Quantitative elementary mode analysis of metabolic pathways: the example of yeast glycolysis

Creating new-to-nature carbon fixation: A guide

Synthetic biology aims at designing new biological functions from first principles. These new designs allow to expand the natural solution space and overcome the limitations of naturally evolved systems. One example is synthetic CO2-fixation pathways that promise to provide more efficient ways for the capture and conversion of CO2 than natural pathways, such as the Calvin Benson Bassham (CBB) cycle of photosynthesis. In this review, we provide a practical guideline for the design and realization of such new-to-nature CO2-fixation pathways. We introduce the concept of "synthetic CO2-fixation", and give a general overview over the enzymology and topology of synthetic pathways, before we derive general principles for their design from their eight naturally evolved analogs. We provide a comprehensive summary of synthetic carbon-assimilation pathways and derive a step-by-step, practical guide from the theoretical design to their practical implementation, before ending with an outlook on new developments in the field.

A Markov constraint to uniquely identify elementary flux mode weights in unimolecular metabolic networks

Elementary flux modes (EFMs) are minimal, steady state pathways characterizing a flux network. Fundamentally, all steady state fluxes in a network are decomposable into a linear combination of EFMs. While there is typically no unique set of EFM weights that reconstructs these fluxes, several optimization-based methods have been proposed to constrain the solution space by enforcing some notion of parsimony. However, it has long been recognized that optimization-based approaches may fail to uniquely identify EFM weights and return different feasible solutions across objective functions and solvers. Here we show that, for flux networks only involving single molecule transformations, these problems can be avoided by imposing a Markovian constraint on EFM weights. Our Markovian constraint guarantees a unique solution to the flux decomposition problem, and that solution is arguably more biophysically plausible than other solutions. We describe an algorithm for computing Markovian EFM weights via steady state analysis of a certain discrete-time Markov chain, based on the flux network, which we call the cycle-history Markov chain. We demonstrate our method with a differential analysis of EFM activity in a lipid metabolic network comparing healthy and Alzheimer's disease patients. Our method is the first to uniquely decompose steady state fluxes into EFM weights for any unimolecular metabolic network.

Minimizing enzyme mass to decompose flux distribution for identifying biologically relevant elementary flux modes

The flux distribution in metabolic network can be decomposed as non-negative linear combinations of elementary flux modes (EFMs). Identifying biologically relevant EFM combination by decomposing flux distribution in metabolic network is a useful method to study metabolisms in systems biology. However, the occurrence of biologically irrelevant EFMs hinders the application of such methods. In this paper, we introduce a novel method for identifying EFM combination by minimizing enzyme mass. Our proposed method, called EMMD (Enzyme Mass Minimization Decomposition), takes into consideration both thermodynamic and enzymatic constraints in stoichiometry metabolic models. By implementing EMMD, we can decompose the flux distributions in metabolic network to detect biologically relevant EFM combinations. We demonstrate the effectiveness of our method by applying it to the core Escherichia coli metabolic network and show that the optimal EFM combinations identified by EMMD are unique. Moreover, the optimal EFM combination identified by EMMD not only aligns more closely with experimental values in terms of estimated growth rate, but it also demonstrates more favorable thermodynamics. Finally, we investigated the growth of the core Escherichia coli metabolic network in Luria-Bertani medium containing different carbon sources, revealing the impact of various carbon sources on the growth rate of flux distribution. EMMD thus could be a promising complement to the existing flux decomposition tools.

Combining Kinetic and Constraint-Based Modelling to Better Understand Metabolism Dynamics

To understand the phenotypic capabilities of organisms, it is useful to characterise cellular metabolism through the analysis of its pathways. Dynamic mathematical modelling of metabolic networks is of high interest as it provides the time evolution of the metabolic components. However, it also has limitations, such as the necessary mechanistic details and kinetic parameters are not always available. On the other hand, large metabolic networks exhibit a complex topological structure which can be studied rather efficiently in their stationary regime by constraint-based methods. These methods produce useful predictions on pathway operations. In this review, we present both modelling techniques and we show how they bring complementary views of metabolism. In particular, we show on a simple example how both approaches can be used in conjunction to shed some light on the dynamics of metabolic networks.

Application of dynamic metabolic flux analysis for process modeling: Robust flux estimation with regularization, confidence bounds, and selection of elementary modes

In macroscopic dynamic models of fermentation processes, elementary modes (EM) derived from metabolic networks are often used to describe the reaction stoichiometry in a simplified manner and to build predictive models by parameterizing kinetic rate equations for the EM. In this procedure, the selection of a set of EM is a key step which is followed by an estimation of their reaction rates and of the associated confidence bounds. In this paper, we present a method for the computation of reaction rates of cellular reactions and EM as well as an algorithm for the selection of EM for process modeling. The method is based on the dynamic metabolic flux analysis (DMFA) proposed by Leighty and Antoniewicz (2011, Metab Eng, 13(6), 745–755) with additional constraints, regularization and analysis of uncertainty. Instead of using estimated uptake or secretion rates, concentration measurements are used directly to avoid an amplification of measurement errors by numerical differentiation. It is shown that the regularized DMFA for EM method is significantly more robust against measurement noise than methods using estimated rates. The confidence intervals for the estimated reaction rates are obtained by bootstrapping. For the selection of a set of EM for a given st oichiometric model, the DMFA for EM method is combined with a multiobjective genetic algorithm. The method is applied to real data from a CHO fed‐batch process. From measurements of six fed‐batch experiments, 10 EM were identified as the smallest subset of EM based upon which the data can be described sufficiently accurately by a dynamic model. The estimated EM reaction rates and their confidence intervals at different process conditions provide useful information for the kinetic modeling and subsequent process optimization.

Finding MEMo: minimum sets of elementary flux modes

Metabolic network reconstructions are widely used in computational systems biology for in silico studies of cellular metabolism. A common approach to analyse these models are elementary flux modes (EFMs), which correspond to minimal functional units in the network. Already for medium-sized networks, it is often impossible to compute the set of all EFMs, due to their huge number. From a practical point of view, this might also not be necessary because a subset of EFMs may already be sufficient to answer relevant biological questions. In this article, we study MEMos or minimum sets of EFMs that can generate all possible steady-state behaviours of a metabolic network. The number of EFMs in a MEMo may be by several orders of magnitude smaller than the total number of EFMs. Using MEMos, we can compute generating sets of EFMs in metabolic networks where the whole set of EFMs is too large to be enumerated.

