Metabolic flux control analysis of branch points: an improved approach to obtain flux control coefficients from large perturbation data

Bayesian inference of metabolic kinetics from genome-scale multiomics data

Modern biological tools generate a wealth of data on metabolite and protein concentrations that can be used to help inform new strain designs. However, learning from these data to predict how a cell will respond to genetic changes, a key need for engineering, remains challenging. A promising technique for leveraging omics measurements in metabolic modeling involves the construction of kinetic descriptions of the enzymatic reactions that occur within a cell. Parameterizing these models from biological data can be computationally difficult, since methods must also quantify the uncertainty in model parameters resulting from the observed data. While the field of Bayesian inference offers a wide range of methods for efficiently estimating distributions in parameter uncertainty, such techniques are poorly suited to traditional kinetic models due to their complex rate laws and resulting nonlinear dynamics. In this paper, we employ linear-logarithmic kinetics to simplify the calculation of steady-state flux distributions and enable efficient sampling and inference methods. We demonstrate that detailed information on the posterior distribution of parameters can be obtained efficiently at a variety of problem scales, including nearly genome-scale kinetic models trained on multiomics datasets. These results allow modern Bayesian machine learning tools to be leveraged in understanding biological data and in developing new, efficient strain designs.

In Silico Knockout Screening of Plasmodium falciparum Reactions and Prediction of Novel Essential Reactions by Analysing the Metabolic Network

Malaria is an infectious disease that affects close to half a million individuals every year and Plasmodium falciparum is a major cause of malaria. The treatment of this disease could be done effectively if the essential enzymes of this parasite are specifically targeted. Nevertheless, the development of the parasite in resisting existing drugs now makes discovering new drugs a core responsibility. In this study, a novel computational model that makes the prediction of new and validated antimalarial drug target cheaper, easier, and faster has been developed. We have identified new essential reactions as potential targets for drugs in the metabolic network of the parasite. Among the top seven (7) predicted essential reactions, four (4) have been previously identified in earlier studies with biological evidence and one (1) has been with computational evidence. The results from our study were compared with an extensive list of seventy-seven (77) essential reactions with biological evidence from a previous study. We present a list of thirty-one (31) potential candidates for drug targets in Plasmodium falciparum which includes twenty-four (24) new potential candidates for drug targets.

Structuring evolution: biochemical networks and metabolic diversification in birds

Background

Recurrence and predictability of evolution are thought to reflect the correspondence between genomic and phenotypic dimensions of organisms, and the connectivity in deterministic networks within these dimensions. Direct examination of the correspondence between opportunities for diversification imbedded in such networks and realized diversity is illuminating, but is empirically challenging because both the deterministic networks and phenotypic diversity are modified in the course of evolution. Here we overcome this problem by directly comparing the structure of a “global” carotenoid network – comprising of all known enzymatic reactions among naturally occurring carotenoids – with the patterns of evolutionary diversification in carotenoid-producing metabolic networks utilized by birds.

Results

We found that phenotypic diversification in carotenoid networks across 250 species was closely associated with enzymatic connectivity of the underlying biochemical network – compounds with greater connectivity occurred the most frequently across species and were the hotspots of metabolic pathway diversification. In contrast, we found no evidence for diversification along the metabolic pathways, corroborating findings that the utilization of the global carotenoid network was not strongly influenced by history in avian evolution.

Conclusions

The finding that the diversification in species-specific carotenoid networks is qualitatively predictable from the connectivity of the underlying enzymatic network points to significant structural determinism in phenotypic evolution.

Electronic supplementary material

The online version of this article (doi:10.1186/s12862-016-0731-z) contains supplementary material, which is available to authorized users.

The Landscape of Evolution: Reconciling Structural and Dynamic Properties of Metabolic Networks in Adaptive Diversifications

The network of the interactions among genes, proteins, and metabolites delineates a range of potential phenotypic diversifications in a lineage, and realized phenotypic changes are the result of differences in the dynamics of the expression of the elements and interactions in this deterministic network. Regulatory mechanisms, such as hormones, mediate the relationship between the structural and dynamic properties of networks by determining how and when the elements are expressed and form a functional unit or state. Changes in regulatory mechanisms lead to variable expression of functional states of a network within and among generations. Functional properties of network elements, and the magnitude and direction of evolutionary change they determine, depend on their location within a network. Here, we examine the relationship between network structure and the dynamic mechanisms that regulate flux through a metabolic network. We review the mechanisms that control metabolic flux in enzymatic reactions and examine structural properties of the network locations that are targets of flux control. We aim to establish a predictive framework to test the contributions of structural and dynamic properties of deterministic networks to evolutionary diversifications.

