Sequence based prediction of relative solvent
accessibility using two-stage support vector
regression with confidence values
Sequence based prediction of relative solvent
accessibility using two-stage support vector
regression with confidence values
1Department of Electrical and Computer Engineering, University of Alberta, T6G 2V4, Edmonton, CANADA. * Correspondence should be
addressed to Lukasz Kurgan ([e-mail]).
tural biology due to the large and exponentially grow-
ABSTRACT ing gap between the number of known protein
sequences and the number of known structures.
Predicted relative solvent accessibility (RSA) Despite several decades of extensive research in ter-
provides useful information for prediction oftiary structure prediction, this task is still a big chal-
binding sites and reconstruction of the 3D-lenge, especially for sequences that do not have a sig-
structure based on a protein sequence.nificant sequence similarity with known structures
Recent years observed development of sev-[1].As a result, the predictions of the solvent accessi-
eral RSA prediction methods including thosebility [2] and the secondary structure [3] are
that generate real values and those that pre-addressed as an intermediate step towards the predic-
dict discrete states (buried vs. exposed). We tion of the tertiary structure. The relative solvent
propose a novel method for real value predic-accessibility (RSA) reflects the degree to which a res-
tion that aims at minimizing the prediction idue interacts with the solvent molecules. Since pro-
error when compared with six existing meth-tein-protein and protein-ligand interactions occur at
ods. The proposed method is based on a two-the protein surface, only the residues that have a
stage Support Vector Regression (SVR) pre-large surface area exposed to the solvent can possibly
dictor. The improved prediction quality is abind to the ligands and other proteins. As a result, pre-
result of the developed composite sequencediction of solvent accessibility provides useful infor-
representation, which includes a custom-mation for prediction of binding sites [4] and is
selected subset of features from the PSI-vitally important for understanding the binding mech-
BLAST profile, secondary structure pre-anism of proteins [5]. Chan and Dill pointed that the
dicted with PSI-PRED, and binary code that burial of core residues is the driving force in protein
indicates position of a given residue with folding, which suggests that knowledge of localiza-
respect to sequence termini. Cross valida-tion of individual residues (surface vs. buried) pro-
tion tests on a benchmark dataset show thatvides useful information to reconstruct the 3D-
our method achieves 14.3 mean absolutestructure of proteins [6-8].
error and 0.68 correlation. We also propose aThe existing solvent accessibility prediction meth-
confidence value that is associated with each ods use the protein sequence, which is converted into
predicted RSA values. The confidence is com-a fixed-size feature-based representation, as an input
puted based on the difference in predictions to predict the RSA for each of the residues. These
from the two-stage SVR and a second two-methods can be divided into two main groups:
stage Linear Regression (LR) predictor. The Real valued predictors predict RSA value (the
confidence values can be used to indicate definition is given in the Materials section). The rep-
the quality of the output RSA predictions.resentative existing methods are based on linear
regression [9], neural network based regression [11],
neural networks [12], support vector regression [10,
13, 15], and look up table [14]. In Ahmad's study,
binary coding of the sequence was taken as the input
features [12], while all other studies used the evolu-
tionary information in the form of the PSSM profile
1. INTRODUCTIONderived with PSI-BLAST as the input features [9-11,
The knowledge of three dimensional protein struc-13-15].
ture plays the key role in understanding protein'sdiscrete valued predictors classify each residue
function. Computational prediction of the tertiaryinto a predefined set classes. The classes are usually
protein structure is one of the central topics in struc-
Keywords: Relative solvent accessibility;
Support vector regression; PSI-BLAST; PSI-
PRED; Secondary protein structure
11 1
Ke Chen, Michal Kurgan & Lukasz Kurgan*
J. Biomedical Science and Engineering, 2008, 1, 1-9Scientific
Research
Publishing
JBiSE
Published Online May 2008 in SciRes.http://www.srpublishing.org/journal/jbise
SciResCopyright ©2008

defined based on a threshold and include buried, given residue that is accessible to the solvent. RSA
intermediate,andexposedclasses(inmostcasesthevalue, which is normalized to [0, 1] interval, is
predictions concern only two classes, i.e., buried vs. defined as the ratio between the solvent accessible
exposed). The corresponding prediction methods surface area (ASA) of a residue within a three-
apply fuzzy-nearest neighbor [17], neural network dimensional structure and ASA of its extended tri-
[16, 20, 22], support vector machine [19, 21], two peptide(Ala-X-Ala)conformation
stage support vector machine [18], information the-
ory [23], and probability profile [24]. Early studies
only use sequence to generate features [20, 23], while
recent studies use the evolutionary information in the
form of the PSSM profile to generate features [18, 19].