Cyclic decomposition explains a photosynthetic down regulation for Chlamydomonas reinhardtii

The regulation of metabolic networks has been shown to be distributed and shared through the action of metabolic cycles. Biochemical cycles play important roles in maintaining flux and substrate availability for multiple pathways to supply cellular energy and contribute to dynamic stability. By understanding the cyclic and acyclic flows of matter through a network, we are closer to understanding how complex dynamic systems distribute flux along interconnected pathways. In this work, we have applied a cycle decomposition algorithm to a genome-scale metabolic model of Chlamydomonas reinhardtii to analyse how acetate supply affects the distribution of fluxes that sustain cellular activity. We examined the role of metabolic cycles which explain the down regulation of photosynthesis that is observed when cells are grown in the presence of acetate. Our results suggest that acetate modulates changes in global metabolism, with the pentose phosphate pathway, the Calvin-Benson cycle and mitochondrial respiration activity being affected whilst reducing photosynthesis. These results show how the decomposition of metabolic flux into cyclic and acyclic components helps to understand the impact of metabolic cycling on organismal behaviour at the genome scale.

From elementary flux modes to elementary flux vectors: Metabolic pathway analysis with arbitrary linear flux constraints

Elementary flux modes (EFMs) emerged as a formal concept to describe metabolic pathways and have become an established tool for constraint-based modeling and metabolic network analysis. EFMs are characteristic (support-minimal) vectors of the flux cone that contains all feasible steady-state flux vectors of a given metabolic network. EFMs account for (homogeneous) linear constraints arising from reaction irreversibilities and the assumption of steady state; however, other (inhomogeneous) linear constraints, such as minimal and maximal reaction rates frequently used by other constraint-based techniques (such as flux balance analysis [FBA]), cannot be directly integrated. These additional constraints further restrict the space of feasible flux vectors and turn the flux cone into a general flux polyhedron in which the concept of EFMs is not directly applicable anymore. For this reason, there has been a conceptual gap between EFM-based (pathway) analysis methods and linear optimization (FBA) techniques, as they operate on different geometric objects. One approach to overcome these limitations was proposed ten years ago and is based on the concept of elementary flux vectors (EFVs). Only recently has the community started to recognize the potential of EFVs for metabolic network analysis. In fact, EFVs exactly represent the conceptual development required to generalize the idea of EFMs from flux cones to flux polyhedra. This work aims to present a concise theoretical and practical introduction to EFVs that is accessible to a broad audience. We highlight the close relationship between EFMs and EFVs and demonstrate that almost all applications of EFMs (in flux cones) are possible for EFVs (in flux polyhedra) as well. In fact, certain properties can only be studied with EFVs. Thus, we conclude that EFVs provide a powerful and unifying framework for constraint-based modeling of metabolic networks.

A principal components method constrained by elementary flux modes: analysis of flux data sets

Background

Non-negative linear combinations of elementary flux modes (EMs) describe all feasible reaction flux distributions for a given metabolic network under the quasi steady state assumption. However, only a small subset of EMs contribute to the physiological state of a given cell.

Results

In this paper, a method is proposed that identifies the subset of EMs that best explain the physiological state captured in reaction flux data, referred to as principal EMs (PEMs), given a pre-specified universe of EM candidates. The method avoids the evaluation of all possible combinations of EMs by using a branch and bound approach which is computationally very efficient. The performance of the method is assessed using simulated and experimental data of Pichia pastoris and experimental fluxome data of Saccharomyces cerevisiae. The proposed method is benchmarked against principal component analysis (PCA), commonly used to study the structure of metabolic flux data sets.

Conclusions

The overall results show that the proposed method is computationally very effective in identifying the subset of PEMs within a large set of EM candidates (cases with ~100 and ~1000 EMs were studied). In contrast to the principal components in PCA, the identified PEMs have a biological meaning enabling identification of the key active pathways in a cell as well as the conditions under which the pathways are activated. This method clearly outperforms PCA in the interpretability of flux data providing additional insights into the underlying regulatory mechanisms.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1063-0) contains supplementary material, which is available to authorized users.

Which sets of elementary flux modes form thermodynamically feasible flux distributions?

Elementary flux modes (EFMs) are non-decomposable steady-state fluxes through metabolic networks. Every possible flux through a network can be described as a superposition of EFMs. The definition of EFMs is based on the stoichiometry of the network, and it has been shown previously that not all EFMs are thermodynamically feasible. These infeasible EFMs cannot contribute to a biologically meaningful flux distribution. In this work, we show that a set of thermodynamically feasible EFMs need not be thermodynamically consistent. We use first principles of thermodynamics to define the feasibility of a flux distribution and present a method to compute the largest thermodynamically consistent sets (LTCSs) of EFMs. An LTCS contains the maximum number of EFMs that can be combined to form a thermodynamically feasible flux distribution. As a case study we analyze all LTCSs found in Escherichia coli when grown on glucose and show that only one LTCS shows the required phenotypical properties. Using our method, we find that in our E. coli model < 10% of all EFMs are thermodynamically relevant.

Identification of active elementary flux modes in mitochondria using selectively permeabilized CHO cells

Metabolic compartmentation is a key feature of mammalian cells. Mitochondria are the powerhouse of eukaryotic cells, responsible for respiration and the TCA cycle. We accessed the mitochondrial metabolism of the economically important Chinese hamster ovary (CHO) cells using selective permeabilization. We tested key substrates without and with addition of ADP. Based on quantified uptake and production rates, we could determine the contribution of different elementary flux modes to the metabolism of a substrate or substrate combination. ADP stimulated the uptake of most metabolites, directly by serving as substrate for the respiratory chain, thus removing the inhibitory effect of NADH, or as allosteric effector. Addition of ADP favored substrate metabolization to CO2 and did not enhance the production of other metabolites. The controlling effect of ADP was more pronounced when we supplied metabolites to the first part of the TCA cycle: pyruvate, citrate, α-ketoglutarate and glutamine. In the second part of the TCA cycle, the rates were primarily controlled by the concentrations of C4-dicarboxylates. Without ADP addition, the activity of the pyruvate carboxylase-malate dehydrogenase-malic enzyme cycle consumed the ATP produced by oxidative phosphorylation, preventing its accumulation and maintaining metabolic steady state conditions. Aspartate was taken up only in combination with pyruvate, whose uptake also increased, a fact explained by complex regulatory effects. Isocitrate dehydrogenase and α-ketoglutarate dehydrogenase were identified as the key regulators of the TCA cycle, confirming existent knowledge from other cells. We have shown that selectively permeabilized cells combined with elementary mode analysis allow in-depth studying of the mitochondrial metabolism and regulation.

