroleukemia cells. MAP kinase pathway activation alters the expression of metabolic enzymes in K562 cells. Our array data show changes in expression of lactate dehydrogenase (LDH) isoforms after treatment with phorbol 12-myristate 13-acetate (PMA), which activates MAP kinase signaling. We model the change in lactate production which occurs when the MAP kinase pathway is activated, using a non-equilibrium, chemical-kinetic model of homolactic fermentation. In particular, we examine the role of LDH isoforms, which catalyse the conversion of pyruvate to lactate. Changes in the isoform ratio are not the primary determinant of the production of lactate. Rather, the total concentration of LDH controls the lactate concentration.     

Modes and cuts in metabolic networks: complexity and algorithms

Constraint-based approaches recently brought new insight into our understanding of metabolism. By making very simple assumptions such as that the system is at steady-state and some reactions are irreversible, and without requiring kinetic parameters, general properties of the system can be derived. A central concept in this methodology is the notion of an elementary mode (EM for short) which represents a minimal functional subsystem. The computation of EMs still forms a limiting step in metabolic studies and several algorithms have been proposed to address this problem leading to increasingly faster methods. However, although a theoretical upper bound on the number of elementary modes that a network may possess has been established, surprisingly, the complexity of this problem has never been systematically studied. In this paper, we give a systematic overview of the complexity of optimisation problems related to modes. We first establish results regarding network consistency. Most consistency problems are easy, i.e., they can be solved in polynomial time. We then establish the complexity of finding and counting elementary modes. We show in particular that finding one elementary mode is easy but that this task becomes hard when a specific EM (i.e. an EM containing some specified reactions) is sought. We then show that counting the number of elementary modes is musical sharpP-complete. We emphasize that the easy problems can be solved using currently existing software packages. We then analyse the complexity of a closely related task which is the computation of so-called minimum reaction cut sets and we show that this problem is hard. We then present two positive results which both allow to avoid computing EMs as a prior to the computation of reaction cuts. The first one is a polynomial approximation algorithm for finding a minimum reaction cut set. The second one is a test for verifying whether a set of reactions constitutes a reaction cut; this test can be readily included in existing algorithms to improve their performance. Finally, we discuss the complexity of other cut-related problems.     

Visual exploration of isotope labeling networks in 3D

Isotope labeling networks (ILNs) are graphs explaining the flow of isotope labeled molecules in a metabolic network. Moreover, they are the structural backbone of metabolic flux analysis (MFA) by isotopic tracers which has been established as a standard experimental tool in fluxomics. To configure an isotope labeling experiment (ILE) for MFA, the structure of the corresponding ILN must be understood to a certain extent even by a practitioner. Graph algorithms help to analyze the network structure but produce rather abstract results. Here, the major obstruction is the high dimension of these networks and the large number of network components which, consequently, are hard to figure out manually. At the interface between theory and experiment, the three-dimensional interactive visualization tool CumoVis has been developed for exploring the network structure in a step by step manner. Navigation and orientation within ILNs are supported by exploiting the natural 3D structure of an underlying metabolite network with stacked labeled particles on top of each metabolite node. Network exploration is facilitated by rotating, zooming, forward and backward path tracing and, most important, network component reduction. All features of CumoVis are explained with an educational example and a realistic network describing carbon flow in the citric acid cycle.     

Uncertainty in allometric exponent estimation: a case study in scaling metabolic rate with body mass

Many factors could influence the allometric scaling exponent β estimation, but have not been explored systematically. We investigated the influences of three factors on the estimate of β based on a data set of 626 species of basal metabolic rate and mass in mammals. The influence of sampling error was tested by re-sampling with different sample sizes using a Monte Carlo method. Small random errors were introduced to measured data to examine their influence on parameter estimations. The influence of analysis method was also evaluated by applying nonlinear and linear regressions to the original data. Results showed that a relative large sample size was required to lower statistical inference errors. When sample size n was 10% of the base population size (n=63), 35% of the samples supported β=2/3, 39% supported β=3/4, and 15% rejected β=0.711, even though the base population had a β=0.711. The controversy surrounding the estimation of β in the literature could be partially attributable to such small sample sizes in many studies. Measurement errors in body mass and base metabolic rate, especially in body mass, could largely increase alpha and beta errors. Analysis methods also affected parameter estimations. Nonlinear regressions provided better estimates of the scaling exponent that were significantly higher than these commonly estimated by linear regressions. This study demonstrated the importance of the quantity and quality of data as well as analysis method in power law analysis, raising caution in interpreting power law results. Meta-data synthesis using data from independent studies seems to be a proper approach in the future, but caution should be taken to make sure that such measurements are made using similar protocols.     

