# A Two-Stage Exon Recognition Model Based on Synergetic Neural Network

Authors: Zhehuang Huang; Yidong Chen
Journal: Computational and Mathematical Methods in Medicine
 (2014)

---

## Abstract

Exon recognition is a fundamental task in bioinformatics to identify the exons of DNA sequence. Currently, exon recognition algorithms based on digital signal processing techniques have been widely used. Unfortunately, these methods require many calculations, resulting in low recognition efficiency. In order to overcome this limitation, a two-stage exon recognition model is proposed and implemented in this paper. There are three main works. Firstly, we use synergetic neural network to rapidly determine initial exon intervals. Secondly, adaptive sliding window is used to accurately discriminate the final exon intervals. Finally, parameter optimization based on artificial fish swarm algorithm is used to determine different species thresholds and corresponding adjustment parameters of adaptive windows. Experimental results show that the proposed model has better performance for exon recognition and provides a practical solution and a promising future for other recognition tasks.


---

## Body

## 1. Introduction

With the completion of human genome project, gene data increase exponentially. Identifying the genes encoding of DNA [1] has important theoretical and practical implications. How to quickly access accurate genetic information is an urgent problem to be solved.Early exon recognition methods were based mainly on statistical models [2], which get their chromosomal order by statistical analysis of different genes. But with the increase of genomic number, statistical methods cannot meet the need for rapid recognition of exons. At present, exon recognition methods based on digital signal processing have also been widely used [3–5]. These techniques select a suitable mapping method and transformation method to get spectral values and identify exons according to fixed length window. Limitations of these methods include slow recognition speed and inability to accurately determine the threshold for different species.Synergetic theory [6] is the science proposed by Haken to describe high dimension and nonlinear problem as a set of low-dimension nonlinear equations. One advantage of synergetic neural network is that the method is robust against noise and the method can better handle the fuzzy matching problem [7–9]. Exon recognition can also be considered a problem of pattern recognition, for which the proposed method can be used to solve.Artificial fish swarm algorithm (AFSA) [10, 11] is a class of swarm intelligence optimization algorithms based on the behavior of animals proposed in 2002; the basic idea of AFSA is to imitate the fish behaviors such as praying, swarming, and following. AFSA is very suitable for solving a variety of numerical optimization problems, making the algorithm become a hot topic in the current optimization field quickly. Because of simplicity in principle and good robustness, AFSA has been applied successfully to all kinds of optimization problems such as image segmentation [12], color quantization [13], neural network [14], fuzzy logic controller [15], multirobot task scheduling [16], fault diagnosis in mine hoist [17], data clustering [18], and other areas.In this paper, we proposed a two-stage exon recognition model based on synergetic neural network and artificial fish swarm algorithm. This paper is organized as follows. Firstly, traditional exon recognition method based on digital signal processing and related work are presented. Secondly, an exon recognition model based on synergetic neural network and parameter optimization method based on artificial fish swarm algorithm are introduced. Finally some experimental tests, results, and conclusions are given on the systems.


## 2. Introduction to Exon Recognition Method Based on Digital Signal Processing

The gene is usually divided into many fragments. The coding sequence is called exons and noncoding part is called introns, as shown in Figure1.Figure 1
Structure of eukaryotic DNA sequence.The objective of gene recognition is to identify the exons of DNA sequence. Gene recognition based on digital signal processing methods consists of several steps [19, 20]. First, gene sequences are transformed into digital symbol sequences using mapping methods [21–24]. This is followed by calculation of the corresponding frequency value by fast Fourier transform and the 3-Cycle properties of the spectrum are then used to identify exons [25, 26]. Finally, fixed sliding window method is used for automatic exon recognition, as shown in Figure 2.Figure 2
Exon recognition algorithm based on 3-Cycle spectrum.


