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Quite generally, constraint-based metabolic flux analysis describes the space of viable flux configurations for a metabolic network as a high-dimensional polytope defined by the linear constraints that enforce the balancing of production…

Molecular Networks · Quantitative Biology 2013-09-24 Francesco Alessandro Massucci , Francesc Font-Clos , Andrea De Martino , Isaac Pérez Castillo

Background: Genome-scale metabolic network models and constraint-based modeling techniques have become important tools for analyzing cellular metabolism. Thermodynamically infeasible cy-cles (TICs) causing unbounded metabolic flux ranges…

Molecular Networks · Quantitative Biology 2017-11-15 Siu Hung Joshua Chan , Lin Wang , Satyakam Dash , Costas D. Maranas

Metabolic flux balance analyses are a standard tool in analysing metabolic reaction rates compatible with measurements, steady-state and the metabolic reaction network stoichiometry. Flux analysis methods commonly place unrealistic…

Current mathematical frameworks for predicting the flux state and macromolecular composition of the cell do not rely on thermodynamic constraints to determine the spontaneous direction of reactions. These predictions may be biologically…

Optimization and Control · Mathematics 2020-08-14 Amir Akbari , Bernhard O. Palsson

13C-Metabolic Flux Analysis (13C-MFA) and Flux Balance Analysis (FBA) are widely used to investigate the operation of biochemical networks in both biological and biotechnological research. Both of these methods use metabolic reaction…

Molecular Networks · Quantitative Biology 2023-03-23 Joshua A. M. Kaste , Yair Shachar-Hill

Constraint-based metabolic modeling is the predominant framework for simulating cellular metabolism. The central assumption of these models is that metabolism operates at a steady state, meaning that the production and consumption rates of…

Quantitative Methods · Quantitative Biology 2026-05-22 Ariel Bruner , Mona Singh

Assuming a steady-state condition within a cell, metabolic fluxes satisfy an under-determined linear system of stoichiometric equations. Characterizing the space of fluxes that satisfy such equations along with given bounds (and possibly…

Biological Physics · Physics 2017-04-10 Alfredo Braunstein , Anna Paola Muntoni , Andrea Pagnani

Flux balance analysis has proven an effective tool for analyzing metabolic networks. In flux balance analysis, reaction rates and optimal pathways are ascertained by solving a linear program, in which the growth rate is maximized subject to…

Optimization and Control · Mathematics 2018-04-10 Amir Akbari , Paul I. Barton

Constraint based methods, such as the Flux Balance Analysis, are widely used to model cellular growth processes without relying on extensive information on the regulatory features. The regulation is instead substituted by an optimization…

Optimization and Control · Mathematics 2017-06-14 Henning Lindhorst , Sergio Lucia , Rolf Findeisen , Steffen Waldherr

Flux analysis is a class of constraint-based approaches to the study of biochemical reaction networks: they are based on determining the reaction flux configurations compatible with given stoichiometric and thermodynamic constraints. One of…

Molecular Networks · Quantitative Biology 2015-05-18 A. De Martino , E. Marinari

Optimization-based models have been used to predict cellular behavior for over 25 years. The constraints in these models are derived from genome annotations, measured macro-molecular composition of cells, and by measuring the cell's growth…

Quantitative Methods · Quantitative Biology 2019-05-21 Laurence Yang , Michael A. Saunders , Jean-Christophe Lachance , Bernhard O. Palsson , José Bento

Scalable sampling of molecular states in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann Generators tackle this problem by pairing a generative model, capable of exact likelihood computation, with…

Machine Learning · Computer Science 2025-12-11 Danyal Rehman , Tara Akhound-Sadegh , Artem Gazizov , Yoshua Bengio , Alexander Tong

One of the long-expected goals of genome-scale metabolic modeling is to evaluate the influence of the perturbed enzymes to the flux distribution. Both ordinary differential equation (ODE) models and the constraint-based models, like Flux…

Molecular Networks · Quantitative Biology 2016-10-05 Zhengwei Xie , Tianyu Zhang , Qi Ouyang

Elementary flux modes (EFMs) are vectors defined from a metabolic reaction network, giving the connections between substrates and products. EFMs-based metabolic flux analysis (MFA) estimates the flux over each EFM from external flux…

Optimization and Control · Mathematics 2015-04-21 Hildur Æsa Oddsdóttir , Erika Hagrot , Veronique Chotteau , Anders Forsgren

Comprehension of metabolic pathways is considerably enhanced by metabolic flux analysis (MFA-ILE) in isotope labeling experiments. The balance equations are given by hundreds of algebraic (stationary MFA) or ordinary differential equations…

Molecular Networks · Quantitative Biology 2016-03-24 Stéphane Mottelet , Gil Gaullier , Georges Sadaka

Accurate quantification of intracellular metabolic fluxes is central to systems biology and biotechnology. Flux estimation relies on biochemical network models, with $^{13}$C metabolic flux analysis (MFA) being the state-of-the-art…

Quantitative Methods · Quantitative Biology 2026-05-26 Johann F. Jadebeck , Anton Stratmann , Martin Beyß , Katharina Nöh

Metabolic flux analysis using 13C labeled substrates is an important tool for metabolic engineering. Although it has now been evolving for more than ten years, metabolic flux analysis has still not reached the limits of its application.…

Optimization and Control · Mathematics 2012-06-25 Stéphane Mottelet

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…

Optimization and Control · Mathematics 2025-05-13 Hannah Troppens , Mathieu Besançon , St. Elmo Wilken , Sebastian Pokutta

13C-based metabolic flux analysis (13C-MFA) is a cornerstone of quantitative systems biology, yet its increasing data complexity and methodological diversity place high demands on simulation software. We introduce 13CFLUX(v3), a…

Quantitative Methods · Quantitative Biology 2025-09-30 Anton Stratmann , Martin Beyß , Johann F. Jadebeck , Wolfgang Wiechert , Katharina Nöh

Elementary flux modes (EFMs) are pathways through a metabolic reaction network that connect external substrates to products. Using EFMs, a metabolic network can be transformed into its macroscopic counterpart, in which the internal…

Optimization and Control · Mathematics 2014-10-13 Hildur Æsa Oddsdóttir , Erika Hagrot , Véronique Chotteau , Anders Forsgren
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