Avoiding the Enumeration of Infeasible Elementary Flux Modes by Including Transcriptional Regulatory Rules in the Enumeration Process Saves Computational Costs

Despite the significant progress made in recent years, the computation of the complete set of elementary flux modes of large or even genome-scale metabolic networks is still impossible. We introduce a novel approach to speed up the calculation of elementary flux modes by including transcriptional regulatory information into the analysis of metabolic networks. Taking into account gene regulation dramatically reduces the solution space and allows the presented algorithm to constantly eliminate biologically infeasible modes at an early stage of the computation procedure. Thereby, computational costs, such as runtime, memory usage, and disk space, are extremely reduced. Moreover, we show that the application of transcriptional rules identifies non-trivial system-wide effects on metabolism. Using the presented algorithm pushes the size of metabolic networks that can be studied by elementary flux modes to new and much higher limits without the loss of predictive quality. This makes unbiased, system-wide predictions in large scale metabolic networks possible without resorting to any optimization principle.

Metabolomics integrated elementary flux mode analysis in large metabolic networks

Elementary flux modes (EFMs) are non-decomposable steady-state pathways in metabolic networks. They characterize phenotypes, quantify robustness or identify engineering targets. An EFM analysis (EFMA) is currently restricted to medium-scale models, as the number of EFMs explodes with the network's size. However, many topologically feasible EFMs are biologically irrelevant. We present thermodynamic EFMA (tEFMA), which calculates only the small(er) subset of thermodynamically feasible EFMs. We integrate network embedded thermodynamics into EFMA and show that we can use the metabolome to identify and remove thermodynamically infeasible EFMs during an EFMA without losing biologically relevant EFMs. Calculating only the thermodynamically feasible EFMs strongly reduces memory consumption and program runtime, allowing the analysis of larger networks. We apply tEFMA to study the central carbon metabolism of E. coli and find that up to 80% of its EFMs are thermodynamically infeasible. Moreover, we identify glutamate dehydrogenase as a bottleneck, when E. coli is grown on glucose and explain its inactivity as a consequence of network embedded thermodynamics. We implemented tEFMA as a Java package which is available for download at https://github.com/mpgerstl/tEFMA.

tEFMA: computing thermodynamically feasible elementary flux modes in metabolic networks

: Elementary flux modes (EFMs) are important structural tools for the analysis of metabolic networks. It is known that many topologically feasible EFMs are biologically irrelevant. Therefore, tools are needed to find the relevant ones. We present thermodynamic tEFM analysis (tEFMA) which uses the cellular metabolome to avoid the enumeration of thermodynamically infeasible EFMs. Specifically, given a metabolic network and a not necessarily complete metabolome, tEFMA efficiently returns the full set of thermodynamically feasible EFMs consistent with the metabolome. Compared with standard approaches, tEFMA strongly reduces the memory consumption and the overall runtime. Thus tEFMA provides a new way to analyze unbiasedly hitherto inaccessible large-scale metabolic networks.

AVAILABILITY AND IMPLEMENTATION

https://github.com/mpgerstl/tEFMA CONTACT: : christian.jungreuthmayer@boku.ac.at or juergen.zanghellini@boku.ac.at

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Estimating biological elementary flux modes that decompose a flux distribution by the minimal branching property

MOTIVATION

Elementary flux mode (EFM) is a useful tool in constraint-based modeling of metabolic networks. The property that every flux distribution can be decomposed as a weighted sum of EFMs allows certain applications of EFMs to studying flux distributions. The existence of biologically infeasible EFMs and the non-uniqueness of the decomposition, however, undermine the applicability of such methods. Efforts have been made to find biologically feasible EFMs by incorporating information from transcriptional regulation and thermodynamics. Yet, no attempt has been made to distinguish biologically feasible EFMs by considering their graphical properties. A previous study on the transcriptional regulation of metabolic genes found that distinct branches at a branch point metabolite usually belong to distinct metabolic pathways. This suggests an intuitive property of biologically feasible EFMs, i.e. minimal branching.

RESULTS

We developed the concept of minimal branching EFM and derived the minimal branching decomposition (MBD) to decompose flux distributions. Testing in the core Escherichia coli metabolic network indicated that MBD can distinguish branches at branch points and greatly reduced the solution space in which the decomposition is often unique. An experimental flux distribution from a previous study on mouse cardiomyocyte was decomposed using MBD. Comparison with decomposition by a minimum number of EFMs showed that MBD found EFMs more consistent with established biological knowledge, which facilitates interpretation. Comparison of the methods applied to a complex flux distribution in Lactococcus lactis similarly showed the advantages of MBD. The minimal branching EFM concept underlying MBD should be useful in other applications.

CONTACT

sinhu@bio.dtu.dk or p.ji@polyu.edu.hk

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A depth-first search algorithm to compute elementary flux modes by linear programming

Background

The decomposition of complex metabolic networks into elementary flux modes (EFMs) provides a useful framework for exploring reaction interactions systematically. Generating a complete set of EFMs for large-scale models, however, is near impossible. Even for moderately-sized models (<400 reactions), existing approaches based on the Double Description method must iterate through a large number of combinatorial candidates, thus imposing an immense processor and memory demand.

Results

Based on an alternative elementarity test, we developed a depth-first search algorithm using linear programming (LP) to enumerate EFMs in an exhaustive fashion. Constraints can be introduced to directly generate a subset of EFMs satisfying the set of constraints. The depth-first search algorithm has a constant memory overhead. Using flux constraints, a large LP problem can be massively divided and parallelized into independent sub-jobs for deployment into computing clusters. Since the sub-jobs do not overlap, the approach scales to utilize all available computing nodes with minimal coordination overhead or memory limitations.

