title: Analytical solution of steady-state equations for chemical reaction networks with bilinear rate laws.
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.
authors: West Virginia University, Morgantown.
authors: Adám M
authors: AM
authors: Halász
authors: West Virginia University, Morgantown.
authors: Hong-Jian
authors: HJ
authors: Lai
authors: University of New Mexico, Albuquerque.
authors: Meghan
authors: M
authors: McCabe Pryor
authors: University of Kentucky, Lexington.
authors: Krishnan
authors: K
authors: Radhakrishnan
authors: University of New Mexico Health Sciences Center, Albuquerque.
authors: Jeremy S
authors: JS
authors: Edwards
mesh_terms: D000465:Algorithms; D002450:Cell Communication; D019295:Computational Biology; D007700:Kinetics; D016014:Linear Models; D008954:Models, Biological; D015398:Signal Transduction; D042461:Vascular Endothelial Growth Factor A
chemical_list: D042461:Vascular Endothelial Growth Factor A