Reliable and efficient solution of genome-scale models of Metabolism and macromolecular Expression

Integration of proteomic data with genome-scale metabolic models: A methodological overview

The integration of proteomics data with constraint-based reconstruction and analysis (COBRA) models plays a pivotal role in understanding the relationship between genotype and phenotype and bridges the gap between genome-level phenomena and functional adaptations. Integrating a generic genome-scale model with information on proteins enables generation of a context-specific metabolic model which improves the accuracy of model prediction. This review explores methodologies for incorporating proteomics data into genome-scale models. Available methods are grouped into four distinct categories based on their approach to integrate proteomics data and their depth of modeling. Within each category section various methods are introduced in chronological order of publication demonstrating the progress of this field. Furthermore, challenges and potential solutions to further progress are outlined, including the limited availability of appropriate in vitro data, experimental enzyme turnover rates, and the trade-off between model accuracy, computational tractability, and data scarcity. In conclusion, methods employing simpler approaches demand fewer kinetic and omics data, consequently leading to a less complex mathematical problem and reduced computational expenses. On the other hand, approaches that delve deeper into cellular mechanisms and aim to create detailed mathematical models necessitate more extensive kinetic and omics data, resulting in a more complex and computationally demanding problem. However, in some cases, this increased cost can be justified by the potential for more precise predictions.

Current State, Challenges, and Opportunities in Genome-Scale Resource Allocation Models: A Mathematical Perspective

Stoichiometric genome-scale metabolic models (generally abbreviated GSM, GSMM, or GEM) have had many applications in exploring phenotypes and guiding metabolic engineering interventions. Nevertheless, these models and predictions thereof can become limited as they do not directly account for protein cost, enzyme kinetics, and cell surface or volume proteome limitations. Lack of such mechanistic detail could lead to overly optimistic predictions and engineered strains. Initial efforts to correct these deficiencies were by the application of precursor tools for GSMs, such as flux balance analysis with molecular crowding. In the past decade, several frameworks have been introduced to incorporate proteome-related limitations using a genome-scale stoichiometric model as the reconstruction basis, which herein are called resource allocation models (RAMs). This review provides a broad overview of representative or commonly used existing RAM frameworks. This review discusses increasingly complex models, beginning with stoichiometric models to precursor to RAM frameworks to existing RAM frameworks. RAM frameworks are broadly divided into two categories: coarse-grained and fine-grained, with different strengths and challenges. Discussion includes pinpointing their utility, data needs, highlighting framework strengths and limitations, and appropriateness to various research endeavors, largely through contrasting their mathematical frameworks. Finally, promising future applications of RAMs are discussed.

Recombinant protein expression in proteome-reduced cells under aerobic and oxygen-limited regimes

Industrial cultures are hindered by the physiological complexity of the host and the limited mass transfer capacity of conventional bioreactors. In this study, a minimal cell approach was combined with genetic devices to overcome such issues. A flavin mononucleotide-based fluorescent protein (FbFP) was expressed in a proteome-reduced Escherichia coli (PR). When FbFP was expressed from a constitutive protein generator (CPG), the PR strain produced 47% and 35% more FbFP than its wild type (WT), in aerobic or oxygen-limited regimes, respectively. Metabolic and expression models predicted more efficient biomass formation at higher fluxes to FbFP, in agreement with these results. A microaerobic protein generator (MPG) and a microaerobic transcriptional cascade (MTC) were designed to induce FbFP expression upon oxygen depletion. The FbFP fluorescence using the MTC in the PR strain was 9% higher than that of the WT bearing the CPG under oxygen limitation. To further improve the PR strain, the pyruvate dehydrogenase complex regulator gene was deleted, and the Vitreoscilla hemoglobin was expressed. Compared to oxygen-limited cultures of the WT, the engineered strains increased the FbFP expression more than 50% using the MTC. Therefore, the designed expression systems can be a valuable alternative for industrial cultivations.

