Constraint-based metabolic models can be used to investigate the intracellular physiology of microorganisms. These models couple genes to reactions, and typically seek to predict metabolite fluxes that optimize some biologically important metric. Classical techniques, like Flux Balance Analysis (FBA), formulate the metabolism of a microbe as an optimization problem where growth rate is maximized. While FBA has found widespread use, it often leads to thermodynamically infeasible solutions that contain internal cycles (loops). To address this shortcoming, Loopless-Flux Balance Analysis (ll-FBA) seeks to predict flux distributions that do not contain these loops. ll-FBA is a disjunctive program, usually reformulated as a mixed-integer program, and is challenging to solve for biological models that often contain thousands of reactions and metabolites. In this paper, we compare various reformulations of ll-FBA and different solution approaches. Overall, the combinatorial Benders' decomposition is the most promising of the tested approaches with which we could solve most instances. However, the model size and numerical instability pose a challenge to the combinatorial Benders' method.

MOTIVATION: Sensitivity analysis is a useful tool to identify key parameters in metabolic models. It is typically only applied to the growth rate, disregarding the sensitivity of other solution variables to parameters. Further, sensitivity analysis of elementary flux modes could provide low-dimensional insights into optimal solutions, but they are not defined when a model is subject to inhomogeneous flux constraints, such as the frequently used ATP maintenance reaction. RESULTS: We introduce optimal flux modes (OFMs), an analogue to elementary flux modes (EFMs), but specifically applied to optimal solutions of constraint-based models. Further, we prove that implicit differentiation can always be used to efficiently calculate the sensitivities of both whole-model solutions and OFM-based solutions to model parameters. This allows for fine-grained sensitivity analysis of the optimal solution, and investigation of how these parameters exert control on the optimal composition of OFMs. This novel framework is implemented in DifferentiableMetabolism.jl, a software package designed to efficiently differentiate solutions of constraint-based models. To demonstrate scalability, we differentiate solutions of 342 yeast models; additionally we show that sensitivities of specific subsystems can guide metabolic engineering. Applying our scheme to an Escherichia coli model, we find that OFM sensitivities predict the effect of knockout experiments on waste product accumulation. Sensitivity analysis of OFMs also provides key insights into metabolic changes resulting from parameter perturbations. AVAILABILITY AND IMPLEMENTATION: Software introduced here is available as open-source Julia packages DifferentiableMetabolism.jl (https://github.com/stelmo/DifferentiableMetabolism.jl) and ElementaryFluxModes.jl (https://github.com/HettieC/ElementaryFluxModes.jl), which both work on all major operating systems and computer architectures. Code to reproduce all results is available from https://github.com/HettieC/DifferentiableOFMPaper, and as an archive from https://doi.org/10.5281/zenodo.15183208.

SUMMARY: Constraint-based metabolic models offer a scalable framework to investigate biological systems using optimality principles. Construction and simulation of detailed models that utilize multiple kinds of constraint systems pose a significant coding overhead, complicating implementation of new types of analyses. We present an improved version of the constraint-based metabolic modeling package COBREXA, which utilizes a hierarchical model construction framework that decouples the implemented analysis algorithms into independent, yet re-combinable, building blocks. By removing the need to re-implement modeling components, assembly of complex metabolic models is simplified, which we demonstrate on use-cases of resource-balanced models, and enzyme-constrained flux balance models of interacting bacterial communities. Notably, these models show improved predictive capabilities in both monoculture and community settings. In perspective, the re-usable model-building components in COBREXA 2 provide a sustainable way to handle increasingly complex models in constraint-based modeling. AVAILABILITY AND IMPLEMENTATION: COBREXA 2 is available from https://github.com/COBREXA/COBREXA.jl, and from Julia package repositories. COBREXA 2 works on all major operating systems and computer architectures. Documentation is available at https://cobrexa.github.io/COBREXA.jl/.

SUMMARY: COBREXA.jl is a Julia package for scalable, high-performance constraint-based reconstruction and analysis of very large-scale biological models. Its primary purpose is to facilitate the integration of modern high performance computing environments with the processing and analysis of large-scale metabolic models of challenging complexity. We report the architecture of the package, and demonstrate how the design promotes analysis scalability on several use-cases with multi-organism community models. AVAILABILITY AND IMPLEMENTATION: https://doi.org/10.17881/ZKCR-BT30. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.