EFMlrs: a Python package for elementary flux mode enumeration via lexicographic reverse search

Background Elementary flux mode (EFM) analysis is a well-established, yet computationally challenging approach to characterize metabolic networks. Standard algorithms require huge amounts of memory and lack scalability which limits their application to single servers and consequently limits a comprehensive analysis to medium-scale networks. Recently, Avis et al. developed —a parallel version of the lexicographic reverse search (lrs) algorithm, which, in principle, enables an EFM analysis on high-performance computing environments (Avis and Jordan. mplrs: a scalable parallel vertex/facet enumeration code. arXiv:1511.06487, 2017). Here we test its applicability for EFM enumeration. Results We developed , a Python package that gives users access to the enumeration capabilities of . uses COBRApy to process metabolic models from sbml files, performs loss-free compressions of the stoichiometric matrix, and generates suitable inputs for as well as , providing support not only for our proposed new method for EFM enumeration but also for already established tools. By leveraging COBRApy, also allows the application of additional reaction boundaries and seamlessly integrates into existing workflows. Conclusion We show that due to ’s properties, the algorithm is perfectly suited for high-performance computing (HPC) and thus offers new possibilities for the unbiased analysis of substantially larger metabolic models via EFM analyses. is an open-source program that comes together with a designated workflow and can be easily installed via pip.

Thermodynamic and Kinetic Modeling of Co-utilization of Glucose and Xylose for 2,3-BDO Production by Zymomonas mobilis

Prior engineering of the ethanologen Zymomonas mobilis has enabled it to metabolize xylose and to produce 2,3-butanediol (2,3-BDO) as a dominant fermentation product. When co-fermenting with xylose, glucose is preferentially utilized, even though xylose metabolism generates ATP more efficiently during 2,3-BDO production on a BDO-mol basis. To gain a deeper understanding of Z. mobilis metabolism, we first estimated the kinetic parameters of the glucose facilitator protein of Z. mobilis by fitting a kinetic uptake model, which shows that the maximum transport capacity of glucose is seven times higher than that of xylose, and glucose is six times more affinitive to the transporter than xylose. With these estimated kinetic parameters, we further compared the thermodynamic driving force and enzyme protein cost of glucose and xylose metabolism. It is found that, although 20% more ATP can be yielded stoichiometrically during xylose utilization, glucose metabolism is thermodynamically more favorable with 6% greater cumulative Gibbs free energy change, more economical with 37% less enzyme cost required at the initial stage and sustains the advantage of the thermodynamic driving force and protein cost through the fermentation process until glucose is exhausted. Glucose-6-phosphate dehydrogenase (g6pdh), glyceraldehyde-3-phosphate dehydrogenase (gapdh) and phosphoglycerate mutase (pgm) are identified as thermodynamic bottlenecks in glucose utilization pathway, as well as two more enzymes of xylose isomerase and ribulose-5-phosphate epimerase in xylose metabolism. Acetolactate synthase is found as potential engineering target for optimized protein cost supporting unit metabolic flux. Pathway analysis was then extended to the core stoichiometric matrix of Z. mobilis metabolism. Growth was simulated by dynamic flux balance analysis and the model was validated showing good agreement with experimental data. Dynamic FBA simulations suggest that a high agitation is preferable to increase 2,3-BDO productivity while a moderate agitation will benefit the 2,3-BDO titer. Taken together, this work provides thermodynamic and kinetic insights of Z. mobilis metabolism on dual substrates, and guidance of bioengineering efforts to increase hydrocarbon fuel production.

Speeding up the core algorithm for the dual calculation of minimal cut sets in large metabolic networks

Background The concept of minimal cut sets (MCS) has become an important mathematical framework for analyzing and (re)designing metabolic networks. However, the calculation of MCS in genome-scale metabolic models is a complex computational problem. The development of duality-based algorithms in the last years allowed the enumeration of thousands of MCS in genome-scale networks by solving mixed-integer linear problems (MILP). A recent advancement in this field was the introduction of the MCS2 approach. In contrast to the Farkas-lemma-based dual system used in earlier studies, the MCS2 approach employs a more condensed representation of the dual system based on the nullspace of the stoichiometric matrix, which, due to its reduced dimension, holds promise to further enhance MCS computations. Results In this work, we introduce several new variants and modifications of duality-based MCS algorithms and benchmark their effects on the overall performance. As one major result, we generalize the original MCS2 approach (which was limited to blocking the operation of certain target reactions) to the most general case of MCS computations with arbitrary target and desired regions. Building upon these developments, we introduce a new MILP variant which allows maximal flexibility in the formulation of MCS problems and fully leverages the reduced size of the nullspace-based dual system. With a comprehensive set of benchmarks, we show that the MILP with the nullspace-based dual system outperforms the MILP with the Farkas-lemma-based dual system speeding up MCS computation with an averaged factor of approximately 2.5. We furthermore present several simplifications in the formulation of constraints, mainly related to binary variables, which further enhance the performance of MCS-related MILP. However, the benchmarks also reveal that some highly condensed formulations of constraints, especially on reversible reactions, may lead to worse behavior when compared to variants with a larger number of (more explicit) constraints and involved variables. Conclusions Our results further enhance the algorithmic toolbox for MCS calculations and are of general importance for theoretical developments as well as for practical applications of the MCS framework.

