Talk:Hill equation (biochemistry)

Wiki Education Foundation-supported course assignment
This article is or was the subject of a Wiki Education Foundation-supported course assignment. Further details are available on the course page. Student editor(s): Abw20. Peer reviewers: Jih24, Blb6175535.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 23:27, 16 January 2022 (UTC)

Reference and Article Cleanup
I have made a lot of changes and added citations. Any feedback would be appreciated! Abw20 (talk) 18:24, 28 November 2016 (UTC)

Edits
'''I don't know if this is the right place to write a comment about this page. Anyway, I think that the figure and the caption are (slightly) wrong: the horizontal axis is [L] and not K_a/[L], otherwise we would have θ(0)=1.''' — Preceding unsigned comment added by Cedric.lh (talk • contribs) 12:17, 7 March 2017 (UTC)

I think the Hill equation of the current version is wrong. The equation looks like the one given by J Biol Chem. 1970 Dec 10;245(23):6335-6., but not the same. Based my derivation from the model and my understanding, I am going to edit the function and if someone thinks mine is not correct, please discuss with me here.

The earlier version was really wrong, but the present form is already correct. Kd is the dissociation constant in the Hill equation, which is obtained from the law of mass action. KA is another constant for the system, denoting the ligand concentration occupying half of the binding sites. Their relationship is: Kd = (KA)n. Using the Hill equation to describe different systems, n (Hill coefficient) may have different meanings. In a complicated system, the meaning of n is also complex.

Request
In the introduction to Hill equations, we read "The Hill-Langmuir equation was originally formulated by Archibald Hill in 1910 to describe the sigmoidal O2 binding curve of haemoglobin." It would be nice to have a figure with this graph, so that the less-sophisticated reader can get a sense of what the sigmoidal binding is, if someone has it.

Rpgoldman (talk) 15:11, 19 November 2019 (UTC)

Disambiguation
The disambiguation at the top of this page is probably not enough. One may also wish to consider the issue of being notable - 15 thousand vs 40 thousand Google hits for the astronomical equation ( i searched for "Hill equation hemoglobin" vs "Hill equation moon". The astronomical equation is important for the entire development of 20th century mathematical physics, whereas the biochemical is a special case of the Langmuir equation. Perhaps it would be better to rename the article as "Hill C oefficient"? For example, a recent paper discussing this has three mentions of the "Hill coefficient" and only one mention of the equation in the abstract. http://www.fasebj.org/cgi/content/abstract/11/11/835  Kotika98 (talk) 13:37, 11 November 2009 (UTC)

Hill Plot and comment on disambiguation
It would be nice to include a section about Hill plots, since a.) this page redirects from "Hill plot", and b.) Hill plots (at least in older literature) are the primary way of measuring the parameters of the Hill equation. Currently Hill plots are not mentioned.

I think searching on "Hill equation hemoglobin" leads to an underestimation of the importance of Hill plots: they can be used to describe the kinetics of any kind of molecule that binds to multiple ligands, not just hemoglobin, as shown by the paper Kotika98 cites. I also like titling the article "Hill equation" because, even if "Hill coefficients" are more commonly discussed, the equation underlies the meaning of the coefficient. Asteen (talk) 12:39, 30 August 2011 (UTC)

Typo in the logistic version of the equation?
I'm no expert on the Hill equation, but shouldn't both terms get the n?:

$$ \log\left( {\theta\over 1-\theta} \right) = n\log{[L]} - \log{K_A}.$$

-->$$ \log\left( {\theta\over 1-\theta} \right) = n(\log{[L]} - \log{K_A}).$$ — Preceding unsigned comment added by 207.198.105.22 (talk) 15:51, 30 September 2015 (UTC)

I agree. The way it's defined in the article, both terms ought to get an n. However, I've seen derivations where, essentially, $$K_H$$ is defined as $$K_A^n$$. Then,

$$ \log\left( {\theta\over 1-\theta} \right) = n\log{[L]} - \log{K_H}.$$

Then, the derivation matches most others.

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I agree. I went ahead and made the change. 129.177.233.236 (talk) 12:00, 10 November 2015 (UTC)

Response Coefficient Section, possible incorrect terminology
The Response Coefficient section is incorrectly named, although it depends on the context. If you're thinking of a single process in a model, such as an enzyme or transcriptional factor that shows cooperative behavior, then the correct terminology is to use the elasticity coefficient. If you're thinking of a system with more than one process, then the correct terminology is the response coefficient. By system, I mean a mathematical model of the system. The reason for the difference in terminology is to distinguish between local responses and systems responses. Hence if someone refers to an elasticity, one immediately knows they are talking about the response of a single process.

The formalism for a single process in a model would be:

$$ \varepsilon^x_y = \frac{\partial y}{\partial x} \frac{x}{y} $$

For a Hill function, it is also possible to algebraically compute the elasticity, which is given by:

$$ \varepsilon^v_s = \frac{n K_H}{K_H + (s/K_H)^n} $$

where K_H is the ligand (s) concentration at half-maximal velocity.

Rhodydog (talk) 18:53, 20 October 2019 (UTC)

Here is a link to Hill's original paper
I don't know how to add this as a reference, but it would be useful to add.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1533698/pdf/jphysiol02248-0004.pdf — Preceding unsigned comment added by 173.228.119.216 (talk) 23:26, 24 December 2020 (UTC)


 * Looks like the reference is cited in the article, citation number 4. Rhodydog (talk) 05:09, 28 January 2023 (UTC)