Estimation of protein secondary structure and error analysis from circular dichroism spectra

The estimation of protein secondary structure from circular dichroism spectra is described by a multivariate linear model with noise (Gauss-Markoff model). With this formalism the adequacy of the linear model is investigated, paying special attention to the estimation of the error in the secondary structure estimates. It is shown that the linear model is only adequate for the alpha-helix class. Since the failure of the linear model is most likely due to nonlinear effects, a locally linearized model is introduced. This model is combined with the selection of the estimate whose fractions of secondary structure summate to approximately one. Comparing the estimation from the CD spectra with the X-ray data (by using the data set of W.C. Johnson Jr., 1988, Annu. Rev. Biophys. Chem. 17, 145-166) the root mean square residuals are 0.09 (alpha-helix), 0.12 (anti-parallel beta-sheet), 0.08 (parallel beta-sheet), 0.07 (beta-turn), and 0.09 (other). These residuals are somewhat larger than the errors estimated from the locally linearized model. In addition to alpha-helix, in this model the beta-turn and "other" class are estimated adequately. But the estimation of the antiparallel and parallel beta-sheet class remains unsatisfactory. We compared the linear model and the locally linearized model with two other methods (S. W. Provencher and J. Gl?ckner, 1981, Biochemistry 20, 1085-1094; P. Manavalan and W. C. Johnson Jr., 1988, Anal. Biochem. 167, 76-85). The locally linearized model and the Provencher and Gl?ckner method provided the smallest residuals. However, an advantage of the locally linearized model is the estimation of the error in the secondary structure estimates.     

Protein secondary structure from circular dichroism spectra

Circular dichroism spectra of proteins are extremely sensitive to secondary structure. Nevertheless, circular dichroism spectra should not be analyzed for protein secondary structure unless they are measured to at least 184 nm. Even if all the various types ofβ-turns are lumped together, there are at least 5 different types of secondary structure in a protein (α-helix, antiparallelβ-sheet, parallelβ-sheet,β-turn, and other structures not included in the first 4 categories). It is not possible to solve for these 5 parameters unless there are 5 equations. Singular value decomposition can be used to show that circular dichroism spectra of proteins measured to 200 nm contain only 2 pieces of information, while spectra measured to 190 nm contain about 4. Adding the constraint that the sum of secondary structures must equal 1 provides another piece of information, but even with this constraint, spectra measured to 190 nm simply do not analyze well for the 5 unknowns in secondary structure. Spectra measured to 184 nm do contain 5 pieces of information and we have used such spectra successfully to analyze a variety of proteins for their component secondary structures.     

Using circular dichroism spectra to estimate protein secondary structure

Circular dichroism (CD) is an excellent tool for rapid determination of the secondary structure and folding properties of proteins that have been obtained using recombinant techniques or purified from tissues. The most widely used applications of protein CD are to determine whether an expressed, purified protein is folded, or if a mutation affects its conformation or stability. In addition, it can be used to study protein interactions. This protocol details the basic steps of obtaining and interpreting CD data, and methods for analyzing spectra to estimate the secondary structural composition of proteins. CD has the advantage that measurements may be made on multiple samples containing < or =20 microg of proteins in physiological buffers in a few hours. However, it does not give the residue-specific information that can be obtained by x-ray crystallography or NMR.     

SOMCD: method for evaluating protein secondary structure from UV circular dichroism spectra

This article presents SOMCD, an improved method for the evaluation of protein secondary structure from circular dichroism spectra, based on Kohonen's self-organizing maps (SOM). Protein circular dichroism (CD) spectra are used to train a SOM, which arranges the spectra on a two-dimensional map. Location in the map reflects the secondary structure composition of a protein. With SOMCD, the prediction of beta-turn has been included. The number of spectra in the training set has been increased, and it now includes 39 protein spectra and 6 reference spectra. Finally, SOM parameters have been chosen to minimize distortion and make the network produce clusters with known properties. Estimation results show improvements compared with the previous version, K2D, which, in addition, estimated only three secondary structure components; the accuracy of the method is more uniform over the different secondary structures.     