Conclusions

The speed of the algorithm was comparable to efmtool, a mainstream Double Description method, when enumerating all EFMs; the attrition power gained from performing flux feasibility tests offsets the increased computational demand of running an LP solver. Unlike the Double Description method, the algorithm enables accelerated enumeration of all EFMs satisfying a set of constraints.

Derivative processes for modelling metabolic fluxes

Motivation: One of the challenging questions in modelling biological systems is to characterize the functional forms of the processes that control and orchestrate molecular and cellular phenotypes. Recently proposed methods for the analysis of metabolic pathways, for example, dynamic flux estimation, can only provide estimates of the underlying fluxes at discrete time points but fail to capture the complete temporal behaviour. To describe the dynamic variation of the fluxes, we additionally require the assumption of specific functional forms that can capture the temporal behaviour. However, it also remains unclear how to address the noise which might be present in experimentally measured metabolite concentrations.

Results: Here we propose a novel approach to modelling metabolic fluxes: derivative processes that are based on multiple-output Gaussian processes (MGPs), which are a flexible non-parametric Bayesian modelling technique. The main advantages that follow from MGPs approach include the natural non-parametric representation of the fluxes and ability to impute the missing data in between the measurements. Our derivative process approach allows us to model changes in metabolite derivative concentrations and to characterize the temporal behaviour of metabolic fluxes from time course data. Because the derivative of a Gaussian process is itself a Gaussian process, we can readily link metabolite concentrations to metabolic fluxes and vice versa. Here we discuss how this can be implemented in an MGP framework and illustrate its application to simple models, including nitrogen metabolism in Escherichia coli.

Availability and implementation: R code is available from the authors upon request.

Contact:j.norkunaite@imperial.ac.uk; m.stumpf@imperial.ac.uk

Supplementary information:Supplementary data are available at Bioinformatics online.

Elementary flux modes in a nutshell: properties, calculation and applications

Elementary flux mode (EFM) analysis allows the unbiased decomposition of a metabolic network into minimal functional units, making it a powerful tool for metabolic engineering. While the use of EFM analysis (EFMA) is still limited by the size of the models it can handle, EFMA has been successfully applied to solve real-world metabolic engineering problems. Here we provide a user-oriented introduction to EFMA, provide examples of recent applications, analyze current research strategies to overcome the computational restrictions and give an overview over current approaches, which aim to identify and calculate only biologically relevant EFMs.

Lysine overproducing Corynebacterium glutamicum is characterized by a robust linear combination of two optimal phenotypic states

A homoserine auxotroph strain of Corynebacterium glutamicum accumulates storage compound trehalose with lysine when limited by growth. Industrially lysine is produced from C. glutamicum through aspartate biosynthetic pathway, where enzymatic activity of aspartate kinase is allosterically controlled by the concerted feedback inhibition of threonine plus lysine. Ample threonine in the medium supports growth and inhibits lysine production (phenotype-I) and its complete absence leads to inhibition of growth in addition to accumulating lysine and trehalose (phenotype-II). In this work, we demonstrate that as threonine concentration becomes limiting, metabolic state of the cell shifts from maximizing growth (phenotype-I) to maximizing trehalose phenotype (phenotype-II) in a highly sensitive manner (with a Hill coefficient of 4). Trehalose formation was linked to lysine production through stoichiometry of the network. The study demonstrated that the net flux of the population was a linear combination of the two optimal phenotypic states, requiring only two experimental measurements to evaluate the flux distribution. The property of linear combination of two extreme phenotypes was robust for various medium conditions including varying batch time, initial glucose concentrations and medium osmolality.

Fast thermodynamically constrained flux variability analysis

MOTIVATION

Flux variability analysis (FVA) is an important tool to further analyse the results obtained by flux balance analysis (FBA) on genome-scale metabolic networks. For many constraint-based models, FVA identifies unboundedness of the optimal flux space. This reveals that optimal flux solutions with net flux through internal biochemical loops are feasible, which violates the second law of thermodynamics. Such unbounded fluxes may be eliminated by extending FVA with thermodynamic constraints.

RESULTS

We present a new algorithm for efficient flux variability (and flux balance) analysis with thermodynamic constraints, suitable for analysing genome-scale metabolic networks. We first show that FBA with thermodynamic constraints is NP-hard. Then we derive a theoretical tractability result, which can be applied to metabolic networks in practice. We use this result to develop a new constraint programming algorithm Fast-tFVA for fast FVA with thermodynamic constraints (tFVA). Computational comparisons with previous methods demonstrate the efficiency of the new method. For tFVA, a speed-up of factor 30-300 is achieved. In an analysis of genome-scale metabolic networks in the BioModels database, we found that in 485 of 716 networks, additional irreversible or fixed reactions could be detected.

AVAILABILITY AND IMPLEMENTATION

Fast-tFVA is written in C++ and published under GPL. It uses the open source software SCIP and libSBML. There also exists a Matlab interface for easy integration into Matlab. Fast-tFVA is available from page.mi.fu-berlin.de/arnem/fast-tfva.html.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Systems biology tools for toxicology

An important goal of toxicology is to understand and predict the adverse effects of drugs and other xenobiotics. For pharmaceuticals, such effects often emerge unexpectedly in man even when absent from trials in vitro and in animals. Although drugs and xenobiotics act on molecules, it is their perturbation of intracellular networks that matters. The tremendous complexity of these networks makes it difficult to understand the effects of xenobiotics on their ability to function. Because systems biology integrates data concerning molecules and their interactions into an understanding of network behaviour, it should be able to assist toxicology in this respect. This review identifies how in silico systems biology tools, such as kinetic modelling, and metabolic control, robustness and flux analyse, may indeed help understanding network-mediated toxicity. It also shows how these approaches function by implementing them vis-à-vis the glutathione network, which is important for the detoxification of reactive drug metabolites. The tools enable the appreciation of the steady state concept for the detoxification network and make it possible to simulate and then understand effects of perturbations of the macromolecules in the pathway that are counterintuitive. We review how a glutathione model has been used to explain the impact of perturbation of the pathway at various molecular sites, as would be the effect of single-nucleotide polymorphisms. We focus on how the mutations impact the levels of glutathione and of two candidate biomarkers of hepatic glutathione status. We conclude this review by sketching how the various systems biology tools may help in the various phases of drug development in the pharmaceutical industry.

