Principles of proteome allocation are revealed using proteomic data and genome-scale models

Bacterial cell size modulation along the growth curve across nutrient conditions

Under stable growth conditions, bacteria maintain cell size homeostasis through coordinated elongation and division. However, fluctuations in nutrient availability result in dynamic regulation of the target cell size. Using microscopy imaging and mathematical modelling, we examine how bacterial cell volume changes over the growth curve in response to nutrient conditions. We find that two rod-shaped bacteria, Escherichia coli and Salmonella enterica, exhibit similar cell volume distributions in stationary phase cultures irrespective of growth media. Cell resuspension in rich media results in a transient peak with a five-fold increase in cell volume ≈ 2h after resuspension. This maximum cell volume, which depends on nutrient composition, subsequently decreases to the stationary phase cell size. Continuous nutrient supply sustains the maximum volume. In poor nutrient conditions, cell volume shows minimal changes over the growth curve, but a markedly decreased cell width compared to other conditions. The observed cell volume dynamics translate into non-monotonic dynamics in the ratio between biomass (optical density) and cell number (colony-forming units), highlighting their non-linear relationship. Our findings support a heuristic model comparing modulation of cell division relative to growth across nutrient conditions and providing novel insight into the mechanisms of cell size control under dynamic environmental conditions.

Proteome allocation is linked to transcriptional regulation through a modularized transcriptome

It has proved challenging to quantitatively relate the proteome to the transcriptome on a per-gene basis. Recent advances in data analytics have enabled a biologically meaningful modularization of the bacterial transcriptome. We thus investigate whether matched datasets of transcriptomes and proteomes from bacteria under diverse conditions can be modularized in the same way to reveal novel relationships between their compositions. We find that; (1) the modules of the proteome and the transcriptome are comprised of a similar list of gene products, (2) the modules in the proteome often represent combinations of modules from the transcriptome, (3) known transcriptional and post-translational regulation is reflected in differences between two sets of modules, allowing for knowledge-mapping when interpreting module functions, and (4) through statistical modeling, absolute proteome allocation can be inferred from the transcriptome alone. Quantitative and knowledge-based relationships can thus be found at the genome-scale between the proteome and transcriptome in bacteria.

Resource allocation in mammalian systems

Cells execute biological functions to support phenotypes such as growth, migration, and secretion. Complementarily, each function of a cell has resource costs that constrain phenotype. Resource allocation by a cell allows it to manage these costs and optimize their phenotypes. In fact, the management of resource constraints (e.g., nutrient availability, bioenergetic capacity, and macromolecular machinery production) shape activity and ultimately impact phenotype. In mammalian systems, quantification of resource allocation provides important insights into higher-order multicellular functions; it shapes intercellular interactions and relays environmental cues for tissues to coordinate individual cells to overcome resource constraints and achieve population-level behavior. Furthermore, these constraints, objectives, and phenotypes are context-dependent, with cells adapting their behavior according to their microenvironment, resulting in distinct steady-states. This review will highlight the biological insights gained from probing resource allocation in mammalian cells and tissues.

StressME: Unified computing framework of Escherichia coli metabolism, gene expression, and stress responses

Generalist microbes have adapted to a multitude of environmental stresses through their integrated stress response system. Individual stress responses have been quantified by E. coli metabolism and expression (ME) models under thermal, oxidative and acid stress, respectively. However, the systematic quantification of cross-stress & cross-talk among these stress responses remains lacking. Here, we present StressME: the unified stress response model of E. coli combining thermal (FoldME), oxidative (OxidizeME) and acid (AcidifyME) stress responses. StressME is the most up to date ME model for E. coli and it reproduces all published single-stress ME models. Additionally, it includes refined rate constants to improve prediction accuracy for wild-type and stress-evolved strains. StressME revealed certain optimal proteome allocation strategies associated with cross-stress and cross-talk responses. These stress-optimal proteomes were shaped by trade-offs between protective vs. metabolic enzymes; cytoplasmic vs. periplasmic chaperones; and expression of stress-specific proteins. As StressME is tuned to compute metabolic and gene expression responses under mild acid, oxidative, and thermal stresses, it is useful for engineering and health applications. The modular design of our open-source package also facilitates model expansion (e.g., to new stress mechanisms) by the computational biology community.