Drug-efficacy depends on the inhibitor type and the target position in a metabolic network--a systematic study

Drug discovery usually focuses on candidate molecules that affect individual reactions with presumed essential functions in the cellular reaction network, especially in the development of diseases. Unfortunately, appropriately designed drugs often fail to show the expected biological effect, since the multitude of interactions in the biochemical reaction network buffers the individual changes or causes significant side effects. We address this problem through a computational approach, which considers the effect of drug application within a generalized biochemical pathway and by studying the effect of changes regarding the type and strength of inhibitors on the reduction of flux. This allows us to systematically search for the appropriate target and for type and concentration of the optimal inhibitor. We propose the flux selectivity as a measure for the discrimination of the effect on different pathways. Since the calculation of the flux selectivity is based on flux control coefficients that are calculated in the non-affected state, it is also a means for predicting the inhibitor efficacy. Furthermore, we will propose how to increase discriminative inhibition in the case of a parasitic disease by using multi-target drugs.This work is devoted to the memorial of our teacher Reinhart Heinrich, who made important contributions to the investigation of the regulation of metabolic networks, namely by introducing and applying the concept of metabolic control.     

Inferring phylogenetic networks by the maximum parsimony criterion: a case study

Horizontal gene transfer (HGT) may result in genes whose evolutionary histories disagree with each other, as well as with the species tree. In this case, reconciling the species and gene trees results in a network of relationships, known as the "phylogenetic network" of the set of species. A phylogenetic network that incorporates HGT consists of an underlying species tree that captures vertical inheritance and a set of edges which model the "horizontal" transfer of genetic material. In a series of papers, Nakhleh and colleagues have recently formulated a maximum parsimony (MP) criterion for phylogenetic networks, provided an array of computationally efficient algorithms and heuristics for computing it, and demonstrated its plausibility on simulated data. In this article, we study the performance and robustness of this criterion on biological data. Our findings indicate that MP is very promising when its application is extended to the domain of phylogenetic network reconstruction and HGT detection. In all cases we investigated, the MP criterion detected the correct number of HGT events required to map the evolutionary history of a gene data set onto the species phylogeny. Furthermore, our results indicate that the criterion is robust with respect to both incomplete taxon sampling and the use of different site substitution matrices. Finally, our results show that the MP criterion is very promising in detecting HGT in chimeric genes, whose evolutionary histories are a mix of vertical and horizontal evolution. Besides the performance analysis of MP, our findings offer new insights into the evolution of 4 biological data sets and new possible explanations of HGT scenarios in their evolutionary history.     

Elementary network reconstruction: A framework for the analysis of regulatory networks in biological systems

Complexity of regulatory networks arises from the high degree of interaction between network components such as DNA, RNA, proteins, and metabolites. We have developed a modeling tool, elementary network reconstruction (ENR), to characterize these networks. ENR is a knowledge-driven, steady state, deterministic, quantitative modeling approach based on linear perturbation theory. In ENR we demonstrate a novel means of expressing control mechanisms by way of dimensionless steady state gains relating input and output variables, which are purely in terms of species abundances (extensive variables). As a result of systematic enumeration of network species in n×n matrix, the two properties of linear perturbation are manifested in graphical representations: transitive property is evident in a special L-shape structure, and additive property is evident in multiple L-shape structures arriving at the same matrix cell. Upon imposing mechanistic (lowest-level) gains, network self-assembly through transitive and additive properties results in elucidation of inherent topology and explicit cataloging of higher level gains, which in turn can be used to predict perturbation results. Application of ENR to the regulatory network behind carbon catabolite repression in Escherichia coli is presented. Through incorporation of known molecular mechanisms governing transient and permanent repressions, the ENR model correctly predicts several key features of this regulatory network, including a 50% downshift in intracellular cAMP level upon exposure to glucose. Since functional genomics studies are mainly concerned with redistribution of species abundances in perturbed systems, ENR could be exploited in the system-level analysis of biological systems.     