Prediction of protein secondary structure from circular dichroism using theoretically derived spectra

Circular dichroism (CD) is a spectroscopic technique commonly used to investigate the structure of proteins. Major secondary structure types, alpha‐helices and beta‐strands, produce distinctive CD spectra. Thus, by comparing the CD spectrum of a protein of interest to a reference set consisting of CD spectra of proteins of known structure, predictive methods can estimate the secondary structure of the protein. Currently available methods, including K2D2, use such experimental CD reference sets, which are very small in size when compared to the number of tertiary structures available in the Protein Data Bank (PDB). Conversely, given a PDB structure, it is possible to predict a theoretical CD spectrum from it. The methodological framework for this calculation was established long ago but only recently a convenient implementation called DichroCalc has been developed. In this study, we set to determine whether theoretically derived spectra could be used as reference set for accurate CD based predictions of secondary structure. We used DichroCalc to calculate the theoretical CD spectra of a nonredundant set of structures representing most proteins in the PDB, and applied a straightforward approach for predicting protein secondary structure content using these theoretical CD spectra as reference set. We show that this method improves the predictions, particularly for the wavelength interval between 200 and 240 nm and for beta‐strand content. We have implemented this method, called K2D3, in a publicly accessible web server at http://www. ogic.ca/projects/k2d3 . Proteins 2012. © 2011 Wiley Periodicals, Inc.     

Estimation of protein secondary structure from circular dichroism spectra: inclusion of denatured proteins with native proteins in the analysis

We have expanded our reference set of proteins used in the estimation of protein secondary structure by CD spectroscopy from 29 to 37 proteins by including 3 additional globular proteins with known X-ray structure and 5 denatured proteins. We have also modified the self-consistent method for analyzing protein CD spectra, SELCON3, by including a new selection criterion developed by W. C. Johnson, Jr. (Proteins Struct. Funct. Genet. 35, 307-312, 1999). The secondary structure corresponding to the denatured proteins was approximated to be 90% unordered, owing to the spectral similarity of the denatured proteins and unordered structures. We examined the thermal denaturation of ribonuclease T1 by CD using both the original and expanded sets of reference proteins and obtained more consistent results with the expanded set. The expanded set of reference proteins will be helpful for the determination of protein secondary structure from protein CD spectra with higher reliability, especially of proteins with significant unordered structure content and/or in the course of denaturation.     

Accuracy of protein secondary structure determination from circular dichroism spectra based on immunoglobulin examples

Strong contribution of the aromatic amino acid side chain chromophores to the far-UV circular dichroism (CD) spectra substantially distorts a relatively weak CD signal originating from beta sheet, the main type of immunoglobulin secondary structure. In this study we compared the secondary structure calculated from the far-UV CD spectra with the X-ray data for three antibody Fab fragments. Calculations were performed with three different algorithms, using two sets of reference proteins. Low standard deviations between all six estimates indicate stable mathematical solutions. Despite pronounced differences in the shape and amplitude of the CD spectra, we found a strong correlation between CD and X-ray data in the secondary structure for every protein studied. The number and average length of the secondary structure elements estimated from the CD spectra closely resemble those of the X-ray data. Agreement between spectroscopic and crystallographic results demonstrates that modern methods of secondary structure calculation are resilient to distortions of the far-UV CD spectra of immunoglobulins caused by aromatic side chain chromophores.     

Variable selection method improves the prediction of protein secondary structure from circular dichroism spectra

A new procedure based on the statistical method of "variable selection" is used to predict the secondary structure of proteins from circular dichroism spectra. Variable selection adds the flexibility found in the Provencher and Gl?ckner method (S. W. Provencher and J. Gl?ckner, 1981, Biochemistry 20, 33-37) to the method of Hennessey and Johnson (J. P. Hennessey and W. C. Johnson, 1981, Biochemistry 20, 1085-1094). Two analytical methods are presented for choosing a solution from the series generated by the Provencher and Gl?ckner method, and this improves the technique. All three methods are compared and it is shown that both the variable selection method and the improved Provencher and Gl?ckner methods have equivalent reliability superior to the original Hennessey and Johnson method. For the new variable selection method, correlation coefficients calculated between X-ray structure and predicted secondary structures for data measured to 178 nm are: 0.97 for alpha-helix, 0.75 for beta-sheet, 0.50 for beta-turn, and 0.89 for other structures. Although the variable selection method improves the analysis of circular dichroism data truncated at 190 nm, data measured to 178 nm gives superior results. It is shown that improving the fit to the measured CD beyond the accuracy of the data can result in poorer analyses.     