The PSI-BLAST profile [25] was recently intro-2.3. Feature representation
duced as an efficient sequence representation that PSI-BLAST profile. PSI-BLAST is used to compare
improves classification accuracy [16]. Subsequently,different protein sequences to find similar sequences
researchers have found that secondary structure pre-and to discover evolutionary relationships [25]. PSI-
dicted using the PSI-PRED method [3] improves theBLAST generates a profile representing a set of simi-
real value RSA predictions [2].lar protein sequences in the form of a 20Nposition-
This paper investigates whether improved sequence specific scoring matrix, whereNis the length of the
representation, which is based on the information har-sequence (window) and where each amino acid in the
vested from the sequence, the PSI-BLAST profile sequence (window) is described by 20 features. We
and the predicted secondary structure, could lead to used PSI-BLAST with the default parameters and the
improving the RSA predictions. We also investigateBLOSUM62 substitution matrix. The profile was
whether it would be possible to build an index that computed for a 15 residues wide window centered on
would indicate the quality of the predicted RSA value. a target residue and thus it consists of 300 features.
The above hypotheses translate into the two follow-The selected size is motivated by previous studies
ing goals: (1) we aim at proposing a prediction that adopted this window size [18] and obtained good
method that minimizes the RSA prediction error; (2) secondary structure prediction results [3].
the method should provide a confidence value that Secondary structure predicted with PSI-PRED.
indicates the quality of the predicted RSA values. The quality of secondary structure prediction has sig-
The first goal is achieved by designing a custom-nificantly improved in the last decade and nowadays
selected set of features, which is based on performing it is successfully used in prediction of tertiary struc-
feature selection, to represent the input sequence. Asture. Recently, secondary structure predicted with the
suggested in previous studies, the PSI-BLAST pro-PSI-PRED algorithm was shown to improve predic-
file, PSI-PRED predicted secondary structure andtion of solvent accessibility [2]. We used PSI-
additional features that indicate termini of the PRED25 with default parameters to predict second-
sequence were adopted to represent the input ary structure from the protein sequences. PSI-PRED
sequence. In contrast to prior works, we do not use all assigns three probabilities for each residue, which
features from the PSI-BLAST profile, but instead wecorrespond to the probability of assuming helix,
use two feature selection methods to select a subsetstrand, and coil conformation, respectively. These
of best-performing features. This results in a simpli-probabilities were taken as features for the proposed
fied prediction model, reduced computational time,RSA prediction method.
and optimized predictive quality.Binary code. The amino acids that are located at
To address the second goal, the confidence values the two termini of the sequence have larger probabil-
are computed based on the difference in predictionsity of being exposed to the solvent. This fact is imple-
of RSA by two predictors: a support vector regression mented during RSA prediction by using a binary code
and a linear regression. These values can be used to that indicates position of a given residue that is
indicate the quality of the output RSA predictions. located close to either terminus. The following
binary vector
2. MATERIALS
2.1. Dataset
The dataset used in this paper is referred to as the
is used to encode the first five positions at the N ter-
Manesh dataset [23] and consists of 215 low-
minus (denoted by a) and the last five position
similarity, i.e., < 25%, proteins. The sequences are i
available online at http://gibk21.bse.kyutech.ac.jp/at the C terminus (denoted byb). For instance,
i
rvp-net/all-data.tar.gz. The Manesh dataset was the third residue in the sequence is encoded as
widely used by researchers to benchmark prediction (0,0,1,0,0,0,0,0,0,0), while a residue that is out-
methods [2, 12-15, 20, 24], and this motivated us to side of the first and the last five residues in the
use it to design and validate our method.sequence is encoded as (0,0,0,0,0,0,0,0,0,0).
