[PhDstudent]

Hello, I have a doubt about cooperativity in molecules with only one binding site, forming dimers and tetramers. could someboby please help me and  give me a reference to consult this item?  everything I find is related to proteins with more than one binding site, and I am working with a protein which forms aggregates, and the binding ratio molecule: ligand is 2:1, and it forms tetramers and more complex agreggates, and the calculated Hill coefficient is >1, cooperative binding. Thaks!!

[Babcock_Hall]

I am not sure that I entirely follow, but I am proceeding under the assumption that the cooperatively might be associated with the macromolecule's association into aggregates.  You might wish to consult Chapter 6 of "Binding and Linkage" by J. Wyman and S. J. Gill (1990).  It looks like a fairly advanced treatment.

[pgk]

Both hemoglobin and myoglobin have one active site but both have a Hill coefficient that is >1, respectively. Besides, the experimental values are often different than the calculated ones. Please take a look to the follow article and link that might be helpful.
The Hill equation revisited: uses and misuses, The FASEB Journal, 11(11), 835-841, (1997)
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.312.9957&rep=rep1&type=pdf

[Babcock_Hall]

The Hill coefficient of myoglobin is one.  Hemoglobin has one active site per monomer, but it exists (primarily) in the form of an α₂β₂ tetramer in solution, having four active sites, and it normally shows a Hill coefficient of 2.8 to 3.  A few forms are known which have a Hill coefficient of one.  I broadly agree with the article by Weiss in that the Hill coefficient is a measure of cooperatively but not stoichiometry.

[pgk]

Agreed and furthermore:
J.J. Kelly, K.A. Kelly, S.A. Hartley and C.H. Barlow  (1991)  Myoglobin oxygen binding curves determined by phosphorescence quenching of palladium porphyrin.  Appl. Spectrosc.  45(7):1177-1182. A completely optical method was developed for evaluating myoglobin-oxygen saturation. Solution oxygen concentrations were computed from measurements of phosphorescence decay of a soluble palladium porphyrin according the Stern-Volmer quenching relationship. Visible absorption spectra were recorded of myoglobin solutions progressively deoxygenated by bacterial aerobic metabolism. Myoglobin oxygenation curves were obtained from the spectra by two full-spectrum procedures, singular value decomposition (SVD) and curve fitting, and by the traditional dual-wavelength isosbestic method. The calculated P50 for horse heart myoglobin at 24±1°C was 1.2 Torr by SVD, 1.2 Torr by curve fitting, and 1.4 Torr by dual-wavelength spectroscopy. These results compare favorably with a value of 1.1 Torr estimated from the work of Rossi-Fanelli and Antonini for human myoglobin. The Hill coefficient, theoretically 1.00 for myoglobin, was experimentally determined to be 0.96 by SVD and 0.95 by curve fitting the spectral data matrix.

[PhDstudent]

Thanks Babcock_Hall and pgk,
I am still reading the information and it looks really usefull. By now I understand Hill coefficient can be calculated for that binding, forming protein aggregates which bind a ligand, RNA in my case. This coefficient is calculated for the protein but it must be refered to the tetramer or further aggregates, as in my case, when I have got 4 protein molecules against 2 ligands (2 small RNA molecules). On one hand I have got the stoichometry, I know it forms aggregates and how are those, and on the other hand I have calculated the Hill coefficient and it relates to cooperativity but not stoichometry. And this coefficient reinforce the idea that my protein works as aggregates or it is the active form of the protein. am I right?

 

[pgk]

It' up to you to decide by taking another look to the previous replies and to the said article by Weiss. But, are there any references in the literature, about the quaternary structure of your protein?

[Babcock_Hall]

It might be that the problem will become marginally easier if you treat the RNA as the macromolecule and the protein as the ligand.  If you have not yet obtained a copy of the Wyman book, I suggest that you do so.  The authors have some examples in Chapter 6.