Multidimensional optimality of microbial metabolism

Free-energy transduction mechanisms shape the flux space of metabolic networks

The transduction of free energy in metabolic networks represents a thermodynamic mechanism by which the free energy derived from nutrients is converted to drive nonspontaneous, energy-requiring metabolic reactions. This transduction is typically observed in processes that generate energy-rich molecules such as ATP and NAD(P)H, which, in turn, power specific reactions, particularly biosynthetic reactions. This property establishes a pivotal connection between the intricate topology of metabolic networks and their ability to redirect energy for functional purposes. The present study proposes a dedicated framework aimed at exploring the relationship between free-energy dissipation, network topology, and metabolic objectives. The starting point is that, regardless of the network topology, nonequilibrium chemostatting conditions impose stringent thermodynamic constraints on the feasible flux steady states to satisfy energy and entropy balances. An analysis of randomly sampled reaction networks shows that the network topology imposes additional constraints that restrict the accessible flux solution space, depending on key structural features such as the reaction's molecularity, reaction cycles, and conservation laws. Notably, topologies featuring multimolecular reactions that implement free-energy transduction mechanisms tend to extend the accessible flux domains, facilitating the achievement of metabolic objectives such as anabolic flux maximization or flux rerouting capacity. This approach is applied to a coarse-grained model of carbohydrate metabolism, highlighting the structural requirements for optimal biomass yield.

Optimal performance objectives in the highly conserved bone morphogenetic protein signaling pathway

Throughout development, complex networks of cell signaling pathways drive cellular decision-making across different tissues and contexts. The transforming growth factor β (TGF-β) pathways, including the BMP/Smad pathway, play crucial roles in determining cellular responses. However, as the Smad pathway is used reiteratively throughout the life cycle of all animals, its systems-level behavior varies from one context to another, despite the pathway connectivity remaining nearly constant. For instance, some cellular systems require a rapid response, while others require high noise filtering. In this paper, we examine how the BMP-Smad pathway balances trade-offs among three such systems-level behaviors, or "Performance Objectives (POs)": response speed, noise amplification, and the sensitivity of pathway output to receptor input. Using a Smad pathway model fit to human cell data, we show that varying non-conserved parameters (NCPs) such as protein concentrations, the Smad pathway can be tuned to emphasize any of the three POs and that the concentration of nuclear phosphatase has the greatest effect on tuning the POs. However, due to competition among the POs, the pathway cannot simultaneously optimize all three, but at best must balance trade-offs among the POs. We applied the multi-objective optimization concept of the Pareto Front, a widely used concept in economics to identify optimal trade-offs among various requirements. We show that the BMP pathway efficiently balances competing POs across species and is largely Pareto optimal. Our findings reveal that varying the concentration of NCPs allows the Smad signaling pathway to generate a diverse range of POs. This insight identifies how signaling pathways can be optimally tuned for each context.

A hierarchy of metabolite exchanges in metabolic models of microbial species and communities

The metabolic network of an organism can be analyzed as a constraint-based model. This analysis can be biased, optimizing an objective such as growth rate, or unbiased, aiming to describe the full feasible space of metabolic fluxes through pathway analysis or random flux sampling. In particular, pathway analysis can decompose the flux space into fundamental and formally defined metabolic pathways. Unbiased methods scale poorly with network size due to combinatorial explosion, but a promising approach to improve scalability is to focus on metabolic subnetworks, e.g., cells' metabolite exchanges with each other and the environment, rather than the full metabolic networks. Here, we applied pathway enumeration and flux sampling to metabolite exchanges in microbial species and a microbial community, using models ranging from central carbon metabolism to genome-scale and focusing on pathway definitions that allow direct targeting of subnetworks such as metabolite exchanges (elementary conversion modes, elementary flux patterns, and minimal pathways). Enumerating growth-supporting metabolite exchanges, we found that metabolite exchanges from different pathway definitions were related through a hierarchy, and we show that this hierarchical relationship between pathways holds for metabolic networks and subnetworks more generally. Metabolite exchange frequencies, defined as the fraction of pathways in which each metabolite was exchanged, were similar across pathway definitions, with a few specific exchanges explaining large differences in pathway counts. This indicates that biological interpretation of predicted metabolite exchanges is robust to the choice of pathway definition, and it suggests strategies for more scalable pathway analysis. Our results also signal wider biological implications, facilitating detailed and interpretable analysis of metabolite exchanges and other subnetworks in fields such as metabolic engineering and synthetic biology.

Cell Geometry and Membrane Protein Crowding Constrain Growth Rate, Overflow Metabolism, Respiration, and Maintenance Energy

A metabolic theory is presented for predicting maximum growth rate, overflow metabolism, respiration efficiency, and maintenance energy flux based on the intersection of cell geometry, membrane protein crowding, and metabolism. The importance of cytosolic macromolecular crowding on phenotype has been established in the literature but the importance of surface area has been largely overlooked due to incomplete knowledge of membrane properties. We demonstrate that the capacity of the membrane to host proteins increases with growth rate offsetting decreases in surface area-to-volume ratios (SA:V). This increase in membrane protein is hypothesized to be essential to competitive Escherichia coli phenotypes. The presented membrane-centric theory uses biophysical properties and metabolic systems analysis to successfully predict the phenotypes of E. coli K-12 strains, MG1655 and NCM3722, which are genetically similar but have SA:V ratios that differ up to 30%, maximum growth rates on glucose media that differ by 40%, and overflow phenotypes that start at growth rates that differ by 80%. These analyses did not consider cytosolic macromolecular crowding, highlighting the distinct properties of the presented theory. Cell geometry and membrane protein crowding are significant biophysical constraints on phenotype and provide a theoretical framework for improved understanding and control of cell biology.

A global view of T cell metabolism in systemic lupus erythematosus

Impaired metabolism is recognized as an important contributor to pathogenicity of T cells in Systemic Lupus Erythematosus (SLE). Over the last two decades, we have acquired significant knowledge about the signaling and transcriptomic programs related to metabolic rewiring in healthy and SLE T cells. However, our understanding of metabolic network activity derives largely from studying metabolic pathways in isolation. Here, we argue that enzymatic activities are necessarily coupled through mass and energy balance constraints with in-built network-wide dependencies and compensation mechanisms. Therefore, metabolic rewiring of T cells in SLE must be understood in the context of the entire network, including changes in metabolic demands such as shifts in biomass composition and cytokine secretion rates as well as changes in uptake/excretion rates of multiple nutrients and waste products. As a way forward, we suggest cell physiology experiments and integration of orthogonal metabolic measurements through computational modeling towards a comprehensive understanding of T cell metabolism in lupus.

Models and molecular mechanisms for trade-offs in the context of metabolism

Accumulating evidence for trade-offs involving metabolic traits has demonstrated their importance in the evolution of organisms. Metabolic models with different levels of complexity have already been considered when investigating mechanisms that explain various metabolic trade-offs. Here we provide a systematic review of modelling approaches that have been used to study and explain trade-offs between: (i) the kinetic properties of individual enzymes, (ii) rates of metabolic reactions, (iii) the rate and yield of metabolic pathways and networks, (iv) different metabolic objectives in single organisms and in metabolic communities, and (v) metabolic concentrations. In providing insights into the mechanisms underlying these five types of metabolic trade-offs obtained from constraint-based metabolic modelling, we emphasize the relationship of metabolic trade-offs to the classical black box Y-model that provides a conceptual explanation for resource acquisition-allocation trade-offs. In addition, we identify several pressing concerns and offer a perspective for future research in the identification and manipulation of metabolic trade-offs by relying on the toolbox provided by constraint-based metabolic modelling for single organisms and microbial communities.