### 2.1. Z-Curve Mapping

In order to make digital processing, we must transform four nucleotide sequences A, T, G, and C into their corresponding numeric sequence based on certain rules.Let the four instruction sequences be{
u
b
[
n
]
}, b
∈
I
=
{
A
,
C
,
G
,
T
}, and cumulative sequence b
n
(
n
=
0,1
…
,
N
-
1
) is b
n
=
∑
i
=
0
n
-
1
u
b
[
i
]; then we can define three sequences x
[
n
], y
[
n
], and z
[
n
]:
(1)
x
[
n
]
=
2
(
A
n
+
G
n
)
-
n
,
y
[
n
]
=
2
(
A
n
+
C
n
)
-
n
,
z
[
n
]
=
2
(
A
n
+
T
n
)
-
n
.Let(2)
x
[
-
1
]
=
0
,
y
[
-
1
]
=
0
,
z
[
-
1
]
=
0
,
Δ
x
[
n
]
=
x
[
n
]
-
x
[
n
-
1
]
,
Δ
y
[
n
]
=
y
[
n
]
-
y
[
n
-
1
]
,
Δ
z
[
n
]
=
z
[
n
]
-
z
[
n
-
1
]
.Thus we can get theZ-curve mapping:
(3)
(
Δ
x
[
n
]
Δ
y
[
n
]
Δ
z
[
n
]
)
=
(
1
-
1
1
-
1
1
1
-
1
-
1
1
-
1
-
1
1
)
(
u
A
[
n
]
u
C
[
n
]
u
G
[
n
]
u
T
[
n
]
)
.For example, the DNA sequence ofS
(
n
) is ACGTTAG; then the corresponding Z-curve mapping sequence is shown in Table 1.Table 1
Δ
x
[
n
]
1
−1
1
−1
−1
1
1
Δ
y
[
n
]
1
1
−1
−1
−1
1
−1
Δ
z
[
n
]
1
−1
−1
1
1
1
−1


### 2.2. The Power Spectrum

To study the characteristics of DNA coding sequences (exons), we can do the discrete Fourier transform (DFT), respectively, for the instruction sequences:(4)
U
b
[
k
]
=
∑
n
=
0
N
-
1
u
b
[
n
]
e
-
j
(
2
π
n
k
/
N
)
,
k
=
0,1
,
…
,
N
-
1
.Thus we can calculate the power spectrum:(5)
P
z
[
k
]
=
|
Δ
X
[
k
]
|
2
+
|
|
Δ
Y
[
k
]
|
|
2
+
|
Δ
Z
[
k
]
|
2
,
k
=
0,1
,
…
,
N
-
1
,
where Δ
X
[
k
], Δ
Y
[
k
], and Δ
Z
[
k
] are the Fourier transform of Δ
x
[
n
], Δ
y
[
n
], and Δ
z
[
n
], respectively.The spectral peaks of exon sequences are larger ink
=
N
/
3 and k
=
2
N
/
3 of the power spectrum curve, while they are not similar for intron. This statistical phenomenon is known as 3-Cycle. Suppose that the average power spectrum of DNA sequences is
(6)
E
-
=
∑
k
=
0
N
-
1
P
[
k
]
N
.
The power spectrum ratio of the DNA sequence and the average spectrum of the entire sequence are known as SNR (signal-to-noise ratio):
(7)
R
=
P
[
N
/
3
]
E
-
.Figure3 shows the power spectrum of viral genes.Figure 3
The power spectrum of viral gene sequence.From Figure3, we can see that the spectrum presents obvious 3-Cycle. The peaks appear roughly in 2000, 4000, and 6000. So the exon segment can be determined, enabling the recognition of genes.The highest point of power spectrum may not appear ink
=
N
/
3 and k
=
2
N
/
3 but occur in the surrounding. So we can calculate average SNR R
1 and R
2 of intervals [
N
/
3
-
γ, N
/
3
+
γ
] and [
2
N
/
3
-
γ, 2
N
/
3
+
γ
], respectively:
(8)
R
1
=
∑
k
=
N
/
3
-
γ
N
/
3
+
γ
P
[
E
]
(
2
γ
+
1
)
E
-
,
R
2
=
∑
k
=
2
N
/
3
-
γ
2
N
/
3
+
γ
P
[
E
]
(
2
γ
+
1
)
E
-
.


### 2.3. Automatic Recognition Algorithm Based on Fixed Sliding Windows

SupposedM is the length of fixed window; we can do four discrete Fourier transforms (DFT) for instruction sequences {
u
b
[
n
]
}
(
0
≤
n
≤
N
-
1
),
(9)
U
b
[
k
]
=
∑
i
=
n
-
(
M
-
1
)
/
2
i
=
n
+
(
M
-
1
)
/
2
u
b
[
i
]
e
-
j
(
2
π
i
k
/
M
)
,
k
=
0,1
,
…
,
M
-
1
.Then the total spectrump
(
n
;
M
/
3
) at position M
/
3 is
(10)
P
[
M
3
]
=
|
U
A
[
M
3
]
|
2
+
|
U
T
[
M
3
]
|
2
+
|
U
G
[
M
3
]
|
2
+
|
U
C
[
M
3
]
|
2
=
Δ
p
(
n
;
M
3
)
.


