Research Article  Open Access
Ning Zhang, Shan Gao, Lei Zhang, Jishou Ruan, Tao Zhang, "Statistical Analysis of Terminal Extensions of Protein βStrand Pairs", Advances in Bioinformatics, vol. 2013, Article ID 909436, 7 pages, 2013. https://doi.org/10.1155/2013/909436
Statistical Analysis of Terminal Extensions of Protein βStrand Pairs
Abstract
The longrange interactions, required to the accurate predictions of tertiary structures of βsheetcontaining proteins, are still difficult to simulate. To remedy this problem and to facilitate βsheet structure predictions, many efforts have been made by computational methods. However, known efforts on βsheets mainly focus on interresidue contacts or amino acid partners. In this study, to go one step further, we studied βsheets on the strand level, in which a statistical analysis was made on the terminal extensions of paired βstrands. In most cases, the two paired βstrands have different lengths, and terminal extensions exist. The terminal extensions are the extended part of the paired strands besides the common paired part. However, we found that the best pairing required a terminal alignment, and βstrands tend to pair to make bigger common parts. As a result, 96.97% of βstrand pairs have a ratio of 25% of the paired common part to the whole length. Also 94.26% and 95.98% of βstrand pairs have a ratio of 40% of the paired common part to the length of the two βstrands, respectively. Interstrand register predictions by searching interacting βstrands from several alternative offsets should comply with this rule to reduce the computational searching space to improve the performances of algorithms.
1. Introduction
The issue of protein structure prediction is still extremely challenging in bioinformatics [1, 2]. Usually, structural information for protein sequences with no detectable homology to a protein of known structure could be obtained by predicting the arrangement of their secondary structural elements [3]. As we know, the two predominant protein secondary structures are αhelices and βsheets. However, a combination of the early suitable αhelical model systems and sustained researches have resulted in a detailed understanding of αhelix, while comparatively little is known about βsheet [4]. Tertiary structures of βsheetcontaining proteins are especially difficult to simulate [3, 5]. Unlike αhelices, βsheets are more complex resulting from a combination of two or more disjoint peptide segments, called βstrands. Therefore, the βsheet topology is very useful for elucidating protein folding pathways [6, 7] for predicting tertiary structures [3, 8–11], and even for designing new proteins [12–14].
As fundamental components, βsheets are plentifully contained in protein domains. In a βsheet, multiple βstrands held together linked by hydrogen bonds and can be classified into parallel and antiparallel direction styles. Adjacent βstrands bring distant residues on sequences into close special contact with one another and constitute a specific mode of amino acid pairing [1, 15–17], interactions (like DNA base pairing). There is a growing recognition of the importance of the strandtostrand interactions among βsheets [18]. Several studies, including statistical studies examining frequencies of nearestneighbor amino acids in βsheets, found a significantly different preference for certain interstrand amino acid pairs at nonhydrogenbonded and hydrogenbonded sites [1, 17, 19, 20], Dou et al. [21] created a comprehensive database of interchain βsheet (ICBS) interactions. We also developed the SheetsPair database [22] to compile both the interchain and the intrachain amino acid pairs.
Generally speaking, previous work on βsheets mainly focused on the interresidue contacts or amino acid partners [23–28]. Prediction of interresidue contacts in βsheets is interesting, while the prediction by ab initio structure is also useful to understand protein folding [29, 30]. Our previous studies showed that the interstrand amino acid pairs played a significant role to determine the parallel or antiparallel orientation of βstrands [15], and the statistical results could possibly be used to predict the βstrand orientation [16]. Cheng and Baldi [11] introduced BETAPRO method to predict and assemble βstrands into a βsheet, in which a single misprediction of one amino acid pairing from the first stage could be amplified by the next stages and results in serious wrong set of partner assignments between βstrands. However, those studies can be viewed as initial steps of βsheet studies relative to predict strand level pairing [25]. In this paper, to go one step further, we investigate the βstrand pairing on the strand level for exploring the rules of how βstrands form a βsheet.
Many results have shown the importance of statistical analysis in protein structure studies [15, 16]. In particular, statistical information could provide a starting point for de novo computational design methods that are now becoming successful for short, singlechain proteins [14], as well as methods of protein structure predictions and understanding of protein folding mechanisms [31, 32]. Fooks et al. [1] also indicated that such statistical analysis results would be useful for protein structure prediction. Therefore, we advocate using the tools of statistics and informatics to study βsheet and generate new rules for algorithm development. In this study, we focused on the terminal extensions of paired βstrands.
