Metabolic models condense biochemical knowledge about organisms in a structured and standardised way. As large-scale network reconstructions are readily available for many organisms, genome-scale models are being widely used among modellers and engineers. However, these large models can be difficult to analyse and visualise, and occasionally generate predictions that are hard to interpret or even biologically unrealistic. Of the thousands of enzymatic reactions in a typical bacterial metabolism, only a few hundred form the metabolic pathways essential to produce energy carriers and biosynthetic precursors. These pathways carry relatively high flux, are central to maintaining and reproducing the cell, and provide precursors and energy to engineered metabolic pathways. Focusing on these central metabolic subsystems, we present iCH360, a manually curated medium-scale model of energy and biosynthesis metabolism for the well-studied bacterium Escherichia coli K-12 MG1655. The model is a sub-network of the most recent genome-scale reconstruction, iML1515, and comes with an updated layer of database annotations and a range of metabolic maps for visualisation. We enriched the stoichiometric network with extensive biological information and quantitative data, including thermodynamic and kinetic constants, enhancing the scope and applicability of the model. In addition, we assess the properties of this model in comparison to its genome-scale parent and demonstrate the use of the network and supporting data in various scenarios, including enzyme-constrained flux balance analysis, elementary flux mode analysis, and thermodynamic analysis. Overall, this model holds the potential to become a reference medium-scale metabolic model for E. coli.

MOTIVATION: We achieve a significant improvement in thermodynamic-based flux analysis (TFA) by introducing multivariate treatment of thermodynamic variables and leveraging component contribution, the state-of-the-art implementation of the group contribution methodology. Overall, the method greatly reduces the uncertainty of thermodynamic variables. RESULTS: We present multiTFA, a Python implementation of our framework. We evaluated our application using the core Escherichia coli model and achieved a median reduction of 6.8 kJ/mol in reaction Gibbs free energy ranges, while three out of 12 reactions in glycolysis changed from reversible to irreversible. AVAILABILITY AND IMPLEMENTATION: Our framework along with documentation is available on https://github.com/biosustain/multitfa. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Thermodynamics dictates the structure and function of metabolism. Redox reactions drive cellular energy and material flow. Hence, accurately quantifying the thermodynamics of redox reactions should reveal design principles that shape cellular metabolism. However, only few redox potentials have been measured, and mostly with inconsistent experimental setups. Here, we develop a quantum chemistry approach to calculate redox potentials of biochemical reactions and demonstrate our method predicts experimentally measured potentials with unparalleled accuracy. We then calculate the potentials of all redox pairs that can be generated from biochemically relevant compounds and highlight fundamental trends in redox biochemistry. We further address the question of why NAD/NADP are used as primary electron carriers, demonstrating how their physiological potential range fits the reactions of central metabolism and minimizes the concentration of reactive carbonyls. The use of quantum chemistry can revolutionize our understanding of biochemical phenomena by enabling fast and accurate calculation of thermodynamic values.

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.

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: : [email protected].

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.

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.

Standard Gibbs energies of reactions are increasingly being used in metabolic modeling for applying thermodynamic constraints on reaction rates, metabolite concentrations and kinetic parameters. The increasing scope and diversity of metabolic models has led scientists to look for genome-scale solutions that can estimate the standard Gibbs energy of all the reactions in metabolism. Group contribution methods greatly increase coverage, albeit at the price of decreased precision. We present here a way to combine the estimations of group contribution with the more accurate reactant contributions by decomposing each reaction into two parts and applying one of the methods on each of them. This method gives priority to the reactant contributions over group contributions while guaranteeing that all estimations will be consistent, i.e. will not violate the first law of thermodynamics. We show that there is a significant increase in the accuracy of our estimations compared to standard group contribution. Specifically, our cross-validation results show an 80% reduction in the median absolute residual for reactions that can be derived by reactant contributions only. We provide the full framework and source code for deriving estimates of standard reaction Gibbs energy, as well as confidence intervals, and believe this will facilitate the wide use of thermodynamic data for a better understanding of metabolism.

