Tzafriri A R
Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Room 16-343, Cambridge, MA 02139, USA.
Bull Math Biol. 2003 Nov;65(6):1111-29. doi: 10.1016/S0092-8240(03)00059-4.
The total quasi-steady state approximation (tQSSA) for the irreversible Michaelis-Menten scheme is derived in a consistent manner. It is found that self-consistency of the initial transient guarantees the uniform validity of the tQSSA, but does not guarantee the validity of the linearization in the original derivation of Borghans et al. (1996, Bull. Math. Biol., 58, 43-63). Moreover, the present rederivation yielded the noteworthy result that the tQSSA is at least roughly valid for any substrate and enzyme concentrations. This reinforces and extends the original assertion that the parameter domain for which the tQSSA is valid overlaps the domain of validity of the standard quasi-steady state approximation and includes the limit of high enzyme concentrations. The criteria for the uniform validity of the original (linearized) tQSSA are corrected, and are used to derive approximate solutions that are uniformly valid in time. These approximations overlap and extend the domains of validity of the standard and reverse quasi-steady state approximations.
以一种连贯的方式推导了不可逆米氏反应机制的全准稳态近似（tQSSA）。结果发现，初始瞬态的自洽性保证了tQSSA的一致有效性，但不能保证Borghans等人（1996年，《数学生物学公报》，58卷，43 - 63页）原始推导中线性化的有效性。此外，当前的重新推导得出了一个值得注意的结果，即tQSSA对于任何底物和酶浓度至少大致有效。这强化并扩展了原始论断，即tQSSA有效的参数域与标准准稳态近似的有效域重叠，并且包括高酶浓度的极限情况。对原始（线性化）tQSSA一致有效性的标准进行了修正，并用于推导在时间上一致有效的近似解。这些近似解与标准和反向准稳态近似的有效域重叠并进行了扩展。
