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.     

K2D2: Estimation of protein secondary structure from circular dichroism spectra

Background  

Circular dichroism spectroscopy is a widely used technique to analyze the secondary structure of proteins in solution. Predictive methods use the circular dichroism spectra from proteins of known tertiary structure to assess the secondary structure contents of a protein with unknown structure given its circular dichroism spectrum.     

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.     

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.     

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.     

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.     

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.     

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.     

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).     

Determination of the secondary structure of proteins from circular dichroism spectra. IV. Contribution of aromatic amino acid residues into circular dichroism spectra of proteins in the peptide region

A new method for determination of the secondary protein structure from the CD spectra taking into account the contribution of aromatic amino acid residues is proposed. New proteins reference CD spectra for five secondary structures (alpha-helices, antiparallel and parallel beta-structures, beta-bends and irregular form) without contribution of aromatic residues are obtained. By means of this new method the secondary structure of sixteen different proteins was analysed. There is a good correlation of these results with the X-ray data.     

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.     

Secondary-structure analysis of denatured proteins by vacuum-ultraviolet circular dichroism spectroscopy

To elucidate the structure of denatured proteins, we measured the vacuum-ultraviolet circular dichroism (VUVCD) spectra from 260 to 172 nm of three proteins (metmyoglobin, staphylococcal nuclease, and thioredoxin) in the native and the acid-, cold-, and heat-denatured states, using a synchrotron-radiation VUVCD spectrophotometer. The circular dichroism spectra of proteins fully unfolded by guanidine hydrochloride (GdnHCl) were also measured down to 197 nm for comparison. These denatured proteins exhibited characteristic VUVCD spectra that reflected a considerable amount of residual secondary structures. The contents of alpha-helices, beta-strands, turns, poly-L-proline type II (PPII), and unordered structures were estimated for each denatured state of the three proteins using the SELCON3 program with Protein Data Bank data and the VUVCD spectra of 31 reference proteins reported in our previous study. Based on these contents, the characteristics of the four types of denaturation were discussed for each protein. In all types of denaturation, a decrease in alpha-helices was accompanied by increases in beta-strands, PPII, and unordered structures. About 20% beta-strands were present even in the proteins fully unfolded by GdnHCl in which beta-sheets should be broken. From these results, we propose that denatured proteins constitute an ensemble of residual alpha-helices and beta-sheets, partly unfolded (or distorted) alpha-helices and beta-strands, PPII, and unordered structures.     

Singular value decomposition analysis of the secondary structure features contributing to the circular dichroism spectra of model proteins

Amyloid fibril formation occurs in restricted environment, such as the interface between intercellular fluids and bio-membranes. Conformational interconversion from α-helix to β-structure does not progress in fluids; however, it can occur after sedimentary aggregation during amyloid fibril formation induced by heat treatment of hen egg white lysozyme (HEWL). Secondary structures of various proteins and denatured proteins titrated with 2,2,2-trifluoroethanol (TFE) were examined using their CD spectra. Gaussian peak/trough and singular value decompositions (SVD) showed that the spectral pattern of the α-helix comprised a sharp trough at wavelength 207 nm and a broad trough at 220 nm. Conversely, we distinguished two patterns for β-sheet—a spread barrel type, corresponding to ConA, and a tightly weaved type, corresponding to the soybean trypsin inhibitor. Herein, we confirmed that the spectral/conformational interconversion of the heat-treated HEWL was not observed in the dissolved fluid.     

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.     

Deconvolution of the circular dichroism spectra of proteins: the circular dichroism spectra of the antiparallel beta-sheet in proteins.

A recently developed algorithm, called Convex Constraint Analysis (CCA), was successfully applied to determine the circular dichroism (CD) spectra of the pure beta-pleated sheet in globular proteins. On the basis of X-ray diffraction determined secondary structures, the original data set used (Perczel, A., Hollosi, M., Tusnady, G. Fasman, G.D. Convex constraint analysis: A natural deconvolution of circular dichroism curves of proteins, Prot. Eng., 4:669-679, 1991), was improved by the addition of proteins with high beta-pleated sheet content. The analysis yielded CD curves of the pure components of the main secondary structural elements (alpha-helix, antiparallel beta-pleated sheet, beta-turns, and unordered conformation), as well as a curve attributed to the "aromatic contribution" in the wavelength range of 195-240 nm. Upon deconvolution the curves obtained were assigned to various secondary structures. The calculated weights (percentages determining the contributions of each pure component curve in the measured CD spectra of a given protein) were correlated with the X-ray diffraction determined percentages in an assignment procedure and were evaluated. The Pearson product correlation coefficients (R) are significant for all five components. The new pure component curves, which were obtained through deconvolution of the protein CD spectra alone, are promising candidates for determining the percentages of the secondary structural components in globular proteins without the necessity of adopting an X-ray database. The CD spectrum of the CheY protein was interesting because it has the characteristic shape associated with the alpha-helical structure, but upon analysis yielded a considerable amount of beta-sheet in agreement with the X-ray structure.     

On the analysis of membrane protein circular dichroism spectra

Analysis of circular dichroism spectra of proteins provides information about protein secondary structure. Analytical methods developed for such an analysis use structures and spectra of a set of reference proteins. The reference protein sets currently in use include soluble proteins with a wide range of secondary structures, and perform quite well in analyzing CD spectra of soluble proteins. The utility of soluble protein reference sets in analyzing membrane protein CD spectra, however, has been questioned in a recent study that found current reference protein sets to be inadequate for analyzing membrane proteins. We have examined the performance of reference protein sets available in the CDPro software package for analyzing CD spectra of 13 membrane proteins with available crystal structures. Our results indicate that the reference protein sets currently available for CD analysis perform reasonably well in analyzing membrane protein CD spectra, with performance indices comparable to those for soluble proteins. Soluble + membrane protein reference sets, which were constructed by combining membrane proteins with soluble protein reference sets, gave improved performance in both soluble and membrane protein CD analysis.