# Prediction of Four Kinds of Simple Supersecondary Structures in Protein by Using Chemical Shifts

Authors: Feng Yonge
Journal: The Scientific World Journal
 (2014)

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## Abstract

Knowledge of supersecondary structures can provide important information about its spatial structure of protein. Some approaches have been developed for the prediction of protein supersecondary structure. However, the feature used by these approaches is primarily based on amino acid sequences. In this study, a novel model is presented to predict protein supersecondary structure by use of chemical shifts (CSs) information derived from nuclear magnetic resonance (NMR) spectroscopy. Using these CSs as inputs of the method of quadratic discriminant analysis (QD), we achieve the overall prediction accuracy of 77.3%, which is competitive with the same method for predicting supersecondary structures from amino acid compositions in threefold cross-validation. Moreover, our finding suggests that the combined use of different chemical shifts will influence the accuracy of prediction.


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## Body

## 1. Introduction

The prediction of protein structure is always one of the most important research topics in the field of bioinformatics. However, it is very difficult to predict the spatial structure directly from the protein sequence. Therefore, the prediction of supersecondary structure is an important step in the prediction of protein spatial structure. The supersecondary structural motifs are composed of a few secondary structural elements (namely,α or β) connected by loops. At present, there are four kinds of simple supersecondary structures, namely, α-loop-β, α-loop-α, β-loop-α, and β-loop-β. These motifs play an important role in protein folding and stability because a large number of motifs exist in protein spatial structure. Many researches have focused on exploring methods for protein supersecondary structure prediction [1, 2]. In 1995, Sun et al. predicted protein supersecondary structure and achieved an accuracy of between 70 and 80% by using neural networks [3]. Chou and Blinn presented a method for predicting beta turns [4–6], alpha turns [7], and all the tight turns [6]. Cruz et al. identified β-hairpin and non-β-hairpin [8]. Hu and Li identified four kinds of simple supersecondary structures in 2088 proteins and achieved an accuracy of 78~83 % [9]. Zou et al. also predicted four kinds of simple supersecondary structures from 3088 proteins by using support vector machine [10]. And the overall accuracy of 78% was achieved. The features of these studies were mainly derived from the amino acid compositions or dipeptide compositions.Nuclear magnetic resonance (NMR) technique plays an important role in the determination of three-dimensional biological macromolecule structures. NMR chemical shifts encode subtle information about the local chemical environment of nuclear spins. For many years, there has been growing interest to access this information and utilize it for biomolecular structure determination [11, 12]. Recent progress was made by combining chemical shifts with protein structure prediction programs [13–20], showing that chemical shifts information is a power parameter for the determination of protein structure. In this paper, we utilized chemical shifts as parameters to predict four kinds of simple supersecondary structures in protein by the method of quadratic discriminant analysis. Using the benchmark dataset, we achieved the average of sensitivity of 76.3% and specificity of 74.3% and the overall prediction accuracy of 77.3% in threefold cross-validation by using six CSs (C,Cα,Cβ,H,Hα,N) as features. Moreover, we have performed the prediction by combining the different chemical shifts as features. Results showed that the redundant information has great influence on the accuracy.


## 2. Materials and Methods

### 2.1. Database

The chemical shifts of all nuclei (C,Cα,Cβ,H,Hα,N) in proteins were extracted from re-referenced protein chemical shift database (namely, RefDB [21]). The following steps were performed to construct the dataset. Firstly, only proteins with six nuclei assigned CSs were considered. Secondly, only proteins with the supersecondary structures information in ArchDB40 [22] were available. We finally utilized the PISCES program [23] to remove the highly similar sequences. After strictly following the aforementioned procedures, 114 proteins were obtained which have both CSs and supersecondary structures. Among 114 proteins, 92% (105 sequences) proteins have less than 25% sequence identity, and the sequence identity of the remains ranges from 25 to 30%. The appendix lists 114 proteins used in this study. Finally, we obtained 90 α-loop-α (HH), 89 α-loop-β (HE), 97 β-loop-α (EH), and 122 β-loop-β (EE) motifs, including the β-β link and β-β hairpin.


### 2.2. Feature Parameter

In the four data subsets{HH,HE,EH,EE}, we calculated the averaged CSs of six nuclei for a sequence of length l using the following formula:
(1)ti=1l∑i=1lCSi,
where i=C,Cα,Cβ,H,Hα,N. Therefore, a sequence can be converted into a six-dimensional vector R:{ti}.


### 2.3. Prediction Algorithm

To design an efficient and accurate predicted algorithm the key step is in protein supersecondary structure prediction. The quadratic discriminant analysis [24] is a power algorithm that has been widely applied in genomic and proteomic bioinformatics. Thus, we used it here to perform prediction.