## 2.1. Z-Curve Mapping

In order to make digital processing, we must transform four nucleotide sequences A, T, G, and C into their corresponding numeric sequence based on certain rules.Let the four instruction sequences be{
u
b
[
n
]
}, b
∈
I
=
{
A
,
C
,
G
,
T
}, and cumulative sequence b
n
(
n
=
0,1
…
,
N
-
1
) is b
n
=
∑
i
=
0
n
-
1
u
b
[
i
]; then we can define three sequences x
[
n
], y
[
n
], and z
[
n
]:
(1)
x
[
n
]
=
2
(
A
n
+
G
n
)
-
n
,
y
[
n
]
=
2
(
A
n
+
C
n
)
-
n
,
z
[
n
]
=
2
(
A
n
+
T
n
)
-
n
.Let(2)
x
[
-
1
]
=
0
,
y
[
-
1
]
=
0
,
z
[
-
1
]
=
0
,
Δ
x
[
n
]
=
x
[
n
]
-
x
[
n
-
1
]
,
Δ
y
[
n
]
=
y
[
n
]
-
y
[
n
-
1
]
,
Δ
z
[
n
]
=
z
[
n
]
-
z
[
n
-
1
]
.Thus we can get theZ-curve mapping:
(3)
(
Δ
x
[
n
]
Δ
y
[
n
]
Δ
z
[
n
]
)
=
(
1
-
1
1
-
1
1
1
-
1
-
1
1
-
1
-
1
1
)
(
u
A
[
n
]
u
C
[
n
]
u
G
[
n
]
u
T
[
n
]
)
.For example, the DNA sequence ofS
(
n
) is ACGTTAG; then the corresponding Z-curve mapping sequence is shown in Table 1.Table 1
Δ
x
[
n
]
1
−1
1
−1
−1
1
1
Δ
y
[
n
]
1
1
−1
−1
−1
1
−1
Δ
z
[
n
]
1
−1
−1
1
1
1
−1


## 2.2. The Power Spectrum

To study the characteristics of DNA coding sequences (exons), we can do the discrete Fourier transform (DFT), respectively, for the instruction sequences:(4)
U
b
[
k
]
=
∑
n
=
0
N
-
1
u
b
[
n
]
e
-
j
(
2
π
n
k
/
N
)
,
k
=
0,1
,
…
,
N
-
1
.Thus we can calculate the power spectrum:(5)
P
z
[
k
]
=
|
Δ
X
[
k
]
|
2
+
|
|
Δ
Y
[
k
]
|
|
2
+
|
Δ
Z
[
k
]
|
2
,
k
=
0,1
,
…
,
N
-
1
,
where Δ
X
[
k
], Δ
Y
[
k
], and Δ
Z
[
k
] are the Fourier transform of Δ
x
[
n
], Δ
y
[
n
], and Δ
z
[
n
], respectively.The spectral peaks of exon sequences are larger ink
=
N
/
3 and k
=
2
N
/
3 of the power spectrum curve, while they are not similar for intron. This statistical phenomenon is known as 3-Cycle. Suppose that the average power spectrum of DNA sequences is
(6)
E
-
=
∑
k
=
0
N
-
1
P
[
k
]
N
.
The power spectrum ratio of the DNA sequence and the average spectrum of the entire sequence are known as SNR (signal-to-noise ratio):
(7)
R
=
P
[
N
/
3
]
E
-
.Figure3 shows the power spectrum of viral genes.Figure 3
The power spectrum of viral gene sequence.From Figure3, we can see that the spectrum presents obvious 3-Cycle. The peaks appear roughly in 2000, 4000, and 6000. So the exon segment can be determined, enabling the recognition of genes.The highest point of power spectrum may not appear ink
=
N
/
3 and k
=
2
N
/
3 but occur in the surrounding. So we can calculate average SNR R
1 and R
2 of intervals [
N
/
3
-
γ, N
/
3
+
γ
] and [
2
N
/
3
-
γ, 2
N
/
3
+
γ
], respectively:
(8)
R
1
=
∑
k
=
N
/
3
-
γ
N
/
3
+
γ
P
[
E
]
(
2
γ
+
1
)
E
-
,
R
2
=
∑
k
=
2
N
/
3
-
γ
2
N
/
3
+
γ
P
[
E
]
(
2
γ
+
1
)
E
-
.


## 2.3. Automatic Recognition Algorithm Based on Fixed Sliding Windows

SupposedM is the length of fixed window; we can do four discrete Fourier transforms (DFT) for instruction sequences {
u
b
[
n
]
}
(
0
≤
n
≤
N
-
1
),
(9)
U
b
[
k
]
=
∑
i
=
n
-
(
M
-
1
)
/
2
i
=
n
+
(
M
-
1
)
/
2
u
b
[
i
]
e
-
j
(
2
π
i
k
/
M
)
,
k
=
0,1
,
…
,
M
-
1
.Then the total spectrump
(
n
;
M
/
3
) at position M
/
3 is
(10)
P
[
M
3
]
=
|
U
A
[
M
3
]
|
2
+
|
U
T
[
M
3
]
|
2
+
|
U
G
[
M
3
]
|
2
+
|
U
C
[
M
3
]
|
2
=
Δ
p
(
n
;
M
3
)
.