Proteome allocation is linked to transcriptional regulation through a modularized transcriptome

It has proved challenging to quantitatively relate the proteome to the transcriptome on a per-gene basis. Recent advances in data analytics have enabled a biologically meaningful modularization of the bacterial transcriptome. We thus investigated whether matched datasets of transcriptomes and proteomes from bacteria under diverse conditions could be modularized in the same way to reveal novel relationships between their compositions. We found that; 1) the modules of the proteome and the transcriptome are comprised of a similar list of gene products, 2) the modules in the proteome often represent combinations of modules from the transcriptome, 3) known transcriptional and post-translational regulation is reflected in differences between two sets of modules, allowing for knowledge-mapping when interpreting module functions, and 4) through statistical modeling, absolute proteome allocation can be inferred from the transcriptome alone. Quantitative and knowledge-based relationships can thus be found at the genome-scale between the proteome and transcriptome in bacteria.

Reconstruction of a catalogue of genome-scale metabolic models with enzymatic constraints using GECKO 2.0

Genome-scale metabolic models (GEMs) have been widely used for quantitative exploration of the relation between genotype and phenotype. Streamlined integration of enzyme constraints and proteomics data into such models was first enabled by the GECKO toolbox, allowing the study of phenotypes constrained by protein limitations. Here, we upgrade the toolbox in order to enhance models with enzyme and proteomics constraints for any organism with a compatible GEM reconstruction. With this, enzyme-constrained models for the budding yeasts Saccharomyces cerevisiae, Yarrowia lipolytica and Kluyveromyces marxianus are generated to study their long-term adaptation to several stress factors by incorporation of proteomics data. Predictions reveal that upregulation and high saturation of enzymes in amino acid metabolism are common across organisms and conditions, suggesting the relevance of metabolic robustness in contrast to optimal protein utilization as a cellular objective for microbial growth under stress and nutrient-limited conditions. The functionality of GECKO is expanded with an automated framework for continuous and version-controlled update of enzyme-constrained GEMs, also producing such models for Escherichia coli and Homo sapiens. In this work, we facilitate the utilization of enzyme-constrained GEMs in basic science, metabolic engineering and synthetic biology purposes.

Global pleiotropic effects in adaptively evolved Escherichia coli lacking CRP reveal molecular mechanisms that define the growth physiology

Evolution facilitates emergence of fitter phenotypes by efficient allocation of cellular resources in conjunction with beneficial mutations. However, system-wide pleiotropic effects that redress the perturbations to the apex node of the transcriptional regulatory networks remain unclear. Here, we elucidate that absence of global transcriptional regulator CRP in Escherichia coli results in alterations in key metabolic pathways under glucose respiratory conditions, favouring stress- or hedging-related functions over growth-enhancing functions. Further, we disentangle the growth-mediated effects from the CRP regulation-specific effects on these metabolic pathways. We quantitatively illustrate that the loss of CRP perturbs proteome efficiency, as evident from metabolic as well as ribosomal proteome fractions, that corroborated with intracellular metabolite profiles. To address how E. coli copes with such systemic defect, we evolved Δcrp mutant in the presence of glucose. Besides acquiring mutations in the promoter of glucose transporter ptsG, the evolved populations recovered the metabolic pathways to their pre-perturbed state coupled with metabolite re-adjustments, which altogether enabled increased growth. By contrast to Δcrp mutant, the evolved strains remodelled their proteome efficiency towards biomass synthesis, albeit at the expense of carbon efficiency. Overall, we comprehensively illustrate the genetic and metabolic basis of pleiotropic effects, fundamental for understanding the growth physiology.

A Model of Synovial Fluid with a Hyaluronic Acid Source: A Numerical Challenge

Initially motivated by the analysis of the flow dynamics of the synovial fluid, taken as non-Newtonian, this paper also reports on a numerical challenge which occurred unexpectedly while solving the momentum equation of the model. The configuration consists of two infinitely long horizontal parallel flat plates where the top plate is sheared at constant speed and the bottom plate is fixed. The synovial fluid shows a shear-thinning rheology, and furthermore it thickens with the hyaluronic acid (HA) concentration, i.e., it is also chemically-thickening. Accordingly, a modified Cross model is employed to express the shear rate and concentration-dependent viscosity, whose parameter values are determined from experimental data. Another significance of the study is the investigation of the effect of an external stimulus on the flow dynamics via a HA source term. The resulting flow exhibits peculiar features resulting from extremely large and small, but positive, numerical quantities, such as the viscosity and the shear rates. This requires constructing a parametrized zero-machine level solver, up to 300 accurate digits or so, for capturing the correct length scales of the flow physics. As a conclusion, the physical model, although simple, but original, leads to interesting results whose numerical determination turns out to be successful only once the real cause of the numerical trap is identified.