Model Reduction in Large Chemical Systems- an Alternative Method Applying Discrete Approximation

No numerical data. <p><b><br> </b>Dynamic model reduction techniques based on the decomposition of the stoichiometric matrix to find the chemical invariant, break down if axial diffusion is present in a tubular reactor.</p> <p>Straightforward discretization of the partial differential operator does indeed show that the resulting discrete dynamic model cannot generally be partioned to obtain the reaction variant vector and the reaction invariant (asymptotic) vector. However, the paper demonstrate that, if the diffusional tubular reactor is discretely and approximatively represented by tanks-in-series, then matrix approaches to successfully find the chemical variant and invariant vectors of the resulting chemical process model is possible. </p>

Model Reduction in Large Chemical Systems- an Alternative Method Applying Discrete Approximation

No numerical data. <p><b><br> </b>Dynamic model reduction techniques based on the decomposition of the stoichiometric matrix to find the chemical invariant, break down if axial diffusion is present in a tubular reactor.</p> <p>Straightforward discretization of the partial differential operator does indeed show that the resulting discrete dynamic model cannot generally be partioned to obtain the reaction variant vector and the reaction invariant (asymptotic) vector. However, the paper demonstrate that, if the diffusional tubular reactor is discretely and approximatively represented by tanks-in-series, then matrix approaches to successfully find the chemical variant and invariant vectors of the resulting chemical process model is possible. </p>

Exploiting transcriptomic data in genome-scale metabolic networks: new insights into obesity

Systems Biology is a holistic approach, based on the integration of multiscale models and different kinds of data, aimed at studying the underlying mechanisms of complex biological systems. A GEnome-scale metabolic Model (GEM) is the representation of the metabolic structure of a cell in terms of chemical reactions, involved metabolites, and associated genes. GEMs provide a functional scaffold for constraint-based mathematical methods aimed at simulating and predicting metabolic fluxes in living organisms. The most widely used constraint-based method is the Flux Balance Analysis (FBA), that exploits the stoichiometric matrix, a mathematical representation of the relations between substrates and products of all the reactions in the GEM. Recently, the increasing availability of large amounts of high-throughput sequencing data has fostered the research of new approaches in which the structural information described by GEMs is integrated with the knowledge coming from omics data, with the aim to build more accurate descriptions of metabolic states. Here we propose to use a recently published method, in which transcriptomic data are integrated into genome-scale metabolic models through the maximization of the correlation between the steady-state pattern of the predicted fluxes and the corresponding absolute gene expression data generated under the condition of interest. This approach has the interesting property that no cell growth function must be minimized to execute the model. We used this methodology to simulate a novel GEM of the human adipocyte (iAdipocytes1809), with the aim of getting new insights into the metabolic mechanisms underlying obesity and its relationships with cancer. Obesity is a complex disorder associated with an increased risk of developing several comorbid chronic diseases, ranging from cardiovascular alterations to diabetes, hypertension and cancer. In particular, weight increase and obesity have been identified as the most important risk and prognostic factors for breast cancer, especially in postmenopausal women. We discuss some preliminary results obtained with this approach, hilighting the importance of data integration, and the need for developing new methods that could help in improving our interpretation of biological phenomena.

Exploiting transcriptomic data in genome-scale metabolic networks: new insights into obesity

Systems Biology is a holistic approach, based on the integration of multiscale models and different kinds of data, aimed at studying the underlying mechanisms of complex biological systems. A GEnome-scale metabolic Model (GEM) is the representation of the metabolic structure of a cell in terms of chemical reactions, involved metabolites, and associated genes. GEMs provide a functional scaffold for constraint-based mathematical methods aimed at simulating and predicting metabolic fluxes in living organisms. The most widely used constraint-based method is the Flux Balance Analysis (FBA), that exploits the stoichiometric matrix, a mathematical representation of the relations between substrates and products of all the reactions in the GEM. Recently, the increasing availability of large amounts of high-throughput sequencing data has fostered the research of new approaches in which the structural information described by GEMs is integrated with the knowledge coming from omics data, with the aim to build more accurate descriptions of metabolic states. Here we propose to use a recently published method, in which transcriptomic data are integrated into genome-scale metabolic models through the maximization of the correlation between the steady-state pattern of the predicted fluxes and the corresponding absolute gene expression data generated under the condition of interest. This approach has the interesting property that no cell growth function must be minimized to execute the model. We used this methodology to simulate a novel GEM of the human adipocyte (iAdipocytes1809), with the aim of getting new insights into the metabolic mechanisms underlying obesity and its relationships with cancer. Obesity is a complex disorder associated with an increased risk of developing several comorbid chronic diseases, ranging from cardiovascular alterations to diabetes, hypertension and cancer. In particular, weight increase and obesity have been identified as the most important risk and prognostic factors for breast cancer, especially in postmenopausal women. We discuss some preliminary results obtained with this approach, hilighting the importance of data integration, and the need for developing new methods that could help in improving our interpretation of biological phenomena.

Energy-based analysis of biomolecular pathways

Decomposition of biomolecular reaction networks into pathways is a powerful approach to the analysis of metabolic and signalling networks. Current approaches based on analysis of the stoichiometric matrix reveal information about steady-state mass flows (reaction rates) through the network. In this work, we show how pathway analysis of biomolecular networks can be extended using an energy-based approach to provide information about energy flows through the network. This energy-based approach is developed using the engineering-inspired bond graph methodology to represent biomolecular reaction networks. The approach is introduced using glycolysis as an exemplar; and is then applied to analyse the efficiency of free energy transduction in a biomolecular cycle model of a transporter protein [sodium-glucose transport protein 1 (SGLT1)]. The overall aim of our work is to present a framework for modelling and analysis of biomolecular reactions and processes which considers energy flows and losses as well as mass transport.