Local convergence of the Levenberg-Marquardt method under H\"{o}lder metric subregularity

We describe and analyse Levenberg-Marquardt methods for solving systems of nonlinear equations. More specifically, we propose an adaptive formula for the Levenberg-Marquardt parameter and analyse the local convergence of the method under H\"{o}lder metric subregularity of the function defining the equation and H\"older continuity of its gradient mapping. Further, we analyse the local convergence of the method under the additional assumption that the \L{}ojasiewicz gradient inequality holds. We finally report encouraging numerical results confirming the theoretical findings for the problem of computing moiety conserved steady states in biochemical reaction networks. This problem can be cast as finding a solution of a system of nonlinear equations, where the associated mapping satisfies the \L{}ojasiewicz gradient inequality assumption.Comment: 30 pages, 10 figure

Creation and analysis of biochemical constraint-based models: the COBRA Toolbox v3. 0

COnstraint-Based Reconstruction and Analysis (COBRA) provides a molecular mechanistic framework for integrative analysis of experimental data and quantitative prediction of physicochemically and biochemically feasible phenotypic states. The COBRA Toolbox is a comprehensive software suite of interoperable COBRA methods. It has found widespread applications in biology, biomedicine, and biotechnology because its functions can be flexibly combined to implement tailored COBRA protocols for any biochemical network. Version 3.0 includes new methods for quality controlled reconstruction, modelling, topological analysis, strain and experimental design, network visualisation as well as network integration of chemoinformatic, metabolomic, transcriptomic, proteomic, and thermochemical data. New multi-lingual code integration also enables an expansion in COBRA application scope via high-precision, high-performance, and nonlinear numerical optimisation solvers for multi-scale, multi-cellular and reaction kinetic modelling, respectively. This protocol can be adapted for the generation and analysis of a constraint-based model in a wide variety of molecular systems biology scenarios. This protocol is an update to the COBRA Toolbox 1.0 and 2.0. The COBRA Toolbox 3.0 provides an unparalleled depth of constraint-based reconstruction and analysis methods.status: publishe

[Scheda bibliografica]: Popoli dell'Africa mediterranea in et\ue0 romana

Constraint-based reconstruction and analysis (COBRA) provides a molecular mechanistic framework for integrative analysis of experimental molecular systems biology data and quantitative prediction of physicochemically and biochemically feasible phenotypic states. The COBRA Toolbox is a comprehensive desktop software suite of interoperable COBRA methods. It has found widespread application in biology, biomedicine, and biotechnology because its functions can be flexibly combined to implement tailored COBRA protocols for any biochemical network. This protocol is an update to the COBRA Toolbox v.1.0 and v.2.0. Version 3.0 includes new methods for quality-controlled reconstruction, modeling, topological analysis, strain and experimental design, and network visualization, as well as network integration of chemoinformatic, metabolomic, transcriptomic, proteomic, and thermochemical data. New multi-lingual code integration also enables an expansion in COBRA application scope via high-precision, high-performance, and nonlinear numerical optimization solvers for multi-scale, multi-cellular, and reaction kinetic modeling, respectively. This protocol provides an overview of all these new features and can be adapted to generate and analyze constraint-based models in a wide variety of scenarios. The COBRA Toolbox v.3.0 provides an unparalleled depth of COBRA methods.This study was funded by the National Centre of Excellence in Research (NCER) on Parkinson’s disease, the U.S. Department of Energy, Offices of Advanced Scientific Computing Research and the Biological and Environmental Research as part of the Scientific Discovery Through Advanced Computing program, grant no. DE-SC0010429. This project also received funding from the European Union’s HORIZON 2020 Research and Innovation Programme under grant agreement no. 668738 and the Luxembourg National Research Fund (FNR) ATTRACT program (FNR/A12/01) and OPEN (FNR/O16/11402054) grants. N.E.L. was supported by NIGMS (R35 GM119850) and the Novo Nordisk Foundation (NNF10CC1016517). M.A.P.O. was supported by the Luxembourg National Research Fund (FNR) grant AFR/6669348. A.R. was supported by the Lilly Innovation Fellows Award. F.J.P. was supported by the Minister of Economy and Competitiveness of Spain (BIO2016-77998-R) and the ELKARTEK Programme of the Basque Government (KK-2016/00026). I.A. was supported by a Basque Government predoctoral grant (PRE_2016_2_0044). B.Ø.P. was supported by the Novo Nordisk Foundation through the Center for Biosustainability at the Technical University of Denmark (NNF10CC1016517)

Creation and analysis of biochemical constraint-based models using the COBRA Toolbox v.3.0.

Constraint-based reconstruction and analysis (COBRA) provides a molecular mechanistic framework for integrative analysis of experimental molecular systems biology data and quantitative prediction of physicochemically and biochemically feasible phenotypic states. The COBRA Toolbox is a comprehensive desktop software suite of interoperable COBRA methods. It has found widespread application in biology, biomedicine, and biotechnology because its functions can be flexibly combined to implement tailored COBRA protocols for any biochemical network. This protocol is an update to the COBRA Toolbox v.1.0 and v.2.0. Version 3.0 includes new methods for quality-controlled reconstruction, modeling, topological analysis, strain and experimental design, and network visualization, as well as network integration of chemoinformatic, metabolomic, transcriptomic, proteomic, and thermochemical data. New multi-lingual code integration also enables an expansion in COBRA application scope via high-precision, high-performance, and nonlinear numerical optimization solvers for multi-scale, multi-cellular, and reaction kinetic modeling, respectively. This protocol provides an overview of all these new features and can be adapted to generate and analyze constraint-based models in a wide variety of scenarios. The COBRA Toolbox v.3.0 provides an unparalleled depth of COBRA methods