Proteome Regulation Patterns Determine Escherichia coli Wild-Type and Mutant Phenotypes

It is generally recognized that proteins constitute the key cellular component in shaping microbial phenotypes. Due to limited cellular resources and space, optimal allocation of proteins is crucial for microbes to facilitate maximum proliferation rates while allowing a flexible response to environmental changes. To account for the growth condition-dependent proteome in the constraint-based metabolic modeling of Escherichia coli, we consolidated a coarse-grained protein allocation approach with the explicit consideration of enzymatic constraints on reaction fluxes. Besides representing physiologically relevant wild-type phenotypes and flux distributions, the resulting protein allocation model (PAM) advances the predictability of the metabolic responses to genetic perturbations. A main driver of mutant phenotypes was ascribed to inherited regulation patterns in protein distribution among metabolic enzymes. Moreover, the PAM correctly reflected metabolic responses to an augmented protein burden imposed by the heterologous expression of green fluorescent protein. In summary, we were able to model the effects of important and frequently applied metabolic engineering approaches on microbial metabolism. Therefore, we want to promote the integration of protein allocation constraints into classical constraint-based models to foster their predictive capabilities and application for strain analysis and engineering purposes.

IMPORTANCE Predictive metabolic models are important, e.g., for generating biological knowledge and designing microbes with superior performance for target compound production. Yet today’s whole-cell models either show insufficient predictive capabilities or are computationally too expensive to be applied to metabolic engineering purposes. By linking the inherent genotype-phenotype relationship to a complete representation of the proteome, the PAM advances the accuracy of simulated phenotypes and intracellular flux distributions of E. coli. Being equally computationally lightweight as classical stoichiometric models and allowing for the application of established in silico tools, the PAM and related simulation approaches will foster the use of a model-driven metabolic research. Applications range from the investigation of mechanisms of microbial evolution to the determination of optimal strain design strategies in metabolic engineering, thus supporting basic scientists and engineers alike.

Synthesizing Systems Biology Knowledge from Omics Using Genome-Scale Models

Omic technologies have enabled the complete readout of the molecular state of a cell at different biological scales. In principle, the combination of multiple omic data types can provide an integrated view of the entire biological system. This integration requires appropriate models in a systems biology approach. Here, genome-scale models (GEMs) are focused upon as one computational systems biology approach for interpreting and integrating multi-omic data. GEMs convert the reactions (related to metabolism, transcription, and translation) that occur in an organism to a mathematical formulation that can be modeled using optimization principles. A variety of genome-scale modeling methods used to interpret multiple omic data types, including genomics, transcriptomics, proteomics, metabolomics, and meta-omics are reviewed. The ability to interpret omics in the context of biological systems has yielded important findings for human health, environmental biotechnology, bioenergy, and metabolic engineering. The authors find that concurrent with advancements in omic technologies, genome-scale modeling methods are also expanding to enable better interpretation of omic data. Therefore, continued synthesis of valuable knowledge, through the integration of omic data with GEMs, are expected.

Metabolic Modelling as a Framework for Metabolomics Data Integration and Analysis

Metabolic networks are regulated to ensure the dynamic adaptation of biochemical reaction fluxes to maintain cell homeostasis and optimal metabolic fitness in response to endogenous and exogenous perturbations. To this end, metabolism is tightly controlled by dynamic and intricate regulatory mechanisms involving allostery, enzyme abundance and post-translational modifications. The study of the molecular entities involved in these complex mechanisms has been boosted by the advent of high-throughput technologies. The so-called omics enable the quantification of the different molecular entities at different system layers, connecting the genotype with the phenotype. Therefore, the study of the overall behavior of a metabolic network and the omics data integration and analysis must be approached from a holistic perspective. Due to the close relationship between metabolism and cellular phenotype, metabolic modelling has emerged as a valuable tool to decipher the underlying mechanisms governing cell phenotype. Constraint-based modelling and kinetic modelling are among the most widely used methods to study cell metabolism at different scales, ranging from cells to tissues and organisms. These approaches enable integrating metabolomic data, among others, to enhance model predictive capabilities. In this review, we describe the current state of the art in metabolic modelling and discuss future perspectives and current challenges in the field.

