Talk:Michaelis–Menten kinetics

Phase space
I changed the explanation of the quasi-steady-state approximation from:


 * The current derivation, based on the quasi steady state approximation (which asserts that the concentrations of the intermediate complexes initially change so as to approach the set in phase space where their rate of change is zero)

to


 * The current derivation, based on the quasi steady state approximation (that the concentrations of the intermediate complexes remain constant)

The derivation is based on the assumption that the concentrations do not change, no more, no less. The discussion about the representation in phase space might indeed be a more accurate and complete description of the quasi-steady-state approximation, but at that point in the article it's just confusing to non-specialists. --Slashme (talk) 13:43, 5 June 2008 (UTC)


 * Nice, but it should also be explained that the equation always breaks down at low concentration. I.e., at very small [S], substrate binding is always rate limiting, so V approaches k_1 [S], but that's not what the MM equation approaches. I don't see the merit of considering phase space for that matter. Physicsjock (talk) 17:22, 16 July 2008 (UTC)

Mathematical notation
Both TeX and non-TeX math notation conventions were somewhat extensively disregarded in this article; I've (mostly?) fixed that. See Manual of Style (mathematics). In particular, I found this:

$$ E + S \begin{matrix} k_1 \\ \longrightarrow \\ \longleftarrow \\ k_{\textrm{-}1} \end{matrix} ES \begin{matrix} k_2 \\ \longrightarrow\\ \  \end{matrix} E + P $$

and I changed it to this:

E + S \overset{k_1}{\underset{k_{-1}}{\begin{smallmatrix} \displaystyle \longrightarrow \\ \displaystyle \longleftarrow \end{smallmatrix}}} ES  \overset{k_2} {\longrightarrow} E + P $$

Note: In non-TeX notation, italicize variables, but NOT digits and NOT parentheses or other punctuation. Put a space before and after "+", "=", etc. (make in non-breakable when prudent, especially with plus, minus, etc.). In TeX that doesn't matter; the software takes care of it. In non-TeX notation, a minus sign is not just a hyphen:
 * 5 - 3
 * 5 &minus; 3
 * 5 &minus; 3

Michael Hardy (talk) 15:22, 14 August 2008 (UTC)

Mathematical derivations
I tried to clean up the derivation of the Michaelis-Menten approximation,


 * $$ [ES] = \frac{1}{1 + \frac{K_m}{[S]}}, $$

from the quasi-steady-state assumption (QSSA)


 * $$ \frac{d[ES]}{dt} = 0 . $$

It should read much more smoothly now. I also added a short discussion of the mathematical limitations of the QSSA (and therefore also of the Michaelis-Menten kinetics) & a reference to the best reference on the subject. Finally, I tried to uniformize the citation style a bit, as it was a huge mess... Athenray (talk) 20:50, 5 November 2008 (UTC)

More notation issues
Please. Do not write
 * $$ v_{max} \, $$
 * $$ v_{max} \, $$

At the very least, write it as
 * $$ v_\text{max} \, $$
 * $$ v_\text{max} \, $$

instead, with the "max" NOT italicized. Simpler is to write
 * $$ v_\max \, $$
 * $$ v_\max \, $$

coding it as \max rather than as \text{max}, and in some contexts that effects the size of the letters in "max".

(I've just done a bunch of other notation and format edits as well.) Michael Hardy (talk) 17:38, 10 January 2009 (UTC)
 * I've no problem with either; I don't know what's usual in theoretical biochemistry, but italicized subscripts/superscripts are definitely OK in mathematics. But, as I wrote, I've no problem with either.Athenray (talk) 17:38, 13 February 2009 (UTC)
 * This isn't about subscripts or superscripts. "max" should not be italicized regardless of whether it's in a subscript or not; thus:
 * $$ \max\{ f(x) : x \in A\} \, $$
 * is correct, whereas if "max" had been italicized it would fail to follow the usages of TeX and other conventions. Michael Hardy (talk) 20:29, 11 May 2010 (UTC)

A semi-log plot is logarithmic on the y-axis but not on the linear x-axis. The text makes the mistake in several places of calling linear-log plotting semi-log plotting; how amateurish. CarlWesolowski (talk) 23:36, 13 June 2023 (UTC)


 * According to the article on semi-log plots, there are two subtypes of semi-log plot: log-linear with the logarithmic scale on the x-axis, and linear-log with the log scale on the y-axis. So yes, the original Michaelis-Menten graph is an example of linear-log, but since this is one of the two types of semi-log plot it is also correct to call it a semilog plot. Dirac66 (talk) 17:40, 16 June 2023 (UTC)

Km
I changed the equation for Km. It has to be $$\frac{k_{-1}+k_2}{k_1}$$ instead of $$ \frac{k_{-1}+k_2}{k_{-1}}$$. Just solve the equations yourself or look into a textbook to check this. —Preceding unsigned comment added by 129.132.49.164 (talk) 08:42, 11 January 2009 (UTC)
 * This is correct, there was a typo. Thanks for correcting it. --hroest 21:46, 17 March 2009 (UTC)