2.2. Relative solvet accessibility
RSA reflects the percentage of the surface area of a 2.4. Feature selection
2K. Chen et al./J. Biomedical Science and Engineering 1 (2008) 1-9
SciRes JBiSE Copyright © 2008
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PSI-BLAST profile includes 300 features, and thus user. Hence, we tested the performance of different
feature selection methods were used to reduce thenumber of selected features using support vector
dimensionality. We applied thecorrelation-based fea-regression model with default parameters to predict
ture selection (CBFS), and another feature selectionRSA values for the test set of the Monash dataset. The
method, namely correlation-based method for rele-mean absolute error (MAE) steadily decreases to
vance and redundancy analysis (CBRR), which 15.6% by adding up to 70 features, and it saturates
selects a subset of features based on filtering redun-when adding additional features, see . As a
dancy within thefeature set.The CBFS method isresult, the 70 features with the highest Pearson corre-
based on Pearson correlation coefficient r computed lation were selected when using CBFS. The selected
for a pair of variables (X,Y) asfeatures include 65 features from the PSI-BLAST pro-
file, all 3 predicted secondary structure features, and
2 binary code values that correspond to the first and
last position in the sequence, see.
The two feature sets selected by CBRR and CBFS
and the full feature set (313 features) were compared
by predicting RSA values for the test set of the
Manesh dataset using support vector regression with
where x is the mean ofX and y is the mean ofY. The
ii default parameters. The 15 features selected by
value ofris bounded within [-1, 1] interval. Higher CBRR obtain 16.7% MAE, while the 70 features
absolute value of r corresponds to stronger correla-selected by CBFS and the full feature set both result
tion between X and Y. This method ranks individualin 15.6% MAE, see . The features selected
features based on the correlation coefficient between by CBFS provide lower MAE than the features
each feature and the actual RSA values. A subset ofselected by CBRR, and they cover only 23% of the
features with the highest absolute r value is selected.full feature set. As a result, the 70 features selected
The CBRR feature selection method considersBy CBFS were used to design the proposed predic-
both the relevance of the features with respect to thetion model. The selected features are summarized in
target (RSA values), and the redundancy between the
features. It involves two steps: (1) selecting a subsetThe feature selection shows that most of the 300
of relevant features, and (2) selecting predominant features generated by PSI-BLAST are either redun-
features from among the relevant features. The dant and have little or no impact on the RSA
details can be found in [26].Predictions. shows that when predicting RSA
The 300 features corresponding to the PSI-BLAST for the residue A that is located in the center of the
i
profile, 3 features corresponding to the predicted sec-window:
ondary structure and 10 binary code values were pro-the features to encode the two leftmost positions
cessed with both feature selection methods. The fea-(A,A) and the rightmost position (A) were not
ture selection was processed using the training set of i-7 i-6 i+7
Manesh dataset, which includes 30 sequences [14, 20].selected, i.e., these amino acids have no impact on
The CBRR method automatically filters the redun-the prediction of the central amino acid. Therefore, a
dancy among the features and selects the final num-sliding window of size 13 would be sufficient for the
ber of selected features, which in our case was 15. RSA prediction. The two amino acids that are adja-
The selected features include 13 features from thecent to A, i.e.,Aand A, have the most significant
ii-1 i+1
PSI-BLAST profile, and 2 predicted secondary struc-impact on the prediction since they correspond to the
ture features, see . In case of CBFS, the num-largest number of the selected features. Interestingly,
ber of selected features should be specified by the
Figure 1
Table 1
Figure 2
Table 2
Table 2
Table 1
.
Figure 1. The MAE values against the number of selected
features. The MAE is obtained by using support vector
regression with default parameters to predict test set of the
Monash dataset.
Figure 2. Bar chart of MAE values (white) and number of
features (gray) for features selected by CBRR, CBFS, and
the full feature set.
3
K. Chen et al./J. Biomedical Science and Engineering 1 (2008) 1-9
SciRes JBiSE Copyright©2008
(2)
100 110
of features
0.1585
0.158
0.1575
0.157
0.1565
0.156
0.1555
Full feature set

and test a confidence value that is associated with
each predicted RSA value.
