A variational principle for computing nonequilibrium fluxes and potentials in genome-scale biochemical networks.

[1]  M. Tribus,et al.  Probability theory: the logic of science , 2003 .

[2]  Václav Doležal,et al.  Nonlinear networks , 1977 .

[3]  Y. Ye,et al.  Existence of Positive Steady States for Mass Conserving and Mass-Action Chemical Reaction Networks with a Single Terminal-Linkage Class , 2011, 1105.2359.

[4]  Ronan M. T. Fleming,et al.  Integrated stoichiometric, thermodynamic and kinetic modelling of steady state metabolism. , 2010, Journal of theoretical biology.

[5]  E. Gilles,et al.  Thermodynamically feasible kinetic models of reaction networks. , 2007, Biophysical journal.

[6]  Hong Qian,et al.  Phosphorylation energy hypothesis: open chemical systems and their biological functions. , 2007, Annual review of physical chemistry.

[7]  B. Palsson,et al.  A protocol for generating a high-quality genome-scale metabolic reconstruction , 2010 .

[8]  Ronan M. T. Fleming,et al.  Genome-Scale Reconstruction of Escherichia coli's Transcriptional and Translational Machinery: A Knowledge Base, Its Mathematical Formulation, and Its Functional Characterization , 2009, PLoS Comput. Biol..

[9]  Ronan M. T. Fleming,et al.  Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox v2.0 , 2007, Nature Protocols.

[10]  B. Palsson,et al.  Formulating genome-scale kinetic models in the post-genome era , 2008, Molecular systems biology.

[11]  Yinyu Ye,et al.  A Computational Study of the Homogeneous Algorithm for Large-scale Convex Optimization , 1998, Comput. Optim. Appl..

[12]  R. Mahadevan,et al.  Thermodynamic analysis of regulation in metabolic networks using constraint-based modeling , 2010, BMC Research Notes.

[13]  E. Seibert,et al.  Fundamentals of enzyme kinetics. , 2014, Methods in molecular biology.

[14]  V. Hatzimanikatis,et al.  Thermodynamics-based metabolic flux analysis. , 2007, Biophysical journal.

[15]  B. Palsson,et al.  Elimination of thermodynamically infeasible loops in steady-state metabolic models. , 2011, Biophysical journal.

[16]  Hong Qian,et al.  Ab initio prediction of thermodynamically feasible reaction directions from biochemical network stoichiometry. , 2005, Metabolic engineering.

[17]  H. Qian,et al.  Thermodynamics of stoichiometric biochemical networks in living systems far from equilibrium. , 2005, Biophysical chemistry.

[18]  Ronan M. T. Fleming,et al.  von Bertalanffy 1.0: a COBRA toolbox extension to thermodynamically constrain metabolic models , 2011, Bioinform..

[19]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[20]  C. Mathews Thermodynamics of biochemical reactions , 2004 .

[21]  G. Oster,et al.  Network Thermodynamics , 1971, Nature.

[22]  J. Maxwell A Treatise on Electricity and Magnetism , 1873, Nature.

[23]  Keng C. Soh,et al.  Network thermodynamics in the post-genomic era. , 2010, Current opinion in microbiology.

[24]  B. Palsson,et al.  Network analysis of intermediary metabolism using linear optimization. I. Development of mathematical formalism. , 1992, Journal of theoretical biology.

[25]  Bernhard Ø Palsson,et al.  Candidate states of Helicobacter pylori's genome-scale metabolic network upon application of "loop law" thermodynamic constraints. , 2006, Biophysical journal.

[26]  W. Millar CXVI. Some general theorems for non-linear systems possessing resistance , 1951 .

[27]  Matthew D. Jankowski,et al.  Group contribution method for thermodynamic analysis of complex metabolic networks. , 2008, Biophysical journal.

[28]  A. Cornish-Bowden,et al.  Enzymes in context: Kinetic characterization of enzymes for systems biology , 2005 .

[29]  H. Holzhütter The principle of flux minimization and its application to estimate stationary fluxes in metabolic networks. , 2004, European journal of biochemistry.

[30]  Achille Messac,et al.  Integrated Energy and Flux Balance Based Multiobjective Framework for Large-Scale Metabolic Networks , 2007, Annals of Biomedical Engineering.

[31]  Yinyu Ye,et al.  Interior point algorithms: theory and analysis , 1997 .

[32]  J. Rabinowitz,et al.  Absolute Metabolite Concentrations and Implied Enzyme Active Site Occupancy in Escherichia coli , 2009, Nature chemical biology.

[33]  S. Panke,et al.  Putative regulatory sites unraveled by network-embedded thermodynamic analysis of metabolome data , 2006, Molecular systems biology.

[34]  Matthew D. Jankowski,et al.  Genome-scale thermodynamic analysis of Escherichia coli metabolism. , 2006, Biophysical journal.

[35]  Janette L. Jones,et al.  Duality, thermodynamics, and the linear programming problem in constraint-based models of metabolism. , 2007, Physical review letters.

[36]  C. Desoer,et al.  Tellegen's theorem and thermodynamic inequalities. , 1971, Journal of theoretical biology.

[37]  Edda Klipp,et al.  Modular rate laws for enzymatic reactions: thermodynamics, elasticities and implementation , 2010, Bioinform..

[38]  Gilbert Strang,et al.  Introduction to applied mathematics , 1988 .

[39]  H. Qian,et al.  Energy balance for analysis of complex metabolic networks. , 2002, Biophysical journal.

[40]  Vassily Hatzimanikatis,et al.  Thermodynamic analysis of biodegradation pathways , 2009, Biotechnology and bioengineering.

[41]  R. Duffin Nonlinear networks. IIb , 1946 .

[42]  Ronan M. T. Fleming,et al.  Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox v2.0 , 2007, Nature Protocols.

[43]  J. Sadhukhan,et al.  Optimization of Productivity and Thermodynamic Performance of Metabolic Pathways , 2008 .

[44]  H. Krebs,et al.  Energy Transformations in Living Matter , 1957 .

[45]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .

[46]  Bastian Goldlücke,et al.  Variational Analysis , 2014, Computer Vision, A Reference Guide.

[47]  B. Palsson Systems Biology: Properties of Reconstructed Networks , 2006 .

[48]  G. B.,et al.  Treatise on Thermodynamics , 1903, Nature.

[49]  Jeffrey D Orth,et al.  What is flux balance analysis? , 2010, Nature Biotechnology.

[50]  Asen L. Dontchev,et al.  Primal-Dual Solution Perturbations in Convex Optimization , 2001 .

[51]  John Ross,et al.  Thermodynamics and Fluctuations Far From Equilibrium , 2008, Entropy.

[52]  R. Alberty Biochemical thermodynamics: applications of Mathematica. , 2006, Methods of biochemical analysis.

[53]  A. Barrett Network Flows and Monotropic Optimization. , 1984 .

[54]  Ronan M. T. Fleming,et al.  Quantitative assignment of reaction directionality in constraint-based models of metabolism: application to Escherichia coli. , 2009, Biophysical chemistry.