Hi all,
Typically, in a generic ligand binding equation, [L]+[R] -> [LR], the fraction bound receptors ([LR]/([L]+[LR]) can be written as [L]/(Kd+[L]). From this when we plot, fraction bound vs. [L], when the fraction bound is 0.5, the [L] = Kd.
I am trying to observe dimer dissociation constant upon some ligand binding. So the chemical equation would be [M]+[M]+[L]->[D] or 2[M]+[L]-> [D], where M is monomer, D is dimer and L is ligand.
I want to get the dimer dissociation constant under increasing concentrations of ligand. So I think I would like to relate the Kd to dimer fraction([D]/[D]+2[M]) and varying concentrations of [L].
Would deriving the Kd (dimer dissociation constant) possible using [D]/[D]+2[M] vs. [L]?
It's important to be clear about the system. How many different equilibria are there? Is there any dimerization in the absence of the ligand? If so, is there a different affinity of the ligand for the monomer versus the dimer? Is there an equilbrium for the ligand binding to the monomer without dimerization?
Perhaps the analysis in this paper is relevant to your system:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2754295/
I should downvote your question, which shows that you do not understand the basics of chemical equilibria. I would advise you to remove your question from the forum and to read textbooks.
If we take your proposed equilibrium at face value: M+M+LD, where D actually consists of the ternary complex M2L, which I will write as MML, and assuming that to be the only equilibrium (which is doubtful), then Kd = [M]2[L]/[MML] and the fraction of M bound (i.e. in the state MML) is fb = 2[MML]/([M] + 2[MML]), where [M] + 2[MML] is [M]total. Note that the concentration of M bound in the MML state is 2[MML].
Substituting [MML] = [M]2[L]/Kd in the fb relationship leads to
fb = 2[M][L]/(Kd + 2[M][L]).
Therefore, when fb = 0.5 (i.e. 50% of M is in MML), Kd = 2[M][L].
It is very important, when using relationships like this, to realize that the concentrations [M] and [L] are not the total concentrations of M and L, they are the free concentrations.
Quick comments to Adam's answer. The termolecular reactions do not exist. This reaction should be written as a sequence of two bimolecular reactions. You are absolutely right that "the concentrations [M] and [L] are not the total concentrations of M and L, they are the free concentrations." In other words, a mass balance should be taken into account to derive the right equation. Derivations of equilibrium equations are described in the textbooks.
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