References of "Fleming, Ronan MT 50001792"
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See detailAccelerating the DC algorithm for smooth functions
Aragón Artacho, Francisco Javier UL; Fleming, Ronan MT UL; Phan, Vuong UL

E-print/Working paper (2015)

We introduce two new algorithms to minimise smooth difference of convex (DC) functions that accelerate the convergence of the classical DC algorithm (DCA). We prove that the point computed by DCA can be ... [more ▼]

We introduce two new algorithms to minimise smooth difference of convex (DC) functions that accelerate the convergence of the classical DC algorithm (DCA). We prove that the point computed by DCA can be used to define a descent direction for the objective function evaluated at this point. Our algorithms are based on a combination of DCA together with a line search step that uses this descent direction. Convergence of the algorithms is proved and the rate of convergence is analysed under the Łojasiewicz property of the objective function. We apply our algorithms to a class of smooth DC programs arising in the study of biochemical reaction networks, where the objective function is real analytic and thus satisfies the Łojasiewicz property. Numerical tests on various biochemical models clearly show that our algorithms outperforms DCA, being on average more than four times faster in both computational time and the number of iterations. The algorithms are globally convergent to a non-equilibrium steady state of a biochemical network, with only chemically consistent restrictions on the network topology. [less ▲]

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See detailDo Genome-scale Models Need Exact Solvers or Clearer Standards?
Ebrahim, Ali; Almaas, Eivind; Bauer, Eugen UL et al

in Molecular Systems Biology (2015), 11(10), 1

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See detailPrediction of intracellular metabolic states from extracellular metabolomic data
Aurich, Maike Kathrin UL; Paglia, Guiseppe; Rolfsson, Ottar et al

in Metabolomics : Official journal of the Metabolomic Society (2015), 11(3), 603-619

Metabolic models can provide a mechanistic framework to analyze information-rich omics data sets, and are increasingly being used to investigate metabolic alternations in human diseases. An expression of ... [more ▼]

Metabolic models can provide a mechanistic framework to analyze information-rich omics data sets, and are increasingly being used to investigate metabolic alternations in human diseases. An expression of the altered metabolic pathway utilization is the selection of metabolites consumed and released by cells. However, methods for the inference of intracellular metabolic states from extracellular measurements in the context of metabolic models remain underdeveloped compared to methods for other omics data. Herein, we describe a workflow for such an integrative analysis emphasizing on extracellular metabolomics data. We demonstrate, using the lymphoblastic leukemia cell lines Molt-4 and CCRF-CEM, how our methods can reveal differences in cell metabolism. Our models explain metabolite uptake and secretion by predicting a more glycolytic phenotype for the CCRFCEM model and a more oxidative phenotype for the Molt-4 model, which was supported by our experimental data. Gene expression analysis revealed altered expression of gene products at key regulatory steps in those central metabolic pathways, and literature query emphasized the role of these genes in cancer metabolism. Moreover, in silico gene knock-outs identified unique control points for each cell line model, e.g., phosphoglycerate dehydrogenase for the Molt-4 model. Thus, our workflow is well-suited to the characterization of cellular metabolic traits based on extracellular metabolomic data, and it allows the integration of multiple omics data sets into a cohesive picture based on a defined model context. [less ▲]

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See detailA constraint-based modelling approach to metabolic dysfunction in Parkinson's disease
Mao, Longfei UL; Nicolae, Averina UL; Oliveira, Miguel UL et al

in Computational and Structural Biotechnology Journal (2015), 13

Abstract One of the hallmarks of sporadic Parkinson's disease is degeneration of dopaminergic neurons in the pars compacta of the substantia nigra. The aetiopathogenesis of this degeneration is still not ... [more ▼]

Abstract One of the hallmarks of sporadic Parkinson's disease is degeneration of dopaminergic neurons in the pars compacta of the substantia nigra. The aetiopathogenesis of this degeneration is still not fully understood, with dysfunction of many biochemical pathways in different subsystems suggested to be involved. Recent advances in constraint-based modelling approaches hold great potential to systematically examine the relative contribution of dysfunction in disparate pathways to dopaminergic neuronal degeneration, but few studies have employed these methods in Parkinson's disease research. Therefore, this review outlines a framework for future constraint-based modelling of dopaminergic neuronal metabolism to decipher the multi-factorial mechanisms underlying the neuronal pathology of Parkinson's disease. [less ▲]

