Metabolic isotopomer labeling systems. Part I: global dynamic behavior. Export

@article{citeulike:3041976, abstract = {In the last few years metabolic flux analysis (MFA) using carbon labeling experiments (CLE) has become a major diagnostic tool in metabolic engineering. The mathematical centerpiece of MFA is the solution of isotopomer labeling systems (ILS). An ILS is a high-dimensional nonlinear differential equation system that describes the distribution of isotopomers over a metabolic network during a carbon labeling experiment. This contribution presents a global analysis of the dynamic behavior of general ILSs. It is proven that an ILS is globally stable under very weak conditions that are always satisfied in practice. In particular it is shown that in some sense ILSs are a nonlinear extension to the classical theory of compartmental systems. The central stability condition for compartmental systems, i.e., the non-existence of traps in linear compartmental networks, is also the major stability condition for ILSs. As an important side result of the proof, it is shown that ILSs can be transformed to a cascade of linear systems with time-dependent inhomogeneous terms. This cascade structure has considerable consequences for the development of efficient numerical algorithms for the solution of ILSs and thus for MFA.}, address = {IMR, Department of Simulation, University of Siegen, Paul-Bonatz-Str. 9-11, D-57068, Siegen, Germany. wiechert@simtec.mb.uni-siegen.de}, author = {Wiechert, W. and Wurzel, M.}, citeulike-article-id = {3041976}, citeulike-linkout-0 = {http://view.ncbi.nlm.nih.gov/pubmed/11166321}, citeulike-linkout-1 = {http://www.hubmed.org/display.cgi?uids=11166321}, issn = {0025-5564}, journal = {Mathematical biosciences}, keywords = {13c, flux-measurements, mfa}, month = {February}, number = {2}, pages = {173--205}, posted-at = {2008-07-25 09:12:26}, priority = {2}, title = {Metabolic isotopomer labeling systems. Part I: global dynamic behavior.}, url = {http://view.ncbi.nlm.nih.gov/pubmed/11166321}, volume = {169}, year = {2001} }

TY - JOUR ID - citeulike:3041976 L3 - citeulike-article-id:3041976 N2 - In the last few years metabolic flux analysis (MFA) using carbon labeling experiments (CLE) has become a major diagnostic tool in metabolic engineering. The mathematical centerpiece of MFA is the solution of isotopomer labeling systems (ILS). An ILS is a high-dimensional nonlinear differential equation system that describes the distribution of isotopomers over a metabolic network during a carbon labeling experiment. This contribution presents a global analysis of the dynamic behavior of general ILSs. It is proven that an ILS is globally stable under very weak conditions that are always satisfied in practice. In particular it is shown that in some sense ILSs are a nonlinear extension to the classical theory of compartmental systems. The central stability condition for compartmental systems, i.e., the non-existence of traps in linear compartmental networks, is also the major stability condition for ILSs. As an important side result of the proof, it is shown that ILSs can be transformed to a cascade of linear systems with time-dependent inhomogeneous terms. This cascade structure has considerable consequences for the development of efficient numerical algorithms for the solution of ILSs and thus for MFA. IS - 2 JF - Mathematical biosciences SN - 0025-5564 AD - IMR, Department of Simulation, University of Siegen, Paul-Bonatz-Str. 9-11, D-57068, Siegen, Germany. wiechert@simtec.mb.uni-siegen.de EP - 205 TI - Metabolic isotopomer labeling systems. Part I: global dynamic behavior. VL - 169 SP - 173 KW - 13c KW - flux-measurements KW - mfa AU - Wiechert, W AU - Wurzel, M PY - 2001/02// UR - http://view.ncbi.nlm.nih.gov/pubmed/11166321 ER -