Exploring the associations between transcript levels and fluxes in constraint-based models of metabolism

Background Several computational methods have been developed that integrate transcriptomics data with genome-scale metabolic reconstructions to increase accuracy of inferences of intracellular metabolic flux distributions. Even though existing methods use transcript abundances as a proxy for enzyme activity, each method uses a different hypothesis and assumptions. Most methods implicitly assume a proportionality between transcript levels and flux through the corresponding function, although these proportionality constant(s) are often not explicitly mentioned nor discussed in any of the published methods. E-Flux is one such method and, in this algorithm, flux bounds are related to expression data, so that reactions associated with highly expressed genes are allowed to carry higher flux values. Results Here, we extended E-Flux and systematically evaluated the impact of an assumed proportionality constant on model predictions. We used data from published experiments with Escherichia coli and Saccharomyces cerevisiae and we compared the predictions of the algorithm to measured extracellular and intracellular fluxes. Conclusion We showed that detailed modelling using a proportionality constant can greatly impact the outcome of the analysis. This increases accuracy and allows for extraction of better physiological information.

MOFA: Multi-Objective Flux Analysis for the COBRA Toolbox

Multi-objective Optimization (MO) is an important tool for quantitative examination of the trade-offs faced by biological organisms. Using genome-scale constraint-based models of metabolism (GSMs),Multi-Objective Flux Analysis (MOFA) allows MO analyses of trade-offs among key biological tasks. The leading software package for conducting a plethora of different types of constraint-based analyses using GSMs is the COBRA Toolbox for MATLAB. We have developed a new add-on tool for this toolbox using Normalized Normal Constraint (NNC) that performs MOFA for a number of objectives only limited by computation power (n≤10). This development will facilitate MOFA analyses by COBRA's large user base and allow greater multi-faceted examination of metabolic trade-offs in complicated biological systems. Availability and Implementation: The MOFA software is freely available for download from https://bbs.llnl.gov under the GPL v2 license. The program runs on MATLAB with the COBRA software on Windows, Linux, and MacOS. It includes a detailed manual explaining the input and output of a simulation, a listing of the code's functions, and an example MOFA run using a well-curated GSM model of E. coli.

Metabolic flux configuration determination using information entropy

Constraint-based models use steady-state mass balances to define a solution space of flux configurations, which can be narrowed down by measuring as many fluxes as possible. Due to loops and redundant pathways, this process typically yields multiple alternative solutions. To address this ambiguity, flux sampling can estimate the probability distribution of each flux, or a flux configuration can be singled out by further minimizing the sum of fluxes according to the assumption that cellular metabolism favors states where enzyme-related costs are economized. However, flux sampling is susceptible to artifacts introduced by thermodynamically infeasible cycles and is it not clear if the economy of fluxes assumption (EFA) is universally valid. Here, we formulated a constraint-based approach, MaxEnt, based on the principle of maximum entropy, which in this context states that if more than one flux configuration is consistent with a set of experimentally measured fluxes, then the one with the minimum amount of unwarranted assumptions corresponds to the best estimation of the non-observed fluxes. We compared MaxEnt predictions to Escherichia coli and Saccharomyces cerevisiae publicly available flux data. We found that the mean square error (MSE) between experimental and predicted fluxes by MaxEnt and EFA-based methods are three orders of magnitude lower than the median of 1,350,000 MSE values obtained using flux sampling. However, only MaxEnt and flux sampling correctly predicted flux through E. coli’s glyoxylate cycle, whereas EFA-based methods, in general, predict no flux cycles. We also tested MaxEnt predictions at increasing levels of overflow metabolism. We found that MaxEnt accuracy is not affected by overflow metabolism levels, whereas the EFA-based methods show a decreasing performance. These results suggest that MaxEnt is less sensitive than flux sampling to artifacts introduced by thermodynamically infeasible cycles and that its predictions are less susceptible to overfitting than EFA-based methods.

Gapsplit: efficient random sampling for non-convex constraint-based models

Summary Gapsplit generates random samples from convex and non-convex constraint-based models by targeting under-sampled regions of the solution space. Gapsplit provides uniform coverage of linear, mixed-integer and general non-linear models. Availability and implementation Python and Matlab source code are freely available at http://jensenlab.net/tools. Supplementary information Supplementary data are available at Bioinformatics online.

CoBAMP: a Python framework for metabolic pathway analysis in constraint-based models

Summary CoBAMP is a modular framework for the enumeration of pathway analysis concepts, such as elementary flux modes (EFM) and minimal cut sets in genome-scale constraint-based models (CBMs) of metabolism. It currently includes the K-shortest EFM algorithm and facilitates integration with other frameworks involving reading, manipulation and analysis of CBMs. Availability and implementation The software is implemented in Python 3, supported on most operating systems and requires a mixed-integer linear programming optimizer supported by the optlang framework. Source-code is available at https://github.com/BioSystemsUM/cobamp.