### 2.4. Quadratic Discriminant Analysis (QD)

For a sequenceX to be classified, we calculated the averaged CSs of six nuclei using (1). So, the sequence is converted into a six-dimensional vector R:{ti}:
(2)R={ti}(i=C,Cα,Cβ,H,Hα,N).
Here we integrated six-dimensional vector by using quadratic discriminant analysis function. Consider a sequence X is classified into four groups (HH,HE,EH,EE). The discriminant analysis function between group i and group j is defined by
(3)ξij=ln⁡p(ωi∣X)-ln⁡p(ωj∣X).According to Bayes’ Theorem, we deduce(4)ξij=ln⁡pipj-δi-δj2-12ln⁡|Σi||Σj|=(ln⁡pi-12δi-12ln⁡|Σi|)-(ln⁡pj-12δj-12ln⁡|Σj|).
The result can be generalized tofour groups directly and described as follows.Set(5)ηv=ln⁡pv-δv2-12ln⁡|Σv|(v=HH,EH,HE,EE),
where
(6)δv=(R-μv)TΣv-1(R-μv),
where pv denotes the number of samples in group v, δv is the square mahalanobis distance between R and μv with respect to Σv (note: μv and |Σv| are calculated in training set), and μv denotes chemical shift values of six nuclei R:{ti} averaged over group v; |Σv| is the determinant of matrix Σv.The six-dimensional vectorμv can be written as
(7)μv(i)=1pv∑i=1pvti,
where v=HH,EH,HE,EE; i=C,Cα,Cβ,Hα,H,N; Σv is the covariance matrix of 6×6 dimension, quantifying correlations between the chemical shifts of six nuclei:
(8)Σv=[σv1,1σv1,2⋯σv1,6σv2,1σv2,2⋯σv2,6⋮⋮⋮⋮σv6,1σv6,2⋯σv6,6],
where the element
(9)σi,jv=1pv∑(ti-μv(i))(tj-μv(j)).
Here v=HH,EH,HE,EE; i,j=C,Cα,Cβ,Hα,H,N.From (4) and (5), we have concluded
(10)ξij=ηi-ηj.It can be easily proved thatp(ωk∣X) is the maximum of p(ωv∣X), if ηk is the maximal one in ηv (v=HH,EH,HE,EE). Then, we predict that X belongs to group k.


### 2.5. Correction in the Error Allowed Scope

A sequenceX is predicted for four kinds of supersecondary structures by using (1)~(10). If ηi is the maximal one in ηk (k=HH,EH,HE,EE), then we predict that X belongs to group i. However, there are slight differences among ηk (k=HH,EH,HE,EE). To correct predicted results, we define the coefficient of the error allowed scope as
(11)R=ηcorr-ηwroηcorr,
where ηcorr denotes X belonging to itself classη, ηwro denotes X being predicted another class η. For example, if X is the super-secondary structure of HH, then ηcorr is ηHH and ηwro is the maximum among ηEH, ηHE, ηEE.


### 2.6. Performance Evaluation

In statistical prediction, independent dataset test, cross-validation test, and jackknife test can be used to examine a predictor for its effectiveness in practical application. Among the three test methods, the jackknife test is deemed to be the least arbitrary that can always yield a unique result for a given benchmark dataset [25] and has been widely used to examine the performance of various predictors [26–37]. However, in this study we have used the threefold cross-validation to examine the performance of our method; in order to reduce the computational time, we randomly divided the training set into three parts, two of which are for training and the rest for testing. The process is repeated three times. The following three parameters: sensitivity (SNi), specificity (SPi), and overall accuracy (Qtotal), are used to evaluate the predictive performance of our approach:
(12)SNi=TPiTPi+FNi×100%,(13)SPi=TPiTPi+FPi×100%,(14)Qtotal=∑iTPiN×100%,
where i=HH,HE,EH,EE and TP, FN,TN, and FP denote, respectively, true positives, false positives, true negatives, and false positives. N is total number of sequences in four data subsets.


## 2.1. Database

The chemical shifts of all nuclei (C,Cα,Cβ,H,Hα,N) in proteins were extracted from re-referenced protein chemical shift database (namely, RefDB [21]). The following steps were performed to construct the dataset. Firstly, only proteins with six nuclei assigned CSs were considered. Secondly, only proteins with the supersecondary structures information in ArchDB40 [22] were available. We finally utilized the PISCES program [23] to remove the highly similar sequences. After strictly following the aforementioned procedures, 114 proteins were obtained which have both CSs and supersecondary structures. Among 114 proteins, 92% (105 sequences) proteins have less than 25% sequence identity, and the sequence identity of the remains ranges from 25 to 30%. The appendix lists 114 proteins used in this study. Finally, we obtained 90 α-loop-α (HH), 89 α-loop-β (HE), 97 β-loop-α (EH), and 122 β-loop-β (EE) motifs, including the β-β link and β-β hairpin.