Multi-scale models of whole cells: progress and challenges

Whole-cell modeling is "the ultimate goal" of computational systems biology and "a grand challenge for 21st century" (Tomita, Trends in Biotechnology, 2001, 19(6), 205-10). These complex, highly detailed models account for the activity of every molecule in a cell and serve as comprehensive knowledgebases for the modeled system. Their scope and utility far surpass those of other systems models. In fact, whole-cell models (WCMs) are an amalgam of several types of "system" models. The models are simulated using a hybrid modeling method where the appropriate mathematical methods for each biological process are used to simulate their behavior. Given the complexity of the models, the process of developing and curating these models is labor-intensive and to date only a handful of these models have been developed. While whole-cell models provide valuable and novel biological insights, and to date have identified some novel biological phenomena, their most important contribution has been to highlight the discrepancy between available data and observations that are used for the parametrization and validation of complex biological models. Another realization has been that current whole-cell modeling simulators are slow and to run models that mimic more complex (e.g., multi-cellular) biosystems, those need to be executed in an accelerated fashion on high-performance computing platforms. In this manuscript, we review the progress of whole-cell modeling to date and discuss some of the ways that they can be improved.

Cardinality optimization in constraint-based modelling: application to human metabolism

MOTIVATION

Several applications in constraint-based modelling can be mathematically formulated as cardinality optimization problems involving the minimization or maximization of the number of nonzeros in a vector. These problems include testing for stoichiometric consistency, testing for flux consistency, testing for thermodynamic flux consistency, computing sparse solutions to flux balance analysis problems and computing the minimum number of constraints to relax to render an infeasible flux balance analysis problem feasible. Such cardinality optimization problems are computationally complex, with no known polynomial time algorithms capable of returning an exact and globally optimal solution.

RESULTS

By approximating the zero-norm with nonconvex continuous functions, we reformulate a set of cardinality optimization problems in constraint-based modelling into a difference of convex functions. We implemented and numerically tested novel algorithms that approximately solve the reformulated problems using a sequence of convex programs. We applied these algorithms to various biochemical networks and demonstrate that our algorithms match or outperform existing related approaches. In particular, we illustrate the efficiency and practical utility of our algorithms for cardinality optimization problems that arise when extracting a model ready for thermodynamic flux balance analysis given a human metabolic reconstruction.

AVAILABILITY AND IMPLEMENTATION

Open source scripts to reproduce the results are here https://github.com/opencobra/COBRA.papers/2023_cardOpt with general purpose functions integrated within the COnstraint-Based Reconstruction and Analysis toolbox: https://github.com/opencobra/cobratoolbox.

Computation of condition-dependent proteome allocation reveals variability in the macro and micro nutrient requirements for growth

Sustaining a robust metabolic network requires a balanced and fully functioning proteome. In addition to amino acids, many enzymes require cofactors (coenzymes and engrafted prosthetic groups) to function properly. Extensively validated resource allocation models, such as genome-scale models of metabolism and gene expression (ME-models), have the ability to compute an optimal proteome composition underlying a metabolic phenotype, including the provision of all required cofactors. Here we apply the ME-model for Escherichia coli K-12 MG1655 to computationally examine how environmental conditions change the proteome and its accompanying cofactor usage. We found that: (1) The cofactor requirements computed by the ME-model mostly agree with the standard biomass objective function used in models of metabolism alone (M-models); (2) ME-model computations reveal non-intuitive variability in cofactor use under different growth conditions; (3) An analysis of ME-model predicted protein use in aerobic and anaerobic conditions suggests an enrichment in the use of peroxyl scavenging acids in the proteins used to sustain aerobic growth; (4) The ME-model could describe how limitation in key protein components affect the metabolic state of E. coli. Genome-scale models have thus reached a level of sophistication where they reveal intricate properties of functional proteomes and how they support different E. coli lifestyles.

Escherichia coli is capable of growing in many environments, each of which requires a different collection of enzymes to metabolize the nutrients within that environment. Each individual enzyme requires its own set of amino acids and oftentimes cofactors, which are accessory molecules essential for the enzyme to function. Thus, the composition of the micronutrients (amino acids, cofactors, etc.) within a cell will differ depending on its metabolic needs. The presented work is the first effort to employ metabolic models to probe the connection between E. coli’s diverse growth environments and its biomass composition. We first show how differences in model-predicted enzyme use for aerobic or anaerobic growth results in distinct amino acid and cofactor usage. Alternatively, we show that the metabolic models can predict how modifying the cell’s biomass composition will affect growth. For example, by modeling the exposure of E. coli to trimethoprim or sulfamethoxazole—two antibiotics that target folate (vitamin B9) synthesis—we predicted how E. coli could adapt to grow under folate-limited conditions. This work demonstrates how models can be used to study antibiotic resistance of drugs that target amino acid or cofactor synthesis.

