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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., Competing Interests: We declare we have no competing interests., (© 2024 The Authors.)

Constraint-based metabolic models have been used for decades to predict the phenotype of microorganisms in different environments. However, quantitative predictions are limited unless labor-intensive measurements of media uptake fluxes are performed. We show how hybrid neural-mechanistic models can serve as an architecture for machine learning providing a way to improve phenotype predictions. We illustrate our hybrid models with growth rate predictions of Escherichia coli and Pseudomonas putida grown in different media and with phenotype predictions of gene knocked-out Escherichia coli mutants. Our neural-mechanistic models systematically outperform constraint-based models and require training set sizes orders of magnitude smaller than classical machine learning methods. Our hybrid approach opens a doorway to enhancing constraint-based modeling: instead of constraining mechanistic models with additional experimental measurements, our hybrid models grasp the power of machine learning while fulfilling mechanistic constrains, thus saving time and resources in typical systems biology or biological engineering projects., (© 2023. Springer Nature Limited.)

The physiology of biological cells evolved under physical and chemical constraints, such as mass conservation across the network of biochemical reactions, nonlinear reaction kinetics, and limits on cell density. For unicellular organisms, the fitness that governs this evolution is mainly determined by the balanced cellular growth rate. We previously introduced growth balance analysis (GBA) as a general framework to model and analyze such nonlinear systems, revealing important analytical properties of optimal balanced growth states. It has been shown that at optimality, only a minimal subset of reactions can have nonzero flux. However, no general principles have been established to determine if a specific reaction is active at optimality. Here, we extend the GBA framework to study the optimality of each biochemical reaction, and we identify the mathematical conditions determining whether a reaction is active or not at optimal growth in a given environment. We reformulate the mathematical problem in terms of a minimal number of dimensionless variables and use the Karush-Kuhn-Tucker (KKT) conditions to identify fundamental principles of optimal resource allocation in GBA models of any size and complexity. Our approach helps to identify from first principles the economic values of biochemical reactions, expressed as marginal changes in cellular growth rate; these economic values can be related to the costs and benefits of proteome allocation into the reactions' catalysts. Our formulation also generalizes the concepts of Metabolic Control Analysis to models of growing cells. We show how the extended GBA framework unifies and extends previous approaches of cellular modeling and analysis, putting forward a program to analyze cellular growth through the stationarity conditions of a Lagrangian function. GBA thereby provides a general theoretical toolbox for the study of fundamental mathematical properties of balanced cellular growth., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Dourado et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Motivation: Efficient resource allocation can contribute to an organism's fitness and can improve evolutionary success. Resource Balance Analysis (RBA) is a computational framework that models an organism's growth-optimal proteome configurations in various environments. RBA software enables the construction of RBA models on genome scale and the calculation of medium-specific, growth-optimal cell states including metabolic fluxes and the abundance of macromolecular machines. However, existing software lacks a simple programming interface for non-expert users, easy to use and interoperable with other software., Results: The python package RBAtools provides convenient access to RBA models. As a flexible programming interface, it enables the implementation of custom workflows and the modification of existing genome-scale RBA models. Its high-level functions comprise simulation, model fitting, parameter screens, sensitivity analysis, variability analysis and the construction of Pareto fronts. Models and data are represented as structured tables and can be exported to common data formats for fluxomics and proteomics visualization., Availability and Implementation: RBAtools documentation, installation instructions and tutorials are available at https://sysbioinra.github.io/rbatools/. General information about RBA and related software can be found at rba.inrae.fr., (© The Author(s) 2023. Published by Oxford University Press.)

Computational models have great potential to accelerate bioscience, bioengineering, and medicine. However, it remains challenging to reproduce and reuse simulations, in part, because the numerous formats and methods for simulating various subsystems and scales remain siloed by different software tools. For example, each tool must be executed through a distinct interface. To help investigators find and use simulation tools, we developed BioSimulators (https://biosimulators.org), a central registry of the capabilities of simulation tools and consistent Python, command-line and containerized interfaces to each version of each tool. The foundation of BioSimulators is standards, such as CellML, SBML, SED-ML and the COMBINE archive format, and validation tools for simulation projects and simulation tools that ensure these standards are used consistently. To help modelers find tools for particular projects, we have also used the registry to develop recommendation services. We anticipate that BioSimulators will help modelers exchange, reproduce, and combine simulations., (© The Author(s) 2022. Published by Oxford University Press on behalf of Nucleic Acids Research.)

