Michaelis–Menten kinetics
[6] Biochemical reactions involving a single substrate are often assumed to follow Michaelis–Menten kinetics, without regard to the model's underlying assumptions.
Instead they took advantage of the fact that the curve is almost straight in the middle range and has a maximum slope of
[11] His work was taken up by Michaelis and Menten, who investigated the kinetics of invertase, an enzyme that catalyzes the hydrolysis of sucrose into glucose and fructose.
(catalytic rate constant) denote the rate constants,[14] the double arrows between A (substrate) and EA (enzyme-substrate complex) represent the fact that enzyme-substrate binding is a reversible process, and the single forward arrow represents the formation of P (product).
This rate, which is never attained, refers to the hypothetical case in which all enzyme molecules are bound to substrate.
[16] Its value depends both on the identity of the enzyme and that of the substrate, as well as conditions such as temperature and pH.
Michaelis–Menten kinetics have also been applied to a variety of topics outside of biochemical reactions,[14] including alveolar clearance of dusts,[19] the richness of species pools,[20] clearance of blood alcohol,[21] the photosynthesis-irradiance relationship, and bacterial phage infection.
[22] The equation can also be used to describe the relationship between ion channel conductivity and ligand concentration,[23] and also, for example, to limiting nutrients and phytoplankton growth in the global ocean.
As the equation originated with Henri, not with Michaelis and Menten, it is more accurate to call it the Henri–Michaelis–Menten equation,[26] though it was Michaelis and Menten who realized that analysing reactions in terms of initial rates would be simpler, and as a result more productive, than analysing the time course of reaction, as Henri had attempted.
In addition, Michaelis and Menten understood the need for buffers to control the pH, but Henri did not.
When studying urease at about the same time as Michaelis and Menten were studying invertase, Donald Van Slyke and G. E. Cullen[29] made essentially the opposite assumption, treating the first step not as an equilibrium but as an irreversible second-order reaction with rate constant
They assumed that the concentration of the intermediate complex does not change on the time scale over which product formation is measured.
The resulting rate equation is as follows: where This is the generalized definition of the Michaelis constant.
[33] All of the derivations given treat the initial binding step in terms of the law of mass action, which assumes free diffusion through the solution.
However, in the environment of a living cell where there is a high concentration of proteins, the cytoplasm often behaves more like a viscous gel than a free-flowing liquid, limiting molecular movements by diffusion and altering reaction rates.
[35] In practice, therefore, treating the movement of substrates in terms of diffusion is not likely to produce major errors.
Nonetheless, Schnell and Turner consider that is more appropriate to model the cytoplasm as a fractal, in order to capture its limited-mobility kinetics.
[36] Determining the parameters of the Michaelis–Menten equation typically involves running a series of enzyme assays at varying substrate concentrations
Before computing facilities to perform nonlinear regression became available, graphical methods involving linearisation of the equation were used.
[43] From the point of view of visualizaing the data the Eadie–Hofstee plot has an important property: the entire possible range of
occupies a finite range of ordinate scale, making it impossible to choose axes that conceal a poor experimental design.
However, while useful for visualization, all three linear plots distort the error structure of the data and provide less precise estimates of
(Propagation of uncertainty), implying that linear regression of the double-reciprocal plot should include weights of
This was well understood by Lineweaver and Burk,[41] who had consulted the eminent statistician W. Edwards Deming before analysing their data.
[45] This aspect of the work of Lineweaver and Burk received virtually no attention at the time, and was subsequently forgotten.
The direct linear plot is a graphical method in which the observations are represented by straight lines in parameter space, with axes
However, that is correct only if the appropriate weighting scheme is used, preferably on the basis of experimental investigation, something that is almost never done.
As noted above, Burk[45] carried out the appropriate investigation, and found that the error structure of his data was consistent with a uniform standard deviation in
More recent studies found that a uniform coefficient of variation (standard deviation expressed as a percentage) was closer to the truth with the techniques in use in the 1970s.
In practice the error structure of enzyme kinetic data is very rarely investigated experimentally, therefore almost never known, but simply assumed.