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See detailGlobally convergent algorithms for finding zeros of duplomonotone mappings
Aragón Artacho, Francisco Javier UL; Fleming, Ronan MT UL

in Optimization Letters (2015), 3(3), 569584

We introduce a new class of mappings, called duplomonotone, which is strictly broader than the class of monotone mappings. We study some of the main properties of duplomonotone functions and provide ... [more ▼]

We introduce a new class of mappings, called duplomonotone, which is strictly broader than the class of monotone mappings. We study some of the main properties of duplomonotone functions and provide various examples, including nonlinear duplomonotone functions arising from the study of systems of biochemical reactions. Finally, we present three variations of a derivative-free line search algorithm for finding zeros of systems of duplomonotone equations, and we prove their linear convergence to a zero of the function. [less ▲]

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See detailFASTGAPFILL: Efficient gap filling in metabolic networks
Thiele, Ines UL; Vlassis, Nikos UL; Fleming, Ronan MT UL

in Bioinformatics (2014), 30(17), 2529-2531

Motivation: Genome-scale metabolic reconstructions summarize current knowledge about a target organism in a structured manner and as such highlight missing information. Such gaps can be filled ... [more ▼]

Motivation: Genome-scale metabolic reconstructions summarize current knowledge about a target organism in a structured manner and as such highlight missing information. Such gaps can be filled algorithmically. Scalability limitations of available algorithms for gap filling hinder their application to compartmentalized reconstructions. Results:We present FASTGAPFILL, a computationally efficient,tractable extension to the COBRA toolbox that permits theidentification of candidate missing knowledge from a universal biochemical reaction database (e.g., KEGG) for a given (compart-mentalized) metabolic reconstruction. The stoichiometric consistency of the universal reaction database and of the metabolic reconstruction can be tested for permitting the computation of biologically more relevant solutions. We demonstrate the efficiency and scalability of fastGapFill on a range of metabolic reconstructions. [less ▲]

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See detailModeling the effects of commonly used drugs on human metabolism
Sahoo, Swagatika UL; Haraldsdottir, Hulda UL; Fleming, Ronan MT UL et al

in FEBS Journal (2014)

Metabolism contributes significantly to the pharmacokinetics and pharmacodynamics of a drug. In addition, diet and genetics have a profound effect on cellular metabolism under health and disease. Herein ... [more ▼]

Metabolism contributes significantly to the pharmacokinetics and pharmacodynamics of a drug. In addition, diet and genetics have a profound effect on cellular metabolism under health and disease. Herein, we assembled a comprehensive, literature-based drug metabolic reconstruction of the 18 most highly prescribed drug groups including statins, antihypertensives, immunosuppressants, and analgesics. This reconstruction captures in detail our current understanding of their absorption, intra-cellular distribution, metabolism, and elimination. We combined this drug module with the most comprehensive reconstruction of human metabolism, Recon 2, yielding Recon2_DM1796, which accounts for 2803 metabolites and 8161 reactions. By defining 50 specific drug objectives that captured the overall drug metabolism of these compounds, we investigated effects of dietary composition and inherited metabolic disorders on drug metabolism and drug-drug interactions. Our main findings include (i) shift in dietary patterns significantly affect statins and acetaminophen metabolism, (ii) disturbed statin metabolism contributes to the clinical phenotype of mitochondrial energy disorders, and (iii) the interaction between statins and cyclosporine can be explained by several common metabolic and transport pathways other than the previously established CYP3A4 connection. This work holds the potential for studying adverse drug reactions and designing patient-specific therapies. [less ▲]

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See detailExistence of Positive Steady States for Mass Conserving and Mass-Action Chemical Reaction Networks with a Single Terminal-Linkage Class
Fleming, Ronan MT UL; Akle, Santiago; Dalal, Onkar et al

in arXiv preprint arXiv:1105.2359 (2013)

We establish that mass conserving, single terminal-linkage networks of chemical reactions admit positive steady states regardless of network deficiency and the choice of reaction rate constants. This ... [more ▼]

We establish that mass conserving, single terminal-linkage networks of chemical reactions admit positive steady states regardless of network deficiency and the choice of reaction rate constants. This result holds for closed systems without material exchange across the boundary, as well as for open systems with material exchange at rates that satisfy a simple sufficient and necessary condition. Our proof uses a fixed point of a novel convex optimization formulation to find the steady state behavior of chemical reaction networks that satisfy the law of mass-action kinetics. A fixed point iteration can be used to compute these steady states, and we show that it converges for weakly reversible homogeneous systems. We report the results of our algorithm on numerical experiments. [less ▲]