The proposed two-stage prediction model works as
follows:
STAGE1.The input sequences is inputted into
PSIPRED to compute predicted secondary structure
and into PSI-BLAST to compute the PSI-BLAST pro-
file. Next, the input sequence, the predicted second-
ary structure, and the PSI-BLAST profile are used to
compute the selected 70 features using a 15 residues
wide window centered over the being predicted resi-
due, and for each residue in the input sequence. The
residues at i-2 andi+2 positions have relatively small 70 features are used as an input to the LR model and
influence on the prediction.SVR model that predict a real value (predicted RSA
The selected features are almost symmetricallyvalue) for the central residue in a given window.
distributed aroundA, e.g., amino acids E, K, Q, R,
iSTAGE 2. The aim of the stage two is to refine the
and D have similar impact on the solvent accessibil-predictions from stage one. Similarly to other two-
ity of the central residue at the third left position (A)stage designs [13,18], the second stage“smoothes” the
i-3
predictions. It takes the three predicted secondary
and the third right position (A).
i+3 structure features (computed in stage one by
Hydrophilic residues, which include E, K, Q, R, PSIPRED) and a 7 residues wide window from the
and D, may have impact on the solvent accessibilityfirst stage predictions centered over the predicted res-
of A residue which is 3 or 4 positions away from the
iidue as the input to provide the refined real value pre-
these residues. This pattern covers 19 of the selected dictions.
features and we hypothesize that this is related to theSince the prediction quality of SVR is better than
á-helical structures due to the following two reasons.the quality of LR (results are discussed in the follow-
Firstly, these 5 hydrophilic residues have larger prob-ing), the predictions from SVR are taken as the final
ability (above 0.5) to form helical structure than prediction outcome.The LR results serve as a refer-
strand and coil structures [27]. Secondly,á-helix con-ence to evaluate quality of SVR predictions. This
sists of 3.6 residues per turn, and hence if two resi-means that if predictions from SVR and LR are simi-
dues in a helix are separated by 2 or 3 residues in the lar then SVR predictions are assumed to be of high
sequence then they are spatially close to each other,quality. On the other hand, if the two predictions are
which in turn may induce some interactions between different then the SVR prediction is assumed to be of
them. For instance, the hydrogen bond that maintainslower quality. The corresponding confidence value is
the helical structure occurs between two residues that defined as
are separated in a sequence by three other residues,
i.e., A and A.
ii+4
where R is the predicted RSA from SVR, andT is the
3. METHODSii
predicted RSA from LR. A detailed overview of the
3.1. Prediction methodprediction procedure is shown in .
Linear Regression (LR) and Support VectorThe optimization of the prediction, through adjust-
Regression (SVR) were already applied in the RSAment of internal parameters of the predictors and
prediction [10,13,15]. In this paper, we propose anselection of the window size for the second stage,
improved two-stage model, which not only aims at was performed by dividing the Manesh dataset into
reducing the prediction error, but we also propose
Figure 3
Table 1. Summary of the feature selection results.
Features set
PSI-BLAST profile
Binary code
Predicted second.structure
Total
Total #
features
300
10
3
313
# selected
features by
CBFS
65
2
3
70
# selected
features by
CBRR
13
0
2
15
Table 2.Summary of feature selection results for the PSI-BLAST profile by correlation-based feature selection method.
15-wide window
Total # of features
# ofselected features
The selected features
Ai-7
20
0
Ai-6
20
0
Ai-5
20
2
I
L
Ai-4
20
4
E
K
Q
R
Ai-3
20
5
E
K
Q
R
D
Ai-2
20
0
Ai-1
20
8
E
K
Q
R
D
N
P
S
Ai
20
19
C D
E F
G H
I K
L M
N P
Q R
S T
V W
Y
Ai+1
20
7
E
K
Q
H
D
N
G
Ai+2
20
1
P
Ai+3
20
6
E
K
Q
R
D
P
Ai+4
20
6
E
K
Q
R
D
P
Ai+5
20
4
I
L
V
F
Ai+6
20
3
I
L
V
Ai+7
20
0
(3)
Table 1. Summary of the feature selection results.
4K. Chen et al./J. Biomedical Science and Engineering 1 (2008) 1-9
SciRes JBiSE Copyright©2008

two subsets, one used to compute the prediction
model and the other to perform test. Similarly to [14],
30 sequences were used for training and the remain-
ing 185 as the test set. The linear regression is
parameterless and thus it does not require optimiza-
tion. For SVR, RBF kernel was used for both stages.
