Mathematical modelling of kinetic processes with different time scales allows a reduction of the governing equations using quasi-steady-state approximations (QSSA). A QSSA theorem is applied to a mathematical model of the influence that Raf kinase inhibitor protein (RKIP) has on the ERK signalling pathway. On the basis of previously published parameter values, the system of 11 ordinary differential equations is rewritten in a form suitable for model reduction. In accordance with the terminology of the QSSA theorem, it is established that four of the protein and protein-complex concentrations are 'fast varying', such that the corresponding kinetic equations form an attached system. Another concentration is 'medium varying' such that the corresponding equation is reduced with respect to the four fast ones. The other six concentrations are 'slow varying', which means the corresponding kinetic equations also present a reduced system with respect to the others. Analytical solutions, relating the steady-state values of the fast varying protein concentrations and the slow varying ones, are derived and interpreted as restrictions on the regulatory role of RKIP on ERK-pathway.
%0 Journal Article
%1 petrov_reduction_2007
%A Petrov, V
%A Nikolova, E
%A Wolkenhauer, O
%D 2007
%J IET Systems Biology
%K Binding Biology, Computational Dynamics, Extracellular Kinase Kinases, Nonlinear Phosphatidylethanolamine Protein, Rostock SBI Signaling System, Systems biology {MAP} {Signal-Regulated}
%N 1
%P 2--9
%T Reduction of nonlinear dynamic systems with an application to signal transduction pathways
%U http://www.ncbi.nlm.nih.gov/pubmed/17370424
%V 1
%X Mathematical modelling of kinetic processes with different time scales allows a reduction of the governing equations using quasi-steady-state approximations (QSSA). A QSSA theorem is applied to a mathematical model of the influence that Raf kinase inhibitor protein (RKIP) has on the ERK signalling pathway. On the basis of previously published parameter values, the system of 11 ordinary differential equations is rewritten in a form suitable for model reduction. In accordance with the terminology of the QSSA theorem, it is established that four of the protein and protein-complex concentrations are 'fast varying', such that the corresponding kinetic equations form an attached system. Another concentration is 'medium varying' such that the corresponding equation is reduced with respect to the four fast ones. The other six concentrations are 'slow varying', which means the corresponding kinetic equations also present a reduced system with respect to the others. Analytical solutions, relating the steady-state values of the fast varying protein concentrations and the slow varying ones, are derived and interpreted as restrictions on the regulatory role of RKIP on ERK-pathway.
@article{petrov_reduction_2007,
abstract = {Mathematical modelling of kinetic processes with different time scales allows a reduction of the governing equations using quasi-steady-state approximations {(QSSA).} A {QSSA} theorem is applied to a mathematical model of the influence that Raf kinase inhibitor protein {(RKIP)} has on the {ERK} signalling pathway. On the basis of previously published parameter values, the system of 11 ordinary differential equations is rewritten in a form suitable for model reduction. In accordance with the terminology of the {QSSA} theorem, it is established that four of the protein and protein-complex concentrations are 'fast varying', such that the corresponding kinetic equations form an attached system. Another concentration is 'medium varying' such that the corresponding equation is reduced with respect to the four fast ones. The other six concentrations are 'slow varying', which means the corresponding kinetic equations also present a reduced system with respect to the others. Analytical solutions, relating the steady-state values of the fast varying protein concentrations and the slow varying ones, are derived and interpreted as restrictions on the regulatory role of {RKIP} on {ERK-pathway.}},
added-at = {2010-09-17T16:55:15.000+0200},
author = {Petrov, V and Nikolova, E and Wolkenhauer, O},
biburl = {https://www.bibsonomy.org/bibtex/20410eb10e0cd9dc2fe71845b505ed5d3/ra1602},
interhash = {78722db35515e21f7e61c60e09baae27},
intrahash = {0410eb10e0cd9dc2fe71845b505ed5d3},
issn = {1751-8849},
journal = {{IET} Systems Biology},
keywords = {Binding Biology, Computational Dynamics, Extracellular Kinase Kinases, Nonlinear Phosphatidylethanolamine Protein, Rostock SBI Signaling System, Systems biology {MAP} {Signal-Regulated}},
month = jan,
note = {{PMID:} 17370424},
number = 1,
pages = {2--9},
timestamp = {2010-09-17T16:55:22.000+0200},
title = {Reduction of nonlinear dynamic systems with an application to signal transduction pathways},
url = {http://www.ncbi.nlm.nih.gov/pubmed/17370424},
volume = 1,
year = 2007
}