Metabolic control analysis of L-lactate synthesis pathway in Rhizopus oryzae As 3.2686

The relationship between the metabolic flux and the activities of the pyruvate branching enzymes of Rhizopus oryzae As 3.2686 during L-lactate fermentation was investigated using the perturbation method of aeration. The control coefficients for five enzymes, pyruvate dehydrogenase (PDH), pyruvate carboxylase (PC), pyruvate decarboxylase (PDC), lactate dehydrogenase (LDH), and alcohol dehydrogenase (ADH), were calculated. Our results indicated significant correlations between PDH and PC, PDC and LDH, PDC and ADH, LDH and ADH, and PDC and PC. It also appeared that PDH, PC, and LDH strongly controlled the L-lactate flux; PDH and ADH strongly controlled the ethanol flux; while PDH and PC strongly controlled the acetyl coenzyme A flux and the oxaloacetate flux. Further, the flux control coefficient curves indicated that the control of the system gradually transferred from PDC to PC during the steady state. Therefore, PC was the key rate-limiting enzyme that controls the flux distribution.

Tradeoff between robustness and elaboration in carotenoid networks produces cycles of avian color diversification

Background

Resolution of the link between micro- and macroevolution calls for comparing both processes on the same deterministic landscape, such as genomic, metabolic or fitness networks. We apply this perspective to the evolution of carotenoid pigmentation that produces spectacular diversity in avian colors and show that basic structural properties of the underlying carotenoid metabolic network are reflected in global patterns of elaboration and diversification in color displays. Birds color themselves by consuming and metabolizing several dietary carotenoids from the environment. Such fundamental dependency on the most upstream external compounds should intrinsically constrain sustained evolutionary elongation of multi-step metabolic pathways needed for color elaboration unless the metabolic network gains robustness – the ability to synthesize the same carotenoid from an additional dietary starting point.

Results

We found that gains and losses of metabolic robustness were associated with evolutionary cycles of elaboration and stasis in expressed carotenoids in birds. Lack of metabolic robustness constrained lineage’s metabolic explorations to the immediate biochemical vicinity of their ecologically distinct dietary carotenoids, whereas gains of robustness repeatedly resulted in sustained elongation of metabolic pathways on evolutionary time scales and corresponding color elaboration.

Conclusions

The structural link between length and robustness in metabolic pathways may explain periodic convergence of phylogenetically distant and ecologically distinct species in expressed carotenoid pigmentation; account for stasis in carotenoid colors in some ecological lineages; and show how the connectivity of the underlying metabolic network provides a mechanistic link between microevolutionary elaboration and macroevolutionary diversification.

Reviewers

This article was reviewed by Junhyong Kim, Eugene Koonin, and Fyodor Kondrashov. For complete reports, see the Reviewers’ reports section.

Electronic supplementary material

The online version of this article (doi:10.1186/s13062-015-0073-6) contains supplementary material, which is available to authorized users.

Computer-aided design for metabolic engineering

The development and application of biotechnology-based strategies has had a great socio-economical impact and is likely to play a crucial role in the foundation of more sustainable and efficient industrial processes. Within biotechnology, metabolic engineering aims at the directed improvement of cellular properties, often with the goal of synthesizing a target chemical compound. The use of computer-aided design (CAD) tools, along with the continuously emerging advanced genetic engineering techniques have allowed metabolic engineering to broaden and streamline the process of heterologous compound-production. In this work, we review the CAD tools available for metabolic engineering with an emphasis, on retrosynthesis methodologies. Recent advances in genetic engineering strategies for pathway implementation and optimization are also reviewed as well as a range of bionalytical tools to validate in silico predictions. A case study applying retrosynthesis is presented as an experimental verification of the output from Retropath, the first complete automated computational pipeline applicable to metabolic engineering. Applying this CAD pipeline, together with genetic reassembly and optimization of culture conditions led to improved production of the plant flavonoid pinocembrin. Coupling CAD tools with advanced genetic engineering strategies and bioprocess optimization is crucial for enhanced product yields and will be of great value for the development of non-natural products through sustainable biotechnological processes.

The evolution of genes in branched metabolic pathways

Simulation models of the evolution of genes in a branched metabolic pathway subject to stabilizing selection on flux are described and analyzed. The models are based either on metabolic control theory (MCT), with the assumption that enzymes are far from saturation, or on Michaelis-Menten kinetics, which allows for saturation and near saturation. Several predictions emerge from the models: (1) flux control evolves to be concentrated at pathway branch points, including the first enzyme in the pathway. (2) When flux is far from its optimum, adaptive substitutions occur disproportionately often in branching enzymes. (3) When flux is near its optimum, adaptive substitutions occur disproportionately often in nonbranching enzymes. (4) Slightly deleterious substitutions occur disproportionately often in nonbranching enzymes. (5) In terms of both flux control and patterns of substitution, pathway branches are similar to those predicted for linear pathways. These predictions provide null hypotheses for empirical examination of the evolution of genes in metabolic pathways.

