Then you need a quantitative technique that allows you a precise determination of the binding affinity. There are many techniques for affinity determination (e.g. SPR, spectroscopy), but the gold standard nowadays is ITC (isothermal titration calorimetry).

You may perform an experiment titrating protein C into protein A. Then, a second experiment titrating protein C into complex A-B. Just in case, it would be appropriate to perform a third experiment titrating protein B into protein A. The first two experiments will provide the answer to your question.

You may check these two articles concerning heterotropic cooperativity and ternary interactions:

http://www.ncbi.nlm.nih.gov/pubmed/16766617

http://www.ncbi.nlm.nih.gov/pubmed/17192587

Another IP experiment can still help to get a clue on whether B is crucial for A-B to interact with C, and to show that A alone cannot co-IP with C. First you have to show and be sure that, in fact, A, B, and C, do co-IP altogether (repeat IP and run WB to detect C). If so, elimination of B (e.g. by siRNA) should abrogate A-C co-IP, if B is really crucial for this interaction. Do you agree?

The proposed IP experiments should work. But, if B just modulates binding affinity between A and C (that is, in the absence of B, protein A still interact with protein C, with different affinity though), co-IP experiments will not provide a direct answer. It will work fine in two limit cases, either protein B abolish A-C interaction, or protein B is strictly required for A-C interaction.

you can show the complex of all 3 or 2 proteins forming by immune transmission electron microscopy (iTEM) using 3 sizes of gold bead. I did this in a recent paper (Circ Res, see attached figure) as part of a number of experiments to show protein interacting together. We used 3 size beads and measured distances between each of the conditions (less than 20nm was recorded as an interaction. We then backed up findings by co-IP, co-localization, proximity ligation assay (duo link) and analytical Size exclusion chromatography of the purified proteins.

I agree with you Adrian. I guess that the final methodology depends on the degree of precission she wants to achieve in terms of affinity (whether quantitative or just qualitative). So-Jin has the word on this concern. A quick IP experiment should solve the last sentence of your previous comment, and help decide the next methodological approach in case B finely modulates afinity of the A-B complex towards C and on which degree.

Forgive my two cents, but how do you get information about the affinity between two proteins by immunoprecipitation ? IP is certainly not a quantitative method, or is it ?

It might be that the missleading word in this thread iis "affinity". She used that word in her first sentence of her address when she probably ment "interaction", but she never mentioned "to quantitate the degree of affinity". Pierre, IIP will provide qualitative information on protein interactions, but it can also help to show semi-quantitative differences when a co-factor is needed for an interaction to occur. IP/WBs can be quantified using pertinent controls (inputs) and antibodies. Take a look on this paper I just picked as an example: http://www.ncbi.nlm.nih.gov/pubmed/14517248

Forgive my complete ignorance in the subject... but FRET would not work for this? At least it can be performed in a more quantitative way than IIP and I think is less expensive than other more state-of-the-art methods... just my 2 cents.

Cost must be estimated globally: you may use less sample in FRET experiments, but you must label the proteins with the appropriate fluorofores... Besides, labels may potentially distort interactions. Apart from some disadvantages of ITC (by the way, most of them are shared with another binding techniques), ITC remains as the gold standard: no labelling, no immobilization, direct determination of enthalpy and affinity of interaction...

Protein-protein interaction (PPI) networks enable us to better understand the functional organization of the proteome.

http://www.biomedcentral.com/1752-0509/3/112

The biggest problem that you encounter with analytical size exclusion, SPR and I assume ITC (never used it) and any of these is that it requires generation and purification of the single proteins from bacteria or some other method. This can be very complicated even for relatively unfolded easy to generate proteins, requires a lot a equipment that may not be part of a standard (non-chemistry based) lab and is definitely expensive and time consuming. At least by comparison of the proteins in their biological state i.e. in-cell or in lysates (i.e. Co-IP). Practicality vs cost vs importance to the studies should be estimated as stated by Adrian

Thanks to Salvador for the nice paper, where the authors nevertheless used a "more quantitative surface plasmon resonance BiaCore binding assay" to confirm their findings. Going back to So-Jin question, it seems that the experimental gold standard these days to study protein complexes would be some affinity purification(s) followed by mass spec ( http://www.ncbi.nlm.nih.gov/pubmed/17072306 or http://www.ncbi.nlm.nih.gov/pubmed/22610586 ), including of course all proper controls. This would not require protein purification, but could also be costly and not practical in many labs.

Most straightforward and quick way (assuming you have adequate amount of protein through expression and purification) is to perform Isothermal calorimetry (ITC) on these proteins. Although as stated by Scott, it depends on how easy it is to obtain adequate amount. If you did have a good amount you could start with A and determine the free energy of binding with B and then add C and see if your free energy decreases and this will tell you that the binding of B energetically facilitates the formation of the ABC complex etc. I'm sure someone has done this in the literature for three proteins before. Although keep in mind this is in vitro and the affinity can definitely be different in a cell because there are other proteins that may be present who's transient interactions or low affinity may contribute to the formation of the entire complex. That's just my idea and we are planning to use this approach now for a set of 3 large proteins since we can express them separately in enough quantities. Just keep in mind that expression in mammalian cells and bacteria can lead to very different results because of the possibility that your proteins may be glycosylated and glycosylation may also contribute to the affinity of binding.

Not enough info on protein size, purity, etc. and it's not clear if true affinities are being sought (which you can't get by IP) or just relative affinities. For true affinities you have to do SPR or something like that. For relative affinities you can generate saturation binding curves by ELISA. A straightforward way of doing this is described in Kartner et al. J Biol Chem 285:37476 (2010). It's not a 3 way system, but if you use A and AB as ligands and C as analyte, you should still get a number for relative affinity. You might even get away with not so pure protein if you have good antibody and good controls. Being able to label C would be a bonus. As in all methods you still have to worry about things like aggregation artifacts, steric hindrance artifacts due to ligand binding (meaning here the binding of the A or AB to the plate, which may in different ways affect accessibility of C) and possibly steric hindrance artifacts involving antibody accessibility (which may not be an issue if you can e.g. radiolabel C).