To translate metabolic networks into dynamic models, the Structural Kinetic Modelling framework (SKM) assumes a given reference state and replaces the reaction elasticities in this state by random numbers. A new variant, called Structural Thermokinetic Modelling (STM), accounts for reversible reactions and thermodynamics. STM relies on a dependence schema in which some basic variables are sampled, fitted to data, or optimised, while all other variables can be easily computed. Correlated elasticities follow from enzyme saturation values and thermodynamic forces, which are physically independent. Probability distributions in the dependence schema define a model ensemble, which allows for probabilistic predictions even if data are scarce. STM highlights the importance of variabilities, dependencies, and covariances of biological variables. By varying network structure, fluxes, thermodynamic forces, regulation, or types of rate laws, the effects of these model features can be assessed. By choosing the basic variables, metabolic networks can be converted into kinetic models with consistent reversible rate laws. Metabolic control coefficients obtained from these models can tell us about metabolic dynamics, including responses and optimal adaptations to perturbations, enzyme synergies and metabolite correlations, as well as metabolic fluctuations arising from chemical noise. To showcase STM, I study metabolic control, metabolic fluctuations, and enzyme synergies, and how they are shaped by thermodynamic forces. Considering thermodynamics can improve predictions of flux control, enzyme synergies, correlated flux and metabolite variations, and the emergence and propagation of metabolic noise.

Enzyme kinetic constants in vivo are largely unknown, which limits the construction of large metabolic models. Given measured metabolic fluxes, metabolite concentrations, and enzyme concentrations, these constants may be inferred by model fitting, but the estimation problems are hard to solve if models are large. Here we show how consistent kinetic constants, metabolite concentrations, and enzyme concentrations can be determined from data if metabolic fluxes are known. The estimation method, called model balancing, can handle models with a wide range of rate laws and accounts for thermodynamic constraints between fluxes, kinetic constants, and metabolite concentrations. It can be used to estimate in-vivo kinetic constants, to complete and adjust available data, and to construct plausible metabolic states with predefined flux distributions. By omitting one term from the log posterior-a term for penalising low enzyme concentrations-we obtain a convex optimality problem with a unique local optimum. As a demonstrative case, we balance a model of E. coli central metabolism with artificial or experimental data and obtain a physically and biologically plausible parameterisation of reaction kinetics in E. coli central metabolism. The example shows what information about kinetic constants can be obtained from omics data and reveals practical limits to estimating in-vivo kinetic constants. While noise-free omics data allow for a reasonable reconstruction of in-vivo kcat and KM values, prediction from noisy omics data are worse. Hence, adjusting kinetic constants and omics data to obtain consistent metabolic models is the main application of model balancing.

Systems biology has experienced dramatic growth in the number, size, and complexity of computational models. To reproduce simulation results and reuse models, researchers must exchange unambiguous model descriptions. We review the latest edition of the Systems Biology Markup Language (SBML), a format designed for this purpose. A community of modelers and software authors developed SBML Level 3 over the past decade. Its modular form consists of a core suited to representing reaction-based models and packages that extend the core with features suited to other model types including constraint-based models, reaction-diffusion models, logical network models, and rule-based models. The format leverages two decades of SBML and a rich software ecosystem that transformed how systems biologists build and interact with models. More recently, the rise of multiscale models of whole cells and organs, and new data sources such as single-cell measurements and live imaging, has precipitated new ways of integrating data with models. We provide our perspectives on the challenges presented by these developments and how SBML Level 3 provides the foundation needed to support this evolution., (© 2020 California Institute of Technology Published under the terms of the CC BY 4.0 license.)

Some biological networks exhibit oscillations in their components to convert stimuli to time-dependent responses. The eukaryotic cell cycle is such a case, being governed by waves of cyclin-dependent kinase (cyclin/Cdk) activities that rise and fall with specific timing and guarantee its timely occurrence. Disruption of cyclin/Cdk oscillations could result in dysfunction through reduced cell division. Therefore, it is of interest to capture properties of network designs that exhibit robust oscillations. Here we show that a minimal yeast cell cycle network is able to oscillate autonomously, and that cyclin/Cdk-mediated positive feedback loops (PFLs) and Clb3-centered regulations sustain cyclin/Cdk oscillations, in known and hypothetical network designs. We propose that Clb3-mediated coordination of cyclin/Cdk waves reconciles checkpoint and oscillatory cell cycle models. Considering the evolutionary conservation of the cyclin/Cdk network across eukaryotes, we hypothesize that functional ("healthy") phenotypes require the capacity to oscillate autonomously whereas dysfunctional (potentially "diseased") phenotypes may lack this capacity.