Recent advances in constraint and machine learning-based metabolic modeling by leveraging stoichiometric balances, thermodynamic feasibility and kinetic law formalisms

Understanding the governing principles behind organisms' metabolism and growth underpins their effective deployment as bioproduction chassis. A central objective of metabolic modeling is predicting how metabolism and growth are affected by both external environmental factors and internal genotypic perturbations. The fundamental concepts of reaction stoichiometry, thermodynamics, and mass action kinetics have emerged as the foundational principles of many modeling frameworks designed to describe how and why organisms allocate resources towards both growth and bioproduction. This review focuses on the latest algorithmic advancements that have integrated these foundational principles into increasingly sophisticated quantitative frameworks.

Kinetic profiling of metabolic specialists demonstrates stability and consistency of in vivo enzyme turnover numbers

Enzyme turnover numbers (k _cats) are essential for a quantitative understanding of cells. Because k _cats are traditionally measured in low-throughput assays, they can be inconsistent, labor-intensive to obtain, and can miss in vivo effects. We use a data-driven approach to estimate in vivo k _cats using metabolic specialist Escherichia coli strains that resulted from gene knockouts in central metabolism followed by metabolic optimization via laboratory evolution. By combining absolute proteomics with fluxomics data, we find that in vivo k _cats are robust against genetic perturbations, suggesting that metabolic adaptation to gene loss is mostly achieved through other mechanisms, like gene-regulatory changes. Combining machine learning and genome-scale metabolic models, we show that the obtained in vivo k _cats predict unseen proteomics data with much higher precision than in vitro k _cats. The results demonstrate that in vivo k _cats can solve the problem of inconsistent and low-coverage parameterizations of genome-scale cellular models.

The ETFL formulation allows multi-omics integration in thermodynamics-compliant metabolism and expression models

Systems biology has long been interested in models capturing both metabolism and expression in a cell. We propose here an implementation of the metabolism and expression model formalism (ME-models), which we call ETFL, for Expression and Thermodynamics Flux models. ETFL is a hierarchical model formulation, from metabolism to RNA synthesis, that allows simulating thermodynamics-compliant intracellular fluxes as well as enzyme and mRNA concentration levels. ETFL formulates a mixed-integer linear problem (MILP) that enables both relative and absolute metabolite, protein, and mRNA concentration integration. ETFL is compatible with standard MILP solvers and does not require a non-linear solver, unlike the previous state of the art. It also accounts for growth-dependent parameters, such as relative protein or mRNA content. We present ETFL along with its validation using results obtained from a well-characterized E. coli model. We show that ETFL is able to reproduce proteome-limited growth. We also subject it to several analyses, including the prediction of feasible mRNA and enzyme concentrations and gene essentiality.

Accounting for the effects of genetic expression in genome-scale metabolic models is challenging. Here, the authors introduce a model formulation that efficiently simulates thermodynamic-compliant fluxes, enzyme and mRNA concentration levels, allowing omics integration and broad analysis of in silico cellular physiology.

Cellular responses to reactive oxygen species are predicted from molecular mechanisms

Catalysis using iron-sulfur clusters and transition metals can be traced back to the last universal common ancestor. The damage to metalloproteins caused by reactive oxygen species (ROS) can prevent cell growth and survival when unmanaged, thus eliciting an essential stress response that is universal and fundamental in biology. Here we develop a computable multiscale description of the ROS stress response in Escherichia coli, called OxidizeME. We use OxidizeME to explain four key responses to oxidative stress: 1) ROS-induced auxotrophy for branched-chain, aromatic, and sulfurous amino acids; 2) nutrient-dependent sensitivity of growth rate to ROS; 3) ROS-specific differential gene expression separate from global growth-associated differential expression; and 4) coordinated expression of iron-sulfur cluster (ISC) and sulfur assimilation (SUF) systems for iron-sulfur cluster biosynthesis. These results show that we can now develop fundamental and quantitative genotype-phenotype relationships for stress responses on a genome-wide basis.