It is misleading to say that Km is related to affinity, the Km IS NOT "an inverse measure of the substrate's affinity for the enzyme". Affinity is A + B <> AB with rate constants k1 and k-1 (forward and reverse). The dissociation constant is then Kd= k-1/k1. For enzyme kinetics, the general equation is E + A <> EA > E + P with the first two arrow rate constants also k1 and k-1 and the last arrow rate constant being kcat. Thus, Km=(k-1+kcat)/k1, and we can see the extra term kcat is how dissociation constant Kd and Michaelis constant Km differ. Only if you assume that all kcats are equal, then Km can be well correlated with Kd which is not the case. According to: in some enzyme classes (EC) with simple catalytic mechanisms Kd and Km are well correlated, but with more complex mechanisms they are definitely not. Another way of saying this is only when kcat << k-1 (the ES complex dissociates much faster than the following catalytic steps) is Km = Kd.

I think it is very important for this Wikipedia page to be correct and clarify that Km only related to affinity in select circumstances (safest to assume it isn't related), that Km is fundamentally measuring something different than Kd and that association between Km and Kd is the exception not the rule. Since many people use Wikipedia to learn the concepts, stating there is a firm relationship between Km and Kd will confuse people. Start with the basics, then talk about the special cases. — Preceding unsigned comment added by 195.65.131.154 (talk) 13:33, 27 December 2013 (UTC)
 * Unsigned user is correct. I suggest to add the adjective "apparent" before "affinity", then develop why Km is an affinity constant only in the particular case where $$k_2\ll k_{-1}$$, maybe in a subsection entitled "The meaning of the Michaelis constant" ? The section Enzyme_kinetics#Michaelis-Menten_kinetics is clearer about that point, although the use of "quickly" in "The two most important kinetic properties of an enzyme are how quickly the enzyme becomes saturated with a particular substrate, and the maximum rate it can achieve." (Enzyme kinetics#General_principles) is very misleading... I have suggested a change on the corresponding dicussion page. Lewisiscrazy (talk) 08:54, 21 January 2018 (UTC)

Limitations
It would be nice if the limitations were quantified and bounded. For example, Olsen's work is cited when making the point that diffusion is a problem in the cell but the citer didn't include any numbers. (BTW, my reading of Olsen's abstract is that Michaelis-Menten kinetics held up fine.) —Preceding unsigned comment added by Richmc (talk • contribs) 00:34, 15 January 2009 (UTC)
 * What do you mean with 'quantified and bounded'? I guess you mean stating the error (or estimates thereof)? I can do this for the mathematical limitations if needed.Athenray (talk) 17:36, 13 February 2009 (UTC)

Michaelis–Menten Equation?
While most people make the error, the equation is properly known as the Briggs-Haldane Equation (they came up with their version after Michaelis and Menten). Now, almost everyone gets it wrong including most textbooks. The actual Michaelis–Menten equation assumes rapid equilibrium, the Briggs-Haldane does not. So the first paragraph should be altered to include this somehow. Hichris (talk) 19:14, 14 August 2009 (UTC)
 * Anyone interested can look up the corresponding chapter in the Lin & Segel's classic textbook; I was going over it the other day, & they do make a point about different people attributing the work to different people. Apart from Michaelis & Menten or Briggs & Haldane, one can (& often does) cite Henri as well. It's far from clear that a unique proper attribution exists, as Hichris above seems to suggest. I'm for citing all people involved in the derivation of the enzyme kinetics equation, but I'd also request that one looks up the literature first to see who did what.Athenray (talk) 22:47, 4 October 2009 (UTC)
 * I need to revise the above: indeed, the Briggs-Haldane treatment (based on the quasi-steady state approximation/QSSA) differs from the Michaelis-Menten equations (based on rapid equilibrium) in the particulars. (Similarly for the van Slyke-Cullen equations, which employs yet another argument.) The difference, in fact, lies in the definition of the constants: each treatment gets the same functional expression $$v_0 = v_\max {[}S{]} / (K_M + {[}S{]})$$ but a different expression for the constant $$K_M$$ . Segel's Enzyme Kinetics points this out explicitly (p.22 in the 1993 ed.): (b) For many situations, the rapid equilibrium and steady-state treatments yield the same final velocity equation. That is, the form of the velocity equation is the same, but the definitions of the constants are not the same.
 * My personal inclination would be to add all of the variants (Michaelis-Menten-Henri and Van Slyke-Cullen; Briggs-Haldane is already there) into the article, and then point out the differences and that the Briggs-Haldane treatment is what we commonly refer to (somewhat confusingly, as it turns out) as Michaelis-Menten kinetics. I'll give it a try when I find the time, in fact, unless anyone objects in the meantime. Athenray (talk) 08:50, 6 October 2009 (UTC)

i dont know —Preceding unsigned comment added by 196.221.190.214 (talk) 11:41, 29 June 2010 (UTC)