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See detailConsistent Estimation of Gibbs Energy Using Component Contributions
Noor, Elad; Haraldsdottir, Hulda UL; Milo, Ron et al

in PLoS Computational Biology (2013), 9(7), 1003098

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 ... [more ▼]

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. [less ▲]

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See detailRobust flux balance analysis of multi- scale biochemical reaction networks
Sun, Y; Fleming, Ronan MT UL; Thiele, Ines UL et al

in BMC Bioinformatics (2013), 1(14), 240

Background:Biological processes such as metabolism, signaling, and macromolecular synthesis can be modeled as large networks of biochemical reactions. Large and comprehensive networks, like integrated ... [more ▼]

Background:Biological processes such as metabolism, signaling, and macromolecular synthesis can be modeled as large networks of biochemical reactions. Large and comprehensive networks, like integrated networks that represent metabolism and macromolecular synthesis, are inherently multiscale because reaction rates can vary over many orders of magnitude. They require special methods for accurate analysis because naive use of standard optimization systems can produce inaccurate or erroneously infeasible results. Results: We describe techniques enabling off-the-shelf optimization software to compute accurate solutions to the poorly scaled optimization problems arising from flux balance analysis of multiscale biochemical reaction networks. We implement lifting techniques for flux balance analysis within the openCOBRA toolbox and demonstrate our techniques using the first integrated reconstruction of metabolism and macromolecular synthesis for E. coli. Conclusion:Our techniques enable accurate flux balance analysis of multiscale networks using off-the-shelf optimization software. Although we describe lifting techniques in the context of flux balance analysis, our methods can be used to handle a variety of optimization problems arising from analysis of multiscale network reconstructions. [less ▲]

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See detailReal-time optical pH measurement in a standard microfluidic cell culture system
Magnusson, E. B.; Halldorsson, S.; Fleming, Ronan MT UL et al

in Biomedical Optics Express (2013), 4(9), 1749-1758

The rapid growth of microfluidic cell culturing in biological and biomedical research and industry calls for fast, non-invasive and reliable methods of evaluating conditions such as pH inside a ... [more ▼]

The rapid growth of microfluidic cell culturing in biological and biomedical research and industry calls for fast, non-invasive and reliable methods of evaluating conditions such as pH inside a microfluidic system. We show that by careful calibration it is possible to measure pH within microfluidic chambers with high accuracy and precision, using a direct single-pass measurement of light absorption in a commercially available phenol-red-containing cell culture medium. The measurement is carried out using a standard laboratory microscope and, contrary to previously reported methods, requires no modification of the microfluidic device design. We demonstrate the validity of this method by measuring absorption of light transmitted through 30-micrometer thick microfluidic chambers, using an inverted microscope fitted with a scientific-grade digital camera and two bandpass filters. In the pH range of 7\&\#x02013;8, our measurements have a standard deviation and absolute error below 0.05 for a measurement volume smaller than 4 nL. [less ▲]

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See detailSystems-level characterization of a host-microbe metabolic symbiosis in the mammalian gut.
Heinken, Almut Katrin UL; Sahoo, Swagatika UL; Fleming, Ronan MT UL et al

in Gut microbes (2013), 4(1), 28-40

The human gut microbiota consists of ten times more microorganisms than there are cells in our body, processes otherwise indigestible nutrients, and produces important energy precursors, essential amino ... [more ▼]

The human gut microbiota consists of ten times more microorganisms than there are cells in our body, processes otherwise indigestible nutrients, and produces important energy precursors, essential amino acids, and vitamins. In this study, we assembled and validated a genome-scale metabolic reconstruction of Bacteroides thetaiotaomicron (iAH991), a prominent representative of the human gut microbiota, consisting of 1488 reactions, 1152 metabolites, and 991 genes. To create a comprehensive metabolic model of host-microbe interactions, we integrated iAH991 with a previously published mouse metabolic reconstruction, which was extended for intestinal transport and absorption reactions. The two metabolic models were linked through a joint compartment, the lumen, allowing metabolite exchange and providing a route for simulating different dietary regimes. The resulting model consists of 7239 reactions, 5164 metabolites, and 2769 genes. We simultaneously modeled growth of mouse and B. thetaiotaomicron on five different diets varying in fat, carbohydrate, and protein content. The integrated model captured mutually beneficial cross-feeding as well as competitive interactions. Furthermore, we identified metabolites that were exchanged between the two organisms, which were compared with published metabolomics data. This analysis resulted for the first time in a comprehensive description of the co-metabolism between a host and its commensal microbe. We also demonstrate in silico that the presence of B. thetaiotaomicron could rescue the growth phenotype of the host with an otherwise lethal enzymopathy and vice versa. This systems approach represents a powerful tool for modeling metabolic interactions between a gut microbe and its host in health and disease. [less ▲]