Summary: Measured kinetic constants are key input data for metabolic models, but they are often uncertain, inconsistent and incomplete. Parameter balancing translates such data into complete and consistent parameter sets while accounting for predefined ranges and physical constraints. Based on Bayesian regression, it determines a most plausible parameter set as well as uncertainty ranges for all model parameters. Our tools for parameter balancing support standard model and data formats and enable an easy customization of prior distributions and constraints for biochemical constants. Modellers can balance kinetic constants, thermodynamic data and metabolomic data to obtain thermodynamically consistent metabolic states that comply with user-defined flux directions., Availability and Implementation: An online tool for parameter balancing, a stand-alone Python command line tool, a Python package and a Matlab toolbox (which uses the CPLEX solver) are freely available at www.parameterbalancing.net., (© The Author(s) 2019. Published by Oxford University Press.)

Resource Balance Analysis (RBA) is a computational method based on resource allocation, which performs accurate quantitative predictions of whole-cell states (i.e. growth rate, metabolic fluxes, abundances of molecular machines including enzymes) across growth conditions. We present an integrated workflow of RBA together with the Python package RBApy. RBApy builds bacterial RBA models from annotated genome-scale metabolic models by adding descriptions of cellular processes relevant for growth and maintenance. The package includes functions for model simulation and calibration and for interfacing to Escher maps and Proteomaps for visualization. We demonstrate that RBApy faithfully reproduces results obtained by a hand-curated and experimentally validated RBA model for Bacillus subtilis. We also present a calibrated RBA model of Escherichia coli generated from scratch, which obtained excellent fits to measured flux values and enzyme abundances. RBApy makes whole-cell modelling accessible for a wide range of bacterial wild-type and engineered strains, as illustrated with a CO 2 -fixing Escherichia coli strain. AVAILABILITY: RBApy is available at /https://github.com/SysBioInra/RBApy, under the licence GNU GPL version 3, and runs on Linux, Mac and Windows distributions., (Copyright © 2019 International Metabolic Engineering Society. Published by Elsevier Inc. All rights reserved.)

How individual enzymes evolved is relatively well understood. However, individual enzymes rarely confer a physiological advantage on their own. Judging by its current state, the emergence of metabolism seemingly demanded the simultaneous emergence of many enzymes. Indeed, how multicomponent interlocked systems, like metabolic pathways, evolved is largely an open question. This complexity can be unlocked if we assume that survival of the fittest applies not only to genes and enzymes but also to the metabolites they produce. This review develops our current knowledge of enzyme evolution into a wider hypothesis of pathway and network evolution. We describe the current models for pathway evolution and offer an integrative metabolite-enzyme coevolution hypothesis. Our hypothesis addresses the origins of new metabolites and of new enzymes and the order of their recruitment. We aim to not only survey established knowledge but also present open questions and potential ways of addressing them.

Microbes may maximize the number of daughter cells per time or per amount of nutrients consumed. These two strategies correspond, respectively, to the use of enzyme-efficient or substrate-efficient metabolic pathways. In reality, fast growth is often associated with wasteful, yield-inefficient metabolism, and a general thermodynamic trade-off between growth rate and biomass yield has been proposed to explain this. We studied growth rate/yield trade-offs by using a novel modeling framework, Enzyme-Flux Cost Minimization (EFCM) and by assuming that the growth rate depends directly on the enzyme investment per rate of biomass production. In a comprehensive mathematical model of core metabolism in E. coli, we screened all elementary flux modes leading to cell synthesis, characterized them by the growth rates and yields they provide, and studied the shape of the resulting rate/yield Pareto front. By varying the model parameters, we found that the rate/yield trade-off is not universal, but depends on metabolic kinetics and environmental conditions. A prominent trade-off emerges under oxygen-limited growth, where yield-inefficient pathways support a 2-to-3 times higher growth rate than yield-efficient pathways. EFCM can be widely used to predict optimal metabolic states and growth rates under varying nutrient levels, perturbations of enzyme parameters, and single or multiple gene knockouts.

Systems biology models are rapidly increasing in complexity, size and numbers. When building large models, researchers rely on software tools for the retrieval, comparison, combination and merging of models, as well as for version control. These tools need to be able to quantify the differences and similarities between computational models. However, depending on the specific application, the notion of 'similarity' may greatly vary. A general notion of model similarity, applicable to various types of models, is still missing. Here we survey existing methods for the comparison of models, introduce quantitative measures for model similarity, and discuss potential applications of combined similarity measures. To frame model comparison as a general problem, we describe a theoretical approach to defining and computing similarities based on a combination of different model aspects. The six aspects that we define as potentially relevant for similarity are underlying encoding, references to biological entities, quantitative behaviour, qualitative behaviour, mathematical equations and parameters and network structure. We argue that future similarity measures will benefit from combining these model aspects in flexible, problem-specific ways to mimic users' intuition about model similarity, and to support complex model searches in databases., (© The Author 2016. Published by Oxford University Press.)