Interactive effects of cadmium and hypoxia on metabolic responses and bacterial loads of eastern oysters Crassostrea virginica Gmelin

Pollution by toxic metals including cadmium (Cd) and hypoxia are important stressors in estuaries and coastal waters which may interactively affect sessile benthic organisms, such as oysters. We studied metabolic responses to prolonged hypoxic acclimation (2 weeks at 5% O2) in control and Cd-exposed (30 d at 50 μg L(-1) Cd) oysters Crassostrea virginica, and analyzed the effects of these stressors on abundance of Vibrio spp. in oysters. Hypoxia-acclimated oysters retained normal standard metabolic rates (SMR) at 5% O2, in contrast to a decline of SMR observed during acute hypoxia. However, oysters spent more time actively ventilating in hypoxia than normoxia resulting in enhanced Cd uptake and 2.7-fold higher tissue Cd burdens in hypoxia. Cd exposure led to a significant decrease in tissue glycogen stores, increase in free glucose levels and elevated activity of glycolytic enzymes (hexokinase and aldolase) indicating a greater dependence on carbohydrate catabolism. A compensatory increase in activities of two key mitochondrial enzymes (citrate synthase and cytochrome c oxidase) was found during prolonged hypoxia in control oysters but suppressed in Cd-exposed ones. Cd exposure also resulted in a significant increase in abundance of Vibrio parahaemolyticus and Vibrio vulnificus levels during normoxia and hypoxia, respectively. Overall, Cd- and hypoxia-induced changes in metabolic profile, Cd accumulation and bacterial flora of oysters indicate that these stressors can synergistically impact energy homeostasis, performance and survival of oysters in polluted estuaries and have significant consequences for transfer of Cd and bacterial pathogens to the higher levels of the food chain.

Impact of thermodynamic principles in systems biology

It is shown that properties of biological systems which are relevant for systems biology motivated mathematical modelling are strongly shaped by general thermodynamic principles such as osmotic limit, Gibbs energy dissipation, near equilibria and thermodynamic driving force. Each of these aspects will be demonstrated both theoretically and experimentally.

Human liver rate-limiting enzymes influence metabolic flux via branch points and inhibitors

Background

Rate-limiting enzymes, because of their relatively low velocity, are believed to influence metabolic flux in pathways. To investigate their regulatory role in metabolic networks, we look at the global organization and interactions between rate-limiting enzymes and compounds such as branch point metabolites and enzyme inhibitors in human liver.

Results

Based on 96 rate-limiting enzymes and 132 branch point compounds from human liver, we found that rate-limiting enzymes surrounded 76.5% of branch points. In a compound conversion network from human liver, the 128 branch points involved showed a dramatically higher average degree, betweenness centrality and closeness centrality as a whole. Nearly half of the in vivo inhibitors were products of rate-limiting enzymes, and covered 75.34% of the inhibited targets in metabolic inhibitory networks.

Conclusion

From global topological organization, rate-limiting enzymes as a whole surround most of the branch points; so they can influence the flux through branch points. Since nearly half of the in vivo enzyme inhibitors are produced by rate-limiting enzymes in human liver, these enzymes can initiate inhibitory regulation and then influence metabolic flux through their natural products.

Ensemble modeling for aromatic production in Escherichia coli

Ensemble Modeling (EM) is a recently developed method for metabolic modeling, particularly for utilizing the effect of enzyme tuning data on the production of a specific compound to refine the model. This approach is used here to investigate the production of aromatic products in Escherichia coli. Instead of using dynamic metabolite data to fit a model, the EM approach uses phenotypic data (effects of enzyme overexpression or knockouts on the steady state production rate) to screen possible models. These data are routinely generated during strain design. An ensemble of models is constructed that all reach the same steady state and are based on the same mechanistic framework at the elementary reaction level. The behavior of the models spans the kinetics allowable by thermodynamics. Then by using existing data from the literature for the overexpression of genes coding for transketolase (Tkt), transaldolase (Tal), and phosphoenolpyruvate synthase (Pps) to screen the ensemble, we arrive at a set of models that properly describes the known enzyme overexpression phenotypes. This subset of models becomes more predictive as additional data are used to refine the models. The final ensemble of models demonstrates the characteristic of the cell that Tkt is the first rate controlling step, and correctly predicts that only after Tkt is overexpressed does an increase in Pps increase the production rate of aromatics. This work demonstrates that EM is able to capture the result of enzyme overexpression on aromatic producing bacteria by successfully utilizing routinely generated enzyme tuning data to guide model learning.