## 2.2. Feature Parameter

In the four data subsets{HH,HE,EH,EE}, we calculated the averaged CSs of six nuclei for a sequence of length l using the following formula:
(1)ti=1l∑i=1lCSi,
where i=C,Cα,Cβ,H,Hα,N. Therefore, a sequence can be converted into a six-dimensional vector R:{ti}.


## 2.3. Prediction Algorithm

To design an efficient and accurate predicted algorithm the key step is in protein supersecondary structure prediction. The quadratic discriminant analysis [24] is a power algorithm that has been widely applied in genomic and proteomic bioinformatics. Thus, we used it here to perform prediction.


## 2.4. Quadratic Discriminant Analysis (QD)

For a sequenceX to be classified, we calculated the averaged CSs of six nuclei using (1). So, the sequence is converted into a six-dimensional vector R:{ti}:
(2)R={ti}(i=C,Cα,Cβ,H,Hα,N).
Here we integrated six-dimensional vector by using quadratic discriminant analysis function. Consider a sequence X is classified into four groups (HH,HE,EH,EE). The discriminant analysis function between group i and group j is defined by
(3)ξij=ln⁡p(ωi∣X)-ln⁡p(ωj∣X).According to Bayes’ Theorem, we deduce(4)ξij=ln⁡pipj-δi-δj2-12ln⁡|Σi||Σj|=(ln⁡pi-12δi-12ln⁡|Σi|)-(ln⁡pj-12δj-12ln⁡|Σj|).
The result can be generalized tofour groups directly and described as follows.Set(5)ηv=ln⁡pv-δv2-12ln⁡|Σv|(v=HH,EH,HE,EE),
where
(6)δv=(R-μv)TΣv-1(R-μv),
where pv denotes the number of samples in group v, δv is the square mahalanobis distance between R and μv with respect to Σv (note: μv and |Σv| are calculated in training set), and μv denotes chemical shift values of six nuclei R:{ti} averaged over group v; |Σv| is the determinant of matrix Σv.The six-dimensional vectorμv can be written as
(7)μv(i)=1pv∑i=1pvti,
where v=HH,EH,HE,EE; i=C,Cα,Cβ,Hα,H,N; Σv is the covariance matrix of 6×6 dimension, quantifying correlations between the chemical shifts of six nuclei:
(8)Σv=[σv1,1σv1,2⋯σv1,6σv2,1σv2,2⋯σv2,6⋮⋮⋮⋮σv6,1σv6,2⋯σv6,6],
where the element
(9)σi,jv=1pv∑(ti-μv(i))(tj-μv(j)).
Here v=HH,EH,HE,EE; i,j=C,Cα,Cβ,Hα,H,N.From (4) and (5), we have concluded
(10)ξij=ηi-ηj.It can be easily proved thatp(ωk∣X) is the maximum of p(ωv∣X), if ηk is the maximal one in ηv (v=HH,EH,HE,EE). Then, we predict that X belongs to group k.


## 2.5. Correction in the Error Allowed Scope

A sequenceX is predicted for four kinds of supersecondary structures by using (1)~(10). If ηi is the maximal one in ηk (k=HH,EH,HE,EE), then we predict that X belongs to group i. However, there are slight differences among ηk (k=HH,EH,HE,EE). To correct predicted results, we define the coefficient of the error allowed scope as
(11)R=ηcorr-ηwroηcorr,
where ηcorr denotes X belonging to itself classη, ηwro denotes X being predicted another class η. For example, if X is the super-secondary structure of HH, then ηcorr is ηHH and ηwro is the maximum among ηEH, ηHE, ηEE.


## 2.6. Performance Evaluation

In statistical prediction, independent dataset test, cross-validation test, and jackknife test can be used to examine a predictor for its effectiveness in practical application. Among the three test methods, the jackknife test is deemed to be the least arbitrary that can always yield a unique result for a given benchmark dataset [25] and has been widely used to examine the performance of various predictors [26–37]. However, in this study we have used the threefold cross-validation to examine the performance of our method; in order to reduce the computational time, we randomly divided the training set into three parts, two of which are for training and the rest for testing. The process is repeated three times. The following three parameters: sensitivity (SNi), specificity (SPi), and overall accuracy (Qtotal), are used to evaluate the predictive performance of our approach:
(12)SNi=TPiTPi+FNi×100%,(13)SPi=TPiTPi+FPi×100%,(14)Qtotal=∑iTPiN×100%,
where i=HH,HE,EH,EE and TP, FN,TN, and FP denote, respectively, true positives, false positives, true negatives, and false positives. N is total number of sequences in four data subsets.