2. Results
2.1. Dataset
All protein structure data used in this study were taken from a PISCES [33, 34] dataset generated on May 16, 2009. In the dataset, the percentage identity cutoff is 25%, the resolution cutoff is 2.0 angstroms, and the factor cutoff is 0.25. Secondary structures were assigned from the experimentally determined tertiary structures by using the DSSP program. Besides proteins containing disordered regions [35–37], all data were further preprocessed according to the following criteria: (i) no βsheetcontaining protein chains were removed; (ii) protein chains with nonstandard threeletter residue names (such as DPN, EFC, ABA, C5C, PLP, etc.) were removed, since these indicate that the protein chains have covalently bounded ligands or modified residues; (iii) protein chains with uncertain structures or incorrect data were removed. Since βbulges tend to be isolated and rare [11], we did not consider βbulges in this study either, as several previous studies did [1, 3]. Finally, 2,315 protein chains were extracted, containing 19,214 βstrand pairs. Note that in the special case of βbulges, no amino acid pair is assigned.
2.2. The βSheet Structure
The βsheets, where two or more βstrands are arranged in a specific conformation, are illustrated in Figure 1(a), by a protein example (PDB code 1HZT). Adjacent strands, or the socalled strand pairs, can either run in the same (parallel) or in the opposite (antiparallel) direction styles. In protein 1HZT, there are 3 βsheets called A, B, and C, formed by 10 different βstrands numbered from 1 to 10, making 7 different βstrand pairs, respectively. The 10 βstrands can be named by the βsheet each belongs to and the index numbers in the order of partnership. For example, the 3 βstrands forming βsheet A can be called “A1,” “A2,” and “A3,” while other 4 βstrands forming βsheet B can be called “B1,” “B2,” “B3,” and “B4,” respectively. “A1A2,” “A2A3,” “B1B2,” “B2B3,” and “B3B4” are all βstrand pairs. Sequences of the 10 βstrands with their initial and ending residue numbers are also given in Figure 1(b).
2.3. Different Lengths of Paired βStrands
For a βstrand pair, the terminal of one βstrand does not always align with the terminal of the other (Figure 2), making “terminal extensions” besides the common paired parts. Note that only amino acids in the common part construct amino acid pairs.
Why “terminal extensions” exist widely in βstrand pairs? We firstly investigated the lengths of two paired βstrands and then calculated the percent of each case whether the “terminal extensions” exist or not. Results are shown in Table 1.
 
Absolute value of the difference of − . 
As shown in Table 1, the two paired βstrands having the same length only account for 29.53% of all samples. In other 70.47% percent of samples, lengths of the two paired βstrands are different.
2.4. Statistical Results of Variables
We define the following variables.(1)Let and represent the lengths of two paired βstrands, respectively. Length of the βstrand with smaller strand number (strand numbers can be obtained from PDB database) is defined as , while length of the other βstrand is defined as . (2)Let stand for the length of the common part, which is often smaller than and . (3)Terminal extensions can be found in either of the two βstrands. We define the lengths of the two terminal extensions and , respectively. Length of the terminal extension of the βstrand with length is defined as while the other as .(4)Let represent the whole length; .
Then, the paring ratio could be calculated by
The ratio of the common paired part to the length of each βstrand () could be calculated by
A small percent of βstrand pairs have no “terminal extensions,” the , , and values for which will be 100%.
We calculated , , , for all βstrand pairs in the present dataset. Table 2 gives the range of these variables as well as the averages and standard deviations.

We also calculated , , and for all βstrand pairs in the present dataset. The distribution of these variables is shown in Figure 3.
3. Discussion
3.1. Strands Tend to Align Their Terminals
For the 70.47% of samples with different strand lengths, although they have different lengths, the differences are not big for most of them. Only a small percent of samples (below 2.09%) have the difference above 5. In these cases, it is obvious that they cannot align the terminals (with both and ). They have two ways to choose from: either align to only one terminal making another “terminal extension”, or align to none of the two terminals making both “terminal extensions.” However, it can be seen from Table 1 that most βstrands tend to be in the former case. For example, in case of the length difference 1, the former case accounts for 85.18% while the latter only 14.82%. It is consistent with the case of samelength strand pairs, in which βstrands tend to align their terminals with each other. Interestingly, it is suggested that βstrands tend to align their terminals. In differentlength strand pairs, they still retain one terminal alignment, although they can not align both ends.
3.2. Small “Terminal Extensions”
From Table 2, it can be seen that lengths of βstrands are not very long, ranging from 1 to 25 with an average length about 45 amino acids. The averages and the standard deviations are similar between lengths of the two paired βstrands ( and ).
