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Analytical Solution of SteadyState Equations for Chemical Reaction Networks with Bilinear Rate Laws
JulyAug. 2013 (vol. 10 no. 4)
pp. 957969
ASCII Text  x  
Adam M. Halasz, HongJian Lai, Meghan McCabe Pryor, Krishnan Radhakrishnan, Jeremy S. Edwards, "Analytical Solution of SteadyState Equations for Chemical Reaction Networks with Bilinear Rate Laws," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 10, no. 4, pp. 957969, JulyAug., 2013.  
BibTex  x  
@article{ 10.1109/TCBB.2013.41, author = {Adam M. Halasz and HongJian Lai and Meghan McCabe Pryor and Krishnan Radhakrishnan and Jeremy S. Edwards}, title = {Analytical Solution of SteadyState Equations for Chemical Reaction Networks with Bilinear Rate Laws}, journal ={IEEE/ACM Transactions on Computational Biology and Bioinformatics}, volume = {10}, number = {4}, issn = {15455963}, year = {2013}, pages = {957969}, doi = {http://doi.ieeecomputersociety.org/10.1109/TCBB.2013.41}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE/ACM Transactions on Computational Biology and Bioinformatics TI  Analytical Solution of SteadyState Equations for Chemical Reaction Networks with Bilinear Rate Laws IS  4 SN  15455963 SP957 EP969 EPD  957969 A1  Adam M. Halasz, A1  HongJian Lai, A1  Meghan McCabe Pryor, A1  Krishnan Radhakrishnan, A1  Jeremy S. Edwards, PY  2013 KW  chemical reactions KW  algebra KW  biochemistry KW  cellular biophysics KW  EGFErbB1 KW  steadystate equations KW  chemical reaction networks KW  bilinear rate laws KW  living organisms KW  quasisteadystate approximations KW  multistability analysis KW  CRN KW  molecular processes KW  cellular level KW  binary reactions KW  massaction rate laws KW  nonlinear algebraic problem KW  linear conservation laws KW  RTK receptorligand systems KW  VEGF KW  Steadystate KW  Chemical reactions KW  Nonlinear systems KW  minimally parameterized solutions KW  Chemical reaction networks KW  cell signaling KW  VEGF KW  EGF KW  linear conservation laws KW  analytical solution KW  bilinear systems VL  10 JA  IEEE/ACM Transactions on Computational Biology and Bioinformatics ER   
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TCBB.2013.41
Web Extra: View Supplemental Material(PDF)
True steady states are a rare occurrence in living organisms, yet their knowledge is essential for quasisteadystate 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 steadystate solutions to complex systems, resulting from CRN with binary reactions and massaction rate laws. We map the nonlinear algebraic problem of finding steady states onto a linear problem in a higherdimensional space. We show that the linearized version of the steadystate 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 receptorligand systems, VEGF and EGFErbB1.
Index Terms:
chemical reactions,algebra,biochemistry,cellular biophysics,EGFErbB1,steadystate equations,chemical reaction networks,bilinear rate laws,living organisms,quasisteadystate approximations,multistability analysis,CRN,molecular processes,cellular level,binary reactions,massaction rate laws,nonlinear algebraic problem,linear conservation laws,RTK receptorligand systems,VEGF,Steadystate,Chemical reactions,Nonlinear systems,minimally parameterized solutions,Chemical reaction networks,cell signaling,VEGF,EGF,linear conservation laws,analytical solution,bilinear systems
Citation:
Adam M. Halasz, HongJian Lai, Meghan McCabe Pryor, Krishnan Radhakrishnan, Jeremy S. Edwards, "Analytical Solution of SteadyState Equations for Chemical Reaction Networks with Bilinear Rate Laws," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 10, no. 4, pp. 957969, JulyAug. 2013, doi:10.1109/TCBB.2013.41
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