Functional essentiality from topology features in metabolic networks: a case study in yeast

The relation between the position of mutations in Saccharomyces cerevisiae metabolic network and their lethality is the subject of this work. We represent the topology of the network by a directed graph: nodes are metabolites and arcs represent the reactions; a mutation corresponds to the removal of all the arcs referring to the deleted enzyme. Using publicly available knock-out data, we show that lethality corresponds to the lack of alternative paths in the perturbed network linking the nodes affected by the enzyme deletion. Such feature is at the basis of the recently recognized importance of 'marginal' arcs of metabolic networks.     

Optimization-driven identification of genetic perturbations accelerates the convergence of model parameters in ensemble modeling of metabolic networks

The ensemble modeling (EM) approach has shown promise in capturing kinetic and regulatory effects in the modeling of metabolic networks. Efficacy of the EM procedure relies on the identification of model parameterizations that adequately describe all observed metabolic phenotypes upon perturbation. In this study, we propose an optimization-based algorithm for the systematic identification of genetic/enzyme perturbations to maximally reduce the number of models retained in the ensemble after each round of model screening. The key premise here is to design perturbations that will maximally scatter the predicted steady-state fluxes over the ensemble parameterizations. We demonstrate the applicability of this procedure for an Escherichia coli metabolic model of central metabolism by successively identifying single, double, and triple enzyme perturbations that cause the maximum degree of flux separation between models in the ensemble. Results revealed that optimal perturbations are not always located close to reaction(s) whose fluxes are measured, especially when multiple perturbations are considered. In addition, there appears to be a maximum number of simultaneous perturbations beyond which no appreciable increase in the divergence of flux predictions is achieved. Overall, this study provides a systematic way of optimally designing genetic perturbations for populating the ensemble of models with relevant model parameterizations.     

Finding minimal generating set for metabolic network with reversible pathways

Elementary flux modes give a mathematical representation of metabolic pathways in metabolic networks satisfying the constraint of non-decomposability. The large cost of their computation shifts attention to computing a minimal generating set which is a conically independent subset of elementary flux modes. When a metabolic network has reversible reactions and also admits a reversible pathway, the minimal generating set is not unique. A theoretical development and computational framework is provided which outline how to compute the minimal generating set in this case. The method is based on combining existing software to compute the minimal generating set for a “pointed cone” together with standard software to compute the Reduced Row Echelon Form.     

Information capacity and its approximations under metabolic cost in a simple homogeneous population of neurons

We calculate and analyze the information capacity-achieving conditions and their approximations in a simple neuronal system. The input–output properties of individual neurons are described by an empirical stimulus–response relationship and the metabolic cost of neuronal activity is taken into account. The exact (numerical) results are compared with a popular “low-noise” approximation method which employs the concepts of parameter estimation theory. We show, that the approximate method gives reliable results only in the case of significantly low response variability. By employing specialized numerical procedures we demonstrate, that optimal information transfer can be near-achieved by a number of different input distributions. It implies that the precise structure of the capacity-achieving input is of lesser importance than the value of capacity. Finally, we illustrate on an example that an innocuously looking stimulus–response relationship may lead to a problematic interpretation of the obtained Fisher information values.     

The transition from differential equations to Boolean networks: a case study in simplifying a regulatory network model

Methods for modeling cellular regulatory networks as diverse as differential equations and Boolean networks co-exist, however, without much closer correspondence to each other. With the example system of the fission yeast cell cycle control network, we here discuss these two approaches with respect to each other. We find that a Boolean network model can be formulated as a specific coarse-grained limit of the more detailed differential equations model for this system. This demonstrates the mathematical foundation on which Boolean networks can be applied to biological regulatory networks in a controlled way.     