The parameters for the first stage SVR areã=0.01 and
C=1, and for the second stageã=0.15 andC=1. These
parameters, which were based on experiments sum-
marized in , provide the lowest MAE. We note
that the adjustment of C has little impact in the qual-
ity of predictions. The MAE of the final prediction
for the second stage windows sizes of 5, 7, 9, 11, 15,
and 21 equal 0.149, 0.148, 0.148, 0.148, 0.148, and
0.148, respectively. This shows that the window size
of 7 is the best choice to provide accurate predictions.
3.2. Linear regreesion
A linear regression withp coefficients andn data
points (number of samples), assuming thatn>p, cor-
responds to the construction of the following expres-
sion:
3.3. Support vector regression
Given a training set of n data point pairs (x,y), i = 1,
ii
2,…,n, wherex denotes the vector ofp features rep-
i
th
resenting i protein sequence, y denotes the pre-
i
dicted RSA value, finding the optimal SVR is
achieved by solving:
where y is the predicted RSA value, x = (x,x,…,
iii1i2
th
x) is the vector of p features representingi protein
ip
sequence, â(constant) is parameter to be estimated,
i
and å is the standard error. The above formula can besuch that
i
written in vector-matrix form as:
The solution to minimize the mean square error ||å||
i
is
where w is a vector perpendicular to wx-b=0 hyperplane,
*
C is a user defined complexity constant,î and îare
ii
Table 3
First stageSecond stage
MAE
0.150
0.149
0.148
0.148
0.148
0.149
0.148
0.148
0.148
0.148
0.148
0.148
Parameter
C
1
1
1
1
1
1
0.5
0.8
1
2
3
5
Parameter
C
1
1
1
1
1
1
0.5
0.8
1
2
3
5
MAE
0.157
0.153
0.151
0.151
0.152
0.155
0.152
0.151
0.151
0.151
0.151
0.152
Parameter
ã
0.001
0.005
0.01
0.02
0.03
0.05
0.01
0.01
0.01
0.01
0.01
0.01
Parameter
ã
0.01
0.08
0.15
0.2
0.3
0.4
0.15
0.15
0.15
0.15
0.15
0.15
Table 3.Optimization of parameters for two-stage SVR.
Figure 3
Table 1
. RSA prediction with the proposed system; the RSA
th
value for theiresidue is predicted based on the 70 feature
values (see ) that are computed over a 15 residues
th
wide window centered on i residue; the feature values are
inputted into the first-stage predictor (LR and SVR); next, the
first-stage predictions are aggregated into 7 residue wide
windows and inputted, together with the predicted secondary
structure of the central residue, into the second-stage
predictor that provides the RSA values. Finally, compare the
predictions from SVR and LR, and calculate the confidence
value C.
(5)
(6)
(7)
(8)
5
K. Chen et al./J. Biomedical Science and Engineering 1 (2008) 1-9
SciRes JBiSE Copyright©2008
(4)
AA…AAA …A A
12 i-1 ii+1 n-1 n
PSI-PRED Select 15-wide window
AA…A…A A
i-7 i-6 ii+6 i+7
Predicted
secondary
structure
ss ss …ss…ssss
12 in-1 n
Compute 70 features
Features values for the 15-wide window
Input feature vectors for
all residues, i=1,2,…,n
First-stage SVRFirst-stage LR
rr…rrr …r r
12 i-1ii+1n-1ntt…ttt …t t
12 i-1ii+1 n-1n
Select 7-wide window
rr…r…rr
i-3 i-2 ii+2 i+3 tt…t…tt i-3i-2 ii+2 i+3
Input feature vectors for
all residues, i=1,2,…,N
Second-stage SVRSecond-stage LR
TT…T…T T
12 in-1 n
Compute
confidence value
RR…R …RR
12 in-1n
CC…C …CC
12 in-1 n

slack variables that measure the degree of predictionposedmethodequals14.6andthecorresponding
error ofx for a given hyperplane, and z=(x)wherePearson's correlation coefficient (r) equals 0.67.