Integration of graph neural networks and genome-scale metabolic models for predicting gene essentiality

Genome-scale metabolic models are powerful tools for understanding cellular physiology. Flux balance analysis (FBA), in particular, is an optimization-based approach widely employed for predicting metabolic phenotypes. In model microbes such as Escherichia coli, FBA has been successful at predicting essential genes, i.e. those genes that impair survival when deleted. A central assumption in this approach is that both wild type and deletion strains optimize the same fitness objective. Although the optimality assumption may hold for the wild type metabolic network, deletion strains are not subject to the same evolutionary pressures and knock-out mutants may steer their metabolism to meet other objectives for survival. Here, we present FlowGAT, a hybrid FBA-machine learning strategy for predicting essentiality directly from wild type metabolic phenotypes. The approach is based on graph-structured representation of metabolic fluxes predicted by FBA, where nodes correspond to enzymatic reactions and edges quantify the propagation of metabolite mass flow between a reaction and its neighbours. We integrate this information into a graph neural network that can be trained on knock-out fitness assay data. Comparisons across different model architectures reveal that FlowGAT predictions for E. coli are close to those of FBA for several growth conditions. This suggests that essentiality of enzymatic genes can be predicted by exploiting the inherent network structure of metabolism. Our approach demonstrates the benefits of combining the mechanistic insights afforded by genome-scale models with the ability of deep learning to infer patterns from complex datasets.

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.

Tracking alternative versions of the galactose gene network in the genus Saccharomyces and their expansion after domestication

When Saccharomyces cerevisiae grows on mixtures of glucose and galactose, galactose utilization is repressed by glucose, and induction of the GAL gene network only occurs when glucose is exhausted. Contrary to reference GAL alleles, alternative alleles support faster growth on galactose, thus enabling distinct galactose utilization strategies maintained by balancing selection. Here, we report on new wild populations of Saccharomyces cerevisiae harboring alternative GAL versions and, for the first time, of Saccharomyces paradoxus alternative alleles. We also show that the non-functional GAL version found earlier in Saccharomyces kudriavzevii is phylogenetically related to the alternative versions, which constitutes a case of trans-specific maintenance of highly divergent alleles. Strains harboring the different GAL network variants show different levels of alleviation of glucose repression and growth proficiency on galactose. We propose that domestication involved specialization toward thriving in milk from a generalist ancestor partially adapted to galactose consumption in the plant niche.

Optimal enzyme profiles in unbranched metabolic pathways

How to optimize the allocation of enzymes in metabolic pathways has been a topic of study for many decades. Although the general problem is complex and nonlinear, we have previously shown that it can be solved by convex optimization. In this paper, we focus on unbranched metabolic pathways with simplified enzymatic rate laws and derive analytic solutions to the optimization problem. We revisit existing solutions based on the limit of mass-action rate laws and present new solutions for other rate laws. Furthermore, we revisit a known relationship between flux control coefficients and enzyme abundances in optimal metabolic states. We generalize this relationship to models with density constraints on enzymes and metabolites, and present a new local relationship between optimal reaction elasticities and enzyme amounts. Finally, we apply our theory to derive simple kinetics-based formulae for protein allocation during bacterial growth.

Optimal Performance Objectives in the Highly Conserved Bone Morphogenetic Protein Signaling Pathway

Throughout development, complex networks of cell signaling pathways drive cellular decision-making across different tissues and contexts. The transforming growth factor β (TGF-β) pathways, including the BMP/Smad pathway, play crucial roles in these cellular responses. However, as the Smad pathway is used reiteratively throughout the life cycle of all animals, its systems-level behavior varies from one context to another, despite the pathway connectivity remaining nearly constant. For instance, some cellular systems require a rapid response, while others require high noise filtering. In this paper, we examine how the BMP- Smad pathway balances trade-offs among three such systems-level behaviors, or "Performance Objectives (POs)": response speed, noise amplification, and the sensitivity of pathway output to receptor input. Using a Smad pathway model fit to human cell data, we show that varying non-conserved parameters (NCPs) such as protein concentrations, the Smad pathway can be tuned to emphasize any of the three POs and that the concentration of nuclear phosphatase has the greatest effect on tuning the POs. However, due to competition among the POs, the pathway cannot simultaneously optimize all three, but at best must balance trade-offs among the POs. We applied the multi-objective optimization concept of the Pareto Front, a widely used concept in economics to identify optimal trade-offs among various requirements. We show that the BMP pathway efficiently balances competing POs across species and is largely Pareto optimal. Our findings reveal that varying the concentration of NCPs allows the Smad signaling pathway to generate a diverse range of POs. This insight identifies how signaling pathways can be optimally tuned for each context.

Performance and robustness analysis reveals phenotypic trade-offs in yeast

To design strains that can function efficiently in complex industrial settings, it is crucial to consider their robustness, that is, the stability of their performance when faced with perturbations. In the present study, we cultivated 24 Saccharomyces cerevisiae strains under conditions that simulated perturbations encountered during lignocellulosic bioethanol production, and assessed the performance and robustness of multiple phenotypes simultaneously. The observed negative correlations confirmed a trade-off between performance and robustness of ethanol yield, biomass yield, and cell dry weight. Conversely, the specific growth rate performance positively correlated with the robustness, presumably because of evolutionary selection for robust, fast-growing cells. The Ethanol Red strain exhibited both high performance and robustness, making it a good candidate for bioproduction in the tested perturbation space. Our results experimentally map the robustness-performance trade-offs, previously demonstrated mainly by single-phenotype and computational studies.

Improving microbial bioproduction under low-oxygen conditions

Microbial bioconversion provides access to a wide range of sustainably produced chemicals and commodities. However, industrial-scale bioproduction process operations are preferred to be anaerobic due to the cost associated with oxygen transfer. Anaerobic bioconversion generally offers limited substrate utilization profiles, lower product yields, and reduced final product diversity compared with aerobic processes. Bioproduction under conditions of reduced oxygen can overcome the limitations of fully aerobic and anaerobic bioprocesses, but many microbial hosts are not developed for low-oxygen bioproduction. Here, we describe advances in microbial strain engineering involving the use of redox cofactor engineering, genome-scale metabolic modeling, and functional genomics to enable improved bioproduction processes under low oxygen and provide a viable path for scaling these bioproduction systems to industrial scales.

Unveiling abundance-dependent metabolic phenotypes of microbial communities

IMPORTANCE

In nature, organisms live in communities and not as isolated species, and their interactions provide a source of resilience to environmental disturbances. Despite their importance in ecology, human health, and industry, understanding how organisms interact in different environments remains an open question. In this work, we provide a novel approach that, only using genomic information, studies the metabolic phenotype exhibited by communities, where the exploration of suboptimal growth flux distributions and the composition of a community allows to unveil its capacity to respond to environmental changes, shedding light of the degrees of metabolic plasticity inherent to the community.