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See detailA systems biology approach to studying the role of microbes in human health.
Thiele, Ines UL; Heinken, Almut Katrin UL; Fleming, Ronan MT UL

in Current Opinion in Biotechnology (2013), 24(1), 4-12

Host-microbe interactions play a crucial role in human health and disease. Of the various systems biology approaches, reconstruction of genome-scale metabolic networks combined with constraint-based ... [more ▼]

Host-microbe interactions play a crucial role in human health and disease. Of the various systems biology approaches, reconstruction of genome-scale metabolic networks combined with constraint-based modeling has been particularly successful at in silico predicting the phenotypic characteristics of single organisms. Here, we summarize recent studies, which have applied this approach to investigate microbe-microbe and host-microbe metabolic interactions. This approach can be also expanded to investigate the properties of an entire microbial community, as well as single organisms within the community. We illustrate that the constraint-based modeling approach is suitable to model host-microbe interactions at molecular resolution and will enable systematic investigation of metabolic links between the human host and its microbes. Such host-microbe models, combined with experimental data, will ultimately further our understanding of how microbes influence human health. [less ▲]

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See detailA community-driven global reconstruction of human metabolism.
Thiele, Ines UL; Swainston, N.; Fleming, Ronan MT UL et al

in Nature Biotechnology (2013), 31

Multiple models of human metabolism have been reconstructed, but each represents only a subset of our knowledge. Here we describe Recon 2, a community-driven, consensus ‘metabolic reconstruction’, which ... [more ▼]

Multiple models of human metabolism have been reconstructed, but each represents only a subset of our knowledge. Here we describe Recon 2, a community-driven, consensus ‘metabolic reconstruction’, which is the most comprehensive representation of human metabolism that is applicable to computational modeling. Compared with its predecessors, the reconstruction has improved topological and functional features, including ~2× more reactions and ~1.7× more unique metabolites. Using Recon 2 we predicted changes in metabolite biomarkers for 49 inborn errors of metabolism with 77% accuracy when compared to experimental data. Mapping metabolomic data and drug information onto Recon 2 demonstrates its potential for integrating and analyzing diverse data types. Using protein expression data, we automatically generated a compendium of 65 cell type–specific models, providing a basis for manual curation or investigation of cell-specific metabolic properties. Recon 2 will facilitate many future biomedical studies and is freely available at http://humanmetabolism.org/. [less ▲]

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See detailA systems biology approach to drug targets in Pseudomonas aeruginosa biofilm.
Sigurdsson, Gunnar; Fleming, Ronan MT UL; Heinken, Almut Katrin UL et al

in PLoS ONE (2012), 7(4), 34337

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 ... [more ▼]

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. [less ▲]

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See detailMultiscale modeling of metabolism and macromolecular synthesis in E. coli and its application to the evolution of codon usage.
Thiele, Ines UL; Fleming, Ronan MT UL; Que, Richard et al

in PLoS ONE (2012), 7(9), 45635

Biological systems are inherently hierarchal and multiscale in time and space. A major challenge of systems biology is to describe biological systems as a computational model, which can be used to derive ... [more ▼]

Biological systems are inherently hierarchal and multiscale in time and space. A major challenge of systems biology is to describe biological systems as a computational model, which can be used to derive novel hypothesis and drive experiments leading to new knowledge. The constraint-based reconstruction and analysis approach has been successfully applied to metabolism and to the macromolecular synthesis machinery assembly. Here, we present the first integrated stoichiometric multiscale model of metabolism and macromolecular synthesis for Escherichia coli K12 MG1655, which describes the sequence-specific synthesis and function of almost 2000 gene products at molecular detail. We added linear constraints, which couple enzyme synthesis and catalysis reactions. Comparison with experimental data showed improvement of growth phenotype prediction with the multiscale model over E. coli's metabolic model alone. Many of the genes covered by this integrated model are well conserved across enterobacters and other, less related bacteria. We addressed the question of whether the bias in synonymous codon usage could affect the growth phenotype and environmental niches that an organism can occupy. We created two classes of in silico strains, one with more biased codon usage and one with more equilibrated codon usage than the wildtype. The reduced growth phenotype in biased strains was caused by tRNA supply shortage, indicating that expansion of tRNA gene content or tRNA codon recognition allow E. coli to respond to changes in codon usage bias. Our analysis suggests that in order to maximize growth and to adapt to new environmental niches, codon usage and tRNA content must co-evolve. These results provide further evidence for the mutation-selection-drift balance theory of codon usage bias. This integrated multiscale reconstruction successfully demonstrates that the constraint-based modeling approach is well suited to whole-cell modeling endeavors. [less ▲]

