DocumentCode :
66157
Title :
Analytical Solution of Steady-State Equations for Chemical Reaction Networks with Bilinear Rate Laws
Author :
Halasz, Adam M. ; Hong-Jian Lai ; McCabe Pryor, Meghan ; Radhakrishnan, Krishnaja ; Edwards, Jeremy S.
Author_Institution :
Dept. of Math., West Virginia Univ., Morgantown, WV, USA
Volume :
10
Issue :
4
fYear :
2013
fDate :
July-Aug. 2013
Firstpage :
957
Lastpage :
969
Abstract :
True steady states are a rare occurrence in living organisms, yet their knowledge is essential for quasi-steady-state approximations, multistability analysis, and other important tools in the investigation of chemical reaction networks (CRN) used to describe molecular processes on the cellular level. Here, we present an approach that can provide closed form steady-state solutions to complex systems, resulting from CRN with binary reactions and mass-action rate laws. We map the nonlinear algebraic problem of finding steady states onto a linear problem in a higher-dimensional space. We show that the linearized version of the steady-state equations obeys the linear conservation laws of the original CRN. We identify two classes of problems for which complete, minimally parameterized solutions may be obtained using only the machinery of linear systems and a judicious choice of the variables used as free parameters. We exemplify our method, providing explicit formulae, on CRN describing signal initiation of two important types of RTK receptor-ligand systems, VEGF and EGF-ErbB1.
Keywords :
algebra; biochemistry; cellular biophysics; chemical reactions; CRN; EGF-ErbB1; RTK receptor-ligand systems; VEGF; bilinear rate laws; binary reactions; cellular level; chemical reaction networks; linear conservation laws; living organisms; mass-action rate laws; molecular processes; multistability analysis; nonlinear algebraic problem; quasisteady-state approximations; steady-state equations; Chemical reactions; Nonlinear systems; Steady-state; Chemical reaction networks; EGF; VEGF; analytical solution; bilinear systems; cell signaling; linear conservation laws; minimally parameterized solutions;
fLanguage :
English
Journal_Title :
Computational Biology and Bioinformatics, IEEE/ACM Transactions on
Publisher :
ieee
ISSN :
1545-5963
Type :
jour
DOI :
10.1109/TCBB.2013.41
Filename :
6517194
Link To Document :
بازگشت