Systems Biology and Multi-Omics Integration: Viewpoints from the Metabolomics Research Community

The use of multiple omics techniques (i.e., genomics, transcriptomics, proteomics, and metabolomics) is becoming increasingly popular in all facets of life science. Omics techniques provide a more holistic molecular perspective of studied biological systems compared to traditional approaches. However, due to their inherent data differences, integrating multiple omics platforms remains an ongoing challenge for many researchers. As metabolites represent the downstream products of multiple interactions between genes, transcripts, and proteins, metabolomics, the tools and approaches routinely used in this field could assist with the integration of these complex multi-omics data sets. The question is, how? Here we provide some answers (in terms of methods, software tools and databases) along with a variety of recommendations and a list of continuing challenges as identified during a peer session on multi-omics integration that was held at the recent 'Australian and New Zealand Metabolomics Conference' (ANZMET 2018) in Auckland, New Zealand (Sept. 2018). We envisage that this document will serve as a guide to metabolomics researchers and other members of the community wishing to perform multi-omics studies. We also believe that these ideas may allow the full promise of integrated multi-omics research and, ultimately, of systems biology to be realized.

Creation and analysis of biochemical constraint-based models using the COBRA Toolbox v.3.0

Constraint-based reconstruction and analysis (COBRA) provides a molecular mechanistic framework for integrative analysis of experimental molecular systems biology data and quantitative prediction of physicochemically and biochemically feasible phenotypic states. The COBRA Toolbox is a comprehensive desktop software suite of interoperable COBRA methods. It has found widespread application in biology, biomedicine, and biotechnology because its functions can be flexibly combined to implement tailored COBRA protocols for any biochemical network. This protocol is an update to the COBRA Toolbox v.1.0 and v.2.0. Version 3.0 includes new methods for quality-controlled reconstruction, modeling, topological analysis, strain and experimental design, and network visualization, as well as network integration of chemoinformatic, metabolomic, transcriptomic, proteomic, and thermochemical data. New multi-lingual code integration also enables an expansion in COBRA application scope via high-precision, high-performance, and nonlinear numerical optimization solvers for multi-scale, multi-cellular, and reaction kinetic modeling, respectively. This protocol provides an overview of all these new features and can be adapted to generate and analyze constraint-based models in a wide variety of scenarios. The COBRA Toolbox v.3.0 provides an unparalleled depth of COBRA methods.

The genetic basis for adaptation of model-designed syntrophic co-cultures

Understanding the fundamental characteristics of microbial communities could have far reaching implications for human health and applied biotechnology. Despite this, much is still unknown regarding the genetic basis and evolutionary strategies underlying the formation of viable synthetic communities. By pairing auxotrophic mutants in co-culture, it has been demonstrated that viable nascent E. coli communities can be established where the mutant strains are metabolically coupled. A novel algorithm, OptAux, was constructed to design 61 unique multi-knockout E. coli auxotrophic strains that require significant metabolite uptake to grow. These predicted knockouts included a diverse set of novel non-specific auxotrophs that result from inhibition of major biosynthetic subsystems. Three OptAux predicted non-specific auxotrophic strains—with diverse metabolic deficiencies—were co-cultured with an L-histidine auxotroph and optimized via adaptive laboratory evolution (ALE). Time-course sequencing revealed the genetic changes employed by each strain to achieve higher community growth rates and provided insight into mechanisms for adapting to the syntrophic niche. A community model of metabolism and gene expression was utilized to predict the relative community composition and fundamental characteristics of the evolved communities. This work presents new insight into the genetic strategies underlying viable nascent community formation and a cutting-edge computational method to elucidate metabolic changes that empower the creation of cooperative communities.