Determination of protein secondary structure from circular dichroism spectra. III. Protein-derived base spectra of circular dichroism for antiparallel and parallel beta-structures

Protein-derived basic CD spectra for alpha-helix, antiparallel and parallel beta-structures, beta-bends and irregular form of proteins have been determined from the experimental CD spectra of six (myoglobin, lysozyme, ribonuclease A, papain, lactate dehydrogenase, subtilisin BPN') or seven (glyceraldehyde-3-phosphate dehydrogenase added) reference proteins and the analysis of the X-ray data. The secondary structures of thirteen proteins (seven reference and six additional ones) have been analysed using the basic CD spectra thus obtained. The data obtained have been compared with the results of the X-ray data analysis. It is shown that the accuracy of determination of the beta-structure and beta-bends contents using our basic CD spectra is about 2-3 times better than using the basic spectra reported by Chang et al. (Analyt. Biochem. 91, 13-31, 1978).     

DICHROWEB: an interactive website for the analysis of protein secondary structure from circular dichroism spectra

A user-friendly website for the analysis of protein secondary structures from Circular Dichroism (CD) and Synchrotron Radiation Circular Dichroism (SRCD) spectra has been created.     

Analysis of protein circular dichroism spectra for secondary structure using a simple matrix multiplication

Inverse circular dichroism (CD) spectra are presented for each of the five major secondary structures of proteins: alpha-helix, antiparallel and parallel beta-sheet, beta-turn, and other (random) structures. The fraction of the each secondary structure in a protein is predicted by forming the dot product of the corresponding inverse CD spectrum, expressed as a vector, with the CD spectrum of the protein digitized in the same way. We show how this method is based on the construction of the generalized inverse from the singular value decomposition of a set of CD spectra corresponding to proteins whose secondary structures are known from X-ray crystallography. These inverse spectra compute secondary structure directly from protein CD spectra without resorting to least-squares fitting and standard matrix inversion techniques. In addition, spectra corresponding to the individual secondary structures, analogous to the CD spectra of synthetic polypeptides, are generated from the five most significant CD eigenvectors.     

The optimization of protein secondary structure determination with infrared and circular dichroism spectra.

We have used the circular dichroism and infrared spectra of a specially designed 50 protein database [Oberg, K.A., Ruysschaert, J.M. & Goormaghtigh, E. (2003) Protein Sci. 12, 2015-2031] in order to optimize the accuracy of spectroscopic protein secondary structure determination using multivariate statistical analysis methods. The results demonstrate that when the proteins are carefully selected for the diversity in their structure, no smaller subset of the database contains the necessary information to describe the entire set. One conclusion of the paper is therefore that large protein databases, observing stringent selection criteria, are necessary for the prediction of unknown proteins. A second important conclusion is that only the comparison of analyses run on circular dichroism and infrared spectra independently is able to identify failed solutions in the absence of known structure. Interestingly, it was also found in the course of this study that the amide II band has high information content and could be used alone for secondary structure prediction in place of amide I.     

Analyzing protein circular dichroism spectra for accurate secondary structures.

We have developed an algorithm to analyze the circular dichroism of proteins for secondary structure. Its hallmark is tremendous flexibility in creating the basis set, and it also combines the ideas of many previous workers. We also present a new basis set containing the CD spectra of 22 proteins with secondary structures from high quality X-ray diffraction data. High flexibility is obtained by doing the analysis with a variable selection basis set of only eight proteins. Many variable selection basis sets fail to give a good analysis, but good analyses can be selected without any a priori knowledge by using the following criteria: (1) the sum of secondary structures should be close to 1.0, (2) no fraction of secondary structure should be less than -0.03, (3) the reconstructed CD spectrum should fit the original CD spectrum with only a small error, and (4) the fraction of alpha-helix should be similar to that obtained using all the proteins in the basis set. This algorithm gives a root mean square error for the predicted secondary structure for the proteins in the basis set of 3.3% for alpha-helix, 2.6% for 3(10)-helix, 4.2% for beta-strand, 4.2% for beta-turn, 2.7% for poly(L-proline) II type 3(1)-helix, and 5.1% for other structures when compared with the X-ray structure.     