Validation of NCM460 cell model as control in antitumor strategies targeting colon adenocarcinoma metabolic reprogramming: Trichostatin A as a case study

Background

Cancer cells have extremely active metabolism, which supports high proliferation rates. Metabolic profiles of human colon cancer cells have been extensively studied, but comparison with non-tumour counterparts has been neglected.

Methods

Here we compared the metabolic flux redistribution in human colon adenocarcinoma cells (HT29) and the human colon healthy cell line NCM460 in order to identify the main pathways involved in metabolic reprogramming. Moreover, we explore if induction of differentiation in HT29 by trichostatin A (TSA) reverts the metabolic reprogramming to that of NCM460. Cells were incubated with [1,2-¹³C₂]-d-glucose as a tracer, and Mass Isotopomer Distribution Analysis was applied to characterize the changes in the metabolic flux distribution profile of the central carbon metabolism.

Results

We demonstrate that glycolytic rate and pentose phosphate synthesis are 25% lower in NCM460 with respect to HT29 cells. In contrast, Krebs cycle activity in the former was twice that recorded in the latter. Moreover, we show that TSA-induced HT29 cell differentiation reverts the metabolic phenotype to that of healthy NCM460 cells whereas TSA does not affect the metabolism of NCM460 cells.

Conclusions

We conclude that pentose phosphate pathway, glycolysis, and Krebs cycle are key players of colon adenocarcinoma cellular metabolic remodeling and that NCM460 is an appropriate model to evaluate the results of new therapeutic strategies aiming to selectively target metabolic reprogramming.

General significance

Our findings suggest that strategies to counteract robust metabolic adaptation in cancer cells might open up new avenues to design multiple hit and targeted therapies.     

Thermodynamics-based Metabolite Sensitivity Analysis in metabolic networks

The increasing availability of large metabolomics datasets enhances the need for computational methodologies that can organize the data in a way that can lead to the inference of meaningful relationships. Knowledge of the metabolic state of a cell and how it responds to various stimuli and extracellular conditions can offer significant insight in the regulatory functions and how to manipulate them. Constraint based methods, such as Flux Balance Analysis (FBA) and Thermodynamics-based flux analysis (TFA), are commonly used to estimate the flow of metabolites through genome-wide metabolic networks, making it possible to identify the ranges of flux values that are consistent with the studied physiological and thermodynamic conditions. However, unless key intracellular fluxes and metabolite concentrations are known, constraint-based models lead to underdetermined problem formulations. This lack of information propagates as uncertainty in the estimation of fluxes and basic reaction properties such as the determination of reaction directionalities. Therefore, knowledge of which metabolites, if measured, would contribute the most to reducing this uncertainty can significantly improve our ability to define the internal state of the cell. In the present work we combine constraint based modeling, Design of Experiments (DoE) and Global Sensitivity Analysis (GSA) into the Thermodynamics-based Metabolite Sensitivity Analysis (TMSA) method. TMSA ranks metabolites comprising a metabolic network based on their ability to constrain the gamut of possible solutions to a limited, thermodynamically consistent set of internal states. TMSA is modular and can be applied to a single reaction, a metabolic pathway or an entire metabolic network. This is, to our knowledge, the first attempt to use metabolic modeling in order to provide a significance ranking of metabolites to guide experimental measurements.     

CONTROL: software for the analysis of the control of metabolic networks

The program CONTROL is based on metabolic control theory anduses the method developed by Reder (1988). In this theory, twosets of parameters are defined in the vicinity of a steady-state:the elasticity coefficients which describe the local behaviourof the isolated enzymes, and the control coefficients whichexpress the response of the whole metabolic network to perturbationsat a given step. The theory shows that relationships exist betweenthe control coefficients (summation relationships or structuralrelationships) and also between the two types of coefficients(control and elasticity coefficients: connectivity relationships).The program CONTROL is divided into two parts (sub-menus). Thefirst one calculates all the control coefficients (flux andconcentrations) of a metabolic network from the elasticity coefficients.Using the second menu, the symbolic relationships are obtainedbetween the control coefficients (summation relationships) andbetween the control coefficients and the elasticity coefficients(connectivity relationships). These two sub-menus can be appliedindependently to any metabolic network (to date limited to 19steps and 19 metabolites).     