Bacterial growth depends crucially on metabolic fluxes, which are limited by the cell's capacity to maintain metabolic enzymes. The necessary enzyme amount per unit flux is a major determinant of metabolic strategies both in evolution and bioengineering. It depends on enzyme parameters (such as kcat and KM constants), but also on metabolite concentrations. Moreover, similar amounts of different enzymes might incur different costs for the cell, depending on enzyme-specific properties such as protein size and half-life. Here, we developed enzyme cost minimization (ECM), a scalable method for computing enzyme amounts that support a given metabolic flux at a minimal protein cost. The complex interplay of enzyme and metabolite concentrations, e.g. through thermodynamic driving forces and enzyme saturation, would make it hard to solve this optimization problem directly. By treating enzyme cost as a function of metabolite levels, we formulated ECM as a numerically tractable, convex optimization problem. Its tiered approach allows for building models at different levels of detail, depending on the amount of available data. Validating our method with measured metabolite and protein levels in E. coli central metabolism, we found typical prediction fold errors of 4.1 and 2.6, respectively, for the two kinds of data. This result from the cost-optimized metabolic state is significantly better than randomly sampled metabolite profiles, supporting the hypothesis that enzyme cost is important for the fitness of E. coli. ECM can be used to predict enzyme levels and protein cost in natural and engineered pathways, and could be a valuable computational tool to assist metabolic engineering projects. Furthermore, it establishes a direct connection between protein cost and thermodynamics, and provides a physically plausible and computationally tractable way to include enzyme kinetics into constraint-based metabolic models, where kinetics have usually been ignored or oversimplified., Competing Interests: The authors have declared that no competing interests exist.

Objective: Whole-cell (WC) modeling is a promising tool for biological research, bioengineering, and medicine. However, substantial work remains to create accurate comprehensive models of complex cells., Methods: We organized the 2015 Whole-Cell Modeling Summer School to teach WC modeling and evaluate the need for new WC modeling standards and software by recoding a recently published WC model in the Systems Biology Markup Language., Results: Our analysis revealed several challenges to representing WC models using the current standards., Conclusion: We, therefore, propose several new WC modeling standards, software, and databases., Significance: We anticipate that these new standards and software will enable more comprehensive models.

Unlabelled: : SBtab is a table-based data format for Systems Biology, designed to support automated data integration and model building. It uses the structure of spreadsheets and defines conventions for table structure, controlled vocabularies and semantic annotations. The format comes with predefined table types for experimental data and SBML-compliant model structures and can easily be customized to cover new types of data., Availability and Implementation: SBtab documents can be created and edited with any text editor or spreadsheet tool. The website www.sbtab.net provides online tools for syntax validation and conversion to SBML and HTML, as well as software for using SBtab in MS Excel, MATLAB and R. The stand-alone Python code contains functions for file parsing, validation, conversion to SBML and HTML and an interface to SQLite databases, to be integrated into Systems Biology workflows. A detailed specification of SBtab, including examples and descriptions of table types and available tools, can be found at www.sbtab.net, Contact: : wolfram.liebermeister@gmail.com., (© The Author 2016. Published by Oxford University Press.)

Turnover numbers, also known as kcat values, are fundamental properties of enzymes. However, kcat data are scarce and measured in vitro, thus may not faithfully represent the in vivo situation. A basic question that awaits elucidation is: how representative are kcat values for the maximal catalytic rates of enzymes in vivo? Here, we harness omics data to calculate kmax(vivo), the observed maximal catalytic rate of an enzyme inside cells. Comparison with kcat values from Escherichia coli, yields a correlation ofr(2)= 0.62 in log scale (p < 10(-10)), with a root mean square difference of 0.54 (3.5-fold in linear scale), indicating that in vivo and in vitro maximal rates generally concur. By accounting for the degree of saturation of enzymes and the backward flux dictated by thermodynamics, we further refine the correspondence between kmax(vivo) and kcat values. The approach we present here characterizes the quantitative relationship between enzymatic catalysis in vitro and in vivo and offers a high-throughput method for extracting enzyme kinetic constants from omics data.

Constructing a model in a hierarchical fashion is a natural approach to managing model complexity, and offers additional opportunities such as the potential to re-use model components. The SBML Level 3 Version 1 Core specification does not directly provide a mechanism for defining hierarchical models, but it does provide a mechanism for SBML packages to extend the Core specification and add additional syntactical constructs. The SBML Hierarchical Model Composition package for SBML Level 3 adds the necessary features to SBML to support hierarchical modeling. The package enables a modeler to include submodels within an enclosing SBML model, delete unneeded or redundant elements of that submodel, replace elements of that submodel with element of the containing model, and replace elements of the containing model with elements of the submodel. In addition, the package defines an optional "port" construct, allowing a model to be defined with suggested interfaces between hierarchical components; modelers can chose to use these interfaces, but they are not required to do so and can still interact directly with model elements if they so chose. Finally, the SBML Hierarchical Model Composition package is defined in such a way that a hierarchical model can be "flattened" to an equivalent, non-hierarchical version that uses only plain SBML constructs, thus enabling software tools that do not yet support hierarchy to nevertheless work with SBML hierarchical models.