Advanced stoichiometric analysis of metabolic networks of mammalian systems

Metabolic engineering tools have been widely applied to living organisms to gain a comprehensive understanding about cellular networks and to improve cellular properties. Metabolic flux analysis (MFA), flux balance analysis (FBA), and metabolic pathway analysis (MPA) are among the most popular tools in stoichiometric network analysis. Although application of these tools into well-known microbial systems is extensive in the literature, various barriers prevent them from being utilized in mammalian cells. Limited experimental data, complex regulatory mechanisms, and the requirement of more complex nutrient media are some major obstacles in mammalian cell systems. However, mammalian cells have been used to produce therapeutic proteins, to characterize disease states or related abnormal metabolic conditions, and to analyze the toxicological effects of some medicinally important drugs. Therefore, there is a growing need for extending metabolic engineering principles to mammalian cells in order to understand their underlying metabolic functions. In this review article, advanced metabolic engineering tools developed for stoichiometric analysis including MFA, FBA, and MPA are described. Applications of these tools in mammalian cells are discussed in detail, and the challenges and opportunities are highlighted.

Stoichiometry based steady-state hepatic flux analysis: computational and experimental aspects

: The liver has many complex physiological functions, including lipid, protein and carbohydrate metabolism, as well as bile and urea production. It detoxifies toxic substances and medicinal products. It also plays a key role in the onset and maintenance of abnormal metabolic patterns associated with various disease states, such as burns, infections and major traumas. Liver cells have been commonly used in in vitro experiments to elucidate the toxic effects of drugs and metabolic changes caused by aberrant metabolic conditions, and to improve the functions of existing systems, such as bioartificial liver. More recently, isolated liver perfusion systems have been increasingly used to characterize intrinsic metabolic changes in the liver caused by various perturbations, including systemic injury, hepatotoxin exposure and warm ischemia. Metabolic engineering tools have been widely applied to these systems to identify metabolic flux distributions using metabolic flux analysis or flux balance analysis and to characterize the topology of the networks using metabolic pathway analysis. In this context, hepatic metabolic models, together with experimental methodologies where hepatocytes or perfused livers are mainly investigated, are described in detail in this review. The challenges and opportunities are also discussed extensively.

Elementary mode analysis: a useful metabolic pathway analysis tool for reprograming microbial metabolic pathways

Elementary mode analysis is a useful metabolic pathway analysis tool to characterize cellular metabolism. It can identify all feasible metabolic pathways known as elementary modes that are inherent to a metabolic network. Each elementary mode contains a minimal and unique set of enzymatic reactions that can support cellular functions at steady state. Knowledge of all these pathway options enables systematic characterization of cellular phenotypes, analysis of metabolic network properties (e.g. structure, regulation, robustness, and fragility), phenotypic behavior discovery, and rational strain design for metabolic engineering application. This chapter focuses on the application of elementary mode analysis to reprogram microbial metabolic pathways for rational strain design and the metabolic pathway evolution of designed strains.

Projection to latent pathways (PLP): a constrained projection to latent variables (PLS) method for elementary flux modes discrimination

Background

Elementary flux modes (EFM) are unique and non-decomposable sets of metabolic reactions able to operate coherently in steady-state. A metabolic network has in general a very high number of EFM reflecting the typical functional redundancy of biological systems. However, most of these EFM are either thermodynamically unfeasible or inactive at pre-set environmental conditions.

Results

Here we present a new algorithm that discriminates the "active" set of EFM on the basis of dynamic envirome data. The algorithm merges together two well-known methods: projection to latent structures (PLS) and EFM analysis, and is therefore termed projection to latent pathways (PLP). PLP has two concomitant goals: (1) maximisation of correlation between EFM weighting factors and measured envirome data and (2) minimisation of redundancy by eliminating EFM with low correlation with the envirome.

Conclusions

Overall, our results demonstrate that PLP slightly outperforms PLS in terms of predictive power. But more importantly, PLP is able to discriminate the subset of EFM with highest correlation with the envirome, thus providing in-depth knowledge of how the environment controls core cellular functions. This offers a significant advantage over PLS since its abstract structure cannot be associated with the underlying biological structure.

Metabolic response of perfused livers to various oxygenation conditions

Isolated liver perfusion systems have been used to characterize intrinsic metabolic changes in liver as a result of various perturbations, including systemic injury, hepatotoxin exposure, and warm ischemia. Most of these studies were done using hyperoxic conditions (95% O(2)) but without the use of oxygen carriers in the perfusate. Prior literature data do not clearly establish the impact of oxygenation, and in particular that of adding oxygen carriers to the perfusate, on the metabolic functions of the liver. Therefore, herein the effects of oxygen delivery in the perfusion system on liver metabolism were investigated by comparing three modes of oxygenation. Rat livers were perfused via the portal and hepatic veins at a constant flow rate of 3 mL/min/g liver in a recirculating perfusion system. In the first group, the perfusate was equilibrated in a membrane oxygenator with room air (21% O(2)) before entering the liver. In the second group, the perfusate was equilibrated with a 95% O(2)/5% CO(2) gas mixture. In the third group, the perfusate was supplemented with washed bovine red blood cells (RBCs) at 10% hematocrit and also equilibrated with the 95% O(2)/5% CO(2) gas mixture. Oxygen and CO(2) gradients across the liver were measured periodically with a blood gas analyzer. The rate of change in the concentration of major metabolites in the perfusate was measured over time. Net extracellular fluxes were calculated from these measurements and applied to a stoichiometric-based optimization problem to determine the intracellular fluxes and active pathways in the perfused livers. Livers perfused with RBCs consumed oxygen at twice the rate observed using hyperoxic (95% O(2)) perfusate without RBCs, and also produced more urea and ketone bodies. At the flow rate used, the oxygen supply in perfusate without RBCs was just sufficient to meet the average oxygen demand of the liver but would be insufficient if it increased above baseline, as is often the case in response to environmental perturbations. Metabolic pathway analysis suggests that significant anaerobic glycolysis occurred in the absence of RBCs even using hyperoxic perfusate. Conversely, when RBCs were used, glucose production from lactate and glutamate, as well as pathways related to energy metabolism were upregulated. RBCs also reversed an increase in PPP fluxes induced by the use of hyperoxic perfusate alone. In conclusion, the use of oxygen carriers is required to investigate the effect of various perturbations on liver metabolism.