## 3. Results and Discussion

Under the benchmark dataset, we calculated the average chemical shift values using (1). The sequences from four data subsets are converted, respectively, into six-dimensional vectors, which are derived from chemical shift values of six nuclei; then μ is also a six-dimensional mean vector, which is calculated in each of the datasets. In the training sets, determinant and inverse matrix of covariance matrix Σv are calculated. Given a sequence of the testing sets, we may calculate ηv by using (4)~(10) and compare the results. Then the class of sequence X was determined by the maximum of ηv (v=HH,HE,EH,EE). Moreover, the coefficient R given in (11) is used to correct predicted results. The current study utilized R<0.4. The results of threefold cross-validation are listed in Table 1.Table 1
The predicted accuracies by using six CSs as features (3-fold cross-validation).
Classstructure
SN (%)
SP (%)
AverageSN (%)
AverageSP (%)
Q
total (%)
R < 0.4
HH
73.0
71.0
76.3
74.3
77.3
EH
75.8
78.1
HE
69.0
66.7
EE
87.5
81.4From Table1, we can see that the averaged sensitivity, specificity, and overall accuracy of four kinds of supersecondary structures are 76.3%, 74.3%, and 77.3%, respectively, indicating that CSs are highly informative with regard to supersecondary structures.Generally speaking, chemical shift measurements can be incomplete for a multitude of reasons. Often, chemical shifts can only be assigned partially or are missing. To assess the impact of incomplete chemical shift assignments, we performed the prediction by using the combination of the different chemical shifts as features. The results are shown in Table2.Table 2
Predicted results of different feature combinations (R < 0.4).
Featurecombinations
HH
EH
HE
EE
AverageSN (%)
AverageSP (%)
Q
total (%)
SN (%)
SP (%)
SN (%)
SP (%)
SN (%)
SP (%)
SN (%)
SP (%)
C
,
C
α
,
C
β
,
H
,
H
α
63.3
77.0
84.5
45.6
34.8
100
71.3
77.0
63.4
74.9
64.6
C
,
C
α
,
C
β
,
H
α
,
N
90.0
85.3
66.0
97.0
85.4
86.4
93.4
75.5
83.7
86.1
84.2
C
,
C
α
,
C
β
,
N
55.6
87.7
61.9
80
44.9
93.0
95.1
52.5
64.4
78.3
66.8
C
α
,
C
β
,
N
90.0
87.1
94.8
83.6
79.8
93.4
91.0
91.7
88.9
89.0
89.2
C
,
H
α
,
N
90.0
73.6
75.3
82.0
79.8
81.6
73.8
80.4
79.7
79.4
79.1
AAC
73.3
73.6
73.0
77.8
72.4
71.3
77.5
75.8
74.1
74.6
75.8From Table2, we found that omission of some CSs can result in radically different accuracy. Theoretically, incomplete chemical shifts provide relatively less information, so the predicted accuracy is also declined. But it actually did not in prediction. We used CSs of H,Hα,C as features and achieved the highest accuracy of prediction, indicating that the results are affected by the redundant data. According to the performances, we concluded that CSs of N,Cα,Cβ are the most informative features in the prediction of four kinds of protein supersecondary structures. In addition, the information of C,Hα,N is commonly provided in protein database; we achieved the prediction accuracy of 79.1% by using CSs of C,Hα,N as the only inputs.To test the method and facilitate comparison with other features, we used amino acid compositions (AAC) as inputs of the method of quadratic discriminant analysis. The compared results are recorded in Table2. Compared results show that the performances of CSs are superior to that of AAC for supersecondary structures prediction, exceptHE structure (compared with six CSs).


## 4. Conclusions

In this paper, we have introduced a prediction model for supersecondary structures from protein chemical shifts. Our model is both simple and easy to perform. However, owing to the limitation of both information of supersecondary structures and corresponding chemical shifts of six nuclei that should be considered, only 114 proteins have been selected in this study. Based on the benchmark dataset, we investigated the relationship between supersecondary structures and chemical shifts. We achieved the overall accuracy of 77.3% by using six CSs as features and the maximum overall accuracy of 89.2% by using the combination of CSs ofN,Cα,Cβ. Results show that chemical shift is a good parameter for the prediction of four kinds of protein supersecondary structures. In summary, the chemical shifts will become a new parameter in prediction of the protein supersecondary structures in the near future.



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*Source: 978503-2014-06-18.xml*