Complex data analysis.

CD spectroscopy is used often to analyze the secondary structure content of proteins, but this is only one of many applications.

As we already mentioned in the section dealing with advanced experiments, CD is useful any time that there is a conformational change associated with a given process. Possible example are ligand binding, thermal denaturation, pH effect ...

In all these cases, it is possible to report the percentage of observed CD variation (i.e. DCD/DCDmax * 100) versus the variable of interest (i.e. added ligand concentration, temperature, pH ...).

As a first example, consider the case of the binding of a ligand to a protein. In particular, think to a ligand that does not contribute to the CD spectrum in the region under analysis (for example, a metallic ion).

To obtain some useful information from CD data, like stoichiometry and Kd of the process, we must first of all assume that there is a direct dependence between the CD variation (i.e. the observed conformational change of the protein) and the completeness of the process under study (i.e. the amount of formed complex). This is a quite safe assumption, that is not only used in CD spectroscopy, but in all kind of techniques that monitor indirectly the ligand binding (UV-Vis, Fluorescence, I.R. ... ).

Under this assumption, we have in the case of metal binding that:

[Complex] = k * DCD

and so:

[Complex]max = k * DCDmax

Since:

[Complex]/[Complex]max = frcomplex (where frcomplex is the molar fraction of complex)

we have that:

 frcomplex = DCD/DCDmax

This is to say that the normalized variation of CD is equal to the molar fraction of complex in solution. 

We can now build a graph like the following:

In the particular case illustrated by the graph, the curve which best fits the data is a hyperbola, so that a simple binding model with all equivalent binding sites can be assumed. However, in a different experimental situation this can change. The shape of the curve you obtain is informative on the binding process; however, here I will not discuss further how to treat binding data (this is a circular dichroism tutorial after all!).

What is important to outline is that by CD you obtain simultaneously information on the binding equilibrium (Kd, stoichiometry) and on the structural effect of the ligand on your macromolecule. For example, the above curve refers to the binding of calcium to a peptide. The binding of the metal increases the intensity of the 222 nm band of the peptide, so that by CD you can view that the metal binding is coupled to an increase of the helical content of the peptide.