## 3. Related Work

The SNR of exon sequences reflects the distribution of spectrum peak. SNR greater than a given threshold is a characteristic of exons, while introns generally do not have this property.Protein coding regions and noncoding regions can be distinguished using the value of SNR, but this method still has a large predictive error because the spectrum peak varies amongst different biological categories. A fixed threshold is unreasonable to use for different biological categories. Therefore, determining the SNR threshold has great significance for exon recognition. Note that it is difficult to find the proper prediction threshold for biological categories when relying only on prior biological knowledge.Xu [27] proposed a method based on bootstrap algorithm to determine the best SNR threshold that can be obtained from marked exon sequences. The results of that study showed that the average prediction accuracy of the method was 81%, which is 19% higher than other methods that employ empirical thresholds. In paper [28], a novel model was proposed to determine the SNR threshold based on the means of biological categories and improved the recognition performance to some extent.But all the methods mentioned above have problems, such as slow recognition speed, inaccurate determination of the threshold for different species, and the requirement to know the exon fragments of DNA sequences. In the following sections, we propose a novel two-stage exon recognition model based on synergetic neural network and artificial fish swarm algorithm to better deal with these problems.


## 4. A Novel Two-Stage Exon Recognition Model

In this section, a two-stage exon recognition model is presented. In the first stage, synergetic neural network is used to determine initial exon intervals. In the second stage, final accurate exon intervals determination based on adaptive sliding window and parameter optimization algorithm are introduced.


### 4.1. Initial Exon Intervals Determination Based on Synergetic Neural Network

The basic principle of synergetic neural network [29, 30] is that the pattern recognition procedure can be viewed as the competition progress of many order parameters. The strongest order parameter will win by competition and desired pattern will be recognized.A pattern that remained to be recognized,q, is constructed by a dynamic process which translates q into one of prototype pattern vectors v
k through status q
(
t
); namely, this prototype pattern is closest to q
(
0
). The process is described as the following equation:
(11)
q
⟶
q
(
t
)
⟶
v
k
.A dynamic equation can be given for an unrecognized patternq:
(12)
q
˙
=
∑
k
=
1
M
λ
k
v
k
(
v
k
+
q
)
-
B
∑
k
′
≠
k
(
v
k
′
+
q
)
2
(
v
k
+
q
)
v
k
-
C
(
q
+
q
)
q
+
F
(
t
)
,
where q is the status vector of input pattern with initial value q
0, λ
k is attention parameter, v
k is prototype pattern vector, and v
k
+ is the adjoint vector of v
k that satisfies
(13)
(
v
k
+
,
v
k
′
T
)
=
v
k
+
·
v
k
′
T
=
δ
k
k
′
.Corresponding dynamic equation of order parameters is(14)
ξ
˙
k
=
λ
k
ξ
k
-
B
∑
k
′
≠
k
ξ
k
′
2
ξ
k
-
C
|
∑
k
′
=
1
M
ξ
k
′
2
|
ξ
k
.Haken has proved that whenλ
k
=
c
(
c
>
0
), the largest initial order parameter will win and the network will then converge.We firstly introduce the synergetic theory to exon recognition; an exon recognition algorithm based on synergetic neural network is shown in Figure4.Figure 4
Exon recognition based on synergetic neural network.We use synergetic neural network andN equal method to quickly determine the initial exon region, as shown in Algorithm 1.Algorithm 1:Determination of initial exon region based on synergetic neural network.
(1) LetS is a given gene sequence, S
start and S
end are the beginning and end of the
sequence respectively,T
0 is throdthod of spectral values;
(2) UsingZ_Curve mapping converted gene sequence to the corresponding numeric sequence;
(3) Using fast Fourier transform  to get spectral valuesR
1 and R
2 according to the formula (8);
(4) Calculating gene sequence order parameter:
ξ
1
=
R
1
R
1
+
R
2,  ξ
2
=
R
2
R
1
+
R
2;
(5) Setting network parameterλ
k and B
,
C;
(6) Order parameter evolution according to formula (14);
(7) Ifξ
1>T
0 and  ξ
2>T
0, then [
S
start
,
S
end
] is recorded as a possible interal, and S is divided
equally inton interals S
1
,
S
2, …,  S
n, Repeat step 1 to step 7;
(8) End.


