Regulatory design in a simple system integrating membrane potential generation and metabolic ATP consumption. Robustness and the role of energy dissipating processes

Bacterial physiological responses integrate energy-coupling processes at the membrane level with metabolic energy demand. The regulatory design behind these responses remains largely unexplored. Propionigenium modestum is an adequate organism to study these responses because it presents the simplest scheme known integrating membrane potential generation and metabolic ATP consumption. A hypothetical sodium leak is added to the scheme as the sole regulatory site. Allosteric regulation is assumed to be absent. Information of the rate equations is not available. However, relevant features of the patterns of responses may be obtained using Metabolic Control Analysis (MCA) and Metabolic Control Design (MCD). With these tools, we show that membrane potential disturbances can be compensated by adjusting the leak flux, without significant perturbations of ATP consumption. Perturbations of membrane potential by ATP demand are inevitable and also require compensatory changes in the leak. Numerical simulations were performed with a kinetic model exhibiting the responses for small changes obtained with MCA and MCD. A modest leak (10% of input) was assumed for the reference state. We found that disturbances in membrane potential and ATP consumption, produced by environmental perturbations of the cation concentration, may be reverted to the reference state adjusting the leak. Leak changes can also compensate for undesirable effects on membrane potential produced by changes in nutrient availability or ATP demand, in a wide range of values. The system is highly robust to parameter fluctuations. The regulatory role of energy dissipating processes and the trade-off between energetic efficiency and regulatory capacity are discussed.     

Experimental determination of group flux control coefficients in metabolic networks

Grouping of reactions around key metabolite branch points can facilitate the study of metabolic control of complex metabolic networks. This top-down Metabolic Control Analysis is exemplified through the introduction of group (flux, as well as concentration) control coefficients whose magnitudes provide a measure of the relative impact of each reaction group on the overall network flux, as well as on the overall network stability, following enzymatic amplification. In this article, we demonstrate the application of previously developed theory to the determination of group flux control coefficients. Experimental data for the changes in metabolic fluxes obtained in response to the introduction of six different environmental perturbations are used to determine the group flux control coefficients for three reaction groups formed around the phosphoenolpyruvate/pyruvate branch point. The consistency of the obtained group flux control coefficient estimates is systematically analyzed to ensure that all necessary conditions are satisfied. The magnitudes of the determined control coefficients suggest that the control of lysine production flux in Corynebacterium glutamicum cells at a growth base state resides within the lysine biosynthetic pathway that begins with the PEP/PYR carboxylation anaplorotic pathway. Copyright 1998 John Wiley & Sons, Inc.     

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.     

Classification and sensitivity analysis of a proposed primary metabolic reaction network for Streptomyces lividans

Constructing a metabolic flux analysis model is in principle fairly straightforward. However, there are a number of mathematical pitfalls. First, dependent reactions are a recurring problem and, second, the choice of reactions to measure may not be straight-forward. A method for systematic identification of dependent reactions and a thorough reactions classification procedure is presented. A well-defined stoichiometric presentation can provide significant insight into metabolic control mechanisms. Two methods for analyzing the impact of perturbations in the measured fluxes on the remaining metabolism and the impact of changes in biomass composition on the calculated metabolic reactions is developed. A metabolic reaction network proposed for Streptomyces lividans is used as an example to demonstrate the outlined analysis. It is concluded that oxygen utilization has the highest influence on the pathway fluxes and that realistic perturbations in the biomass composition do not significantly alter the flux patterns.     

Integrating cybernetic modeling with pathway analysis provides a dynamic, systems-level description of metabolic control

Cybernetic modeling strives to uncover the inbuilt regulatory programs of biological systems and leverage them toward computational prediction of metabolic dynamics. Because of its focus on incorporating the global aims of metabolism, cybernetic modeling provides a systems-oriented approach for describing regulatory inputs and inferring the impact of regulation within biochemical networks. Combining cybernetic control laws with concepts from metabolic pathway analysis has culminated in a systematic strategy for constructing cybernetic models, which was previously lacking. The newly devised framework relies upon the simultaneous application of local controls that maximize the net flux through each elementary flux mode and global controls that modulate the activities of these modes to optimize the overall nutritional state of the cell. The modeling concepts are illustrated using a simple linear pathway and a larger network representing anaerobic E. coli central metabolism. The E. coli model successfully describes the metabolic shift that occurs upon deleting the pta-ackA operon that is responsible for fermentative acetate production. The model also furnishes predictions that are consistent with experimental results obtained from additional knockout strains as well as strains expressing heterologous genes. Because of the stabilizing influence of the included control variables, the resulting cybernetic models are more robust and reliable than their predecessors in simulating the network response to imposed genetic and environmental perturbations.     