Decomposing flux distributions into elementary flux modes in genome-scale metabolic networks

MOTIVATION

Elementary flux mode (EFM) is a fundamental concept as well as a useful tool in metabolic pathway analysis. One important role of EFMs is that every flux distribution can be decomposed into a set of EFMs and a number of methods to study flux distributions originated from it. Yet finding such decompositions requires the complete set of EFMs, which is intractable in genome-scale metabolic networks due to combinatorial explosion.

RESULTS

In this article, we proposed an algorithm to decompose flux distributions into EFMs in genome-scale networks. It is an iterative scheme of a mixed integer linear program. Unlike previous optimization models to find pathways, any feasible solutions can become EFMs in our algorithm. This advantage enables the algorithm to approximate the EFM of largest contribution to an objective reaction in a flux distribution. Our algorithm is able to find EFMs of flux distributions with complex structures, closer to the realistic case in which a cell is subject to various constraints. A case of Escherichia coli growth in the Lysogeny broth (LB) medium containing various carbon sources was studied. Essential metabolites and their syntheses were located. Information on the contribution of each carbon source not obvious from the apparent flux distribution was also revealed. Our work further confirms the utility of finding EFMs by optimization models in genome-scale metabolic networks.

CONTACT

joshua.chan@connect.polyu.hk

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Cell functional enviromics: unravelling the function of environmental factors

Background

While functional genomics, focused on gene functions and gene-gene interactions, has become a very active field of research in molecular biology, equivalent methodologies embracing the environment and gene-environment interactions are relatively less developed. Understanding the function of environmental factors is, however, of paramount importance given the complex, interactive nature of environmental and genetic factors across multiple time scales.

Results

Here, we propose a systems biology framework, where the function of environmental factors is set at its core. We set forth a "reverse" functional analysis approach, whereby cellular functions are reconstructed from the analysis of dynamic envirome data. Our results show these data sets can be mapped to less than 20 core cellular functions in a typical mammalian cell culture, while explaining over 90% of flux data variance. A functional enviromics map can be created, which provides a template for manipulating the environmental factors to induce a desired phenotypic trait.

Conclusion

Our results support the feasibility of cellular function reconstruction guided by the analysis and manipulation of dynamic envirome data.

Genome-scale integrative data analysis and modeling of dynamic processes in yeast

Building a dynamic model of a complete biological cell is one of the great challenges of the 21st century. While this objective could appear unrealistic until recently, considerable improvements in high-throughput data collection techniques, computational performance, data integration, and modeling approaches now allow us to consider it within reach in the near future. In this chapter, we review recent developments that pave the way toward the construction of genome-scale dynamic models. We first describe methodologies for the integration of heterogeneous "omics" datasets, which enable the interpretation of cellular activity at the genome scale and in fluctuating conditions, providing the necessary input to models. We subsequently discuss principles of such models and describe a series of approaches that open perspectives toward the construction of genome-scale dynamic models.

Pathway analysis of liver metabolism under stressed condition

Pathway analysis is a useful tool which reveals important metabolic network properties. However, the big challenge is to propose an objective function for estimating active pathways, which represent the actual state of network. In order to provide weight values for all possible pathways within the metabolic network, this study presents different approaches, considering the structural and physiological properties of the metabolic network, aiming at a unique decomposition of the flux vector into pathways. These methods were used to analyze the hepatic metabolism considering available data sets obtained from the perfused livers of fasted rats receiving burn injury. Utilizing unique decomposition techniques and different fluxes revealed that higher weights were always attributed to short pathways. Specific pathways, including pyruvate, glutamate and oxaloacetate pools, and urea production from arginine, were found to be important or essential in all methods and experimental conditions. Moreover the pathways, including serine production from glycine and conversion between acetoacetate and B-OH-butyrate, were assigned higher weights. Pathway analysis was also used to identify the main sources for the production of certain products in the hepatic metabolic network to gain a better understanding of the effects of burn injury on liver metabolism.

Phenotypic characterization of Corynebacterium glutamicum using elementary modes towards synthesis of amino acids

Elementary flux mode (EFM) analysis is a powerful tool to represent the metabolic network structure and can be further utilized for flux analysis. The method enables characterization and quantification of feasible phenotypes in microbes. EFM analysis was employed to characterize the phenotype of Corynebacterium glutamicum to yield various amino acids. The metabolic network of C. glutamicum yielded 62 elementary modes by incorporating the accumulation of amino acids namely, lysine, alanine, valine, glutamine and glutamate. The analysis also allowed us to compute the maximum theoretical yield for the synthesis of various amino acids. These 62 elementary modes were further used to obtain optimal phenotypic space towards accumulation of biomass and lysine. The study indicated that the optimal solution space from 62 elementary modes forms a super space which incorporates various mutants including lysine producing strain of C. glutamicum. The analysis was also extended to obtain sensitivity of the network to variation in the stoichiometry of NADP in the definition of biomass.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1007/s11693-011-9073-8) contains supplementary material, which is available to authorized users.

Gradient descent optimization in gene regulatory pathways

Background

Gene Regulatory Networks (GRNs) have become a major focus of interest in recent years. Elucidating the architecture and dynamics of large scale gene regulatory networks is an important goal in systems biology. The knowledge of the gene regulatory networks further gives insights about gene regulatory pathways. This information leads to many potential applications in medicine and molecular biology, examples of which are identification of metabolic pathways, complex genetic diseases, drug discovery and toxicology analysis. High-throughput technologies allow studying various aspects of gene regulatory networks on a genome-wide scale and we will discuss recent advances as well as limitations and future challenges for gene network modeling. Novel approaches are needed to both infer the causal genes and generate hypothesis on the underlying regulatory mechanisms.