Optimal uptake kinetics
I have twice undone additions of information on "optimal uptake kinetics", most recently with this edit. I don't feel that this is the appropriate place for seven paragraphs about this theory, but would appreciate others' views on this. U+003F? 18:53, 29 October 2011 (UTC)
 * I agree that the "optimal uptake kinetics" section is not appropriate for this article. The application of the MM equation to the "nitrate uptake by phytoplankton in the ocean" is way too specialized for this article – and is probably unsuitable for any wikipedia article - secondary sources would be required. Aa77zz (talk) 10:20, 30 October 2011 (UTC)

Turnover number and turnover frequency
I think the next text isn't right, the term should be turnover frequency and not turnover number. Number is the maximum number of reactions an enzyme can do before it is degraded. The term should be turnover frequency as it is a value of the number of reactions per unit time. I haven't corrected yet, and wait for people to agree and change it (perhaps i'm wrong)

"the turnover number, is the maximum number of substrate molecules converted to product per enzyme molecule per second." — Preceding unsigned comment added by 77.173.73.102 (talk) 23:13, 16 December 2013 (UTC)

by User:Ansjovis86

rate as a function of substrate concentration graph
I was trying to learn about Km and affinity from this page. But I found confusing the very first graph you have on the page! There is no explanation if the concentration is of a substrate or of a product. The main formula, which relates to the graph, has both substrate and product concentrations in it. Only after looking at other web pages I could understand that the graph is talking about the substrate concentration.

Related to the above problem is a missing graph of d[P]/dt even though the formula is given at the very beginning of the page. And I don't think that the graph to the right for the rate/[S] is the graph of that function.

Assessment comment
Substituted at 23:56, 29 April 2016 (UTC)

Unexplained deletion by author and classmate?

 * I am wondering why the five edits by two Hunter college students were deleted again by one of them? In my opinion they were useful and well-sourced additions to the article, which I would have restored if they had been deleted by someone else. Are either or both of these two editors interested in restoring all or part of the deleted text? Dirac66 (talk) 02:02, 18 December 2017 (UTC)
 * I am wondering why the five edits by two Hunter college students were deleted again by one of them? In my opinion they were useful and well-sourced additions to the article, which I would have restored if they had been deleted by someone else. Are either or both of these two editors interested in restoring all or part of the deleted text? Dirac66 (talk) 02:02, 18 December 2017 (UTC)
 * I am wondering why the five edits by two Hunter college students were deleted again by one of them? In my opinion they were useful and well-sourced additions to the article, which I would have restored if they had been deleted by someone else. Are either or both of these two editors interested in restoring all or part of the deleted text? Dirac66 (talk) 02:02, 18 December 2017 (UTC)

Common sense in punctuation
Apparently somebody thought that the way to put a period at the end of a sentence is this: That is silly. I changed it to this: Michael Hardy (talk) 18:02, 18 March 2019 (UTC)


 * It's rarely necessary or helpful to put punctuation in equations at all. I would omit the full stop. Athel cb (talk) 18:52, 1 April 2023 (UTC)

Michaelis–Menten equation vs Briggs-Haldane equation
It seems as if the equation mentioned in the lead is commonly referred to as the Briggs-Haldane equation (and not the Michaelis–Menten equation).

If we want to have the Michaelis–Menten equation in the lead, then we have to change the Km to Kd. The Michaelis–Menten equation assumes equilibrium, while the Briggs-Haldane equation assumes a steady state. 81.191.81.174 (talk) 18:14, 7 December 2022 (UTC)


 * The mechanism proposed by Michaelis and Menten assumed equilibrium, yes, but today nearly everyone takes the Michaelis–Menten equation to be the form derived by Briggs and Haldane. Athel cb (talk) 18:48, 1 April 2023 (UTC)

Assumptions and limitations
I find this subsection too advanced in style for the general level of the article. I would prefer a dumbed-down version that gives appropriate references to Schnell. Athel cb (talk) 18:56, 1 April 2023 (UTC)

"Michaelis–Menten plot"
Is it misleading to use "Michaelis–Menten plot" for a diagram of v over a? After all, such a plot would show data fitted to the Michaelis-Menten equation, so the name matches quite well. V was plotted over log a in the original paper, yes it's true. This way of plotting is not used anymore for this data, also true. Unnecessary techniques should become forgotten over time. There is enough other information on the Michaelis-Menten equation relevant today that we should care about. The section "Michaelis–Menten plot" might be dispensable. 2003:F8:3F1D:1BC8:DC57:32A4:5900:6ED2 (talk) 19:59, 5 February 2024 (UTC)