Proteomics techniques generate an avalanche of data and promise to satisfy biologists' long-held desire to measure absolute protein abundances on a genome-wide scale. However, can this knowledge be translated into a clearer picture of how cells invest their protein resources? This article aims to give a broad perspective on the composition of proteomes as gleaned from recent quantitative proteomics studies. We describe proteomaps, an approach for visualizing the composition of proteomes with a focus on protein abundances and functions. In proteomaps, each protein is shown as a polygon-shaped tile, with an area representing protein abundance. Functionally related proteins appear in adjacent regions. General trends in proteomes, such as the dominance of metabolism and protein production, become easily visible. We make interactive visualizations of published proteome datasets accessible at www.proteomaps.net. We suggest that evaluating the way protein resources are allocated by various organisms and cell types in different conditions will sharpen our understanding of how and why cells regulate the composition of their proteomes.

In metabolism research, thermodynamics is usually used to determine the directionality of a reaction or the feasibility of a pathway. However, the relationship between thermodynamic potentials and fluxes is not limited to questions of directionality: thermodynamics also affects the kinetics of reactions through the flux-force relationship, which states that the logarithm of the ratio between the forward and reverse fluxes is directly proportional to the change in Gibbs energy due to a reaction (ΔrG'). Accordingly, if an enzyme catalyzes a reaction with a ΔrG' of -5.7 kJ/mol then the forward flux will be roughly ten times the reverse flux. As ΔrG' approaches equilibrium (ΔrG' = 0 kJ/mol), exponentially more enzyme counterproductively catalyzes the reverse reaction, reducing the net rate at which the reaction proceeds. Thus, the enzyme level required to achieve a given flux increases dramatically near equilibrium. Here, we develop a framework for quantifying the degree to which pathways suffer these thermodynamic limitations on flux. For each pathway, we calculate a single thermodynamically-derived metric (the Max-min Driving Force, MDF), which enables objective ranking of pathways by the degree to which their flux is constrained by low thermodynamic driving force. Our framework accounts for the effect of pH, ionic strength and metabolite concentration ranges and allows us to quantify how alterations to the pathway structure affect the pathway's thermodynamics. Applying this methodology to pathways of central metabolism sheds light on some of their features, including metabolic bypasses (e.g., fermentation pathways bypassing substrate-level phosphorylation), substrate channeling (e.g., of oxaloacetate from malate dehydrogenase to citrate synthase), and use of alternative cofactors (e.g., quinone as an electron acceptor instead of NAD). The methods presented here place another arrow in metabolic engineers' quiver, providing a simple means of evaluating the thermodynamic and kinetic quality of different pathway chemistries that produce the same molecules.

The quantitative effects of environmental and genetic perturbations on metabolism can be studied in silico using kinetic models. We present a strategy for large-scale model construction based on a logical layering of data such as reaction fluxes, metabolite concentrations, and kinetic constants. The resulting models contain realistic standard rate laws and plausible parameters, adhere to the laws of thermodynamics, and reproduce a predefined steady state. These features have not been simultaneously achieved by previous workflows. We demonstrate the advantages and limitations of the workflow by translating the yeast consensus metabolic network into a kinetic model. Despite crudely selected data, the model shows realistic control behaviour, a stable dynamic, and realistic response to perturbations in extracellular glucose concentrations. The paper concludes by outlining how new data can continuously be fed into the workflow and how iterative model building can assist in directing experiments.

Steady-state metabolite concentrations in a microorganism typically span several orders of magnitude. The underlying principles governing these concentrations remain poorly understood. Here, we hypothesize that observed variation can be explained in terms of a compromise between factors that favor minimizing metabolite pool sizes (e.g. limited solvent capacity) and the need to effectively utilize existing enzymes. The latter requires adequate thermodynamic driving force in metabolic reactions so that forward flux substantially exceeds reverse flux. To test this hypothesis, we developed a method, metabolic tug-of-war (mTOW), which computes steady-state metabolite concentrations in microorganisms on a genome-scale. mTOW is shown to explain up to 55% of the observed variation in measured metabolite concentrations in E. coli and C. acetobutylicum across various growth media. Our approach, based strictly on first thermodynamic principles, is the first method that successfully predicts high-throughput metabolite concentration data in bacteria across conditions.