Many basic characteristics underlying the establishment of cooperative growth in bacterial communities have not been studied in detail. The presented work sought to understand the adaptation of syntrophic communities by first employing a new computational method to generate a comprehensive catalog of E. coli auxotrophic mutants. Many of the knockouts in the catalog had the predicted effect of disabling a major biosynthetic process. As a result, these strains were predicted to be capable of growing when supplemented with many different individual metabolites (i.e., a non-specific auxotroph), but the strains would require a high amount of metabolic cooperation to grow in community. Three such non-specific auxotroph mutants from this catalog were co-cultured with a proven auxotrophic partner in vivo and evolved via adaptive laboratory evolution. In order to successfully grow, each strain in co-culture had to evolve under a pressure to grow cooperatively in its new niche. The non-specific auxotrophs further had to adapt to significant homeostatic changes in cell’s metabolic state caused by knockouts in metabolic genes. The genomes of the successfully growing communities were sequenced, thus providing unique insights into the genetic changes accompanying the formation and optimization of the viable communities. A computational model was further developed to predict how finite protein availability, a fundamental constraint on cell metabolism, could impact the composition of the community (i.e., the relative abundances of each community member).

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.

Machine learning applied to enzyme turnover numbers reveals protein structural correlates and improves metabolic models

Knowing the catalytic turnover numbers of enzymes is essential for understanding the growth rate, proteome composition, and physiology of organisms, but experimental data on enzyme turnover numbers is sparse and noisy. Here, we demonstrate that machine learning can successfully predict catalytic turnover numbers in Escherichia coli based on integrated data on enzyme biochemistry, protein structure, and network context. We identify a diverse set of features that are consistently predictive for both in vivo and in vitro enzyme turnover rates, revealing novel protein structural correlates of catalytic turnover. We use our predictions to parameterize two mechanistic genome-scale modelling frameworks for proteome-limited metabolism, leading to significantly higher accuracy in the prediction of quantitative proteome data than previous approaches. The presented machine learning models thus provide a valuable tool for understanding metabolism and the proteome at the genome scale, and elucidate structural, biochemical, and network properties that underlie enzyme kinetics.

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.

COBRAme: A computational framework for genome-scale models of metabolism and gene expression

Genome-scale models of metabolism and macromolecular expression (ME-models) explicitly compute the optimal proteome composition of a growing cell. ME-models expand upon the well-established genome-scale models of metabolism (M-models), and they enable a new fundamental understanding of cellular growth. ME-models have increased predictive capabilities and accuracy due to their inclusion of the biosynthetic costs for the machinery of life, but they come with a significant increase in model size and complexity. This challenge results in models which are both difficult to compute and challenging to understand conceptually. As a result, ME-models exist for only two organisms (Escherichia coli and Thermotoga maritima) and are still used by relatively few researchers. To address these challenges, we have developed a new software framework called COBRAme for building and simulating ME-models. It is coded in Python and built on COBRApy, a popular platform for using M-models. COBRAme streamlines computation and analysis of ME-models. It provides tools to simplify constructing and editing ME-models to enable ME-model reconstructions for new organisms. We used COBRAme to reconstruct a condensed E. coli ME-model called iJL1678b-ME. This reformulated model gives functionally identical solutions to previous E. coli ME-models while using 1/6 the number of free variables and solving in less than 10 minutes, a marked improvement over the 6 hour solve time of previous ME-model formulations. Errors in previous ME-models were also corrected leading to 52 additional genes that must be expressed in iJL1678b-ME to grow aerobically in glucose minimal in silico media. This manuscript outlines the architecture of COBRAme and demonstrates how ME-models can be created, modified, and shared most efficiently using the new software framework.

Quantitative systems pharmacology and the personalized drug-microbiota-diet axis

Precision medicine is an emerging paradigm that aims at maximizing the benefits and minimizing the adverse effects of drugs. Realistic mechanistic models are needed to understand and limit heterogeneity in drug responses. While pharmacokinetic models describe in detail a drug's absorption and metabolism, they generally do not account for individual variations in response to environmental influences, in addition to genetic variation. For instance, the human gut microbiota metabolizes drugs and is modulated by diet, and it exhibits significant variation among individuals. However, the influence of the gut microbiota on drug failure or drug side effects is under-researched. Here, we review recent advances in computational modeling approaches that could contribute to a better, mechanism-based understanding of drug-microbiota-diet interactions and their contribution to individual drug responses. By integrating systems biology and quantitative systems pharmacology with microbiology and nutrition, the conceptually and technologically demand for novel approaches could be met to enable the study of individual variability, thereby providing breakthrough support for progress in precision medicine.