Segmentation and zooid formation in animals with a posterior growing region: the case for metabolic gradients and Turing waves

The discovery of periodic propagation of anteriorly moving pulses/stripes of gene expression in the presomitic mesoderm (PSM) of vertebrates has given new life to the clock and wavefront model, and other models of morphogenesis based on a molecular oscillator where the time periodicity is translated into spatial periodicity. Instead we suggest that segmentation, somitogenesis and metamerism in vertebrates and in invertebrates with a posterior growing region are based on a Turing-Child metabolic gradient that is progressively shifted posteriorly with the PSM as elongation, segmentation and somitogenesis proceed. This gradient corresponds to anteriorly propagating metabolic front in the PSM that drives the anteriorly propagating mRNA synthesis and which, together with mRNA degradation, explains stripe formation and spatial periodicity.The process of segmentation has been compared to zooid formation. We show that for annelids the metabolic profile behaves as a Turing field in the sense that an increase in the length of the system or a decrease of the Turing wavelength results in an additional peak in the posterior growing region as predicted by Turing theory. In particular, it is shown that the metabolic gradient that drives the segmentation is based on a Turing system.     

FASIMU: flexible software for flux-balance computation series in large metabolic networks

Background  

Flux-balance analysis based on linear optimization is widely used to compute metabolic fluxes in large metabolic networks and gains increasingly importance in network curation and structural analysis. Thus, a computational tool flexible enough to realize a wide variety of FBA algorithms and able to handle batch series of flux-balance optimizations is of great benefit.     

Predicting synthetic rescues in metabolic networks

An important goal of medical research is to develop methods to recover the loss of cellular function due to mutations and other defects. Many approaches based on gene therapy aim to repair the defective gene or to insert genes with compensatory function. Here, we propose an alternative, network‐based strategy that aims to restore biological function by forcing the cell to either bypass the functions affected by the defective gene, or to compensate for the lost function. Focusing on the metabolism of single‐cell organisms, we computationally study mutants that lack an essential enzyme, and thus are unable to grow or have a significantly reduced growth rate. We show that several of these mutants can be turned into viable organisms through additional gene deletions that restore their growth rate. In a rather counterintuitive fashion, this is achieved via additional damage to the metabolic network. Using flux balance‐based approaches, we identify a number of synthetically viable gene pairs, in which the removal of one enzyme‐encoding gene results in a non‐viable phenotype, while the deletion of a second enzyme‐encoding gene rescues the organism. The systematic network‐based identification of compensatory rescue effects may open new avenues for genetic interventions.     

PathwayBooster: a tool to support the curation of metabolic pathways

Background

Despite several recent advances in the automated generation of draft metabolic reconstructions, the manual curation of these networks to produce high quality genome-scale metabolic models remains a labour-intensive and challenging task.

Results

We present PathwayBooster, an open-source software tool to support the manual comparison and curation of metabolic models. It combines gene annotations from GenBank files and other sources with information retrieved from the metabolic databases BRENDA and KEGG to produce a set of pathway diagrams and reports summarising the evidence for the presence of a reaction in a given organism’s metabolic network. By comparing multiple sources of evidence within a common framework, PathwayBooster assists the curator in the identification of likely false positive (misannotated enzyme) and false negative (pathway hole) reactions. Reaction evidence may be taken from alternative annotations of the same genome and/or a set of closely related organisms.

Conclusions

By integrating and visualising evidence from multiple sources, PathwayBooster reduces the manual effort required in the curation of a metabolic model. The software is available online at http://www.theosysbio.bio.ic.ac.uk/resources/pathwaybooster/.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0447-2) contains supplementary material, which is available to authorized users.