Mass conserved elementary kinetics is sufficient for the existence of a non-equilibrium steady state concentration

Living systems are forced away from thermodynamic equilibrium by exchange of mass and energy with their environment. In order to model a biochemical reaction network in a non-equilibrium state one requires a mathematical formulation to mimic this forcing. We provide a general formulation to force an arbitrary large kinetic model in a manner that is still consistent with the existence of a non-equilibrium steady state. We can guarantee the existence of a non-equilibrium steady state assuming only two conditions; that every reaction is mass balanced and that continuous kinetic reaction rate laws never lead to a negative molecule concentration. These conditions can be verified in polynomial time and are flexible enough to permit one to force a system away from equilibrium. In an expository biochemical example we show how a reversible, mass balanced perpetual reaction, with thermodynamically infeasible kinetic parameters, can be used to perpetually force a kinetic model of anaerobic glycolysis in a manner consistent with the existence of a steady state. Easily testable existence conditions are foundational for efforts to reliably compute non-equilibrium steady states in genome-scale biochemical kinetic models.Comment: 11 pages, 2 figures (v2 is now placed in proper context of the excellent 1962 paper by James Wei entitled "Axiomatic treatment of chemical reaction systems". In addition, section 4, on "Utility of steady state existence theorem" has been expanded.

MetaboTools: A comprehensive toolbox for analysis of genome-scale metabolic models

Metabolomic data sets provide a direct read-out of cellular phenotypes and are increasingly generated to study biological questions. Our previous work revealed the potential of analyzing extracellular metabolomic data in the context of the metabolic model using constraint-based modeling. Through this work, which consists of a protocol, a toolbox, and tutorials of two use cases, we make our methods available to the broader scientific community. The protocol describes, in a step-wise manner, the workflow of data integration and computational analysis. The MetaboTools comprise the Matlab code required to complete the workflow described in the protocol. Tutorials explain the computational steps for integration of two different data sets and demonstrate a comprehensive set of methods for the computational analysis of metabolic models and stratification thereof into different phenotypes. The presented workflow supports integrative analysis of multiple omics data sets. Importantly, all analysis tools can be applied to metabolic models without performing the entire workflow. Taken together, this protocol constitutes a comprehensive guide to the intra-model analysis of extracellular metabolomic data and a resource offering a broad set of computational analysis tools for a wide biomedical and non-biomedical research community

Conditions for duality between fluxes and concentrations in biochemical networks

Mathematical and computational modelling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modelling from either perspective equivalent to the other? Mathematical duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one manner. We present a novel stoichiometric condition that is necessary and sufficient for duality between unidirectional fluxes and concentrations. Our numerical experiments, with computational models derived from a range of genome-scale biochemical networks, suggest that this flux-concentration duality is a pervasive property of biochemical networks. We also provide a combinatorial characterisation that is sufficient to ensure flux-concentration duality. That is, for every two disjoint sets of molecular species, there is at least one reaction complex that involves species from only one of the two sets. When unidirectional fluxes and molecular species concentrations are dual vectors, this implies that the behaviour of the corresponding biochemical network can be described entirely in terms of either concentrations or unidirectional fluxes

A pilot study demonstrating the altered gut microbiota functionality in stable adults with Cystic Fibrosis

peer-reviewedCystic Fibrosis (CF) and its treatment result in an altered gut microbiota composition compared to non-CF controls. However, the impact of this on gut microbiota functionality has not been extensively characterised. Our aim was to conduct a proof-of-principle study to investigate if measurable changes in gut microbiota functionality occur in adult CF patients compared to controls. Metagenomic DNA was extracted from faecal samples from six CF patients and six non-CF controls and shotgun metagenomic sequencing was performed on the MiSeq platform. Metabolomic analysis using gas chromatography-mass spectrometry was conducted on faecal water. The gut microbiota of the CF group was significantly different compared to the non-CF controls, with significantly increased Firmicutes and decreased Bacteroidetes. Functionality was altered, with higher pathway abundances and gene families involved in lipid (e.g. PWY 6284 unsaturated fatty acid biosynthesis (p = 0.016)) and xenobiotic metabolism (e.g. PWY-5430 meta-cleavage pathway of aromatic compounds (p = 0.004)) in CF patients compared to the controls. Significant differences in metabolites occurred between the two groups. This proof-of-principle study demonstrates that measurable changes in gut microbiota functionality occur in CF patients compared to controls. Larger studies are thus needed to interrogate this further

A Systems Biology Approach to Drug Targets in Pseudomonas aeruginosa Biofilm

Antibiotic resistance is an increasing problem in the health care system and we are in a constant race with evolving bacteria. Biofilm-associated growth is thought to play a key role in bacterial adaptability and antibiotic resistance. We employed a systems biology approach to identify candidate drug targets for biofilm-associated bacteria by imitating specific microenvironments found in microbial communities associated with biofilm formation. A previously reconstructed metabolic model of Pseudomonas aeruginosa (PA) was used to study the effect of gene deletion on bacterial growth in planktonic and biofilm-like environmental conditions. A set of 26 genes essential in both conditions was identified. Moreover, these genes have no homology with any human gene. While none of these genes were essential in only one of the conditions, we found condition-dependent genes, which could be used to slow growth specifically in biofilm-associated PA. Furthermore, we performed a double gene deletion study and obtained 17 combinations consisting of 21 different genes, which were conditionally essential. While most of the difference in double essential gene sets could be explained by different medium composition found in biofilm-like and planktonic conditions, we observed a clear effect of changes in oxygen availability on the growth performance. Eight gene pairs were found to be synthetic lethal in oxygen-limited conditions. These gene sets may serve as novel metabolic drug targets to combat particularly biofilm-associated PA. Taken together, this study demonstrates that metabolic modeling of human pathogens can be used to identify oxygen-sensitive drug targets and thus, that this systems biology approach represents a powerful tool to identify novel candidate antibiotic targets

Genome-Scale Reconstruction of Escherichia coli's Transcriptional and Translational Machinery: A Knowledge Base, Its Mathematical Formulation, and Its Functional Characterization

Metabolic network reconstructions represent valuable scaffolds for ‘-omics’ data integration and are used to computationally interrogate network properties. However, they do not explicitly account for the synthesis of macromolecules (i.e., proteins and RNA). Here, we present the first genome-scale, fine-grained reconstruction of Escherichia coli's transcriptional and translational machinery, which produces 423 functional gene products in a sequence-specific manner and accounts for all necessary chemical transformations. Legacy data from over 500 publications and three databases were reviewed, and many pathways were considered, including stable RNA maturation and modification, protein complex formation, and iron–sulfur cluster biogenesis. This reconstruction represents the most comprehensive knowledge base for these important cellular functions in E. coli and is unique in its scope. Furthermore, it was converted into a mathematical model and used to: (1) quantitatively integrate gene expression data as reaction constraints and (2) compute functional network states, which were compared to reported experimental data. For example, the model predicted accurately the ribosome production, without any parameterization. Also, in silico rRNA operon deletion suggested that a high RNA polymerase density on the remaining rRNA operons is needed to reproduce the reported experimental ribosome numbers. Moreover, functional protein modules were determined, and many were found to contain gene products from multiple subsystems, highlighting the functional interaction of these proteins. This genome-scale reconstruction of E. coli's transcriptional and translational machinery presents a milestone in systems biology because it will enable quantitative integration of ‘-omics’ datasets and thus the study of the mechanistic principles underlying the genotype–phenotype relationship