Conditionally unutilized proteins and their profound effects on growth and adaptation across microbial species

Protein synthesis is an important determinant of microbial growth and response that demands a high amount of metabolic and biosynthetic resources. Despite these costs, microbial species from different taxa and habitats massively synthesize proteins that are not utilized in the conditions they currently experience. Based on resource allocation models, recent studies have begun to reconcile the costs and benefits of these conditionally unutilized proteins (CUPs) in the context of varying environmental conditions. Such massive synthesis of CUPs is crucial to consider in different areas of modern microbiology, from the systematic investigation of cell physiology, via the prediction of evolution in laboratory and natural environments, to the rational design of strains in biotechnology applications.

Local flux coordination and global gene expression regulation in metabolic modeling

Genome-scale metabolic networks (GSMs) are fundamental systems biology representations of a cell's entire set of stoichiometrically balanced reactions. However, such static GSMs do not incorporate the functional organization of metabolic genes and their dynamic regulation (e.g., operons and regulons). Specifically, there are numerous topologically coupled local reactions through which fluxes are coordinated; the global growth state often dynamically regulates many gene expression of metabolic reactions via global transcription factor regulators. Here, we develop a GSM reconstruction method, Decrem, by integrating locally coupled reactions and global transcriptional regulation of metabolism by cell state. Decrem produces predictions of flux and growth rates, which are highly correlated with those experimentally measured in both wild-type and mutants of three model microorganisms Escherichia coli, Saccharomyces cerevisiae, and Bacillus subtilis under various conditions. More importantly, Decrem can also explain the observed growth rates by capturing the experimentally measured flux changes between wild-types and mutants. Overall, by identifying and incorporating locally organized and regulated functional modules into GSMs, Decrem achieves accurate predictions of phenotypes and has broad applications in bioengineering, synthetic biology, and microbial pathology.

The Architecture of Metabolic Networks Constrains the Evolution of Microbial Resource Hierarchies

Microbial strategies for resource use are an essential determinant of their fitness in complex habitats. When facing environments with multiple nutrients, microbes often use them sequentially according to a preference hierarchy, resulting in well-known patterns of diauxic growth. In theory, the evolutionary diversification of metabolic hierarchies could represent a mechanism supporting coexistence and biodiversity by enabling temporal segregation of niches. Despite this ecologically critical role, the extent to which substrate preference hierarchies can evolve and diversify remains largely unexplored. Here, we used genome-scale metabolic modeling to systematically explore the evolution of metabolic hierarchies across a vast space of metabolic network genotypes. We find that only a limited number of metabolic hierarchies can readily evolve, corresponding to the most commonly observed hierarchies in genome-derived models. We further show how the evolution of novel hierarchies is constrained by the architecture of central metabolism, which determines both the propensity to change ranks between pairs of substrates and the effect of specific reactions on hierarchy evolution. Our analysis sheds light on the genetic and mechanistic determinants of microbial metabolic hierarchies, opening new research avenues to understand their evolution, evolvability, and ecology.

Uses of Multi-Objective Flux Analysis for Optimization of Microbial Production of Secondary Metabolites

Secondary metabolites are not essential for the growth of microorganisms, but they play a critical role in how microbes interact with their surroundings. In addition to this important ecological role, secondary metabolites also have a variety of agricultural, medicinal, and industrial uses, and thus the examination of secondary metabolism of plants and microbes is a growing scientific field. While the chemical production of certain secondary metabolites is possible, industrial-scale microbial production is a green and economically attractive alternative. This is even more true, given the advances in bioengineering that allow us to alter the workings of microbes in order to increase their production of compounds of interest. This type of engineering requires detailed knowledge of the "chassis" organism's metabolism. Since the resources and the catalytic capacity of enzymes in microbes is finite, it is important to examine the tradeoffs between various bioprocesses in an engineered system and alter its working in a manner that minimally perturbs the robustness of the system while allowing for the maximum production of a product of interest. The in silico multi-objective analysis of metabolism using genome-scale models is an ideal method for such examinations.

Long-term history dependence of growth rates of E. coli after nutrient shifts

According to a widely accepted paradigm of microbiology, steady-state growth rates are determined solely by current growth conditions1-3 and adaptations between growth states are rapid, as recently recapitulated by simple resource allocation models4. However, even in microbes overlapping regulatory networks can yield multi-stability or long-term cellular memory. Species like Listeria monocytogenes5 and Bacillus subtilis "distinguish" distinct histories for the commitment to sporulation6, but it is unclear if these states can persist over many generations. Remarkably, studying carbon co-utilization of Escherichia coli, we found that growth rates on combinations of carbon sources can depend critically on the previous growth condition. Growing in identical conditions, we observed differences in growth rates of up to 25% and we did not observe convergence of growth rates over 15 generations. We observed this phenomenon occurs across combinations of different phosphotransferase (PTS) substrates with various gluconeogenic carbon sources and found it to depend on the transcription factor Mlc.

A genome-scale dynamic constraint-based modelling (gDCBM) framework predicts growth dynamics, medium composition and intracellular flux distributions in CHO clonal variations

Optimizing mammalian cell growth and bioproduction is a tedious task. However, due to the inherent complexity of eukaryotic cells, heuristic experimental approaches such as, metabolic engineering and bioprocess design, are frequently integrated with mathematical models of cell culture to improve biological process efficiency and find paths for improvement. Constraint-based metabolic models have evolved over the last two decades to be used for dynamic modelling in addition to providing a linear description of steady-state metabolic systems. Formulation and implementation of the underlying optimization problems require special attention to the model's performance and feasibility, lack of defects in the definition of system components, and consideration of optimal alternate solutions, in addition to processing power limitations. Here, the time-resolved dynamics of a genome-scale metabolic network of Chinese hamster ovary (CHO) cell metabolism are shown using a genome-scale dynamic constraint-based modelling framework (gDCBM). The metabolic network was adapted from a reference model of CHO genome-scale metabolic model (GSMM), iCHO_DG44_v1, and dynamic restrictions were imposed to its exchange fluxes based on experimental results. We used this framework for predicting physiological changes in CHO clonal variants. Because of the methodical creation of the components for the flux balance analysis optimization problem and the integration of a switch time, this model can generate sequential predictions of intracellular fluxes during growth and non-growth phases (per hour of culture time) and transparently reveal the shortcomings in such practice. As a result of the differences exploited by various clones, we can understand the relevance of changes in intracellular flux distribution and exometabolomics. The integration of various omics data into the given gDCBM framework, as well as the reductionist analysis of the model, can further help bioprocess optimization.

More is Different: Metabolic Modeling of Diverse Microbial Communities

Microbial consortia drive essential processes, ranging from nitrogen fixation in soils to providing metabolic breakdown products to animal hosts. However, it is challenging to translate the composition of microbial consortia into their emergent functional capacities. Community-scale metabolic models hold the potential to simulate the outputs of complex microbial communities in a given environmental context, but there is currently no consensus for what the fitness function of an entire community should look like in the presence of ecological interactions and whether community-wide growth operates close to a maximum. Transitioning from single-taxon genome-scale metabolic models to multitaxon models implies a growth cone without a well-specified growth rate solution for individual taxa. Here, we argue that dynamic approaches naturally overcome these limitations, but they come at the cost of being computationally expensive. Furthermore, we show how two nondynamic, steady-state approaches approximate dynamic trajectories and pick ecologically relevant solutions from the community growth cone with improved computational scalability.