Complementary identification of multiple flux distributions and multiple metabolic pathways

Cell robustness and complexity have been recognized as unique features of biological systems. Such robustness and complexity of metabolic-reaction systems can be explored by discovering, or identifying, the multiple flux distributions (MFD) and redundant pathways that lead to a given external state; however, this is exceedingly cumbersome to accomplish. It is, therefore, highly desirable to establish an effective computational method for their identification, which, in turn, gives rise to a novel insight into the cellular function. An effective approach is proposed for complementarily identifying MFD in metabolic flux analysis and multiple metabolic pathways (MMP) in structural pathway analysis. This approach judiciously integrates flux balance analysis (FBA) based on linear programming and the graph-theoretic method for determining reaction pathways. A single metabolic pathway, with the concomitant flux distribution and the overall reaction manifesting itself as the desired phenotype under some environmental conditions, is determined by FBA from the initial candidate sequence of metabolic reactions. Subsequently, the graph-theoretic method recovers all feasible MMP and the corresponding MFD. The approach's efficacy is demonstrated by applying it to the in silico Escherichia coli model under various culture conditions. The resultant MMP and MFD attaining a unique external state reveal the surprising adaptability and robustness of the intricate cellular network as a key to cell survival against environmental or genetic changes. These results indicate that the proposed approach would be useful in facilitating drug discovery.     

The definitions of metabolic control analysis revisited.

Various definitions of coefficients in metabolic control analysis are examined with respect to their theoretical consistency and practical applicability. We suggest agreement upon a definition for control coefficients which is clearly distinct from that for response coefficients, in such a way that the former describe inherent properties of the metabolic system while the latter refer to the influence of special parameters. Advantages and drawbacks of using normalized or non-normalized control coefficients are studied. It is shown that normalized control coefficients have the advantage of being invariant to a different rescaling of the particular fluxes. We demonstrate that some problems are easier to tackle if the consistency of time-independent control coefficients with their time-dependent counterparts is taken into account. It is shown that the matrix of flux control coefficients is an indempotent matrix. This allows an interpretation in terms of the transduction of the effect of parameter perturbations. Several aspects of the experimental measurement of control coefficients are discussed, with special reference to the different definitions.     

ΔFBA—Predicting metabolic flux alterations using genome-scale metabolic models and differential transcriptomic data

Genome-scale metabolic models (GEMs) provide a powerful framework for simulating the entire set of biochemical reactions in a cell using a constraint-based modeling strategy called flux balance analysis (FBA). FBA relies on an assumed metabolic objective for generating metabolic fluxes using GEMs. But, the most appropriate metabolic objective is not always obvious for a given condition and is likely context-specific, which often complicate the estimation of metabolic flux alterations between conditions. Here, we propose a new method, called ΔFBA (deltaFBA), that integrates differential gene expression data to evaluate directly metabolic flux differences between two conditions. Notably, ΔFBA does not require specifying the cellular objective. Rather, ΔFBA seeks to maximize the consistency and minimize inconsistency between the predicted flux differences and differential gene expression. We showcased the performance of ΔFBA through several case studies involving the prediction of metabolic alterations caused by genetic and environmental perturbations in Escherichia coli and caused by Type-2 diabetes in human muscle. Importantly, in comparison to existing methods, ΔFBA gives a more accurate prediction of flux differences.     

A new framework for the estimation of control parameters in metabolic pathways using lin-log kinetics.