iAfter the second stage, the MAE value is reduced to
k(x,x')=(x)(x') is a user defined kernel function.14.3 andr is improved to 0.68. compares the
The SVR was trained using sequential minimal proposed two-stage SVR with recent methods for
optimization algorithm [28] that was further opti-RSA prediction, which include neural network and
mized by Shevade and colleagues [29]. The proposedsupport vector regression models [2, 12, 13, 15]. The
SVR uses RBF kernel proposed method obtains 0.6 to 3.7 lower MAE when
compared with the abovementioned methods. This
translates into 4% to 20% error reduction, respec-
for both stages.tively. Since some methods predict discrete valued
classes (exposed vs. buried), we also examined the
performance of our method by converting the real
4. RESULTSAND DISCUSSIONvalue prediction into the two states prediction. We fol-
The SVR and LR predictors were implemented in lowed the standard approach, in which the state is
Weka [30], which is a comprehensive open-sourcedefined based on the predicted RSA value and a pre-
library of machine learning methods. The Manesh defined threshold. For instance, a 5% threshold
dataset consists of 50682 instances (individual resi-means that the residues having an RSA value (%)
dues). The evaluation was performed using two testgreater or equal 5 are defined as exposed, and other-
types to allow for a comprehensive comparison with wise they are classified as buried. The threshold's
previous studies. To compare with [2] and [12], 5-value is usually adjusted between 5% and 50%. We
folds cross validation was executed. On the other note that for all thresholds, our method provides the
hand, following several other prior studies [14, 20,highest accuracy, see. The proposed two-
24], Manesh dataset was divided into two subsets, 30stage model provides 0.3%-0.6% higher accuracies
sequences were used for training and the remainingthan the prediction coming from the first stage for var-
185 as independent test set. The results of both tests, ious thresholds. When compared to the best perform-
i.e., 5 folds cross-validation and independent test, ing, existing two-stage SVR method [13], our predic-
were reported in . In total, the pro-tions are characterized by lower MAE and more accu-
posed method was compared with six real value RSArate two states predictions.
prediction methods [2, 12-15, 24] and one methodFor the independent test, the MAE value for the
that aims at prediction of discrete states [20].first stage of the proposed method equals 15.0 and the
We note that in statistical prediction, the following corresponding Pearson's correlation coefficientr
three cross-validation methods are often used to equals 0.66. After the second stage, the MAE value is
examine a predictor for its effectiveness in practicalreduced to 14.8 andr is improved to 0.67.Table 5
application: independent dataset test, sub-sampling compares the proposed two-stage SVR with recent
(such as 5-fold and 7-fold) test, and jackknife test [31].methods for RSA prediction, which include neural
However, as elucidated by [32] and demonstrated innetwork and look-up table based methods [14, 20, 24].
[33], among the three cross-validation methods, the The proposed method obtains 1.5 to 4.0 lower MAE
jackknife test is deemed the most objective that canwhen compared with the above three methods. This
always yield a unique result for a given benchmark translates into 9% to 21% error reduction, respec-
dataset, and hence has been increasingly used bytively. Similarly to the 5-folds cross validation test,
investigators to examine the accuracy of various pre-we also examined the performance of our method by
dictors [34-42].converting the real value prediction into the two
states prediction. The threshold's value was adjusted
4.1. Comparison with competing prediction between 5 and 50%.
methods For all thresholds our method consistently pro-
For the 5 folds cross-validation test, the mean abso-vides the highest accuracy, see. The two-
lute error (MAE) value of the first stage of the pro-
Table 4
Table 4
Tables 4 and 5
Table 5
Table 4. Experimental comparison between the proposed two-stage SVR and other reported methods; the results were
reported based on 3 or 5-folds cross validation test; the real valued predictions were converted to two state prediction (buried
vs. exposed) with different threshold (5%~50%); unreported results are denoted by “-“; best results are shown in bold.