Parameter Identification in Metabolic Reaction Networks by Means of Multiple Steady-State Measurements

In this work, we investigate some theoretical aspects related to the estimation approach proposed by Liebermeister and Klipp, 2006, in which general rate laws, derived from standardized enzymatic mechanisms, are exploited to kinetically describe the fluxes of a metabolic reaction network, and multiple metabolic steady-state measurements are exploited to estimate the unknown kinetic parameters. Further mathematical details are deeply investigated, and necessary conditions on the amount of information required to solve the identification problem are given. Moreover, theoretical results for the parameter identifiability are provided, and symmetrical and modular properties of the proposed approach are highlighted when the global identification problem is decoupled into smaller and simpler identification problems related to the single reactions of the network. Among the advantages of the proposed innovative approach are (i) non-restrictive conditions to guarantee the solvability of the parameter estimation problem, (ii) the unburden of the usual computational complexity for such identification problems, and (iii) the ease of obtaining the required number of measurements, which are actually steady-state data, experimentally easier to obtain with respect to the time-dependent ones. A simple example concludes the paper, highlighting the mentioned advantages of the method and the implementation of the related theoretical result.

Modeling the metabolic dynamics at the genome-scale by optimized yield analysis

The hybrid cybernetic model (HCM) approach is a dynamic modeling framework that integrates enzyme synthesis and activity regulation. It has been widely applied in bioreaction engineering, particularly in the simulation of microbial growth in different mixtures of carbon sources. In a HCM, the metabolic network is decomposed into elementary flux modes (EFMs), whereby the network can be reduced into a few pathways by yield analysis. However, applying the HCM approach on conventional genome-scale metabolic models (GEMs) is still a challenge due to the high computational demands. Here, we present a HCM strategy that introduced an optimized yield analysis algorithm (opt-yield-FBA) to simulate metabolic dynamics at the genome-scale without the need for EFMs calculation. The opt-yield-FBA is a flux-balance analysis (FBA) based method that can calculate optimal yield solutions and yield space for GEM. With the opt-yield-FBA algorithm, the HCM strategy can be applied to get the yield spaces and avoid the computational burden of EFMs, and it can therefore be applied for developing dynamic models for genome-scale metabolic networks. Here, we illustrate the strategy by applying the concept to simulate the dynamics of microbial communities.

Coordination of CcpA and CodY Regulators in Staphylococcus aureus USA300 Strains

The complex cross talk between metabolism and gene regulatory networks makes it difficult to untangle individual constituents and study their precise roles and interactions. To address this issue, we modularized the transcriptional regulatory network (TRN) of the Staphylococcus aureus USA300 strain by applying independent component analysis (ICA) to 385 RNA sequencing samples. We then combined the modular TRN model with a metabolic model to study the regulation of carbon and amino acid metabolism. Our analysis showed that regulation of central carbon metabolism by CcpA and amino acid biosynthesis by CodY are closely coordinated. In general, S. aureus increases the expression of CodY-regulated genes in the presence of preferred carbon sources such as glucose. This transcriptional coordination was corroborated by metabolic model simulations that also showed increased amino acid biosynthesis in the presence of glucose. Further, we found that CodY and CcpA cooperatively regulate the expression of ribosome hibernation-promoting factor, thus linking metabolic cues with translation. In line with this hypothesis, expression of CodY-regulated genes is tightly correlated with expression of genes encoding ribosomal proteins. Together, we propose a coarse-grained model where expression of S. aureus genes encoding enzymes that control carbon flux and nitrogen flux through the system is coregulated with expression of translation machinery to modularly control protein synthesis. While this work focuses on three key regulators, the full TRN model we present contains 76 total independently modulated sets of genes, each with the potential to uncover other complex regulatory structures and interactions. IMPORTANCE Staphylococcus aureus is a versatile pathogen with an expanding antibiotic resistance profile. The biology underlying its clinical success emerges from an interplay of many systems such as metabolism and gene regulatory networks. This work brings together models for these two systems to establish fundamental principles governing the regulation of S. aureus central metabolism and protein synthesis. Studies of these fundamental biological principles are often confined to model organisms such as Escherichia coli. However, expanding these models to pathogens can provide a framework from which complex and clinically important phenotypes such as virulence and antibiotic resistance can be better understood. Additionally, the expanded gene regulatory network model presented here can deconvolute the biology underlying other important phenotypes in this pathogen.

Amino acid variability, tradeoffs and optimality in human diet

Studies at the molecular level demonstrate that dietary amino acid intake produces substantial effects on health and disease by modulating metabolism. However, how these effects may manifest in human food consumption and dietary patterns is unknown. Here, we develop a series of algorithms to map, characterize and model the landscape of amino acid content in human food, dietary patterns, and individual consumption including relations to health status, covering over 2,000 foods, ten dietary patterns, and over 30,000 dietary profiles. We find that the type of amino acids contained in foods and human consumption is highly dynamic with variability far exceeding that of fat and carbohydrate. Some amino acids positively associate with conditions such as obesity while others contained in the same food negatively link to disease. Using linear programming and machine learning, we show that these health trade-offs can be accounted for to satisfy biochemical constraints in food and human eating patterns to construct a Pareto front in dietary practice, a means of achieving optimality in the face of trade-offs that are commonly considered in economic and evolutionary theories. Thus this study may enable the design of human protein quality intake guidelines based on a quantitative framework.

Optimal transcriptional regulation of dynamic bacterial responses to sudden drug exposures

Cellular responses to the presence of toxic compounds in their environment require prompt expression of the correct levels of the appropriate enzymes, which are typically regulated by transcription factors that control gene expression for the duration of the response. The characteristics of each response dictate the choice of regulatory parameters such as the affinity of the transcription factor to its binding sites and the strength of the promoters it regulates. Although much is known about the dynamics of cellular responses, we still lack a framework to understand how different regulatory strategies evolved in natural systems relate to the selective pressures acting in each particular case. Here, we analyze a dynamical model of a typical antibiotic response in bacteria, where a transcriptionally repressed enzyme is induced by a sudden exposure to the drug that it processes. We identify strategies of gene regulation that optimize this response for different types of selective pressures, which we define as a set of costs associated with the drug, enzyme, and repressor concentrations during the response. We find that regulation happens in a limited region of the regulatory parameter space. While responses to more costly (toxic) drugs favor the usage of strongly self-regulated repressors, responses where expression of enzyme is more costly favor the usage of constitutively expressed repressors. Only a very narrow range of selective pressures favor weakly self-regulated repressors. We use this framework to determine which costs and benefits are most critical for the evolution of a variety of natural cellular responses that satisfy the approximations in our model and to analyze how regulation is optimized in new environments with different demands.