Michaelis and Menten's mechanism for enzymatic catalysis is remarkable both in its simplicity and its wide applicability. The extension for reversible processes, as done by Haldane, makes it even more relevant as most enzymes catalyze reactions that are reversible in nature and carry in vivo flux in both directions. Here, we decompose the reversible Michaelis-Menten equation into three terms, each with a clear physical meaning: catalytic capacity, substrate saturation and thermodynamic driving force. This decomposition facilitates a better understanding of enzyme kinetics and highlights the relationship between thermodynamics and kinetics, a relationship which is often neglected. We further demonstrate how our separable rate law can be understood from different points of view, shedding light on factors shaping enzyme catalysis., (Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.)

Contrary to the textbook portrayal of glycolysis as a single pathway conserved across all domains of life, not all sugar-consuming organisms use the canonical Embden-Meyerhoff-Parnass (EMP) glycolytic pathway. Prokaryotic glucose metabolism is particularly diverse, including several alternative glycolytic pathways, the most common of which is the Entner-Doudoroff (ED) pathway. The prevalence of the ED pathway is puzzling as it produces only one ATP per glucose--half as much as the EMP pathway. We argue that the diversity of prokaryotic glucose metabolism may reflect a tradeoff between a pathway's energy (ATP) yield and the amount of enzymatic protein required to catalyze pathway flux. We introduce methods for analyzing pathways in terms of thermodynamics and kinetics and show that the ED pathway is expected to require several-fold less enzymatic protein to achieve the same glucose conversion rate as the EMP pathway. Through genomic analysis, we further show that prokaryotes use different glycolytic pathways depending on their energy supply. Specifically, energy-deprived anaerobes overwhelmingly rely upon the higher ATP yield of the EMP pathway, whereas the ED pathway is common among facultative anaerobes and even more common among aerobes. In addition to demonstrating how protein costs can explain the use of alternative metabolic strategies, this study illustrates a direct connection between an organism's environment and the thermodynamic and biochemical properties of the metabolic pathways it employs.

Protein levels are a dominant factor shaping natural and synthetic biological systems. Although proper functioning of metabolic pathways relies on precise control of enzyme levels, the experimental ability to balance the levels of many genes in parallel is a major outstanding challenge. Here, we introduce a rapid and modular method to span the expression space of several proteins in parallel. By combinatorially pairing genes with a compact set of ribosome-binding sites, we modulate protein abundance by several orders of magnitude. We demonstrate our strategy by using a synthetic operon containing fluorescent proteins to span a 3D color space. Using the same approach, we modulate a recombinant carotenoid biosynthesis pathway in Escherichia coli to reveal a diversity of phenotypes, each characterized by a distinct carotenoid accumulation profile. In a single combinatorial assembly, we achieve a yield of the industrially valuable compound astaxanthin 4-fold higher than previously reported. The methodology presented here provides an efficient tool for exploring a high-dimensional expression space to locate desirable phenotypes.

Bacteria adapt to environmental stimuli by adjusting their transcriptomes in a complex manner, the full potential of which has yet to be established for any individual bacterial species. Here, we report the transcriptomes of Bacillus subtilis exposed to a wide range of environmental and nutritional conditions that the organism might encounter in nature. We comprehensively mapped transcription units (TUs) and grouped 2935 promoters into regulons controlled by various RNA polymerase sigma factors, accounting for ~66% of the observed variance in transcriptional activity. This global classification of promoters and detailed description of TUs revealed that a large proportion of the detected antisense RNAs arose from potentially spurious transcription initiation by alternative sigma factors and from imperfect control of transcription termination.

Adaptation of cells to environmental changes requires dynamic interactions between metabolic and regulatory networks, but studies typically address only one or a few layers of regulation. For nutritional shifts between two preferred carbon sources of Bacillus subtilis, we combined statistical and model-based data analyses of dynamic transcript, protein, and metabolite abundances and promoter activities. Adaptation to malate was rapid and primarily controlled posttranscriptionally compared with the slow, mainly transcriptionally controlled adaptation to glucose that entailed nearly half of the known transcription regulation network. Interactions across multiple levels of regulation were involved in adaptive changes that could also be achieved by controlling single genes. Our analysis suggests that global trade-offs and evolutionary constraints provide incentives to favor complex control programs.

Background: To enable automatic searches, alignments, and model combination, the elements of systems biology models need to be compared and matched across models. Elements can be identified by machine-readable biological annotations, but assigning such annotations and matching non-annotated elements is tedious work and calls for automation., Results: A new method called "semantic propagation" allows the comparison of model elements based not only on their own annotations, but also on annotations of surrounding elements in the network. One may either propagate feature vectors, describing the annotations of individual elements, or quantitative similarities between elements from different models. Based on semantic propagation, we align partially annotated models and find annotations for non-annotated model elements., Conclusions: Semantic propagation and model alignment are included in the open-source library semanticSBML, available on sourceforge. Online services for model alignment and for annotation prediction can be used at http://www.semanticsbml.org.