A quantitative method for proteome reallocation using minimal regulatory interventions

Engineering resource allocation in biological systems is an ongoing challenge. Organisms allocate resources for ensuring survival, reducing the productivity of synthetic biology functions. Here we present a new approach for engineering the resource allocation of Escherichia coli by rationally modifying its transcriptional regulatory network. Our method (ReProMin) identifies the minimal set of genetic interventions that maximizes the savings in cell resources. To this end, we categorized transcription factors according to the essentiality of its targets and we used proteomic data to rank them. We designed the combinatorial removal of transcription factors that maximize the release of resources. Our resulting strain containing only three mutations, theoretically releasing 0.5% of its proteome, had higher proteome budget, increased production of an engineered metabolic pathway and showed that the regulatory interventions are highly specific. This approach shows that combining proteomic and regulatory data is an effective way of optimizing strains using conventional molecular methods.

Genome-scale model of metabolism and gene expression provides a multi-scale description of acid stress responses in Escherichia coli

Response to acid stress is critical for Escherichia coli to successfully complete its life-cycle by passing through the stomach to colonize the digestive tract. To develop a fundamental understanding of this response, we established a molecular mechanistic description of acid stress mitigation responses in E. coli and integrated them with a genome-scale model of its metabolism and macromolecular expression (ME-model). We considered three known mechanisms of acid stress mitigation: 1) change in membrane lipid fatty acid composition, 2) change in periplasmic protein stability over external pH and periplasmic chaperone protection mechanisms, and 3) change in the activities of membrane proteins. After integrating these mechanisms into an established ME-model, we could simulate their responses in the context of other cellular processes. We validated these simulations using RNA sequencing data obtained from five E. coli strains grown under external pH ranging from 5.5 to 7.0. We found: i) that for the differentially expressed genes accounted for in the ME-model, 80% of the upregulated genes were correctly predicted by the ME-model, and ii) that these genes are mainly involved in translation processes (45% of genes), membrane proteins and related processes (18% of genes), amino acid metabolism (12% of genes), and cofactor and prosthetic group biosynthesis (8% of genes). We also demonstrated several intervention strategies on acid tolerance that can be simulated by the ME-model. We thus established a quantitative framework that describes, on a genome-scale, the acid stress mitigation response of E. coli that has both scientific and practical uses.

Basics of genome-scale metabolic modeling and applications on C1-utilization

It is fundamental to understand the relationship between genotype and phenotype in biology. This requires comprehensive knowledge of metabolic pathways, genetic information and well-defined mathematic modeling. Integration of knowledge on metabolism with mathematical modeling results in genome-scale metabolic models which have proven useful to investigate bacterial metabolism and to engineer bacterial strains capable of producing value-added biochemical. Single carbon substrates such as methane and carbon monoxide have drawn interests and they assumed one of next-generation feedstocks because of their high abundance and low price. The methylotroph and acetogen-based biorefineries hold promises for bioconversion of C1 substrates into biofuels and high value compounds. As an effort on expanding our knowledge on C1 utilization approaches, in silico computational framework of C1-metabolism in methylotrophic and acetogenic bacteria has been developed. In this review, genome-scale metabolic models for C1-utilizing bacteria and well-established analysis tools are presented for potential uses for study of C1 metabolism at the genome scale and its application in metabolic engineering.

Machine and deep learning meet genome-scale metabolic modeling

Omic data analysis is steadily growing as a driver of basic and applied molecular biology research. Core to the interpretation of complex and heterogeneous biological phenotypes are computational approaches in the fields of statistics and machine learning. In parallel, constraint-based metabolic modeling has established itself as the main tool to investigate large-scale relationships between genotype, phenotype, and environment. The development and application of these methodological frameworks have occurred independently for the most part, whereas the potential of their integration for biological, biomedical, and biotechnological research is less known. Here, we describe how machine learning and constraint-based modeling can be combined, reviewing recent works at the intersection of both domains and discussing the mathematical and practical aspects involved. We overlap systematic classifications from both frameworks, making them accessible to nonexperts. Finally, we delineate potential future scenarios, propose new joint theoretical frameworks, and suggest concrete points of investigation for this joint subfield. A multiview approach merging experimental and knowledge-driven omic data through machine learning methods can incorporate key mechanistic information in an otherwise biologically-agnostic learning process.

DynamicME: dynamic simulation and refinement of integrated models of metabolism and protein expression

BACKGROUND

Genome-scale models of metabolism and macromolecular expression (ME models) enable systems-level computation of proteome allocation coupled to metabolic phenotype.