The control properties of biochemical pathways can be described by control coefficients and elasticities, as defined in the framework of metabolic control analysis. The determination of these parameters using the traditional metabolic control analysis relationships is, however, limited by experimental difficulties (e.g. realizing and measuring small changes in biological systems) and lack of appropriate mathematical procedures (e.g. when the more practical large changes are made). In this paper, the recently developed lin-log approach is proposed to avoid the above-mentioned problems and is applied to estimate control parameters from measurements obtained in steady state experiments. The lin-log approach employs approximative linear-logarithmic kinetics parameterized by elasticities and provides analytical solutions for fluxes and metabolite concentrations when large changes are made. Published flux and metabolite concentration data are used, obtained from a reconstructed section of glycolysis converting 3-phosphoglycerate to pyruvate [Giersch, C. (1995) Eur. J. Biochem. 227, 194-201]. With the lin-log approach, all data from different experiments can be combined to give realistic elasticity and flux control coefficient estimates by linear regression. Despite the large changes, a good agreement of fluxes and metabolite concentrations is obtained between the measured and calculated values according to the lin-log model. Furthermore, it is shown that the lin-log approach allows a rigorous statistical evaluation to identify the optimal reference state and the optimal model structure assumption. In conclusion, the lin-log approach addresses practical problems encountered in the traditional metabolic control analysis-based methods by introducing suitable nonlinear kinetics, thus providing a novel framework with improved procedures for the estimation of elasticities and control parameters from large perturbation experiments.     

Effects of introducing heterologous pathways on microbial metabolism with respect to metabolic optimality

Although optimality of microbial metabolism under genetic and environmental perturbations is well studied, the effects of introducing heterologous reactions on the overall metabolism are not well understood. This point is important in the field of metabolic engineering because heterologous reactions are more frequently introduced into various microbial hosts. The genome-scale metabolic simulations of Escherichia coli strains engineered to produce 1,4-butanediol, 1,3-propanediol, and amorphadiene suggest that microbial metabolism shows much different responses to the introduced heterologous reactions in a strain-specific manner than typical gene knockouts in terms of the energetic status (e.g., ATP and biomass generation) and chemical production capacity. The 1,4-butanediol and 1,3-propanediol producers showed greater metabolic optimality than the wild-type strains and gene knockout mutants for the energetic status, while the amorphadiene producer was metabolically less optimal. For the optimal chemical production capacity, additional gene knockouts were most effective for the strain producing 1,3-propanediol, but not for the one producing 1,4-butanediol. These observations suggest that strains having heterologous metabolic reactions have metabolic characteristics significantly different from those of the wild-type strain and single gene knockout mutants. Finally, comparison of the theoretically predicted and ¹³C-based flux values pinpoints pathways with non-optimal flux values, which can be considered as engineering targets in systems metabolic engineering strategies. To our knowledge, this study is the first attempt to quantitatively characterize microbial metabolisms with different heterologous reactions. The suggested potential reasons behind each strain’s different metabolic responses to the introduced heterologous reactions should be carefully considered in strain designs.     

Toward predicting metabolic fluxes in metabolically engineered strains

Predicting metabolic fluxes of a genetically engineered organism is an important step toward rational pathway design. However, because of various regulatory mechanisms, which are complex, often ill-characterized, and sometimes undiscovered, predicting metabolic fluxes using kinetic simulation is difficult. We propose to incorporate regulatory constraints in flux calculation to allow prediction of the steady-state fluxes without complete kinetics. The regulatory constraint, in its linear form, is derived from the dynamic metabolic control theory and involves the flux control coefficients. It is shown that with these constraints, the responses to metabolic perturbation can be predicted. Conversely, the regulatory constraints and the control coefficients can be determined by comparing the experimental data with the prediction. Therefore, this approach may offer a practical direction toward prediction of fluxes for metabolically engineered organisms.     

From annotated genomes to metabolic flux models and kinetic parameter fitting

Significant advances in system-level modeling of cellular behavior can be achieved based on constraints derived from genomic information and on optimality hypotheses. For steady-state models of metabolic networks, mass conservation and reaction stoichiometry impose linear constraints on metabolic fluxes. Different objectives, such as maximization of growth rate or minimization of flux distance from a reference state, can be tested in different organisms and conditions. In particular, we have suggested that the metabolic properties of mutant bacterial strains are best described by an algorithm that performs a minimization of metabolic adjustment (MOMA) upon gene deletion. The increasing availability of many annotated genomes paves the way for a systematic application of these flux balance methods to a large variety of organisms. However, such a high throughput goal crucially depends on our capacity to build metabolic flux models in a fully automated fashion. Here we describe a pipeline for generating models from annotated genomes and discuss the current obstacles to full automation. In addition, we propose a framework for the integration of flux modeling results and high throughput proteomic data, which can potentially help in the inference of whole-cell kinetic parameters.     

