aIndicate the sheet ID and strand number (as described in PDB file) of the two paired β-strands.bShow the sequence of the common part of each pair of β-strands. Also shown are the initial and ending residue numbers of the segment.cThe distinguishing results by SVM. The SVM used here is trained with randomly selected 6/7 parts of the whole dataset, with protein 1HZT not containing in the training set.Full-size tableTable optionsView in workspaceDownload as CSVDiscussionSteward and Thornton [1] argued that the energetic contribution of individual interstrand residue pairs was one of many factors determining the global fold of a protein, but was insufficient to predict a protein’s three-dimensional conformation. Moreover, studies ought to be performed separately on more concrete aspects. Determining the parallel or antiparallel orientation of β-strands is one of the most important steps in β-sheet formation.Indeed, there are notable differences between the interstrand amino
6 his pairs on parallel and antiparallel β-strands [1], although the relative frequencies of some types of residue pairs are similar. For instance, antiparallel β-strands favor polar residues, as opposed to aromatic residues. Antiparallel β-strands have a larger proportion of exposed residue positions, and are more likely to contain a β-bridge with an edge strand, which may be solvent exposed on one edge [1]. Indeed, antiparallel and parallel β-strands were considered separately in many recent studies, such as [1], [5] and [18]. However, from these preference differences, it is not immediately clear how the interstrand amino acid pairs contribute to the formation of β-strands.We investigated this question, by extracting features (21-dimentional vectors) from the amino acid pairs within parallel and antiparallel β-strands. From Fig. 2, it is evident that the cumulative contributions of the singular values derived from MpaveMpave and MapaveMapave matrices are significantly different. The cumulative contributions of the top 21 singular values are 92.16% for parallel, while only 63.46% for antiparallel. Since the two matrices are both average matrices, this indicates that the distribution centers of the two types of β-strands are different.In addition, the selection of the top 21 singular values (10%) is rational, because the cumulative contributions of the top 21 exceed 60%. Although the antiparallel value is smaller, at 63.46%, for parallel the value is up to 92.16%. The cumulative information suggests little further increase for the parallel case. Overall, the top 21 singular values encompass the most information. Therefore, we select the top 21 singular values (10%) to balance out as much as possible the tradeoff between distinguishing the two types of β-strand and reducing the dimension of the input space.In order to examine whether or not features extracted from the two types of β-strand can be separated from each other in such a 21-dimensional space, we adopt the support vector machine (SVM) method. It is somewhat surprising that we obtain almost perfect results: up to 99.40% accuracy, 0.9867 MCC, and over 98% sensitivity and specificity. This indicates that the hyperplane output of the SVM has grasped the complicated relationship between the interstrand amino
acid pairs and the β-strands orientations. Although the method presented here cannot be directly used for the parallel and antiparallel orientation prediction, from Table 4, it can be seen that features derived from parallel and antiparallel β-strands in protein 1HZT can be distinguished from each other dramatically. Parallel and antiparallel arrangements of β-strands not only differ in their pairing preferences, but can also be separated from each other very well based on the amino acid pairing features extracted in 21-dimensional space. Note that we do treat each pair of β-strands in isolation during the feature extracting procedure. The RFMp and RFMap matrices do not contain information either about other secondary structural models, or about protein topology and protein tertiary structures. Therefore, although other factors should also be taken into account when examining protein folding pathways, our results suggest that the parallel or antiparallel orientation of β-strands is considerably correlated with the interstrand amino acid pairs. We see that a small number of interstrand amino acid pairs appear to play a significant role in the determination of parallel or antiparallel orientation during β-sheet formation. Although the result presented here is not sufficient to deduce a protein’s fold, it does allow us to differentiate between contributions made by the amino acid pairs and those due to the surroundings.