Colicins of Escherichia coli Lead to Resistance against the Diarrhea-Causing Pathogen Enterotoxigenic E. coli in Pigs

Gut microbes can affect host adaptation to various environment conditions. Escherichia coli is a common gut species, including pathogenic strains and nonpathogenic strains. This study was conducted to investigate the effects of different E. coli strains in the gut on the health of pigs. In this study, the complete genomes of two E. coli strains isolated from pigs were sequenced. The whole genomes of Y18J and the enterotoxigenic E. coli strain W25K were compared to determine their roles in pig adaptation to disease. Y18J was isolated from feces of healthy piglets and showed strong antimicrobial activity against W25K in vitro. Gene knockout experiments and complementation analysis followed by modeling the microbe-microbe interactions demonstrated that the antagonistic mechanism of Y18J against W25K relied on the bacteriocins colicin B and colicin M. Compared to W25K, Y18J is devoid of exotoxin-coding genes and has more secondary-metabolite-biosynthetic gene clusters. W25K carries more genes involved in genome replication, in accordance with a shorter cell cycle observed during a growth experiment. The analysis of gut metagenomes in different pig breeds showed that colicins B and M were enriched in Laiwu pigs, a Chinese local breed, but were scarce in boars and Duroc pigs. IMPORTANCE This study revealed the heterogeneity of E. coli strains from pigs, including two strains studied by both in silico and wet experiments in detail and 14 strains studied by bioinformatics analysis. E. coli Y18J may improve the adaptability of pigs toward disease resistance through the production of colicins B and M. Our findings could shed light on the pathogenic and harmless roles of E. coli in modern animal husbandry, leading to a better understanding of intestinal-microbe-pathogen interactions in the course of evolution.

Cooperative stability renders protein complex formation more robust and controllable

Protein complexes are the fundamental units of many biological functions. Despite their many advantages, one major adverse impact of protein complexes is accumulations of unassembled subunits that may disrupt other processes or exert cytotoxic effects. Synthesis of excess subunits can be inhibited via negative feedback control or they can be degraded more efficiently than assembled subunits, with this latter being termed cooperative stability. Whereas controlled synthesis of complex subunits has been investigated extensively, how cooperative stability acts in complex formation remains largely unexplored. To fill this knowledge gap, we have built quantitative models of heteromeric complexes with or without cooperative stability and compared their behaviours in the presence of synthesis rate variations. A system displaying cooperative stability is robust against synthesis rate variations as it retains high dimer/monomer ratios across a broad range of parameter configurations. Moreover, cooperative stability can alleviate the constraint of limited supply of a given subunit and makes complex abundance more responsive to unilateral upregulation of another subunit. We also conducted an in silico experiment to comprehensively characterize and compare four types of circuits that incorporate combinations of negative feedback control and cooperative stability in terms of eight systems characteristics pertaining to optimality, robustness and controllability. Intriguingly, though individual circuits prevailed for distinct characteristics, the system with cooperative stability alone achieved the most balanced performance across all characteristics. Our study provides theoretical justification for the contribution of cooperative stability to natural biological systems and represents a guideline for designing synthetic complex formation systems with desirable characteristics.

Trade-offs predicted by metabolic network structure give rise to evolutionary specialization and phenotypic diversification

Mitigating trade-offs between different resource-utilization functions is key to an organism's ecological and evolutionary success. These trade-offs often reflect metabolic constraints with a complex molecular underpinning; therefore, their consequences for evolutionary processes have remained elusive. Here, we investigate how metabolic architecture induces resource utilization constraints and how these constraints, in turn, elicit evolutionary specialization and diversification. Guided by the metabolic network structure of the bacterium Lactococcus cremoris, we selected two carbon sources (fructose and galactose) with predicted co-utilization constraints. By evolving L. cremoris on either fructose, galactose or a mix of both sugars, we imposed selection favoring divergent metabolic specializations or co-utilization of both resources, respectively. Phenotypic characterization revealed the evolution of either fructose or galactose specialists in the single-sugar treatments. In the mixed sugar regime, we observed adaptive diversification: both specialists coexisted, and no generalist evolved. Divergence from the ancestral phenotype occurred at key pathway junctions in the central carbon metabolism. Fructose specialists evolved mutations in the fbp and pfk genes that appear to balance anabolic and catabolic carbon fluxes. Galactose specialists evolved increased expression of pgmA (the primary metabolic bottleneck of galactose metabolism) and silencing of ptnABCD (the main glucose transporter) and ldh (regulator/enzyme of downstream carbon metabolism). Overall, our study shows how metabolic network architecture and historical contingency serve to predict targets of selection and inform the functional interpretation of evolved mutations. The elucidation of the relationship between molecular constraints and phenotypic trade-offs contributes to an integrative understanding of evolutionary specialization and diversification.

OptDesign: Identifying Optimum Design Strategies in Strain Engineering for Biochemical Production

Computational tools have been widely adopted for strain optimization in metabolic engineering, contributing to numerous success stories of producing industrially relevant biochemicals. However, most of these tools focus on single metabolic intervention strategies (either gene/reaction knockout or amplification alone) and rely on hypothetical optimality principles (e.g., maximization of growth) and precise gene expression (e.g., fold changes) for phenotype prediction. This paper introduces OptDesign, a new two-step strain design strategy. In the first step, OptDesign selects regulation candidates that have a noticeable flux difference between the wild type and production strains. In the second step, it computes optimal design strategies with limited manipulations (combining regulation and knockout), leading to high biochemical production. The usefulness and capabilities of OptDesign are demonstrated for the production of three biochemicals in Escherichia coli using the latest genome-scale metabolic model iML1515, showing highly consistent results with previous studies while suggesting new manipulations to boost strain performance. The source code is available at https://github.com/chang88ye/OptDesign.

Protein cost minimization promotes the emergence of coenzyme redundancy

Metabolism relies on a small class of molecules (coenzymes) that serve as universal donors and acceptors of key chemical groups and electrons. Although metabolic networks crucially depend on structurally redundant coenzymes [e.g., NAD(H) and NADP(H)] associated with different enzymes, the criteria that led to the emergence of this redundancy remain poorly understood. Our combination of modeling and structural and sequence analysis indicates that coenzyme redundancy may not be essential for metabolism but could rather constitute an evolved strategy promoting efficient usage of enzymes when biochemical reactions are near equilibrium. Our work suggests that early metabolism may have operated with fewer coenzymes and that adaptation for metabolic efficiency may have driven the rise of coenzyme diversity in living systems.

Coenzymes distribute a variety of chemical moieties throughout cellular metabolism, participating in group (e.g., phosphate and acyl) and electron transfer. For a variety of reactions requiring acceptors or donors of specific resources, there often exist degenerate sets of molecules [e.g., NAD(H) and NADP(H)] that carry out similar functions. Although the physiological roles of various coenzyme systems are well established, it is unclear what selective pressures may have driven the emergence of coenzyme redundancy. Here, we use genome-wide metabolic modeling approaches to decompose the selective pressures driving enzymatic specificity for either NAD(H) or NADP(H) in the metabolic network of Escherichia coli. We found that few enzymes are thermodynamically constrained to using a single coenzyme, and in principle a metabolic network relying on only NAD(H) is feasible. However, structural and sequence analyses revealed widespread conservation of residues that retain selectivity for either NAD(H) or NADP(H), suggesting that additional forces may shape specificity. Using a model accounting for the cost of oxidoreductase enzyme expression, we found that coenzyme redundancy universally reduces the minimal amount of protein required to catalyze coenzyme-coupled reactions, inducing individual reactions to strongly prefer one coenzyme over another when reactions are near thermodynamic equilibrium. We propose that protein minimization generically promotes coenzyme redundancy and that coenzymes typically thought to exist in a single pool (e.g., coenzyme A [CoA]) may exist in more than one form (e.g., dephospho-CoA).