### 4.2. Get Precise Exon Intervals Using Adaptive Smoothing Window

We can obtain several possible exon intervals by Algorithm1. In this section, we propose an adaptive sliding window algorithm to get more accurate intervals, as shown in Algorithm 2.Algorithm 2:Precise exon regions based on adaptive smoothing window.
(1) LetW is a given gene sequence, W
start and W
end are the beginning and the end of
the sequence respectively;
(2) UsingZ_Curve mapping converted gene sequence [
W
start
,
W
end
] to the
corresponding numeric sequence;
(3) Using fast Fourier transform  to get spectral values;
(4) Calculating gene sequence order parameter:
ξ
1
=
R
1
R
1
+
R
2,   ξ
2
=
R
2
R
1
+
R
2;
(5) Order parameter evolution according to formula (14);
(6) Ifξ
1>T
0, ξ
2>T
0 and W
start
+
γ
<
W
end
-
γ, Then W
start
=
W
start
+
γ,
W
end
=
W
end
-
γ,
Repeat step 2 to step 6;
(7) Output the final interval[
W
start
,
W
end
].


### 4.3. Parameter Optimization Based on Artificial Fish Swarm Algorithm

The parametersT
0 and γ directly influence the performance of exon recognition. The adjustment of the parameters is a global behaviour and has no general research theory to control the parameters in the recognition process at present. In this section, artificial fish swarm algorithm is used to search the global optimum parameters (
T
0
,
γ
) in the corresponding parameter space.The parameter optimization based on artificial fish swarm algorithm is shown as Algorithm3.Algorithm 3:Parameter optimization based on artificial fish swarm algorithm.
(1) Initialize the parameters of artificial fish, such ass
t
e
p, v
i
s
u
a
l, the number of exploratory,
maximum number of iterations, and randomly generatedn fishes;
(2) Set bulletin board to record the current status of each fish, and select the optimal value;
(3) Implementation of prey behavior, swarm behavior and follow behavior;
(4) Optimal value in bulletin board is updated;
(5) If termination condition is satisfied, output the result; otherwise return to step 2.


## 4.1. Initial Exon Intervals Determination Based on Synergetic Neural Network

The basic principle of synergetic neural network [29, 30] is that the pattern recognition procedure can be viewed as the competition progress of many order parameters. The strongest order parameter will win by competition and desired pattern will be recognized.A pattern that remained to be recognized,q, is constructed by a dynamic process which translates q into one of prototype pattern vectors v
k through status q
(
t
); namely, this prototype pattern is closest to q
(
0
). The process is described as the following equation:
(11)
q
⟶
q
(
t
)
⟶
v
k
.A dynamic equation can be given for an unrecognized patternq:
(12)
q
˙
=
∑
k
=
1
M
λ
k
v
k
(
v
k
+
q
)
-
B
∑
k
′
≠
k
(
v
k
′
+
q
)
2
(
v
k
+
q
)
v
k
-
C
(
q
+
q
)
q
+
F
(
t
)
,
where q is the status vector of input pattern with initial value q
0, λ
k is attention parameter, v
k is prototype pattern vector, and v
k
+ is the adjoint vector of v
k that satisfies
(13)
(
v
k
+
,
v
k
′
T
)
=
v
k
+
·
v
k
′
T
=
δ
k
k
′
.Corresponding dynamic equation of order parameters is(14)
ξ
˙
k
=
λ
k
ξ
k
-
B
∑
k
′
≠
k
ξ
k
′
2
ξ
k
-
C
|
∑
k
′
=
1
M
ξ
k
′
2
|
ξ
k
.Haken has proved that whenλ
k
=
c
(
c
>
0
), the largest initial order parameter will win and the network will then converge.We firstly introduce the synergetic theory to exon recognition; an exon recognition algorithm based on synergetic neural network is shown in Figure4.Figure 4
Exon recognition based on synergetic neural network.We use synergetic neural network andN equal method to quickly determine the initial exon region, as shown in Algorithm 1.Algorithm 1:Determination of initial exon region based on synergetic neural network.
(1) LetS is a given gene sequence, S
start and S
end are the beginning and end of the
sequence respectively,T
0 is throdthod of spectral values;
(2) UsingZ_Curve mapping converted gene sequence to the corresponding numeric sequence;
(3) Using fast Fourier transform  to get spectral valuesR
1 and R
2 according to the formula (8);
(4) Calculating gene sequence order parameter:
ξ
1
=
R
1
R
1
+
R
2,  ξ
2
=
R
2
R
1
+
R
2;
(5) Setting network parameterλ
k and B
,
C;
(6) Order parameter evolution according to formula (14);
(7) Ifξ
1>T
0 and  ξ
2>T
0, then [
S
start
,
S
end
] is recorded as a possible interal, and S is divided
equally inton interals S
1
,
S
2, …,  S
n, Repeat step 1 to step 7;
(8) End.


