Source and regulation of flux variability in Escherichia coli

Sensitivity analysis and adaptive mutation strategy differential evolution algorithm for optimizing enzymes' turnover numbers in metabolic models

Genome-scale metabolic network model (GSMM) based on enzyme constraints greatly improves general metabolic models. The turnover number ( k cat ${k}_{\mathrm{cat}}$ ) of enzymes is used as a parameter to limit the reaction when extending GSMM. Therefore, turnover number plays a crucial role in the prediction accuracy of cell metabolism. In this work, we proposed an enzyme-constrained GSMM parameter optimization method. First, sensitivity analysis of the parameters was carried out to select the parameters with the greatest influence on predicting the specific growth rate. Then, differential evolution (DE) algorithm with adaptive mutation strategy was adopted to optimize the parameters. This algorithm can dynamically select five different mutation strategies. Finally, the specific growth rate prediction, flux variability, and phase plane of the optimized model were analyzed to further evaluate the model. The enzyme-constrained GSMM of Saccharomyces cerevisiae, ecYeast8.3.4, was optimized. Results of the sensitivity analysis showed that the optimization variables can be divided into three groups based on sensitivity: most sensitive (149 k cat ${k}_{\mathrm{cat}}$ c), highly sensitive (1759 k cat ${k}_{\mathrm{cat}}$ ), and nonsensitive (2502 k cat ${k}_{\mathrm{cat}}$ ) groups. Six optimization strategies were developed based on the results of the sensitivity analysis. The results showed that the DE with adaptive mutation strategy can indeed improve the model by optimizing highly sensitive parameters. Retaining all parameters and optimizing the highly sensitive parameters are the recommended optimization strategy.

Silk fibroin production in Escherichia coli is limited by a positive feedback loop between metabolic burden and toxicity stress

To investigate the metabolic elasticity and production bottlenecks for recombinant silk proteins in Escherichia coli, we performed a comprehensive characterization of one elastin-like peptide strain (ELP) and two silk protein strains (A5 4mer, A5 16mer). Our approach included ¹³C metabolic flux analysis, genome-scale modeling, transcription analysis, and ¹³C-assisted media optimization experiments. Three engineered strains maintained their central flux network during growth, while measurable metabolic flux redistributions (such as the Entner-Doudoroff pathway) were detected. Under metabolic burdens, the reduced TCA fluxes forced the engineered strain to rely more on substrate-level phosphorylation for ATP production, which increased acetate overflow. Acetate (as low as 10 mM) in the media was highly toxic to silk-producing strains, which reduced 4mer production by 43% and 16mer by 84%, respectively. Due to the high toxicity of large-size silk proteins, 16mer's productivity was limited, particularly in the minimal medium. Therefore, metabolic burden, overflow acetate, and toxicity of silk proteins may form a vicious positive feedback loop that fractures the metabolic network. Three solutions could be applied: 1) addition of building block supplements (i.e., eight key amino acids: His, Ile, Phe, Pro, Tyr, Lys, Met, Glu) to reduce metabolic burden; 2) disengagement of growth and production; and 3) use of non-glucose based substrate to reduce acetate overflow. Other reported strategies were also discussed in light of decoupling this positive feedback loop.

Reconstruction and Analysis of Thermodynamically Constrained Models Reveal Metabolic Responses of a Deep-Sea Bacterium to Temperature Perturbations

Microbial acclimation to different temperature conditions can involve broad changes in cell composition and metabolic efficiency. A systems-level view of these metabolic responses in nonmesophilic organisms, however, is currently missing. In this study, thermodynamically constrained genome-scale models were applied to simulate the metabolic responses of a deep-sea psychrophilic bacterium, Shewanella psychrophila WP2, under suboptimal (4°C), optimal (15°C), and supraoptimal (20°C) growth temperatures. The models were calibrated with experimentally determined growth rates of WP2. Gibbs free energy change of reactions (Δ_rG'), metabolic fluxes, and metabolite concentrations were predicted using random simulations to characterize temperature-dependent changes in the metabolism. The modeling revealed the highest metabolic efficiency at the optimal temperature, and it suggested distinct patterns of ATP production and consumption that could lead to lower metabolic efficiency under suboptimal or supraoptimal temperatures. The modeling also predicted rearrangement of fluxes through multiple metabolic pathways, including the glycolysis pathway, Entner-Doudoroff pathway, tricarboxylic acid (TCA) cycle, and electron transport system, and these predictions were corroborated through comparisons to WP2 transcriptomes. Furthermore, predictions of metabolite concentrations revealed the potential conservation of reducing equivalents and ATP in the suboptimal temperature, consistent with experimental observations from other psychrophiles. Taken together, the WP2 models provided mechanistic insights into the metabolism of a psychrophile in response to different temperatures. IMPORTANCE Metabolic flexibility is a central component of any organism's ability to survive and adapt to changes in environmental conditions. This study represents the first application of thermodynamically constrained genome-scale models in simulating the metabolic responses of a deep-sea psychrophilic bacterium to various temperatures. The models predicted differences in metabolic efficiency that were attributed to changes in metabolic pathway utilization and metabolite concentration during growth under optimal and nonoptimal temperatures. Experimental growth measurements were used for model calibration, and temperature-dependent transcriptomic changes corroborated the model-predicted rearrangement of metabolic fluxes. Overall, this study highlights the utility of modeling approaches in studying the temperature-driven metabolic responses of an extremophilic organism.