Enabling technologies: fermentation and downstream processing

Efficient parallel tools for bioprocess design, consequent application of the concepts for metabolic process analysis as well as innovative downstream processing techniques are enabling technologies for new industrial bioprocesses from an engineering point of view. Basic principles, state-of-the-art techniques and cutting-edge technologies are briefly reviewed. Emphasis is on parallel bioreactors for bioprocess design, biochemical systems characterization and metabolic control analysis, as well as on preparative chromatography, affinity filtration and protein crystallization on a process scale.

A method for estimation of elasticities in metabolic networks using steady state and dynamic metabolomics data and linlog kinetics

Background

Dynamic modeling of metabolic reaction networks under in vivo conditions is a crucial step in order to obtain a better understanding of the (dis)functioning of living cells. So far dynamic metabolic models generally have been based on mechanistic rate equations which often contain so many parameters that their identifiability from experimental data forms a serious problem. Recently, approximative rate equations, based on the linear logarithmic (linlog) format have been proposed as a suitable alternative with fewer parameters.

Results

In this paper we present a method for estimation of the kinetic model parameters, which are equal to the elasticities defined in Metabolic Control Analysis, from metabolite data obtained from dynamic as well as steady state perturbations, using the linlog kinetic format. Additionally, we address the question of parameter identifiability from dynamic perturbation data in the presence of noise. The method is illustrated using metabolite data generated with a dynamic model of the glycolytic pathway of Saccharomyces cerevisiae based on mechanistic rate equations. Elasticities are estimated from the generated data, which define the complete linlog kinetic model of the glycolysis. The effect of data noise on the accuracy of the estimated elasticities is presented. Finally, identifiable subset of parameters is determined using information on the standard deviations of the estimated elasticities through Monte Carlo (MC) simulations.

Conclusion

The parameter estimation within the linlog kinetic framework as presented here allows the determination of the elasticities directly from experimental data from typical dynamic and/or steady state experiments. These elasticities allow the reconstruction of the full kinetic model of Saccharomyces cerevisiae, and the determination of the control coefficients. MC simulations revealed that certain elasticities are potentially unidentifiable from dynamic data only. Addition of steady state perturbation of enzyme activities solved this problem.

Control by cytochrome c oxidase of the cellular oxidative phosphorylation system depends on the mitochondrial energy state

Recent measurements of the flux control exerted by cytochrome c oxidase on the respiratory activity in intact cells have led to a re-appraisal of its regulatory function. We have further extended this in vivo study in the framework of the Metabolic Control Analysis and evaluated the impact of the mitochondrial transmembrane electrochemical potential (Deltamu(H+)) on the control strength of the oxidase. The results indicate that, under conditions mimicking the mitochondrial State 4 of respiration, both the flux control coefficient and the threshold value of cytochrome oxidase are modified with respect to the uncoupled condition. The results obtained are consistent with a model based on changes in the assembly state of the oxidative phosphorylation enzyme complexes and possible implications in the understanding of exercise-intolerance of human neuromuscular degenerative diseases are discussed.

Application of metabolome data in functional genomics: A conceptual strategy

A gene with yet unknown physiological function can be studied by changing its expression level followed by analysis of the resulting phenotype. This type of functional genomics study can be complicated by the occurrence of 'silent mutations', the phenotypes of which are not easily observable in terms of metabolic fluxes (e.g., the growth rate). Nevertheless, genetic alteration may give rise to significant yet complicated changes in the metabolome. We propose here a conceptual functional genomics strategy based on microbial metabolome data, which identifies changes in in vivo enzyme activities in the mutants. These predicted changes are used to formulate hypotheses to infer unknown gene functions. The required metabolome data can be obtained solely from high-throughput mass spectrometry analysis, which provides the following in vivo information: (1) the metabolite concentrations in the reference and the mutant strain; (2) the metabolic fluxes in both strains and (3) the enzyme kinetic parameters of the reference strain. We demonstrate in silico that changes in enzyme activities can be accurately predicted by this approach, even in 'silent mutants'.

Approximative kinetic formats used in metabolic network modeling

An overview is presented of the different approximative enzyme kinetic formats that have been proposed for use in metabolic modeling studies. It is considered that the following four general properties are relevant for approximative kinetics: the rate must be proportional to enzyme level; at high metabolite concentrations, there is downward concave behavior of rate versus concentration; the number of kinetic parameters should be as small as possible; analytical solutions of steady-state network balances are desirable. Six different approximative kinetic formats are evaluated (linear, logarithmic-linear, power law GMA, power law S-systems, thermokinetic, linear-logarithmic) and it is concluded that only the recently proposed linear-logarithmic approach combines all desired properties and therefore seems a most appropriate approximate kinetic format.