The exploding number of computational models produced by Systems Biologists over the last years is an invitation to structure and exploit this new wealth of information. Researchers would like to trace models relevant to specific scientific questions, to explore their biological content, to align and combine them, and to match them with experimental data. To automate these processes, it is essential to consider semantic annotations, which describe their biological meaning. As a prerequisite for a wide range of computational methods, we propose general and flexible similarity measures for Systems Biology models computed from semantic annotations. By using these measures and a large extensible ontology, we implement a platform that can retrieve, cluster, and align Systems Biology models and experimental data sets. At present, its major application is the search for relevant models in the BioModels Database, starting from initial models, data sets, or lists of biological concepts. Beyond similarity searches, the representation of models by semantic feature vectors may pave the way for visualisation, exploration, and statistical analysis of large collections of models and corresponding data.

The kinetic parameters of enzymes are key to understanding the rate and specificity of most biological processes. Although specific trends are frequently studied for individual enzymes, global trends are rarely addressed. We performed an analysis of k(cat) and K(M) values of several thousand enzymes collected from the literature. We found that the "average enzyme" exhibits a k(cat) of ~0 s(-1) and a k(cat)/K(M) of ~10(5) s(-1) M(-1), much below the diffusion limit and the characteristic textbook portrayal of kinetically superior enzymes. Why do most enzymes exhibit moderate catalytic efficiencies? Maximal rates may not evolve in cases where weaker selection pressures are expected. We find, for example, that enzymes operating in secondary metabolism are, on average, ~30-fold slower than those of central metabolism. We also find indications that the physicochemical properties of substrates affect the kinetic parameters. Specifically, low molecular mass and hydrophobicity appear to limit K(M) optimization. In accordance, substitution with phosphate, CoA, or other large modifiers considerably lowers the K(M) values of enzymes utilizing the substituted substrates. It therefore appears that both evolutionary selection pressures and physicochemical constraints shape the kinetic parameters of enzymes. It also seems likely that the catalytic efficiency of some enzymes toward their natural substrates could be increased in many cases by natural or laboratory evolution.

Systems biology models can be reused within new simulation scenarios, as parts of more complex models or as sources of biochemical knowledge. Reusability does not come by itself but has to be ensured while creating a model. Most important, models should be designed to remain valid in different contexts-for example, for different experimental conditions-and be published in a standardized and well-documented form. Creating reusable models is worthwhile, but it requires some efforts when a model is developed, implemented, documented, and published. Minimum requirements for published systems biology models have been formulated by the MIRIAM initiative. Main criteria are completeness of information and documentation, availability of machine-readable models in standard formats, and semantic annotations connecting the model elements with entries in biological Web resources. In this chapter, we discuss the assumptions behind bottom-up modeling; present important standards like MIRIAM, the Systems Biology Markup Language (SBML), and the Systems Biology Graphical Notation (SBGN); and describe software tools and services for handling semantic annotations. Finally, we show how standards can facilitate the construction of large metabolic network models., (Copyright © 2011 Elsevier Inc. All rights reserved.)

Kinetic modeling of metabolic pathways has become a major field of systems biology. It combines structural information about metabolic pathways with quantitative enzymatic rate laws. Some of the kinetic constants needed for a model could be collected from ever-growing literature and public web resources, but they are often incomplete, incompatible, or simply not available. We address this lack of information by parameter balancing, a method to complete given sets of kinetic constants. Based on Bayesian parameter estimation, it exploits the thermodynamic dependencies among different biochemical quantities to guess realistic model parameters from available kinetic data. Our algorithm accounts for varying measurement conditions in the input data (pH value and temperature). It can process kinetic constants and state-dependent quantities such as metabolite concentrations or chemical potentials, and uses prior distributions and data augmentation to keep the estimated quantities within plausible ranges. An online service and free software for parameter balancing with models provided in SBML format (Systems Biology Markup Language) is accessible at www.semanticsbml.org. We demonstrate its practical use with a small model of the phosphofructokinase reaction and discuss its possible applications and limitations. In the future, parameter balancing could become an important routine step in the kinetic modeling of large metabolic networks.