Estimation of protein secondary structure from circular dichroism spectra: comparison of CONTIN, SELCON, and CDSSTR methods with an expanded reference set

We have expanded the reference set of proteins used in SELCON3 by including 11 additional proteins (selected from the reference sets of Yang and co-workers and Keiderling and co-workers). Depending on the wavelength range and whether or not denatured proteins are included in the reference set, five reference sets were constructed with the number of reference proteins varying from 29 to 48. The performance of three popular methods for estimating protein secondary structure fractions from CD spectra (implemented in software packages CONTIN, SELCON3, and CDSSTR) and a variant of CONTIN, CONTIN/LL, that incorporates the variable selection method in the locally linearized model in CONTIN, were examined using the five reference sets described here, and a 22-protein reference set. Secondary structure assignments from DSSP were used in the analysis. The performances of all three methods were comparable, in spite of the differences in the algorithms used in the three software packages. While CDSSTR performed the best with a smaller reference set and larger wavelength range, and CONTIN/LL performed the best with a larger reference set and smaller wavelength range, the performances for individual secondary structures were mixed. Analyzing protein CD spectra using all three methods should improve the reliability of predicted secondary structural fractions. The three programs are provided in CDPro software package and have been modified for easier use with the different reference sets described in this paper. CDPro software is available at the website: http://lamar.colostate.edu/ approximately sreeram/CDPro.     

Determination of secondary structure of globular proteins using circular dichroism spectra

A ridge regression method is presented for prediction of the secondary structure of proteins by the circular dichroism spectra (CD) from 190 to 236 nm. Eight types of the secondary structure were calculated on a microcalculator. The method is based on the X-ray data of Kabsh and Sander. The teaching rule is constructed on CD spectra of 30 proteins of all structural classes of the globular proteins (alpha, alpha/beta, alpha + beta and beta-proteins). The errors of the methods are analysed by removing each protein from the reference set and analyzing its structure in terms of the remaining proteins. Correlation coefficients and root-mean square deviations between CD and X-ray data were: 0.99 and 0.03 for alpha-helix, 0.86 and 0.02 for 3(10)-helix, 0.92 and 0.06 for antiparallel beta-sheet, 0.86 and 0.03 for parallel beta-sheet, 0.94 and 0.01 for T3 beta-turn, 0.85 and 0.02 for other beta-turn, 0.84 and 0.03 for S-bends, 0.83 and 0.04 for "random" structure.     

Overestimated accuracy of circular dichroism in determining protein secondary structure

Circular dichroism (CD) is a spectroscopic technique widely used for estimating protein secondary structures in aqueous solution, but its accuracy has been doubted in recent work. In the present paper, the contents of nine globular proteins with known secondary structures were determined by CD spectroscopy and Fourier transform infrared spectroscopy (FTIR) in aqueous solution. A large deviation was found between the CD spectra and X-ray data, even when the experimental conditions were optimized. The content determined by FTIR was in good agreement with the X-ray crystallography data. Therefore, CD spectra are not recommended for directly calculating the content of a protein’s secondary structure.     

Concentration-independent estimation of protein secondary structure by circular dichroism: a comparison of methods

Estimation of a protein's secondary structure from its circular dichroism spectrum usually requires accurate knowledge of the concentration and pathlength of the sample. Two recently described methods avoid this problem by analysis of g-factor spectra (McPhie, Anal. Biochem. 293, 109-119) or scaling of relative intensities (Raussens et al., Anal. Biochem. 319, 114-121). Application of the two methods to the same samples shows that they can have similar efficacies. Calculation with the latter method is more rapid, but the performance of the former is maintained over reduced wavelength ranges.