Integration of temporal analysis and control analysis of metabolic systems.

A theory is developed that integrates approaches to the analysis of pathway transient response and metabolic control analysis. A Temporal Control Coefficient is defined that is a measure of the system's transient response to modulation of enzyme activity or concentration. The approach allows for the analysis of the establishment of a steady state from rest, of the system's 'agility' of response to minor perturbations of a pre-existing steady state and of the macroscopic transition between steady states. In the last-mentioned case it is shown that, like the transient time itself, the control of transient response retains the property of independence from the mechanism of the transition. In consequence, the Temporal Control Coefficient can be defined in terms of the control properties of the initial and final states alone without reference to the mechanism of transition. A summation property is shown to apply to the Temporal Control Coefficients in each case. Connectivity relationships between elasticities and Temporal Control Coefficients are also established.     

Isotopically nonstationary 13C metabolic flux analysis in resting and activated human platelets

Platelet metabolism is linked to platelet hyper- and hypoactivity in numerous human diseases. Developing a detailed understanding of the link between metabolic shifts and platelet activation state is integral to improving human health. Here, we show the first application of isotopically nonstationary ¹³C metabolic flux analysis to quantitatively measure carbon fluxes in both resting and thrombin activated platelets. Metabolic flux analysis results show that resting platelets primarily metabolize glucose to lactate via glycolysis, while acetate is oxidized to fuel the tricarboxylic acid cycle. Upon activation with thrombin, a potent platelet agonist, platelets increase their uptake of glucose 3-fold. This results in an absolute increase in flux throughout central metabolism, but when compared to resting platelets they redistribute carbon dramatically. Activated platelets decrease relative flux to the oxidative pentose phosphate pathway and TCA cycle from glucose and increase relative flux to lactate. These results provide the first report of reaction-level carbon fluxes in platelets and allow us to distinguish metabolic fluxes with much higher resolution than previous studies.     

Ensemble modeling of metabolic networks

Complete modeling of metabolic networks is desirable, but it is difficult to accomplish because of the lack of kinetics. As a step toward this goal, we have developed an approach to build an ensemble of dynamic models that reach the same steady state. The models in the ensemble are based on the same mechanistic framework at the elementary reaction level, including known regulations, and span the space of all kinetics allowable by thermodynamics. This ensemble allows for the examination of possible phenotypes of the network upon perturbations, such as changes in enzyme expression levels. The size of the ensemble is reduced by acquiring data for such perturbation phenotypes. If the mechanistic framework is approximately accurate, the ensemble converges to a smaller set of models and becomes more predictive. This approach bypasses the need for detailed characterization of kinetic parameters and arrives at a set of models that describes relevant phenotypes upon enzyme perturbations.     

Comparison of metabolic states using genome-scale metabolic models

Genome-scale metabolic models (GEMs) are comprehensive knowledge bases of cellular metabolism and serve as mathematical tools for studying biological phenotypes and metabolic states or conditions in various organisms and cell types. Given the sheer size and complexity of human metabolism, selecting parameters for existing analysis methods such as metabolic objective functions and model constraints is not straightforward in human GEMs. In particular, comparing several conditions in large GEMs to identify condition- or disease-specific metabolic features is challenging. In this study, we showcase a scalable, model-driven approach for an in-depth investigation and comparison of metabolic states in large GEMs which enables identifying the underlying functional differences. Using a combination of flux space sampling and network analysis, our approach enables extraction and visualisation of metabolically distinct network modules. Importantly, it does not rely on known or assumed objective functions. We apply this novel approach to extract the biochemical differences in adipocytes arising due to unlimited vs blocked uptake of branched-chain amino acids (BCAAs, considered as biomarkers in obesity) using a human adipocyte GEM (iAdipocytes1809). The biological significance of our approach is corroborated by literature reports confirming our identified metabolic processes (TCA cycle and Fatty acid metabolism) to be functionally related to BCAA metabolism. Additionally, our analysis predicts a specific altered uptake and secretion profile indicating a compensation for the unavailability of BCAAs. Taken together, our approach facilitates determining functional differences between any metabolic conditions of interest by offering a versatile platform for analysing and comparing flux spaces of large metabolic networks.