Laboratory Evolution to Alternating Substrate Environments Yields Distinct Phenotypic and Genetic Adaptive Strategies

Adaptive laboratory evolution (ALE) experiments are often designed to maintain a static culturing environment to minimize confounding variables that could influence the adaptive process, but dynamic nutrient conditions occur frequently in natural and bioprocessing settings. To study the nature of carbon substrate fitness tradeoffs, we evolved batch cultures of Escherichia coli via serial propagation into tubes alternating between glucose and either xylose, glycerol, or acetate. Genome sequencing of evolved cultures revealed several genetic changes preferentially selected for under dynamic conditions and different adaptation strategies depending on the substrates being switched between; in some environments, a persistent "generalist" strain developed, while in another, two "specialist" subpopulations arose that alternated dominance. Diauxic lag phenotype varied across the generalists and specialists, in one case being completely abolished, while gene expression data distinguished the transcriptional strategies implemented by strains in pursuit of growth optimality. Genome-scale metabolic modeling techniques were then used to help explain the inherent substrate differences giving rise to the observed distinct adaptive strategies. This study gives insight into the population dynamics of adaptation in an alternating environment and into the underlying metabolic and genetic mechanisms. Furthermore, ALE-generated optimized strains have phenotypes with potential industrial bioprocessing applications.IMPORTANCE Evolution and natural selection inexorably lead to an organism's improved fitness in a given environment, whether in a laboratory or natural setting. However, despite the frequent natural occurrence of complex and dynamic growth environments, laboratory evolution experiments typically maintain simple, static culturing environments so as to reduce selection pressure complexity. In this study, we investigated the adaptive strategies underlying evolution to fluctuating environments by evolving Escherichia coli to conditions of frequently switching growth substrate. Characterization of evolved strains via a number of different data types revealed the various genetic and phenotypic changes implemented in pursuit of growth optimality and how these differed across the different growth substrates and switching protocols. This work not only helps to establish general principles of adaptation to complex environments but also suggests strategies for experimental design to achieve desired evolutionary outcomes.

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

Integrating omics data to refine or make context-specific models is an active field of constraint-based modeling. Proteomics now cover over 95% of the Escherichia coli proteome by mass. Genome-scale models of Metabolism and macromolecular Expression (ME) compute proteome allocation linked to metabolism and fitness. Using proteomics data, we formulated allocation constraints for key proteome sectors in the ME model. The resulting calibrated model effectively computed the "generalist" (wild-type) E. coli proteome and phenotype across diverse growth environments. Across 15 growth conditions, prediction errors for growth rate and metabolic fluxes were 69% and 14% lower, respectively. The sector-constrained ME model thus represents a generalist ME model reflecting both growth rate maximization and "hedging" against uncertain environments and stresses, as indicated by significant enrichment of these sectors for the general stress response sigma factor σS. Finally, the sector constraints represent a general formalism for integrating omics data from any experimental condition into constraint-based ME models. The constraints can be fine-grained (individual proteins) or coarse-grained (functionally-related protein groups) as demonstrated here. This flexible formalism provides an accessible approach for narrowing the gap between the complexity captured by omics data and governing principles of proteome allocation described by systems-level models.

solveME: fast and reliable solution of nonlinear ME models

Background

Genome-scale models of metabolism and macromolecular expression (ME) significantly expand the scope and predictive capabilities of constraint-based modeling. ME models present considerable computational challenges: they are much (>30 times) larger than corresponding metabolic reconstructions (M models), are multiscale, and growth maximization is a nonlinear programming (NLP) problem, mainly due to macromolecule dilution constraints.

Results

Here, we address these computational challenges. We develop a fast and numerically reliable solution method for growth maximization in ME models using a quad-precision NLP solver (Quad MINOS). Our method was up to 45 % faster than binary search for six significant digits in growth rate. We also develop a fast, quad-precision flux variability analysis that is accelerated (up to 60× speedup) via solver warm-starts. Finally, we employ the tools developed to investigate growth-coupled succinate overproduction, accounting for proteome constraints.

Conclusions

Just as genome-scale metabolic reconstructions have become an invaluable tool for computational and systems biologists, we anticipate that these fast and numerically reliable ME solution methods will accelerate the wide-spread adoption of ME models for researchers in these fields.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1240-1) contains supplementary material, which is available to authorized users.