Methodology

In the present article, we introduce a new method for identifying a set of optimal gene regulatory pathways by using structural equations as a tool for modeling gene regulatory networks. The method, first of all, generates data on reaction flows in a pathway. A set of constraints is formulated incorporating weighting coefficients. Finally the gene regulatory pathways are obtained through optimization of an objective function with respect to these weighting coefficients. The effectiveness of the present method is successfully tested on ten gene regulatory networks existing in the literature. A comparative study with the existing extreme pathway analysis also forms a part of this investigation. The results compare favorably with earlier experimental results. The validated pathways point to a combination of previously documented and novel findings.

Conclusions

We show that our method can correctly identify the causal genes and effectively output experimentally verified pathways. The present method has been successful in deriving the optimal regulatory pathways for all the regulatory networks considered. The biological significance and applicability of the optimal pathways has also been discussed. Finally the usefulness of the present method on genetic engineering is depicted with an example.

Organising metabolic networks: Cycles in flux distributions

Metabolic networks are among the most widely studied biological systems. The topology and interconnections of metabolic reactions have been well described for many species. This is, however, not sufficient to understand how their activity is regulated in living organisms. These descriptions depict a static set of possible chains of reactions, with no information about the dynamic activity of reaction fluxes. Cyclic structures are thought to play a central role in the homeostasis of biological systems and in their resilience to a changing environment. In this work, we present a methodology to help investigating dynamic fluxes associated to biochemical reactions in metabolic networks. We introduce an algorithm for partitioning fluxes between cyclic and acyclic sub-networks, adapted from an algorithm initially developed to study fluxes in trophic networks. Using this algorithm, we analyse three metabolic systems: the central metabolism of wild type and a deletion mutant of Escherichia coli, erythrocyte metabolism and the central metabolism of the bacterium Methylobacterium extorquens. This methodology unveils the role of cycles in driving and maintaining metabolic fluxes under perturbations in these examples, and may be used to further investigate and understand the organisational invariance of biological systems.

Which metabolic pathways generate and characterize the flux space? A comparison among elementary modes, extreme pathways and minimal generators

Important efforts are being done to systematically identify the relevant pathways in a metabolic network. Unsurprisingly, there is not a unique set of network-based pathways to be tagged as relevant, and at least four related concepts have been proposed: extreme currents, elementary modes, extreme pathways, and minimal generators. Basically, there are two properties that these sets of pathways can hold: they can generate the flux space--if every feasible flux distribution can be represented as a nonnegative combination of flux through them--or they can comprise all the nondecomposable pathways in the network. The four concepts fulfill the first property, but only the elementary modes fulfill the second one. This subtle difference has been a source of errors and misunderstandings. This paper attempts to clarify the intricate relationship between the network-based pathways performing a comparison among them.

Streamlining the construction of large-scale dynamic models using generic kinetic equations

MOTIVATION

Studying biological systems, not just at an individual component level but at a system-wide level, gives us great potential to understand fundamental functions and essential biological properties. Despite considerable advances in the topological analysis of metabolic networks, inadequate knowledge of the enzyme kinetic rate laws and their associated parameter values still hampers large-scale kinetic modelling. Furthermore, the integration of gene expression and protein levels into kinetic models is not straightforward.

RESULTS

The focus of our research is on streamlining the construction of large-scale kinetic models. A novel software tool was developed, which enables the generation of generic rate equations for all reactions in a model. It encompasses an algorithm for estimating the concentration of proteins for a reaction to reach a particular steady state when kinetic parameters are unknown, and two robust methods for parameter estimation. It also allows for the seamless integration of gene expression or protein levels into a reaction and can generate equations for both transcription and translation. We applied this methodology to model the yeast glycolysis pathway; our results show that the behaviour of the system can be accurately described using generic kinetic equations.

AVAILABILITY AND IMPLEMENTATION

The software tool, together with its source code in Java, is available from our project web site at http://www.bioinf.manchester.ac.uk/schwartz/grape

CONTACT

jean-marc.schwartz@manchester.ac.uk

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

In response to 'Can sugars be produced from fatty acids? A test case for pathway analysis tools'

MOTIVATION

In their article entitled 'Can sugars be produced from fatty acids? A test case for pathway analysis tools' de Figueiredo and co-authors assess the performance of three pathway prediction tools (METATOOL, PathFinding and Pathway Hunter Tool) using the synthesis of glucose-6-phosphate (G6P) from acetyl-CoA in humans as a test case. We think that this article is biased for three reasons: (i) the metabolic networks used as input for the respective tools were of very different sizes; (ii) the 'assessment' is restricted to two study cases; (iii) developers are inherently more skilled to use their own tools than those developed by other people. We extended the analyses led by de Figueiredo and clearly show that the apparent superior performance of their tool (METATOOL) is partly due to the differences in input network sizes. We also see a conceptual problem in the comparison of tools that serve different purposes. In our opinion, metabolic path finding and elementary mode analysis are answering different biological questions, and should be considered as complementary rather than competitive approaches.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Cross-species analysis of the glycolytic pathway by comparison of molecular interaction fields

The electrostatic potential of an enzyme is a key determinant of its substrate interactions and catalytic turnover. Here we invoke comparative analysis of protein electrostatic potentials, along with sequence and structural analysis, to classify and characterize all the enzymes in an entire pathway across a set of different organisms. The electrostatic potentials of the enzymes from the glycolytic pathway of 11 eukaryotes were analyzed by qPIPSA (quantitative protein interaction property similarity analysis). The comparison allows the functional assignment of neuron-specific isoforms of triosephosphate isomerase from zebrafish, the identification of unusual protein surface interaction properties of the mosquito glucose-6-phosphate isomerase and the functional annotation of ATP-dependent phosphofructokinases and cofactor-dependent phosphoglycerate mutases from plants. We here show that plants possess two parallel pathways to convert glucose. One is similar to glycolysis in humans, the other is specialized to let plants adapt to their environmental conditions. We use differences in electrostatic potentials to estimate kinetic parameters for the triosephosphate isomerases from nine species for which published parameters are not available. Along the core glycolytic pathway, phosphoglycerate mutase displays the most conserved electrostatic potential. The largest cross-species variations are found for glucose-6-phosphate isomerase, enolase and fructose-1,6-bisphosphate aldolase. The extent of conservation of electrostatic potentials along the pathway is consistent with the absence of a single rate-limiting step in glycolysis.