Reference
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Prediction
method
Neural Network
Neural Network
Two-stage SVR
SVR
One-stage SVR
Two-stage SVR
MAE (%)
15.2
18.0
14.9
16.3
14.6
14.3
Correlation
coefficient r
0.67
0.50
0.68
0.58
0.67
0.68
5%
74.9%
-
81.1%
-
80.5%
81.1%
20%
77.7%
-
77.6%
-
78.3%
78.8%
10%
77.2%
-
78.5%
-
79.1%
79.7%
30%
77.8%
-
-
-
78.3%
78.6%
40%
78.1%
-
-
-
78.3%
78.8%
50%
80.5%
-
79.5%
-
80.5%
80.8%
Accuracy for two-states (buried vs. exposed) prediction
6K. Chen et al./J. Biomedical Science and Engineering 1 (2008) 1-9
SciRes JBiSE Copyright©2008
(9)

stage model provides 0.3%-0.5% higher accuracies between 0 and 0.294. As a result, the confidence
than the one-stage model for various thresholds. valueC distributed in the interval [0.706, 1] for the
When compared with the best-performing, compet-Maneshdataset.HigherC values indicate that the pre-
ing method based on neural network [24], our predic-dictions from SVR and LR are more consistent, and
tions result in higher accuracies over all thresholds,thereforethecorrespondingpredictions fromthe
i.e., the differences range between 4% and 5.8%, and two-stageSVRareassumedtobemoreaccurate.
better MAE and correlation coefficient value.TheC value of 7101 samples, which covers
The three main observations based on the per-7101/50682= 14% of the dataset, are greater than
formed empirical evaluation include: (1) the pro-0.99, and the corresponding MAE of these samples
posed two-state predictor obtains favorable (lower)equals0.122,see.TheCvalue of 12846 sam-
error rates when compared with six competing meth-ples,whichcovers12846/50682=25.3%ofthe
ods; (2) the improvements are obtained for both real dataset, are greater than 0.98, and the corresponding
value and two-state predictions; and (3) the introduc-MAE of these samples equals 0.131. The C value of
tion of the second stage in our design allows for 18174samples,whichcovers18174/50682=35.9%
obtaining improved predictions when compared withof the dataset, are greater than 0.97, and the MAE of
aonestagedesign.these samples is 0.136. When the threshold forC
value is set equal or lower than 0.96, the MAE satu-
4.2. Confidence value for RSA predictionrates at 0.143, see, which is equal to the
As one of the goals of this work, we defined confi-MAE for the entire dataset (without using the confi-
dence values to measure the quality of the predicteddence values). This shows that the confidence values
RSA. The confidence values are based on the differ-can be used to identify a subset of the predictions
ence of predictions made by the two-stage SVR and which on average have better quality than the remain-
the two-stage LR. The following discussion is baseding predictions. This way, the user could select a
on results of five folds cross-validation tests. desired fraction of best performing predictions.
The MAE for two-stage SVR is 0.143 and for two-Additionally, the user could inspect quality of predic-
stage LR is 0.155. The difference between the predic-tion for specific amino acids or groupings of amino
tions from SVR and LR for the same residues ranges acids that share certain properties such as hydrophobicity,
charge, size, etc.
5. CONCLUSIONS
This paper proposes a novel method for the real value
RSA prediction. The proposed method addresses two
goals, which include improving the quality of RSA
prediction, and development of a confidence value
that allows for selection of better performing RSA
predictions.
Empirical tests with the Manesh dataset show that
the proposed method is characterized by lower pre-
diction error when compared with six competing real
value RSA prediction methods. We also show that the
PSI-BLAST profile that is commonly used to repre-
sent sequences can by largely reduced by using fea-
ture selection, which results a simpler, interpretable
model and in reduction of the computational time
required to develop the prediction model. Our model
indicates that window size of 13 is sufficient and only
about 22% of the PSI-BLAST features are useful for
Figure 4
Figure 4
Table 5. Experimental comparison between the proposed two-stage SVR and other reported methods; the results were
reported based on a test on the independent dataset (30 sequences for training and 185 sequences for test); the real valued
predictions were converted to two state prediction (buried vs. exposed) with different threshold (5%~50%); unreported
results are denoted by “-“; best results are shown in bold.
Reference
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This paper
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Prediction
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Look-up table
Neural Network
Neural Network
One-stage SVR
Two-stage SVR
MAE (%)
18.8
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16.3
15.0
14.8
Correlation
coefficient r
0.48
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0.58
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0.67
Accuracy for two-states (buried vs. exposed) prediction
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K. Chen et al./J. Biomedical Science and Engineering 1 (2008) 1-9
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