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Hirsch, M.W. and Smale, S. (1974) Differential equations, dynamical systems, and linear algebra. Academic Press Inc., New York.

• 作者: 宗凯, 于建平, 吴素萍, 孙永利

期刊名称: 《Advances in Applied Mathematics》, Vol.4 No.2, 2015-05-08

摘要: 在生物系统和生命活动中，酶都发挥着非常重要的作用，并且参与了几乎所有的化学反应。因此，酶动力学的分析对化学反应的研究至关重要。所以从二十世纪早期就有许多专家学者致力于对酶促系统进行动力学分析，并且做出了许多杰出的贡献。酶动力学的分析对于研究如何控制酶的活性，如何利用药物控制酶，以及酶在代谢中的作用等均有重要作用。本文通过严格的数学分析基础的酶动力学模型，即包含单一底物被酶催化转化为单一产物的反应模型，基于计算机代数技术和动力系统的定性理论。本文的方法是在没有任何假设的情况下提出的并且得到了模型的解析解。在文章的最后给出了一些例子来验证该方法并给出曲线表示。此外，该方法也可以用于研究其它学科，例如生物物理等。 Enzyme plays an important role in the living system as well as life process, and is involved in almost every chemical reaction; thus the enzyme kinetics is fundamental to the research of the chemical reactions. Therefore, from the early part of twentieth century, many researchers were dedicated to the study of the analysis of kinetics of enzymatic system, and a lot of excellent work has been done, because the analysis of the enzyme kinetics can help us find how the activity of enzyme is controlled, how the drug inhibits the enzyme, its role in metabolism, and so on. In this paper, we present a method by rigorous mathematics to analyze the general enzyme kinetics model, which is concerned with a single substrate catalyzed by enzyme and transformed into a single product, and it is based on computer algebra technique and the qualitative theory of dynamical system. Our method does not need any assumption and all the solutions here are analytical. Finally, some examples are given to test this method and make it readable by simulated progress curves, so that almost everyone may understand it. Furthermore, the techniques in this study can be used to the research of other disciplines, such as biophysics, and so on.