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See detailMonitoring metabolites consumption and secretion in cultured cells using ultra-performance liquid chromatography quadrupole-time of flight mass spectrometry (UPLC-Q-ToF-MS).
Paglia, Giuseppe; Hrafnsdottir, Sigrun; Magnusdottir, Manuela et al

in Analytical and Bioanalytical Chemistry (2012), 402(3), 1183-98

Here we present an ultra-performance liquid chromatography-mass spectrometry (UPLC-MS) method for extracellular measurements of known and unexpected metabolites in parallel. The method was developed by ... [more ▼]

Here we present an ultra-performance liquid chromatography-mass spectrometry (UPLC-MS) method for extracellular measurements of known and unexpected metabolites in parallel. The method was developed by testing 86 metabolites, including amino acids, organic acids, sugars, purines, pyrimidines, vitamins, and nucleosides, that can be resolved by combining chromatographic and m/z dimensions. Subsequently, a targeted quantitative method was developed for 80 metabolites. The presented method combines a UPLC approach using hydrophilic interaction liquid chromatography (HILIC) and MS detection achieved by a hybrid quadrupole-time of flight (Q-ToF) mass spectrometer. The optimal setup was achieved by evaluating reproducibility and repeatability of the analytical platforms using pooled quality control samples to minimize the drift in instrumental performance over time. Then, the method was validated by analyzing extracellular metabolites from acute lymphoblastic leukemia cell lines (MOLT-4 and CCRF-CEM) treated with direct (A-769662) and indirect (AICAR) AMP activated kinase (AMPK) activators, monitoring uptake and secretion of the targeted compound over time. This analysis pointed towards a perturbed purine and pyrimidine catabolism upon AICAR treatment. Our data suggest that the method presented can be used for qualitative and quantitative analysis of extracellular metabolites and it is suitable for routine applications such as in vitro drug screening. [less ▲]

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See detailQuantitative Assignment of Reaction Directionality in a Multicompartmental Human Metabolic Reconstruction
Haraldsdottir, Hulda UL; Thiele, Ines UL; Fleming, Ronan MT UL

in Biophysical Journal (2012), 102(8), 17031711

Reaction directionality is a key constraint in the modeling of genome-scale metabolic networks. We thermodynamically constrained reaction directionality in a multicompartmental genome-scale model of human ... [more ▼]

Reaction directionality is a key constraint in the modeling of genome-scale metabolic networks. We thermodynamically constrained reaction directionality in a multicompartmental genome-scale model of human metabolism, Recon 1, by calculating, in vivo, standard transformed reaction Gibbs energy as a function of compartment-specific pH, electrical potential, and ionic strength. We show that compartmental pH is an important determinant of thermodynamically determined reaction directionality. The effects of pH on transport reaction thermodynamics are only seen to their full extent when metabolites are represented as pseudoisomer groups of multiple protonated species. We accurately predict the irreversibility of 387 reactions, with detailed propagation of uncertainty in input data, and manually curate the literature to resolve conflicting directionality assignments. In at least half of all cases, a prediction of a reversible reaction directionality is due to the paucity of compartment-specific quantitative metabolomic data, with remaining cases due to uncertainty in estimation of standard reaction Gibbs energy. This study points to the pressing need for 1), quantitative metabolomic data, and 2), experimental measurement of thermochemical properties for human metabolites. [less ▲]

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See detailMass conserved elementary kinetics is sufficient for the existence of a non-equilibrium steady state concentration.
Fleming, Ronan MT UL; Thiele, Ines UL

in Journal of Theoretical Biology (2012), 314

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 ... [more ▼]

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. With expository biochemical examples we show how reversible, mass balanced perpetual reaction(s), with thermodynamically infeasible kinetic parameters, can be used to perpetually force various kinetic models 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. [less ▲]

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