## 4.2. Get Precise Exon Intervals Using Adaptive Smoothing Window

We can obtain several possible exon intervals by Algorithm1. In this section, we propose an adaptive sliding window algorithm to get more accurate intervals, as shown in Algorithm 2.Algorithm 2:Precise exon regions based on adaptive smoothing window.
(1) LetW is a given gene sequence, W
start and W
end are the beginning and the end of
the sequence respectively;
(2) UsingZ_Curve mapping converted gene sequence [
W
start
,
W
end
] to the
corresponding numeric sequence;
(3) Using fast Fourier transform  to get spectral values;
(4) Calculating gene sequence order parameter:
ξ
1
=
R
1
R
1
+
R
2,   ξ
2
=
R
2
R
1
+
R
2;
(5) Order parameter evolution according to formula (14);
(6) Ifξ
1>T
0, ξ
2>T
0 and W
start
+
γ
<
W
end
-
γ, Then W
start
=
W
start
+
γ,
W
end
=
W
end
-
γ,
Repeat step 2 to step 6;
(7) Output the final interval[
W
start
,
W
end
].


## 4.3. Parameter Optimization Based on Artificial Fish Swarm Algorithm

The parametersT
0 and γ directly influence the performance of exon recognition. The adjustment of the parameters is a global behaviour and has no general research theory to control the parameters in the recognition process at present. In this section, artificial fish swarm algorithm is used to search the global optimum parameters (
T
0
,
γ
) in the corresponding parameter space.The parameter optimization based on artificial fish swarm algorithm is shown as Algorithm3.Algorithm 3:Parameter optimization based on artificial fish swarm algorithm.
(1) Initialize the parameters of artificial fish, such ass
t
e
p, v
i
s
u
a
l, the number of exploratory,
maximum number of iterations, and randomly generatedn fishes;
(2) Set bulletin board to record the current status of each fish, and select the optimal value;
(3) Implementation of prey behavior, swarm behavior and follow behavior;
(4) Optimal value in bulletin board is updated;
(5) If termination condition is satisfied, output the result; otherwise return to step 2.


## 5. Experiment

### 5.1. Data Description

In our experiments, we use some gene sequences provided by Chinese Graduate Mathematical Contest in Modeling. Chinese graduate Mathematical Contest in modeling is aimed at improving the students’ comprehensive abilities of mathematical modeling and computer to solve practical problems. From different points of view, the integrated use of a variety of mathematical methods established the mathematical model of the characteristic.We selected 100 human gene sequences, 100 rodent gene sequences (includingMus musculus and Sewer rat), and 200 mammalian gene sequences for testing. The signal-to-noise ratios of the sequences are gotten by SPSS statistical analysis software, as shown in Table 2.Table 2
The signal-to-noise ratio of four different gene sequences.
Gene categories
Exon
Intron
Number
R-mean
Variance
Number
R-mean
Variance
Human
35
3.02
3.071
26
0.82
0.533
Mus musculus
357
2.46
2.508
275
0.68
0.414
Sewer rat
45
3
5.233
35
0.83
0.624
Mammalian
827
2.72
6.243
626
0.67
0.394From Table2, we can find out that the difference between SNR standard deviation of exons is greater than SNR standard deviation of introns.At the same time, we analyze the SNR distribution of exons and introns of 200 mammalian gene sequences, as shown in Figure5 and Figure 6.Figure 5
The SNR distribution of 200 mammalian exons.Figure 6
The SNR distribution of 200 mammalian introns.From Figure5 and Figure 6, we can see that the mammalian introns are mostly less than 2, while exons are mostly distributed in the range of [
0,2
], which accounts for 55.38%. Therefore, it is unreasonable to set SNR threshold of different categories as fixed value. How to accurately determine SNR threshold of each kind of biological gene has important significance.


