Analysis of the circular dichroism spectrum of proteins using the convex constraint algorithm: a practical guide

Due to the time scale of circular dichroism (CD) measurements, it is theoretically possible to deconvolute such a spectrum if the pure CD spectra differ significantly from one another. In the last decade several methods have been published aiming at obtaining the conformational weights, or percentages (which are the coefficients for a linear combination) of the so-called typical secondary structural elements making up the three-dimensional structure of proteins. Two methods that can be used to determine the secondary structures of proteins are described here. The first method, called LINCOMB, is a simple algorithm based on a least-squares fit with a set of reference spectra representing the known secondary structures and yielding an estimation of weights attributed to alpha-helix, beta-pleated sheet (mainly antiparallel), beta-turns, unordered form, and aromatic/disulfide (or nonpeptide) contributions of the protein being analyzed. This method requires a "template" or reference curve set, which was obtained from the second method. The second method, "convex constraint analysis," is a general deconvolution method for a CD spectra set of any variety of conformational type. The algorithm, based on a set of three constraints, is able to deconvolute a set of CD curves to its common "pure"-component curves and conformational weights. To analyze a single CD spectrum with this method, the spectrum is appended to the data set used as a reference data set. As a way to determine the reliability of the algorithm and provide a guideline to its usage, some applications are presented.