RESULTS

We develop DynamicME, an algorithm enabling time-course simulation of cell metabolism and protein expression. DynamicME correctly predicted the substrate utilization hierarchy on a mixed carbon substrate medium. We also found good agreement between predicted and measured time-course expression profiles. ME models involve considerably more parameters than metabolic models (M models). We thus generate an ensemble of models (each model having its rate constants perturbed), and then analyze the models by identifying archetypal time-course metabolite concentration profiles. Furthermore, we use a metaheuristic optimization method to calibrate ME model parameters using time-course measurements such as from a (fed-) batch culture. Finally, we show that constraints on protein concentration dynamics ("inertia") alter the metabolic response to environmental fluctuations, including increased substrate-level phosphorylation and lowered oxidative phosphorylation.

CONCLUSIONS

Overall, DynamicME provides a novel method for understanding proteome allocation and metabolism under complex and transient environments, and to utilize time-course cell culture data for model-based interpretation or model refinement.

Formation of dominant mode by evolution in biological systems

A reduction in high-dimensional phenotypic states to a few degrees of freedom is essential to understand biological systems. Here, we show evolutionary robustness causes such reduction which restricts possible phenotypic changes in response to a variety of environmental conditions. First, global protein expression changes in Escherichia coli after various environmental perturbations were shown to be proportional across components, across different types of environmental conditions. To examine if such dimension reduction is a result of evolution, we analyzed a cell model-with a huge number of components, that reproduces itself via a catalytic reaction network-and confirmed that common proportionality in the concentrations of all components is shaped through evolutionary processes. We found that the changes in concentration across all components in response to environmental and evolutionary changes are constrained to the changes along a one-dimensional major axis, within a huge-dimensional state space. On the basis of these observations, we propose a theory in which such constraints in phenotypic changes are achieved both by evolutionary robustness and plasticity and formulate this proposition in terms of dynamical systems. Accordingly, broad experimental and numerical results on phenotypic changes caused by evolution and adaptation are coherently explained.

Modeling the multi-scale mechanisms of macromolecular resource allocation

As microbes face changing environments, they dynamically allocate macromolecular resources to produce a particular phenotypic state. Broad 'omics' data sets have revealed several interesting phenomena regarding how the proteome is allocated under differing conditions, but the functional consequences of these states and how they are achieved remain open questions. Various types of multi-scale mathematical models have been used to elucidate the genetic basis for systems-level adaptations. In this review, we outline several different strategies by which microbes accomplish resource allocation and detail how mathematical models have aided in our understanding of these processes. Ultimately, such modeling efforts have helped elucidate the principles of proteome allocation and hold promise for further discovery.

Cellular trade-offs and optimal resource allocation during cyanobacterial diurnal growth

Cyanobacteria are an integral part of Earth's biogeochemical cycles and a promising resource for the synthesis of renewable bioproducts from atmospheric CO₂ Growth and metabolism of cyanobacteria are inherently tied to the diurnal rhythm of light availability. As yet, however, insight into the stoichiometric and energetic constraints of cyanobacterial diurnal growth is limited. Here, we develop a computational framework to investigate the optimal allocation of cellular resources during diurnal phototrophic growth using a genome-scale metabolic reconstruction of the cyanobacterium Synechococcus elongatus PCC 7942. We formulate phototrophic growth as an autocatalytic process and solve the resulting time-dependent resource allocation problem using constraint-based analysis. Based on a narrow and well-defined set of parameters, our approach results in an ab initio prediction of growth properties over a full diurnal cycle. The computational model allows us to study the optimality of metabolite partitioning during diurnal growth. The cyclic pattern of glycogen accumulation, an emergent property of the model, has timing characteristics that are in qualitative agreement with experimental findings. The approach presented here provides insight into the time-dependent resource allocation problem of phototrophic diurnal growth and may serve as a general framework to assess the optimality of metabolic strategies that evolved in phototrophic organisms under diurnal conditions.

Bacterial persistence from a system-level perspective

In recent years, our understanding about bacterial persistence has significantly advanced: we comprehend the persister phenotype better, more triggers for persistence entry have been found, and more insights in the involvement and role of toxin-antitoxin systems and other molecular mechanisms have been unravelled. In this review, we attempt to put these findings into an integrated, system-level perspective. From this point of view, persistence can be seen as a response to a strong perturbation of metabolic homeostasis, either triggered environmentally, or by means of intracellular stochasticity. Metabolic-flux-regulated resource allocation ensures stress protection, and several feedback mechanisms stabilize the cells in this protected state. We hope that this novel view can advance our understanding about persistence.