### 5.2. Experiment Results

Suppose that sensitivityS
N
=
T
P
/
(
T
p
+
F
N
) and specificity S
P
=
T
N
/
(
T
N
+
F
P
), where T
P is the number of exons which are correctly identified, T
N is the number of introns which are correctly identified, F
P is the number of exons which are not correctly identified, and F
N is the number of introns which are not correctly identified. Then we can compute the accurate rate A
c
=
(
S
N
+
S
P
)
/
2.For comparison, we use four strategies.(1)
Baseline: automatic recognition algorithm with thresholdR
0
=
2.
(2)
Bootstrap: the threshold selection algorithm based on bootstrap method.
(3)
SNN: exon recognition based on synergetic neural network.
(4)
SNN + AFSA: two-stage exon recognition model based on synergetic neural network and artificial fish swarm algorithm.The testing performance of Baseline is shown as in Table3.Table 3
The testing performance of Baseline.
Gene categories
T
P
F
N
S
N
T
N
F
P
S
P
A
c
Human
17
18
0.485
24
2
0.923
0.71
Mus musculus
146
211
0.409
271
4
0.985
0.70
Sewer rat
17
28
0.378
31
4
0.886
0.63
Mammalian
369
458
0.446
621
5
0.992
0.72The experiments showed that when the exon length is short, the recognition accuracy rate is low. In the short gene coding sequence, 3-base periodicity is not absolutely satisfied.In our experiments, we complete a two-stage exon recognition model based on synergetic neural network and artificial fish swarm algorithm. The parameter settings of artificial fish swarm algorithm are shown in Table4.Table 4
The parameter settings of artificial fish swarm algorithm.
Algorithm
Fish number
Visual
Delta
Step
Number of iterations
AFSA
100
2.85
9
1
60In the experiment, we set the recognition accuracy rate as score function.The testing performance of SNN + AFSA is shown as in Table5.Table 5
The test performance of SNN + AFSA.
Gene categories
T
P
F
N
S
N
T
N
F
P
S
P
A
c
Human
30
5
0.857
19
7
0.731
0.79
Mus musculus
295
62
0.826
220
55
0.80
0.81
Sewer rat
36
9
0.80
28
7
0.80
0.80
Mammalian
630
197
0.762
607
19
0.97
0.87Table5 shows that the two-stage exon recognition algorithm improves precision compared to the Baseline system. Experiments also indicate that the improved model has a more powerful global exploration ability and a reasonable convergence speed.The accurate rateA
c of different methods is shown in Table 6.Table 6
The test performance comparison among different methods.
Gene categories
Baseline
Bootstrap
SNN
SNN + AFSA
Human
0.71
0.76
0.78
0.79
Mus musculus
0.70
0.78
0.80
0.81
Sewer rat
0.63
0.75
0.77
0.80
Mammalian
0.72
0.84
0.85
0.87Detailed comparisons of results are given in Table6. Experimental results show that the proposed model SNN and SNN + AFSA have good performance for exon recognition. The accurate rate we obtained for all four corpuses is comparable to the state-of-the-art systems, such as Baseline and bootstrap method. Through the evaluating of order parameter equation of SNN to obtain the best threshold, we can further improve the exon recognition performance.At the same time, we can see that the performance of SNN + AFSA is better than SNN model. This is because the attention parameters are very important for SNN and optimization algorithm is essential for better performance. Experimental results show that improved AFSA algorithm has better global and local parameter searching capabilities and thus a better recognition result.It is worth noting that experimental results show that run times of our proposed model reduced with good speedup ratio compared with Baseline. Further studies show that the procedure exhibits data parallelism, so it can be effectively parallelized by running it concurrently. In the future work, we will utilize parallel processing techniques for rapid exon recognition based on SNN to further reduce the run time.


## 5.1. Data Description

In our experiments, we use some gene sequences provided by Chinese Graduate Mathematical Contest in Modeling. Chinese graduate Mathematical Contest in modeling is aimed at improving the students’ comprehensive abilities of mathematical modeling and computer to solve practical problems. From different points of view, the integrated use of a variety of mathematical methods established the mathematical model of the characteristic.We selected 100 human gene sequences, 100 rodent gene sequences (includingMus musculus and Sewer rat), and 200 mammalian gene sequences for testing. The signal-to-noise ratios of the sequences are gotten by SPSS statistical analysis software, as shown in Table 2.Table 2
The signal-to-noise ratio of four different gene sequences.
Gene categories
Exon
Intron
Number
R-mean
Variance
Number
R-mean
Variance
Human
35
3.02
3.071
26
0.82
0.533
Mus musculus
357
2.46
2.508
275
0.68
0.414
Sewer rat
45
3
5.233
35
0.83
0.624
Mammalian
827
2.72
6.243
626
0.67
0.394From Table2, we can find out that the difference between SNR standard deviation of exons is greater than SNR standard deviation of introns.At the same time, we analyze the SNR distribution of exons and introns of 200 mammalian gene sequences, as shown in Figure5 and Figure 6.Figure 5
The SNR distribution of 200 mammalian exons.Figure 6
The SNR distribution of 200 mammalian introns.From Figure5 and Figure 6, we can see that the mammalian introns are mostly less than 2, while exons are mostly distributed in the range of [
0,2
], which accounts for 55.38%. Therefore, it is unreasonable to set SNR threshold of different categories as fixed value. How to accurately determine SNR threshold of each kind of biological gene has important significance.


