2006/11/30 by Matt S. Calder, David Siegel · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Medicine · #Applied mathematics #Asymptotic expansion #Diffusion and Search Dynamics #Enzyme #Infinity #Manifold (fluid mechanics) #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Michaelis–Menten kinetics #Nonlinear Dynamics and Pattern Formation #Physics #Space (punctuation) #Uniqueness #math.CA #math.DS #msc:34C05 #msc:34E05 #msc:92C45
paper · pdf · doi:10.1016/j.jmaa.2007.06.078
published as J. Math. Anal. Appl. 339 (2008) 1044-1064 · 29 pages, 8 figures, corrected a few typos and incorporated reviewer suggestions
openalex publication_date 2007/08/02 · arxiv created 2010/03/21 · arxiv updated 2010/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the two-dimensional reduction of the Michaelis-Menten reaction of enzyme kinetics. First, we prove the existence and uniqueness of a slow manifold between the horizontal and vertical isoclines. Second, we determine the concavity of all solutions in the first quadrant. Third, we establish the asymptotic behaviour of all solutions near the origin, which generally is not given by a Taylor series. Finally, we determine the asymptotic behaviour of the slow manifold at infinity.