Dear community,
I will greatly appreciate an expert view and possible links to further reading on the following. Imagine we have a protein and its ligand, and we measure corrsponding dissociation constant Kd (for example, by ITC) and Ki by a competitive assay (for example, using a fluorescent tracer engaging the same binding pocket as the ligand). In a simplest case when the ligand and the protein are relatively rigid, Kd should be equal Ki. Imagine now the highly flexible protein and ligand; in particular, assume that the protein has its binding pocket hidden and needs to undergo relatively slow conformational rearragement BEFORE the ligands bind, in order to open the pocket. In even more complex case, ligands binding can proceed in several consecutive steps, during which the protein rearranges, also in several steps. The question is: should the Ki and Kd be equal in this case? Ki is measured usually under "stoichiometric" conditions, when the protein and the tracer are bound. Their dissociation might produce the protein possessing its binding pocket already open. Therefore, the k(on) of the ligand can be lower; if k(off) is the same, it means Ki could be larger than Kd measured without the tracer. Does it make sense?
If you measure the two equilibrium constants, without and with competitive ligand, the dissociation constant in the presence of competitor will be larger. And this occurs with or without a conformational change coupled tonthe binding.
In fact, the dissociation constant in the presence of a competitor could be either larger or lower than without competitor, there are many literature examples where they differ significantly in both directions (see, e.g. DOI 10.4161/cc.9.22.13871; 10.1039/c4sc00045e).
They also can be equal (dx.doi.org/10.1021/jm300078z), within the errors of measures.
Can we rationally explain this?
One explanation could use allostery, the case when the ligand and competitor interact with binding sites that are topographically distinct (DOI 10.1111/bph.2010.161.issue-6). But what if the binding sites of are apparently the same, like in DOI 10.1039/c4sc00045e? Can someone recommend a comprehensive reading on this?
If the two ligands, A and B, are truly competitors (either direct orthosteric competition at the same binding site or allosteric competition in different binding sites through a conformational change), the dissociation constant for ligand A in the presence of ligand B at a certain concentration [B], Kd,A/B, is larger than the intrinsic dissociation constant in the absence of the other ligand, Kd,A (for [B]=0):
Kd,A/B = Kd,A (1+[B]/Kd,B)
where Kd,B is the dissociation constant for ligand B.
This is a particular case of a more general case, where the heterotropic interaction between ligand A and B is reflected by:
Kd,A/B = Kd,A (1+[B]/Kd,B)/(1+[B]/alphaKd,B)
where alpha is the heterotropic interaction constant between ligands A and B.
If alpha = infinity (i.e., very large), ligands A and B are excluding or competitive ligands (maximal negative binding cooperativity).
If alpha > 1, ligands A and B show negative binding cooperativity.
If alpha = 1, ligands A and B bind independently to the macromolecule.
If alpha < 1, ligands A and B show positive binding cooperativity.
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