## 5.2. Experiment Results

Suppose that sensitivityS
N
=
T
P
/
(
T
p
+
F
N
) and specificity S
P
=
T
N
/
(
T
N
+
F
P
), where T
P is the number of exons which are correctly identified, T
N is the number of introns which are correctly identified, F
P is the number of exons which are not correctly identified, and F
N is the number of introns which are not correctly identified. Then we can compute the accurate rate A
c
=
(
S
N
+
S
P
)
/
2.For comparison, we use four strategies.(1)
Baseline: automatic recognition algorithm with thresholdR
0
=
2.
(2)
Bootstrap: the threshold selection algorithm based on bootstrap method.
(3)
SNN: exon recognition based on synergetic neural network.
(4)
SNN + AFSA: two-stage exon recognition model based on synergetic neural network and artificial fish swarm algorithm.The testing performance of Baseline is shown as in Table3.Table 3
The testing performance of Baseline.
Gene categories
T
P
F
N
S
N
T
N
F
P
S
P
A
c
Human
17
18
0.485
24
2
0.923
0.71
Mus musculus
146
211
0.409
271
4
0.985
0.70
Sewer rat
17
28
0.378
31
4
0.886
0.63
Mammalian
369
458
0.446
621
5
0.992
0.72The experiments showed that when the exon length is short, the recognition accuracy rate is low. In the short gene coding sequence, 3-base periodicity is not absolutely satisfied.In our experiments, we complete a two-stage exon recognition model based on synergetic neural network and artificial fish swarm algorithm. The parameter settings of artificial fish swarm algorithm are shown in Table4.Table 4
The parameter settings of artificial fish swarm algorithm.
Algorithm
Fish number
Visual
Delta
Step
Number of iterations
AFSA
100
2.85
9
1
60In the experiment, we set the recognition accuracy rate as score function.The testing performance of SNN + AFSA is shown as in Table5.Table 5
The test performance of SNN + AFSA.
Gene categories
T
P
F
N
S
N
T
N
F
P
S
P
A
c
Human
30
5
0.857
19
7
0.731
0.79
Mus musculus
295
62
0.826
220
55
0.80
0.81
Sewer rat
36
9
0.80
28
7
0.80
0.80
Mammalian
630
197
0.762
607
19
0.97
0.87Table5 shows that the two-stage exon recognition algorithm improves precision compared to the Baseline system. Experiments also indicate that the improved model has a more powerful global exploration ability and a reasonable convergence speed.The accurate rateA
c of different methods is shown in Table 6.Table 6
The test performance comparison among different methods.
Gene categories
Baseline
Bootstrap
SNN
SNN + AFSA
Human
0.71
0.76
0.78
0.79
Mus musculus
0.70
0.78
0.80
0.81
Sewer rat
0.63
0.75
0.77
0.80
Mammalian
0.72
0.84
0.85
0.87Detailed comparisons of results are given in Table6. Experimental results show that the proposed model SNN and SNN + AFSA have good performance for exon recognition. The accurate rate we obtained for all four corpuses is comparable to the state-of-the-art systems, such as Baseline and bootstrap method. Through the evaluating of order parameter equation of SNN to obtain the best threshold, we can further improve the exon recognition performance.At the same time, we can see that the performance of SNN + AFSA is better than SNN model. This is because the attention parameters are very important for SNN and optimization algorithm is essential for better performance. Experimental results show that improved AFSA algorithm has better global and local parameter searching capabilities and thus a better recognition result.It is worth noting that experimental results show that run times of our proposed model reduced with good speedup ratio compared with Baseline. Further studies show that the procedure exhibits data parallelism, so it can be effectively parallelized by running it concurrently. In the future work, we will utilize parallel processing techniques for rapid exon recognition based on SNN to further reduce the run time.


## 6. Conclusions

In the paper, we proposed a two-stage exon recognition model based on synergetic neural network and artificial fish swarm algorithm. Experiments show that the proposed model can improve the precision of exon recognition.We got the following conclusions.(1)
The exon recognition procedure can be viewed as the competition progress of many order parameters. The proposed model based on synergetic neural network andN equal method can quickly determine the exon intervals.
(2)
Artificial fish swarm algorithm has both global and local search ability and can effectively choose the parameters of our proposed model.
(3)
UsingN equal algorithm to obtain exon intervals may still miss some intervals which are in the middle; we will further improve the algorithm or use different pattern recognition algorithm in the future.It must be noted that, although we have made some efforts to explore the intelligent exon recognition algorithm in this paper. But due to the special nature of life science itself, there are many problems such as how to accurately determine that the exon interval needs further study. But we believe that with the development of social progress and technology, gene identification technology will become increasingly perfect; we expect it can bring gospel to manking in the near future.



---

*Source: 503132-2014-03-25.xml*