Integration of enzyme constraints in a genome-scale metabolic model of Aspergillus niger improves phenotype predictions

Background

Genome-scale metabolic model (GSMM) is a powerful tool for the study of cellular metabolic characteristics. With the development of multi-omics measurement techniques in recent years, new methods that integrating multi-omics data into the GSMM show promising effects on the predicted results. It does not only improve the accuracy of phenotype prediction but also enhances the reliability of the model for simulating complex biochemical phenomena, which can promote theoretical breakthroughs for specific gene target identification or better understanding the cell metabolism on the system level.

Results

Based on the basic GSMM model iHL1210 of Aspergillus niger, we integrated large-scale enzyme kinetics and proteomics data to establish a GSMM based on enzyme constraints, termed a GEM with Enzymatic Constraints using Kinetic and Omics data (GECKO). The results show that enzyme constraints effectively improve the model’s phenotype prediction ability, and extended the model’s potential to guide target gene identification through predicting metabolic phenotype changes of A. niger by simulating gene knockout. In addition, enzyme constraints significantly reduced the solution space of the model, i.e., flux variability over 40.10% metabolic reactions were significantly reduced. The new model showed also versatility in other aspects, like estimating large-scale \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{cat}}$$\end{document}kcat values, predicting the differential expression of enzymes under different growth conditions.

Conclusions

This study shows that incorporating enzymes’ abundance information into GSMM is very effective for improving model performance with A. niger. Enzyme-constrained model can be used as a powerful tool for predicting the metabolic phenotype of A. niger by incorporating proteome data. In the foreseeable future, with the fast development of measurement techniques, and more precise and rich proteomics quantitative data being obtained for A. niger, the enzyme-constrained GSMM model will show greater application space on the system level.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12934-021-01614-2.

Self-Organization and Information Processing: From Basic Enzymatic Activities to Complex Adaptive Cellular Behavior

One of the main aims of current biology is to understand the origin of the molecular organization that underlies the complex dynamic architecture of cellular life. Here, we present an overview of the main sources of biomolecular order and complexity spanning from the most elementary levels of molecular activity to the emergence of cellular systemic behaviors. First, we have addressed the dissipative self-organization, the principal source of molecular order in the cell. Intensive studies over the last four decades have demonstrated that self-organization is central to understand enzyme activity under cellular conditions, functional coordination between enzymatic reactions, the emergence of dissipative metabolic networks (DMN), and molecular rhythms. The second fundamental source of order is molecular information processing. Studies on effective connectivity based on transfer entropy (TE) have made possible the quantification in bits of biomolecular information flows in DMN. This information processing enables efficient self-regulatory control of metabolism. As a consequence of both main sources of order, systemic functional structures emerge in the cell; in fact, quantitative analyses with DMN have revealed that the basic units of life display a global enzymatic structure that seems to be an essential characteristic of the systemic functional metabolism. This global metabolic structure has been verified experimentally in both prokaryotic and eukaryotic cells. Here, we also discuss how the study of systemic DMN, using Artificial Intelligence and advanced tools of Statistic Mechanics, has shown the emergence of Hopfield-like dynamics characterized by exhibiting associative memory. We have recently confirmed this thesis by testing associative conditioning behavior in individual amoeba cells. In these Pavlovian-like experiments, several hundreds of cells could learn new systemic migratory behaviors and remember them over long periods relative to their cell cycle, forgetting them later. Such associative process seems to correspond to an epigenetic memory. The cellular capacity of learning new adaptive systemic behaviors represents a fundamental evolutionary mechanism for cell adaptation.

Acetate and glycerol are not uniquely suited for the evolution of cross-feeding in E. coli

The evolution of cross-feeding among individuals of the same species can help generate genetic and phenotypic diversity even in completely homogeneous environments. Cross-feeding Escherichia coli strains, where one strain feeds on a carbon source excreted by another strain, rapidly emerge during experimental evolution in a chemically minimal environment containing glucose as the sole carbon source. Genome-scale metabolic modeling predicts that cross-feeding of 58 carbon sources can emerge in the same environment, but only cross-feeding of acetate and glycerol has been experimentally observed. Here we use metabolic modeling to ask whether acetate and glycerol cross-feeding are especially likely to evolve, perhaps because they require less metabolic change, and thus perhaps also less genetic change than other cross-feeding interactions. However, this is not the case. The minimally required metabolic changes required for acetate and glycerol cross feeding affect dozens of chemical reactions, multiple biochemical pathways, as well as multiple operons or regulons. The complexity of these changes is consistent with experimental observations, where cross-feeding strains harbor multiple mutations. The required metabolic changes are also no less complex than those observed for multiple other of the 56 cross feeding interactions we study. We discuss possible reasons why only two cross-feeding interactions have been discovered during experimental evolution and argue that multiple new cross-feeding interactions may await discovery.