Quantitative metabolic fluxes regulated by trans-omic networks

Cells change their metabolism in response to internal and external conditions by regulating the trans-omic network, which is a global biochemical network with multiple omic layers. Metabolic flux is a direct measure of the activity of a metabolic reaction that provides valuable information for understanding complex trans-omic networks. Over the past decades, techniques to determine metabolic fluxes, including 13C-metabolic flux analysis (13C-MFA), flux balance analysis (FBA), and kinetic modeling, have been developed. Recent studies that acquire quantitative metabolic flux and multi-omic data have greatly advanced the quantitative understanding and prediction of metabolism-centric trans-omic networks. In this review, we present an overview of 13C-MFA, FBA, and kinetic modeling as the main techniques to determine quantitative metabolic fluxes, and discuss their advantages and disadvantages. We also introduce case studies with the aim of understanding complex metabolism-centric trans-omic networks based on the determination of metabolic fluxes.

Pinpointing Cancer Sub-Type Specific Metabolic Tasks Facilitates Identification of Anti-cancer Targets

Metabolic reprogramming is one of the hallmarks of tumorigenesis. Understanding the metabolic changes in cancer cells may provide attractive therapeutic targets and new strategies for cancer therapy. The metabolic states are not the same in different cancer types or subtypes, even within the same sample of solid tumors. In order to understand the heterogeneity of cancer cells, we used the Pareto tasks inference method to analyze the metabolic tasks of different cancers, including breast cancer, lung cancer, digestive organ cancer, digestive tract cancer, and reproductive cancer. We found that cancer subtypes haves different propensities toward metabolic tasks, and the biological significance of these metabolic tasks also varies greatly. Normal cells treat metabolic tasks uniformly, while different cancer cells focus on different pathways. We then integrated the metabolic tasks into the multi-objective genome-scale metabolic network model, which shows higher accuracy in the in silico prediction of cell states after gene knockout than the conventional biomass maximization model. The predicted potential single drug targets could potentially turn into biomarkers or drug design targets. We further implemented the multi-objective genome-scale metabolic network model to predict synthetic lethal target pairs of the Basal and Luminal B subtypes of breast cancer. By analyzing the predicted synthetic lethal targets, we found that mitochondrial enzymes are potential targets for drug combinations. Our study quantitatively analyzes the metabolic tasks of cancer and establishes cancer type-specific metabolic models, which opens a new window for the development of specific anti-cancer drugs and provides promising treatment plans for specific cancer subtypes.

Metabolic signatures of regulation by phosphorylation and acetylation

Acetylation and phosphorylation are highly conserved posttranslational modifications (PTMs) that regulate cellular metabolism, yet how metabolic control is shared between these PTMs is unknown. Here we analyze transcriptome, proteome, acetylome, and phosphoproteome datasets in E. coli, S. cerevisiae, and mammalian cells across diverse conditions using CAROM, a new approach that uses genome-scale metabolic networks and machine learning to classify targets of PTMs. We built a single machine learning model that predicted targets of each PTM in a condition across all three organisms based on reaction attributes (AUC>0.8). Our model predicted phosphorylated enzymes during a mammalian cell-cycle, which we validate using phosphoproteomics. Interpreting the machine learning model using game theory uncovered enzyme properties including network connectivity, essentiality, and condition-specific factors such as maximum flux that differentiate targets of phosphorylation from acetylation. The conserved and predictable partitioning of metabolic regulation identified here between these PTMs may enable rational rewiring of regulatory circuits.

Identification of flux trade-offs in metabolic networks

Trade-offs are inherent to biochemical networks governing diverse cellular functions, from gene expression to metabolism. Yet, trade-offs between fluxes of biochemical reactions in a metabolic network have not been formally studied. Here, we introduce the concept of absolute flux trade-offs and devise a constraint-based approach, termed FluTO, to identify and enumerate flux trade-offs in a given genome-scale metabolic network. By employing the metabolic networks of Escherichia coli and Saccharomyces cerevisiae, we demonstrate that the flux trade-offs are specific to carbon sources provided but that reactions involved in the cofactor and prosthetic group biosynthesis are present in trade-offs across all carbon sources supporting growth. We also show that absolute flux trade-offs depend on the biomass reaction used to model the growth of Arabidopsis thaliana under different carbon and nitrogen conditions. The identified flux trade-offs reflect the tight coupling between nitrogen, carbon, and sulphur metabolisms in leaves of C₃ plants. Altogether, FluTO provides the means to explore the space of alternative metabolic routes reflecting the constraints imposed by inherent flux trade-offs in large-scale metabolic networks.

Multiple functions of flagellar motility and chemotaxis in bacterial physiology

Most swimming bacteria are capable of following gradients of nutrients, signaling molecules and other environmental factors that affect bacterial physiology. This tactic behavior became one of the most-studied model systems for signal transduction and quantitative biology, and underlying molecular mechanisms are well characterized in Escherichia coli and several other model bacteria. In this review, we focus primarily on less understood aspect of bacterial chemotaxis, namely its physiological relevance for individual bacterial cells and for bacterial populations. As evident from multiple recent studies, even for the same bacterial species flagellar motility and chemotaxis might serve multiple roles, depending on the physiological and environmental conditions. Among these, finding sources of nutrients and more generally locating niches that are optimal for growth appear to be one of the major functions of bacterial chemotaxis, which could explain many chemoeffector preferences as well as flagellar gene regulation. Chemotaxis might also generally enhance efficiency of environmental colonization by motile bacteria, which involves intricate interplay between individual and collective behaviors and trade-offs between growth and motility. Finally, motility and chemotaxis play multiple roles in collective behaviors of bacteria including swarming, biofilm formation and autoaggregation, as well as in their interactions with animal and plant hosts.

Modeling Drosophila gut microbe interactions reveals metabolic interconnectivity

We know a lot about varying gut microbiome compositions. Yet, how the bacteria affect each other remains elusive. In mammals, this is largely based on the sheer complexity of the microbiome with at least hundreds of different species. Thus, model organisms such as Drosophila melanogaster are commonly used to investigate mechanistic questions as the microbiome consists of only about 10 leading bacterial species. Here, we isolated gut bacteria from laboratory-reared Drosophila, sequenced their respective genomes, and used this information to reconstruct genome-scale metabolic models. With these, we simulated growth in mono- and co-culture conditions and different media including a synthetic diet designed to grow Drosophila melanogaster. Our simulations reveal a synergistic growth of some but not all gut microbiome members, which stems on the exchange of distinct metabolites including tricarboxylic acid cycle intermediates. Culturing experiments confirmed our predictions. Our study thus demonstrates the possibility to predict microbiome-derived growth-promoting cross-feeding.

Learning Extremal Representations with Deep Archetypal Analysis

Archetypes represent extreme manifestations of a population with respect to specific characteristic traits or features. In linear feature space, archetypes approximate the data convex hull allowing all data points to be expressed as convex mixtures of archetypes. As mixing of archetypes is performed directly on the input data, linear Archetypal Analysis requires additivity of the input, which is a strong assumption unlikely to hold e.g. in case of image data. To address this problem, we propose learning an appropriate latent feature space while simultaneously identifying suitable archetypes. We thus introduce a generative formulation of the linear archetype model, parameterized by neural networks. By introducing the distance-dependent archetype loss, the linear archetype model can be integrated into the latent space of a deep variational information bottleneck and an optimal representation, together with the archetypes, can be learned end-to-end. Moreover, the information bottleneck framework allows for a natural incorporation of arbitrarily complex side information during training. As a consequence, learned archetypes become easily interpretable as they derive their meaning directly from the included side information. Applicability of the proposed method is demonstrated by exploring archetypes of female facial expressions while using multi-rater based emotion scores of these expressions as side information. A second application illustrates the exploration of the chemical space of small organic molecules. By using different kinds of side information we demonstrate how identified archetypes, along with their interpretation, largely depend on the side information provided.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11263-020-01390-3.