Motivation: Standard rate laws are a key requisite for systematically turning metabolic networks into kinetic models. They should provide simple, general and biochemically plausible formulae for reaction velocities and reaction elasticities. At the same time, they need to respect thermodynamic relations between the kinetic constants and the metabolic fluxes and concentrations., Results: We present a family of reversible rate laws for reactions with arbitrary stoichiometries and various types of regulation, including mass-action, Michaelis-Menten and uni-uni reversible Hill kinetics as special cases. With a thermodynamically safe parameterization of these rate laws, parameter sets obtained by model fitting, sampling or optimization are guaranteed to lead to consistent chemical equilibrium states. A reformulation using saturation values yields simple formulae for rates and elasticities, which can be easily adjusted to the given stationary flux distributions. Furthermore, this formulation highlights the role of chemical potential differences as thermodynamic driving forces. We compare the modular rate laws to the thermodynamic-kinetic modelling formalism and discuss a simplified rate law in which the reaction rate directly depends on the reaction affinity. For automatic handling of modular rate laws, we propose a standard syntax and semantic annotations for the Systems Biology Markup Language., Availability: An online tool for inserting the rate laws into SBML models is freely available at www.semanticsbml.org., Supplementary Information: Supplementary data are available at Bioinformatics online.

Motivation: The availability of modern sequencing techniques has led to a rapid increase in the amount of reconstructed metabolic networks. Using these models as a platform for the analysis of high throughput transcriptomic, proteomic and metabolomic data can provide valuable insight into conditional changes in the metabolic activity of an organism. While transcriptomics and proteomics provide important insights into the hierarchical regulation of metabolic flux, metabolomics shed light on the actual enzyme activity through metabolic regulation and mass action effects. Here we introduce a new method, termed integrative omics-metabolic analysis (IOMA) that quantitatively integrates proteomic and metabolomic data with genome-scale metabolic models, to more accurately predict metabolic flux distributions. The method is formulated as a quadratic programming (QP) problem that seeks a steady-state flux distribution in which flux through reactions with measured proteomic and metabolomic data, is as consistent as possible with kinetically derived flux estimations., Results: IOMA is shown to successfully predict the metabolic state of human erythrocytes (compared to kinetic model simulations), showing a significant advantage over the commonly used methods flux balance analysis and minimization of metabolic adjustment. Thereafter, IOMA is shown to correctly predict metabolic fluxes in Escherichia coli under different gene knockouts for which both metabolomic and proteomic data is available, achieving higher prediction accuracy over the extant methods. Considering the lack of high-throughput flux measurements, while high-throughput metabolomic and proteomic data are becoming readily available, we expect IOMA to significantly contribute to future research of cellular metabolism.

Background: Yeast cells live in a highly fluctuating environment with respect to temperature, nutrients, and especially osmolarity. The Hog1 mitogen-activated protein kinase (MAPK) pathway is crucial for the adaption of yeast cells to external osmotic changes., Methodology/principal Findings: To better understand the osmo-adaption mechanism in the budding yeast Saccharomyces cerevisiae, we have developed a mathematical model and quantitatively investigated the Hog1 response to osmotic stress. The model agrees well with various experimental data for the Hog1 response to different types of osmotic changes. Kinetic analyses of the model indicate that budding yeast cells have evolved to protect themselves economically: while they show almost no response to fast pulse-like changes of osmolarity, they respond periodically and are well-adapted to osmotic changes with a certain frequency. To quantify the signal transduction efficiency of the osmo-adaption network, we introduced a measure of the signal response gain, which is defined as the ratio of output change integral to input (signal) change integral. Model simulations indicate that the Hog1 response gain shows bell-shaped response curves with respect to the duration of a single osmotic pulse and to the frequency of periodic square osmotic pulses, while for up-staircase (ramp) osmotic changes, the gain depends on the slope., Conclusions/significance: The model analyses suggest that budding yeast cells have selectively evolved to be optimized to some specific types of osmotic changes. In addition, our work implies that the signaling output can be dynamically controlled by fine-tuning the signal input profiles.

Summary: Systems Biology Markup Language (SBML) is the leading exchange format for mathematical models in Systems Biology. Semantic annotations link model elements with external knowledge via unique database identifiers and ontology terms, enabling software to check and process models by their biochemical meaning. Such information is essential for model merging, one of the key steps towards the construction of large kinetic models. SemanticSBML is a tool that helps users to check and edit MIRIAM annotations and SBO terms in SBML models. Using a large collection of biochemical names and database identifiers, it supports modellers in finding the right annotations and in merging existing models. Initially, an element matching is derived from the MIRIAM annotations and conflicting element attributes are categorized and highlighted. Conflicts can then be resolved automatically or manually, allowing the user to control the merging process in detail., Availability: SemanticSBML comes as a free software written in Python and released under the GPL 3. A Debian package, a source package for other Linux distributions, a Windows installer and an online version of semanticSBML with limited functionality are available at http://www.semanticsbml.org. A preinstalled version can be found on the Linux live DVD SB.OS, available at http://www.sbos.eu., Supplementary Information: Supplementary data are available at Bioinformatics online.