Goličnik Marko
Institute of Biochemistry, Faculty of Medicine, University of Ljubljana, Vrazov trg 2, 1000 Ljubljana, Slovenia.
Biochem Mol Biol Educ. 2011 Mar-Apr;39(2):117-25. doi: 10.1002/bmb.20479.
The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate V, and the Michaelis constant K(M) ) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to understand fully, or can even be misunderstood, by students when based only on the differential form of the Michaelis-Menten equation, and the variety of methods available to calculate the kinetic constants from rate versus substrate concentration "textbook data." Consequently, enzyme kinetics can be confusing if an analytical solution of the Michaelis-Menten equation is not available. Therefore, the still rarely known exact solution to the Michaelis-Menten equation is presented here through the explicit closed-form equation in terms of the Lambert W(x) function. Unfortunately, as the W(x) is not available in standard curve-fitting computer programs, the practical use of this direct solution is limited for most life-science students. Thus, the purpose of this article is to provide analytical approximations to the equation for modeling Michaelis-Menten kinetics. The elementary and explicit nature of these approximations can provide students with direct and simple estimations of kinetic parameters from raw experimental time-course data. The Michaelis-Menten kinetics studied in the latter context can provide an ideal alternative to the 100-year-old problems of data transformation, graphical visualization, and data analysis of enzyme-catalyzed reactions. Hence, the content of the course presented here could gradually become an important component of the modern biochemistry curriculum in the 21st century.
米氏速率方程在大多数普通生物化学教科书中都能找到,其中底物的时间导数是两个动力学参数(极限速率V和米氏常数K(M))以及底物量的双曲函数。然而,仅基于米氏方程的微分形式,酶动力学的基本概念可能很难被学生完全理解,甚至可能被误解,而且从速率与底物浓度的“教科书数据”计算动力学常数的方法多种多样。因此,如果没有米氏方程的解析解,酶动力学可能会令人困惑。所以,本文通过用兰伯特W(x)函数表示的显式封闭形式方程,给出了米氏方程仍然鲜为人知的精确解。不幸的是,由于标准曲线拟合计算机程序中没有W(x)函数,这种直接解的实际应用对大多数生命科学专业的学生来说是有限的。因此,本文的目的是为米氏动力学建模方程提供解析近似。这些近似的基本性和显式性可以为学生提供从原始实验时间进程数据直接简单估计动力学参数的方法。在后一种情况下研究的米氏动力学可以为酶催化反应的数据转换、图形可视化和数据分析这一有着百年历史的问题提供理想的替代方法。因此,本文所呈现课程的内容可能会逐渐成为21世纪现代生物化学课程的重要组成部分。