Discovering Essential Multiple Gene Effects Through Large Scale Optimization: An Application to Human Cancer Metabolism

Computational modelling of metabolic processes has proven to be a useful approach to formulate our knowledge and improve our understanding of core biochemical systems that are crucial to maintaining cellular functions. Towards understanding the broader role of metabolism on cellular decision-making in health and disease conditions, it is important to integrate the study of metabolism with other core regulatory systems and omics within the cell, including gene expression patterns. After quantitatively integrating gene expression profiles with a genome-scale reconstruction of human metabolism, we propose a set of combinatorial methods to reverse engineer gene expression profiles and to find pairs and higher-order combinations of genetic modifications that simultaneously optimize multi-objective cellular goals. This enables us to suggest classes of transcriptomic profiles that are most suitable to achieve given metabolic phenotypes. We demonstrate how our techniques are able to compute beneficial, neutral or "toxic" combinations of gene expression levels. We test our methods on nine tissue-specific cancer models, comparing our outcomes with the corresponding normal cells, identifying genes as targets for potential therapies. Our methods open the way to a broad class of applications that require an understanding of the interplay among genotype, metabolism, and cellular behaviour, at scale.

Microeconomics of Metabolism: The Warburg Effect as Giffen Behaviour

Metabolic behaviours of proliferating cells are often explained as a consequence of rational optimization of cellular growth rate, whereas microeconomics formulates consumption behaviours as optimization problems. Here, we pushed beyond the analogy to precisely map metabolism onto the theory of consumer choice. We thereby revealed the correspondence between long-standing mysteries in both fields: the Warburg effect, a seemingly wasteful but ubiquitous strategy where cells favour aerobic glycolysis over more energetically efficient oxidative phosphorylation, and Giffen behaviour, the unexpected consumer behaviour where a good is demanded more as its price rises. We identified the minimal, universal requirements for the Warburg effect: a trade-off between oxidative phosphorylation and aerobic glycolysis and complementarity, i.e. impossibility of substitution for different metabolites. Thus, various hypotheses for the Warburg effect are integrated into an identical optimization problem with the same universal structure. Besides, the correspondence between the Warburg effect and Giffen behaviour implies that oxidative phosphorylation is counter-intuitively stimulated when its efficiency is decreased by metabolic perturbations such as drug administration or mitochondrial dysfunction; the concept of Giffen behaviour bridges the Warburg effect and the reverse Warburg effect. This highlights that the application of microeconomics to metabolism can offer new predictions and paradigms for both biology and economics.

Intelligent host engineering for metabolic flux optimisation in biotechnology

Optimising the function of a protein of length N amino acids by directed evolution involves navigating a 'search space' of possible sequences of some 20N. Optimising the expression levels of P proteins that materially affect host performance, each of which might also take 20 (logarithmically spaced) values, implies a similar search space of 20P. In this combinatorial sense, then, the problems of directed protein evolution and of host engineering are broadly equivalent. In practice, however, they have different means for avoiding the inevitable difficulties of implementation. The spare capacity exhibited in metabolic networks implies that host engineering may admit substantial increases in flux to targets of interest. Thus, we rehearse the relevant issues for those wishing to understand and exploit those modern genome-wide host engineering tools and thinking that have been designed and developed to optimise fluxes towards desirable products in biotechnological processes, with a focus on microbial systems. The aim throughput is 'making such biology predictable'. Strategies have been aimed at both transcription and translation, especially for regulatory processes that can affect multiple targets. However, because there is a limit on how much protein a cell can produce, increasing kcat in selected targets may be a better strategy than increasing protein expression levels for optimal host engineering.

Importance of the biomass formulation for cancer metabolic modeling and drug prediction

Genome-scale metabolic reconstructions include all known biochemical reactions occurring in a cell. A typical application is the prediction of potential drug targets for cancer treatment. The precision of these predictions relies on the definition of the objective function. Generally, the biomass reaction is used to illustrate the growth capacity of a cancer cell. Today, seven human biomass reactions can be identified in published metabolic models. The impact of these differences on the metabolic model predictions has not been explored in detail. We explored this impact on cancer metabolic model predictions and showed that the metabolite composition and the associated coefficients had a large impact on the growth rate prediction accuracy, whereas gene essentiality predictions were mainly affected by the metabolite composition. Our results demonstrate the importance of defining a consensus biomass reaction compatible with most human models, which would contribute to ensuring the reproducibility and consistency of the results.

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The definition of the biomass reaction is of utmost importance for model predictions

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Growth rate predictions are affected by metabolite composition and their coefficients

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Gene essentiality predictions are mainly affected by the metabolite composition

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Need to find a standard biomass reaction for reproducibility and consistency purposes

Retinoic Acid Fluctuation Activates an Uneven, Direction-Dependent Network-Wide Robustness Response in Early Embryogenesis

Robustness is a feature of regulatory pathways to ensure signal consistency in light of environmental changes or genetic polymorphisms. The retinoic acid (RA) pathway, is a central developmental and tissue homeostasis regulatory signal, strongly dependent on nutritional sources of retinoids and affected by environmental chemicals. This pathway is characterized by multiple proteins or enzymes capable of performing each step and their integration into a self-regulating network. We studied RA network robustness by transient physiological RA signaling disturbances followed by kinetic transcriptomic analysis of the recovery during embryogenesis. The RA metabolic network was identified as the main regulated module to achieve signaling robustness using an unbiased pattern analysis. We describe the network-wide responses to RA signal manipulation and found the feedback autoregulation to be sensitive to the direction of the RA perturbation: RA knockdown exhibited an upper response limit, whereas RA addition had a minimal feedback-activation threshold. Surprisingly, our robustness response analysis suggests that the RA metabolic network regulation exhibits a multi-objective optimization, known as Pareto optimization, characterized by trade-offs between competing functionalities. We observe that efficient robustness to increasing RA is accompanied by worsening robustness to reduced RA levels and vice versa. This direction-dependent trade-off in the network-wide feedback response, results in an uneven robustness capacity of the RA network during early embryogenesis, likely a significant contributor to the manifestation of developmental defects.

A morphospace of functional configuration to assess configural breadth based on brain functional networks

The quantification of human brain functional (re)configurations across varying cognitive demands remains an unresolved topic. We propose that such functional configurations may be categorized into three different types: (a) network configural breadth, (b) task-to task transitional reconfiguration, and (c) within-task reconfiguration. Such functional reconfigurations are rather subtle at the whole-brain level. Hence, we propose a mesoscopic framework focused on functional networks (FNs) or communities to quantify functional (re)configurations. To do so, we introduce a 2D network morphospace that relies on two novel mesoscopic metrics, trapping efficiency (TE) and exit entropy (EE), which capture topology and integration of information within and between a reference set of FNs. We use this framework to quantify the network configural breadth across different tasks. We show that the metrics defining this morphospace can differentiate FNs, cognitive tasks, and subjects. We also show that network configural breadth significantly predicts behavioral measures, such as episodic memory, verbal episodic memory, fluid intelligence, and general intelligence. In essence, we put forth a framework to explore the cognitive space in a comprehensive manner, for each individual separately, and at different levels of granularity. This tool that can also quantify the FN reconfigurations that result from the brain switching between mental states.

