Absorption Spectroscopy to Probe Ligand Binding
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When a ligand solution is added to a solution of biomacromolecules, if it does not bind to the macromolecules, then the UV–visible spectrum will simply be the sum of the macromolecule spectrum and the ligand spectrum. If the ligand does bind to the macromolecules, then the spectrum of the complex will be (at least slightly) different from the sum spectrum. One should note that the observed spectrum is probably a complicated mixture of the spectrum of bound and unbound ligands and free and complexed macromolecules.
Titrations to Determining Data for Binding Constant Calculations
The term “titration” is used to cover experiments where spectra are collected as a function of concentration, ionic strength, pH, etc. To minimize macromolecule consumption and also (perhaps surprisingly) to minimize concentration errors, the best way to proceed is often to add solution to the cuvette. A simple way to avoid dilution effects is to proceed as follows. Consider a starting sample that has concentration x M of species X. Each time y cm3 of Y is added, also add y cm3 of a 2 x M solution of X. The concentration of X remains constant at x M. Many variants on this theme may be derived though all rely on the species in the solution establishing a new equilibrium. If the binding is extremely strong (e.g., covalent), then independent samples at the required molar ratios will usually need to be made.
If the shape of the changes (i.e., the spectrum of bound minus spectrum of free) induced into a ligand or macromolecule spectrum remains unchanged during a titration experiment, but the magnitude changes in a manner that is proportional to the concentration of bound ligand, then we can conclude that the ligands are binding in one binding mode or in constant proportions in more than one mode (meaning site, orientation, sequence, etc.). In such cases, spectroscopic data can be used to determine the equilibrium binding constant, K. The data must be of very high quality for absorbance (or any other spectroscopic data) to be used to determine K. A simple plot of change in absorbance versus either total macromolecule or total ligand concentration (whichever is being varied) will probably enable the quality of the data set to be determined. It should be a smooth curve. There are many ways of proceeding from such a curve to a value for K. The one outlined below is designed to indicate the principles rather than necessarily being the best approach.
Whichever data analysis method one chooses, it is very important to check that its assumptions are valid for your situation. For example, the one developed by Schmechel and Crothers (1971) requires one binding site per base pair and small binding ratio. It has been popularized (Pyle et al. 1989) for any situation and so can be misleading.
where c b is the concentration of bound ligand and c f is the concentration of the free ligand.
Application of this equation requires knowledge of the absorbance of free and bound ligand. Determining the latter requires measuring an absorbance spectrum under conditions where it is known that all the ligands are bound to the macromolecules. K may then be determined directly. A more accurate value of K will be achieved if the data are used to perform a Scatchard plot (Scatchard 1949) or fitted directly. The disadvantage of the Scatchard plot is it does not weight all data points equally. Its major advantage is that the curve should be a straight line, so it is obvious to the eye if Eqs. 2 or 3 is not appropriate for the system being studied.
So, a plot of r/c f versus r has slope − K and y-intercept K/n. The x-intercept occurs where r = n.
- Schmechel DEV, Crothers DMB (1971) Kinetic and hydrodynamic studies of the complex of proflavine with poly A·poly U. Biolopymers 10:465–480Google Scholar