The length of the common part has a range similar to that of lengths of βstrands. This indicates that although “terminal extensions” exist, common pairing parts occupy most of βstrands, while “terminal extensions” occupy least. The fact that the maximum value of is 29, only a little bigger than that of lengths of βstrands, and the fact that in average both the “terminal extensions” only have about 1 amino acid ( and ) also support this assumption.
Figure 3 gives percent of samples for , , and in each range of their possible values (from 0% to 100%), respectively. It can be seen that the distributions of and are similar. More than half of the βstrand pairs have these two variables above 95% (or in the range (95–100)). Big or means big common part of βstrands, or small “terminal extensions.” Rare βstrand pairs have smaller values of , , and , which indicates that most βstrands do not pair by means of small “common part” or big “terminal extensions.” It could be concluded from the results that βstrands tend to pair with bigger pairing common parts, leaving smaller “terminal extensions.”
3.3. Possible Reasons for βStrand Extensions
Why “terminal extensions” exist so widely in βstrand pairs? The fact that lengths of two paired βstrands are not the same in most cases as shown in Table 1 may be one of the possible reasons. If paired βstrands have the same lengths, most of them (82.95%) tend to align their terminals with each other, leaving no “terminal extensions.”
A βstrand is led to pair with another by several kinds of potential forces. Steward and Thornton [3] indicated that a single βstrand was still able to recognize a noninteracting βstrand with greater accuracy than that in the case of between two random sequences. The potential forces include hydrogen bonds, van der Waals forces, electrostatic interaction, ionic bonds, hydrophobic effects, and so forth. Parisien and Major [38] revealed that among all the forces, the most important one was the construction of a hydrophobic face. It is conceivable that one residue of a βstrand prefers to pair with the residue of another resulting in a stable state of hydrophobic effects. Optimizing such interactions may result in extensions, which could be the second reason, since more often than not the “terminal alignment” is not the case of optimized pairing style.
A third possible reason could be due to the nucleation events that initiate the βsheet folding. Amino acids in the central part could pair firstly and then fold to extend to terminals.
Another reason is the roles of the nonpaired terminal amino acids in stabilizing the βsheet structure. Several other studies have identified their key roles in modulating protein folding rates, stability, and folding mechanism [39–43]. Therefore, the βstrand terminals could also be important factors for a βsheet formation.
3.4. Ratio Rule of Pairing Strand Alignment
To quantify the pairing common part of paired βstrands, we calculated the cumulative percent of variables , , and and depicted them in Figure 4.
From Figure 4, it can be seen that when and , the cumulative percentages reach 94.26% and 95.98%, respectively, while when only 89.89%. When , the cumulative percentages reach up to 96.97%. Therefore, a rule can be made of the alignment of βstrand pair as follows:
Almost all samples (above 94%) obey this rule.
In a βstrand alignment prediction algorithm, all possible pairings should be examined and scored; it is a timeconsuming task. Kato et al. [44] stated that prediction of planar βsheet structures was NPhard in the present state of our knowledge (http://en.wikipedia.org/wiki/NPhard). However, this previous rule should be used as a constraint of the relative positions in βstrand alignment to reduce the computational searching space, which could be used to develop highspeed βstrand topology prediction algorithms.
4. Conclusion
At the most straightforward level, full “identification” of a βstrand pair could consist of (i) finding the interacting partner βstrand(s), (ii) predicting the relative orientation (i.e. parallel or antiparallel), and (iii) shifting the relative positions of the two interacting βstrands [15, 16]. In this study, we focused on the third aspect. The formation of protein structure and protein folding mechanism are very complex, and the mechanisms of βsheet formation are unclear [45]. However, simple rules could contribute to developing new algorithms in the step of full prediction of βsheet and understanding of protein folding pathways in ongoing research.
In this study, to go one step further, we studied βsheets on the strand level instead of amino acid level. Statistical analyses of the terminal extensions of paired βstrands were performed and a simple rule “% and %, ” was made. Steward and Thornton [3] developed an information theory approach to predict the relative offset positions by shifting one βstrand up to 10 residues either side of that observed. Such a rule could be used in similar studies. We certainly believe that the conclusions presented in this study could contribute to predict protein structures and to develop βsheet prediction methods.
Conflict of Interests
The authors have declared that no conflict of interests exists.
Acknowledgment
This work was supported by Grants from the National Natural Science Foundation of China (nos. 31171053, 11232005, 81171342, 68075049, and 10671100).
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Copyright © 2013 Ning Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.