A possibilistic framework for constraint-based metabolic flux analysis

BACKGROUND

Constraint-based models allow the calculation of the metabolic flux states that can be exhibited by cells, standing out as a powerful analytical tool, but they do not determine which of these are likely to be existing under given circumstances. Typical methods to perform these predictions are (a) flux balance analysis, which is based on the assumption that cell behaviour is optimal, and (b) metabolic flux analysis, which combines the model with experimental measurements.

RESULTS

Herein we discuss a possibilistic framework to perform metabolic flux estimations using a constraint-based model and a set of measurements. The methodology is able to handle inconsistencies, by considering sensors errors and model imprecision, to provide rich and reliable flux estimations. The methodology can be cast as linear programming problems, able to handle thousands of variables with efficiency, so it is suitable to deal with large-scale networks. Moreover, the possibilistic estimation does not attempt necessarily to predict the actual fluxes with precision, but rather to exploit the available data--even if those are scarce--to distinguish possible from impossible flux states in a gradual way.

CONCLUSION

We introduce a possibilistic framework for the estimation of metabolic fluxes, which is shown to be flexible, reliable, usable in scenarios lacking data and computationally efficient.

Maximum entropy decomposition of flux distribution at steady state to elementary modes

Enzyme Control Flux (ECF) is a method of correlating enzyme activity and flux distribution. The advantage of ECF is that the measurement integrates proteome data with metabolic flux analysis through Elementary Modes (EMs). But there are a few methods of effectively determining the Elementary Mode Coefficient (EMC) in cases where no objective biological function is available. Therefore, we proposed a new algorithm implementing the maximum entropy principle (MEP) as an objective function for estimating the EMC. To demonstrate the feasibility of using the MEP in this way, we compared it with Linear Programming and Quadratic Programming for modeling the metabolic networks of Chinese Hamster Ovary, Escherichia coli, and Saccharomyces cerevisiae cells. The use of the MEP presents the most plausible distribution of EMCs in the absence of any biological hypotheses describing the physiological state of cells, thereby enhancing the prediction accuracy of the flux distribution in various mutants.

A hybrid model of anaerobic E. coli GJT001: combination of elementary flux modes and cybernetic variables

Flux balance analysis (FBA) in combination with the decomposition of metabolic networks into elementary modes has provided a route to modeling cellular metabolism. It is dependent, however, on the availability of external fluxes such as substrate uptake or growth rate before estimates can become available of intracellular fluxes. The framework classically does not allow modeling of metabolic regulation or the formulation of dynamic models except through dynamic measurement of external fluxes. The cybernetic modeling approach of Ramkrishna and coworkers provides a dynamic framework for modeling metabolic systems because of its focus on describing regulatory processes based on cybernetic arguments and hence has the capacity to describe both external and internal fluxes. In this article, we explore the alternative of developing hybrid models combining cybernetic models for the external fluxes with the flux balance approach for estimation of the internal fluxes. The approach has the merit of the simplicity of the early cybernetic models and hence computationally facile while also providing detailed information on intracellular fluxes. The hybrid model of this article is based on elementary mode decomposition of the metabolic network. The uptake rates for the various elementary modes are combined using global cybernetic variables based on maximizing substrate uptake rates. Estimation of intracellular metabolism is based on its stoichiometric coupling with the external fluxes under the assumption of (pseudo-) steady state conditions. The set of parameters of the hybrid model was estimated with the aid of nonlinear optimization routine, by fitting simulations with dynamic experimental data on concentrations of biomass, substrate, and fermentation products. The hybrid model estimations were tested with FBA (based on measured substrate uptake rate) for two different metabolic networks (one is a reduced network which fixes ATP contribution to the biomass and maintenance requirement of ATP, and the other network is a more complex network which has a separate reaction for maintenance.) for the same experiment involving anaerobic growth of E. coli GJT001. The hybrid model estimated glucose consumption and all fermentation byproducts to better than 10%. The FBA makes similar estimations of fermentation products, however, with the exception of succinate. The simulation results show that the global cybernetic variables alone can regulate the metabolic reactions obtaining a very satisfactory fit to the measured fermentation byproducts. In view of the hybrid model's ability to predict biomass growth and fermentation byproducts of anaerobic E. coli GJT001, this reduced order model offers a computationally efficient alternative to more detailed models of metabolism and hence useful for the simulation of bioreactors.

Elementary mode analysis: a useful metabolic pathway analysis tool for characterizing cellular metabolism

Elementary mode analysis is a useful metabolic pathway analysis tool to identify the structure of a metabolic network that links the cellular phenotype to the corresponding genotype. The analysis can decompose the intricate metabolic network comprised of highly interconnected reactions into uniquely organized pathways. These pathways consisting of a minimal set of enzymes that can support steady state operation of cellular metabolism represent independent cellular physiological states. Such pathway definition provides a rigorous basis to systematically characterize cellular phenotypes, metabolic network regulation, robustness, and fragility that facilitate understanding of cell physiology and implementation of metabolic engineering strategies. This mini-review aims to overview the development and application of elementary mode analysis as a metabolic pathway analysis tool in studying cell physiology and as a basis of metabolic engineering.

Nanovehicular intracellular delivery systems

This article provides an overview of principles and barriers relevant to intracellular drug and gene transport, accumulation and retention (collectively called as drug delivery) by means of nanovehicles (NV). The aim is to deliver a cargo to a particular intracellular site, if possible, to exert a local action. Some of the principles discussed in this article apply to noncolloidal drugs that are not permeable to the plasma membrane or to the blood-brain barrier. NV are defined as a wide range of nanosized particles leading to colloidal objects which are capable of entering cells and tissues and delivering a cargo intracelullarly. Different localization and targeting means are discussed. Limited discussion on pharmacokinetics and pharmacodynamics is also presented. NVs are contrasted to micro-delivery and current nanotechnologies which are already in commercial use. Newer developments in NV technologies are outlined and future applications are stressed. We also briefly review the existing modeling tools and approaches to quantitatively describe the behavior of targeted NV within the vascular and tumor compartments, an area of particular importance. While we list "elementary" phenomena related to different level of complexity of delivery to cancer, we also stress importance of multi-scale modeling and bottom-up systems biology approach.