The common approaches to feature extraction in speech processing are generative and parametric although they are highly sensitive to violations of their model assumptions. Here, we advocate the non-parametric Information Bottleneck (IB). IB is an information theoretic approach that extends minimal sufficient statistics. However, unlike minimal sufficient statistics which does not allow any relevant data loss, IB method enables a principled tradeoff between compactness and the amount of target-related information. IB's ability to improve a broad range of recognition tasks is illustrated for model dimension reduction tasks for speaker recognition and model clustering for age-group verification.

MOTIVATION: The laws of thermodynamics describe a direct, quantitative relationship between metabolite concentrations and reaction directionality. Despite great efforts, thermodynamic data suffer from limited coverage, scattered accessibility and non-standard annotations. We present a framework for unifying thermodynamic data from multiple sources and demonstrate two new techniques for extrapolating the Gibbs energies of unmeasured reactions and conditions. RESULTS: Both methods account for changes in cellular conditions (pH, ionic strength, etc.) by using linear regression over the ΔG(○) of pseudoisomers and reactions. The Pseudoisomeric Reactant Contribution method systematically infers compound formation energies using measured K' and pK(a) data. The Pseudoisomeric Group Contribution method extends the group contribution method and achieves a high coverage of unmeasured reactions. We define a continuous index that predicts the reversibility of a reaction under a given physiological concentration range. In the characteristic physiological range 3μM-3mM, we find that roughly half of the reactions in Escherichia coli's metabolism are reversible. These new tools can increase the accuracy of thermodynamic-based models, especially in non-standard pH and ionic strengths. The reversibility index can help modelers decide which reactions are reversible in physiological conditions. AVAILABILITY: Freely available on the web at: http://equilibrator.weizmann.ac.il. Website implemented in Python, MySQL, Apache and Django, with all major browsers supported. The framework is open-source (code.google.com/p/milo-lab), implemented in pure Python and tested mainly on Linux. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

What governs the concentrations of metabolites within living cells? Beyond specific metabolic and enzymatic considerations, are there global trends that affect their values? We hypothesize that the physico-chemical properties of metabolites considerably affect their in-vivo concentrations. The recently achieved experimental capability to measure the concentrations of many metabolites simultaneously has made the testing of this hypothesis possible. Here, we analyze such recently available data sets of metabolite concentrations within E. coli, S. cerevisiae, B. subtilis and human. Overall, these data sets encompass more than twenty conditions, each containing dozens (28-108) of simultaneously measured metabolites. We test for correlations with various physico-chemical properties and find that the number of charged atoms, non-polar surface area, lipophilicity and solubility consistently correlate with concentration. In most data sets, a change in one of these properties elicits a ~100 fold increase in metabolite concentrations. We find that the non-polar surface area and number of charged atoms account for almost half of the variation in concentrations in the most reliable and comprehensive data set. Analyzing specific groups of metabolites, such as amino-acids or phosphorylated nucleotides, reveals even a higher dependence of concentration on hydrophobicity. We suggest that these findings can be explained by evolutionary constraints imposed on metabolite concentrations and discuss possible selective pressures that can account for them. These include the reduction of solute leakage through the lipid membrane, avoidance of deleterious aggregates and reduction of non-specific hydrophobic binding. By highlighting the global constraints imposed on metabolic pathways, future research could shed light onto aspects of biochemical evolution and the chemical constraints that bound metabolic engineering efforts.

This paper explores a novel approach for the extraction of relevant information in speaker recognition tasks. This approach uses a principled information theoretic framework-the Information Bottleneck method (IB). In our application, the method compresses the acoustic data while preserving mostly the relevant information for speaker identification. This paper focuses on a continuous version of the IB method known as the Gaussian Information Bottleneck (GIB). This version assumes that both the source and target variables are high dimensional multivariate Gaussian variables. The GIB was applied in our work to the Super Vector (SV) dimension reduction conundrum. Experiments were conducted on the male part of the NIST SRE 2005 corpora. The GIB representation was compared to other dimension reduction techniques and to a baseline system. In our experiments, the GIB outperformed the baseline system; achieving a 6.1% Equal Error Rate (EER) compared to the 15.1 % EER of a baseline system.