Enhancing in silico strain design predictions through next generation metabolic modeling approaches

The reconstruction and analysis of metabolic models has garnered increasing attention due to the multitude of applications in which these have proven to be practical. The growing number of generated metabolic models has been accompanied by an exponentially expanding arsenal of tools used to analyze them. In this work, we discussed the biological relevance of a number of promising modeling frameworks, focusing on the questions and hypotheses each method is equipped to address. To this end, we critically analyzed the steady-state modeling approaches focusing on resource allocation and incorporation of thermodynamic considerations which produce promising results and aid in the generation and experimental validation of numerous predictions. For smaller networks involving more complex regulation, we addressed kinetic modeling techniques which show encouraging results in addressing questions outside the scope of steady-state modeling. Finally, we discussed the potential application of the discussed frameworks within the field of strain design. Adoption of such methodologies is believed to significantly enhance the accuracy of in silico predictions and hence decrease the number of design-build-test cycles required.

Picking the right metaphors for addressing microbial systems: economic theory helps understanding biological complexity

Any descriptive language is necessarily metaphoric and interpretative. Two somewhat overlapping-but not identical-languages have been thoroughly employed in the last decade to address the issue of regulatory complexity in biological systems: the terminology of network theory and the jargon of electric circuitry. These approaches have found many formal equivalences between the layout of extant genetic circuits and the architecture of man-made counterparts. However, these languages still fail to describe accurately key features of biological objects, in particular the diversity of signal-transfer molecules and the diffusion that is inherent to any biochemical system. Furthermore, current formalisms associated with networks and circuits can hardly face the problem of multi-scale regulatory complexity-from single molecules to entire ecosystems. We argue that the language of economic theory might be instrumental not only to portray accurately many features of regulatory networks, but also to unveil aspects of the biological complexity problem that remain opaque to other types of analyses. The main perspective opened by the economic metaphor when applied to control of microbiological activities is a focus on metabolism, not gene selfishness, as the necessary background to make sense of regulatory phenomena. As an example, we analyse and reinterpret the widespread phenomenon of catabolite repression with the formal frame of the consumer's choice theory.

Pareto optimality between growth-rate and lag-time couples metabolic noise to phenotypic heterogeneity in Escherichia coli

Despite mounting evidence that in clonal bacterial populations, phenotypic variability originates from stochasticity in gene expression, little is known about noise-shaping evolutionary forces and how expression noise translates to phenotypic differences. Here we developed a high-throughput assay that uses a redox-sensitive dye to couple growth of thousands of bacterial colonies to their respiratory activity and show that in Escherichia coli, noisy regulation of lower glycolysis and citric acid cycle is responsible for large variations in respiratory metabolism. We found that these variations are Pareto optimal to maximization of growth rate and minimization of lag time, two objectives competing between fermentative and respiratory metabolism. Metabolome-based analysis revealed the role of respiratory metabolism in preventing the accumulation of toxic intermediates of branched chain amino acid biosynthesis, thereby supporting early onset of cell growth after carbon starvation. We propose that optimal metabolic tradeoffs play a key role in shaping and preserving phenotypic heterogeneity and adaptation to fluctuating environments.

The quantitative metabolome is shaped by abiotic constraints

Living systems formed and evolved under constraints that govern their interactions with the inorganic world. These interactions are definable using basic physico-chemical principles. Here, we formulate a comprehensive set of ten governing abiotic constraints that define possible quantitative metabolomes. We apply these constraints to a metabolic network of Escherichia coli that represents 90% of its metabolome. We show that the quantitative metabolomes allowed by the abiotic constraints are consistent with metabolomic and isotope-labeling data. We find that: (i) abiotic constraints drive the evolution of high-affinity phosphate transporters; (ii) Charge-, hydrogen- and magnesium-related constraints underlie transcriptional regulatory responses to osmotic stress; and (iii) hydrogen-ion and charge imbalance underlie transcriptional regulatory responses to acid stress. Thus, quantifying the constraints that the inorganic world imposes on living systems provides insights into their key characteristics, helps understand the outcomes of evolutionary adaptation, and should be considered as a fundamental part of theoretical biology and for understanding the constraints on evolution.

Genome-scale metabolic modelling when changes in environmental conditions affect biomass composition

Genome-scale metabolic modeling is an important tool in the study of metabolism by enhancing the collation of knowledge, interpretation of data, and prediction of metabolic capabilities. A frequent assumption in the use of genome-scale models is that the in vivo organism is evolved for optimal growth, where growth is represented by flux through a biomass objective function (BOF). While the specific composition of the BOF is crucial, its formulation is often inherited from similar organisms due to the experimental challenges associated with its proper determination.

A cell’s macro-molecular composition is not fixed and it responds to changes in environmental conditions. As a consequence, initiatives for the high-fidelity determination of cellular biomass composition have been launched. Thus, there is a need for a mathematical and computational framework capable of using multiple measurements of cellular biomass composition in different environments. Here, we propose two different computational approaches for directly addressing this challenge: Biomass Trade-off Weighting (BTW) and Higher-dimensional-plane InterPolation (HIP).

In lieu of experimental data on biomass composition-variation in response to changing nutrient environment, we assess the properties of BTW and HIP using three hypothetical, yet biologically plausible, BOFs for the Escherichia coli genome-scale metabolic model iML1515. We find that the BTW and HIP formulations have a significant impact on model performance and phenotypes. Furthermore, the BTW method generates larger growth rates in all environments when compared to HIP. Using acetate secretion and the respiratory quotient as proxies for phenotypic changes, we find marked differences between the methods as HIP generates BOFs more similar to a reference BOF than BTW. We conclude that the presented methods constitute a conceptual step in developing genome-scale metabolic modelling approaches capable of addressing the inherent dependence of cellular biomass composition on nutrient environments.

Changes in the environment promote changes in an organism’s metabolism. To achieve balanced growth states for near-optimal function, cells respond through metabolic rearrangements, which may influence the biosynthesis of metabolic precursors for building a cell’s molecular constituents. Therefore, it is necessary to take the dependence of biomass composition on environmental conditions into consideration. While measuring the biomass composition for some environments is possible, and should be done, it cannot be completed for all possible environments.

In this work, we propose two main approaches, BTW and HIP, for addressing the challenge of estimating biomass composition in response to environmental changes. We evaluate the phenotypic consequences of BTW and HIP by characterizing their effect on growth, secretion potential, respiratory efficiency, and gene essentiality of a cell.

Our work constitutes a first conceptual step in accounting for the influence of growth conditions on biomass composition, and in turn the biomass composition’s effect on metabolic phenotypic traits, within constraint-based modelling. As such, we believe it will improve the relevance of constraint-based methods in metabolic engineering and drug discovery, since the biosynthetic potential of microbes for generating industrially relevant products or drugs often is closely linked to their biomass composition.