The evolution of cross-feeding interactions, where one organism thrives by consuming the excretions of others, can create diversity even in simple and homogeneous environments. In past work, we had predicted that 58 cross-feeding interactions could evolve in populations of E. coli grown in glucose minimal media, yet only two have been experimentally observed, those involving acetate and glycerol. We hypothesized that multiple mutations might be required for the evolution of computationally predicted but not experimentally observed cross-feeding interactions. To answer this question, we developed a method that searches for the minimal number of metabolic changes required for individuals to change their metabolic state (from an ancestral glucose-consuming state to an evolved state that produces or consumes other metabolite). We observed that the metabolic changes required for the evolution of acetate and glycerol cross-feeding are no less complex than those required for the evolution of the other predicted cross-feeding interactions, which suggests that multiple cross-feeding interactions may still await discovery.

Enhanced flux prediction by integrating relative expression and relative metabolite abundance into thermodynamically consistent metabolic models

The ever-increasing availability of transcriptomic and metabolomic data can be used to deeply analyze and make ever-expanding predictions about biological processes, as changes in the reaction fluxes through genome-wide pathways can now be tracked. Currently, constraint-based metabolic modeling approaches, such as flux balance analysis (FBA), can quantify metabolic fluxes and make steady-state flux predictions on a genome-wide scale using optimization principles. However, relating the differential gene expression or differential metabolite abundances in different physiological states to the differential flux profiles remains a challenge. Here we present a novel method, named REMI (Relative Expression and Metabolomic Integrations), that employs genome-scale metabolic models (GEMs) to translate differential gene expression and metabolite abundance data obtained through genetic or environmental perturbations into differential fluxes to analyze the altered physiology for any given pair of conditions. REMI allows for gene-expression, metabolite abundance, and thermodynamic data to be integrated into a single framework, then uses optimization principles to maximize the consistency between the differential gene-expression levels and metabolite abundance data and the estimated differential fluxes and thermodynamic constraints. We applied REMI to integrate into the Escherichia coli GEM publicly available sets of expression and metabolomic data obtained from two independent studies and under wide-ranging conditions. The differential flux distributions obtained from REMI corresponding to the various perturbations better agreed with the measured fluxomic data, and thus better reflected the different physiological states, than a traditional model. Compared to the similar alternative method that provides one solution from the solution space, REMI was able to enumerate several alternative flux profiles using a mixed-integer linear programming approach. Using this important advantage, we performed a high-frequency analysis of common genes and their associated reactions in the obtained alternative solutions and identified the most commonly regulated genes across any two given conditions. We illustrate that this new implementation provides more robust and biologically relevant results for a better understanding of the system physiology.

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.

Elements of the cellular metabolic structure

A large number of studies have demonstrated the existence of metabolic covalent modifications in different molecular structures, which are able to store biochemical information that is not encoded by DNA. Some of these covalent mark patterns can be transmitted across generations (epigenetic changes). Recently, the emergence of Hopfield-like attractor dynamics has been observed in self-organized enzymatic networks, which have the capacity to store functional catalytic patterns that can be correctly recovered by specific input stimuli. Hopfield-like metabolic dynamics are stable and can be maintained as a long-term biochemical memory. In addition, specific molecular information can be transferred from the functional dynamics of the metabolic networks to the enzymatic activity involved in covalent post-translational modulation, so that determined functional memory can be embedded in multiple stable molecular marks. The metabolic dynamics governed by Hopfield-type attractors (functional processes), as well as the enzymatic covalent modifications of specific molecules (structural dynamic processes) seem to represent the two stages of the dynamical memory of cellular metabolism (metabolic memory). Epigenetic processes appear to be the structural manifestation of this cellular metabolic memory. Here, a new framework for molecular information storage in the cell is presented, which is characterized by two functionally and molecularly interrelated systems: a dynamic, flexible and adaptive system (metabolic memory) and an essentially conservative system (genetic memory). The molecular information of both systems seems to coordinate the physiological development of the whole cell.

Predictive sulfur metabolism - a field in flux

The key role of sulfur metabolites in response to biotic and abiotic stress in plants, as well as their importance in diet and health has led to a significant interest and effort in trying to understand and manipulate the production of relevant compounds. Metabolic engineering utilizes a set of theoretical tools to help rationally design modifications that enhance the production of a desired metabolite. Such approaches have proven their value in bacterial systems, however, the paucity of success stories to date in plants, suggests that challenges remain. Here, we review the most commonly used methods for understanding metabolic flux, focusing on the sulfur assimilatory pathway. We highlight known issues with both experimental and theoretical approaches, as well as presenting recent methods for integrating different modeling strategies, and progress toward an understanding of flux at the whole plant level.