Volume 1, Issue 1 of Mathematical Biosciences was the venue for a now-classic paper on the application of singular perturbation theory in enzyme kinetics, "On the mathematical status of the pseudo-steady state hypothesis of biochemical kinetics" by F. G. Heineken, H. M. Tsuchiya and R. Aris. More than 50 years have passed, and yet this paper continues to be studied and mined for insights. This perspective discusses both the strengths and weaknesses of the work presented in this paper. For many, the justification of the pseudo-steady-state approximation using singular perturbation theory is the main achievement of this paper. However, there is so much more material here, which laid the foundation for a great deal of research in mathematical biochemistry in the intervening decades. The parameterization of the equations, construction of the first-order uniform singular-perturbation solution, and an attempt to apply similar principles to the pseudo-equilibrium approximation are discussed in particular detail.

中文翻译：

---

喜力（Heineken），土屋（Tsuchiya）和阿里斯（Aris）关于伪稳态假设的数学状态：《数学生物科学》第1卷的经典之作。

数学生物科学第1卷第1期是关于奇异摄动理论在酶动力学中的应用的经典论文的场所，该论文“土生化学的FG Heineken撰写，关于生化动力学的拟稳态假设的数学状态”和R. Aris。50多年过去了，然而，本文仍在继续研究和挖掘以获取见识。这种观点既讨论了本文提出的工作的优点，也讨论了缺点。对于许多人来说，使用奇异摄动理论证明拟稳态近似是正确的。但是，这里的材料太多了，这为随后的几十年中数学生物化学的大量研究奠定了基础。方程的参数化