I guess you need to use Flourescence Anisotropy to measure the Kd of their interaction? If there will be strong interaction then you will see a big change in anisotropy due o increase in side of combined molecule. However, you might need flouroscent tag or so.

Another fluorescence-based method is FRET (fluorescence resonance energy transfer). In this method, one of the proteins requires a donor fluorophore and the other requires an acceptor. This could be done with chemical labels if you have purified proteins, but it could also be done in cells (or with purified proteins) by expressing each protein as a fusion with a suitable fluorescent protein. Measuring the Kd in cells would be challenging because it would require knowing the concentrations of the proteins, but it would be straightforward with purified proteins.

With purified proteins, you could also use non-fluorescence-based techniques, such as isothermal titration calorimetry and surface plasmon resonance.

Thanks for the answer. The only I know about FRET is that it will not work in this case. And yes, the proteins are purified. 

Why do you say that FRET will not work?

Because the two transcription factors are quite similar: At least the truncated versions are. They each have ONE tryptophan residue and as far as I understand there must be a donor AND an acceptor for FRET to work.

Extrinsic fluorophores can be attached to purified proteins by chemical means. With a donor attached to one of the proteins and an acceptor attached to the other, FRET experiments can be done. Some engineering may be needed to create suitable labeling sites. The best situation is to have a single surface-exposed Cys residue in each protein, because Cys can be specifically labeled with commercially available reagents. The selection of fluorophores is an important consideration because it affects the distance between them over which FRET occurs. The position of the Cys residue, similarly, can make a big difference in the size of the FRET signal. The acceptor doesn't have to be fluorescent, by the way; it could be a quencher, too. You could also make fusion proteins with a FRET pair of fluorescent proteins, or take advantage of various tags for introducing the FRET donor/acceptor.

Okay. How would you change the concentration of one construct and keep the concentration of the other construct constant in a single cuvette box??

The FRET donor-labeled protein concentration should be held constant and the acceptor-labeled protein concentration should be varied. The reduction of the onor fluorescence should be measured as a function of the acceptor concentration.

If possible, you should minimize the dimensions of the cuvette. The reason for this is to minimize the inner filter effect (It also reduces the amount of materials needed for the experiment), which is directly proportional to the path length. 4 x 4 mm fluorescence cuvettes are commercially available.

The inner filter effect is a reduction in observed fluorescence caused by absorbance of light by a fluorophore. When titrating the acceptor concentration, you may require concentrations high enough that the absorbance of the donor's emitted light by the acceptor becomes a significant effect, making the FRET efficiency appear higher than it really is.

To deal with this problem, you can measure the inner filter effect by replacing the donor-labeled protein with free donor fluorophore. Since there should be no binding between the free fluorophore and the acceptor-labeled protein, any reduction in free donor fluorophore fluorescence can be attributed to the inner filter effect. Calculate a correction factor based on this measurement. For example, if the inner filter effect results on a reduction in fluorescence intensity of the free donor fluorophore from 3000 to 2000 RFU, the correction would consist of multiplying the fluorescence of the donor-labeled protein fluorescence at the same acceptor concentration by 3000/2000 = 1.5.