In this section, we briefly explain the proposed model, feature encoding techniques, and baseline models.
Feature encoding techniques
A DNA sequence is comprised of the A, C, G, and T nucleotides. To perform computational operations, the sequence must be translated into a numerical representation. Feature encoding schemes play a vital role in creating optimal predictors. The input size should be the same for all sequences. We apply the zero-filled method to make every DNA sequence with an equal length of 99 bp. This technique was previously applied by DPProm (Wang et al., 2022). In this study, we find the best feature encoding technique among the 10 different techniques. The details of each encoding scheme are presented below.
One-hot feature encoding
One-hot encoding techniques are used by many state-of-the-art bioinformatics tools (Umarov and Solovyev, 2017; Liu and Li, 2019; Shujaat et al., 2021; Kim et al., 2022). Each nucleotide in a DNA sequence is represented by a four-dimensional vector, which is a vector of zeros with a single one. Nucleotide A is encoded as (1,0,0,0), C (0,1,0,0), G (0,0,1,0), and T (0, 0,0,1). Each DNA sequence can be represented by a (99,4) two-dimensional vector.
Nucleotide chemical property feature encoding
The chemical characteristics of the four DNA nucleic acids differ (Jeong et al., 2014). Nucleotides are classified into three types based on their chemical characteristics: hydrogen-bond strength, base type, and functional groups. Purines with two rings are represented by the letters A and G, whereas pyrimidines with one ring are represented by the letters C and T. The hydrogen bonds between A and T are weak, whereas the hydrogen bonds between C and G are strong. In terms of functional groups, the amino group includes A and C, whereas the keto group includes G and T. Each DNA sequence is represented by a three-dimensional vector (b, c, p) based on chemical properties, where
n
i
denotes the nucleotide n at position i; hence, b, c, and, p were computed as follows:
b
i
=
{
1
if
n
i
∈
{
A
,
C
}
0
if
n
i
∈
{
G
,
T
}
,
c
i
=
{
1
if
n
i
∈
{
A
,
G
}
0
if
n
i
∈
{
C
,
T
}
,
p
i
=
{
1
if
n
i
∈
{
A
,
T
}
0
if
n
i
∈
{
C
,
G
}
Dinucleotide-based auto-cross covariance feature encoding
DACC is a combination of dinucleotide-based auto-covariance (DAC) and dinucleotide-based cross covariance (DCC) encoding. DAC computes the correlation of the same physicochemical index between two dinucleotides separated by a lag distance along the sequence. DAC is calculated as:
DAC
(
u
,lag
)
=
∑
i
=
1
L
−
lag
−
1
(
(
P
u
(
R
i
R
i
+
1
)
−
P
↼
u
)
(
P
u
(
R
i
+
lag
R
i
+
lag
+
1
)
−
P
↼
u
)
/
(
L
−
lag
−
1
)
)
where
u
,
L
represent the physicochemical index and length of the sequence, respectively, and the physicochemical index
u
for the dinucleotide
(
R
i
R
i
+
1
)
at position
i
is expressed numerically as
P
u
(
R
i
R
i
+
1
)
.
P
↼
u
represents the average value of the physicochemical index
u
along the whole sequence, and is calculated as:
P
↼
u
=
∑
j
=
1
L
−
1
P
u
(
R
j
R
j
+
1
)
/
(
L
−
1
)
The DAC feature vector has a dimension of
N
×
LAG
, where LAG is the maximum lag (lag = 1, 2,…, LAG) and N is the total number of physicochemical indices. DCC computes the correlation of two different physicochemical indices between two dinucleotides along the sequence separated by lag nucleic acids. Mathematically, DCC can be represented as
DCC
(
u
1
,
u
2
,lag
)
=
∑
i
=
1
L
−
lag
−
1
(
P
u
1
(
R
i
R
i
+
1
)
−
P
↼
u
1
)
(
P
u
2
(
R
i
+
lag
R
i
+
lag
+
1
)
−
P
↼
u
2
)
/
(
L
−
lag
−
1
)
where
u
1
,
u
2
and
L
represent the physicochemical indices and length of the nucleotide sequence, respectively,
P
u
1
(
R
i
R
i
+
1
)
is the numerical value of the physicochemical index
u
1
for the dinucleotide
(
R
i
R
i
+
1
)
at position
i
, and
P
↼
u
a
is the average value for the physicochemical index
u
a
along the whole sequence, calculated as:
P
↼
u
a
=
∑
j
=
1
L
−
1
P
u
a
(
R
j
R
j
+
1
)
/
(
L
−
1
)
The DCC feature vector has dimensions of
N
×
(
N
−
1
)
×
LAG
, where LAG is the maximum lag (lag = 1, 2,.., LAG) and N is the total number of physicochemical indices. Thus, the dimension of the DACC encoding is N × N × LAG, where N is the number of physicochemical indices and LAG is the maximum lag (lag = 1, 2, …, LAG).
Pseudo dinucleotide composition
PseDNC encoding incorporates both contiguous local and global sequence order information into a feature vector of the nucleotide sequence. PseDNC is mathematically defined as follows:
S
=
[
s
1
,
s
2
,
…
,
s
16
,
s
16
+
1
,
…
,
s
16
+
1
,
…
,s
16
+
λ
]
T
Whereas:
s
k
=
{
f
k
∑
i
=
1
16
f
i
+
w
∑
j
=
1
λ
θ
j
,
(
1
≤
k
≤
16
)
w
θ
k
−
16
∑
i
=
1
16
f
i
+
w
∑
j
=
1
λ
θ
j
,
(
17
≤
k
≤
16
+
λ
)
where
f
k
(k = 1, 2,…, 16) is the normalized frequency of dinucleotide occurrence in the nucleotide sequence,
λ
represents the highest counted rank (or tie) of the correlation along the nucleotide sequence, w is the weight factor ranging from 0 to 1, and
θ
j
(j = 1,2,…,
λ
) is the jth correlation factor and is defined as
{
θ
1
=
1
L
−
2
∑
i
=
1
L
−
2
θ
(
R
i
R
i
+
1
,
R
i
+
1
R
i
+
2
)
θ
1
=
1
L
−
2
∑
i
=
1
L
−
3
θ
(
R
i
R
i
+
1
,
R
i
+
2
R
i
+
3
)
θ
1
=
1
L
−
2
∑
i
=
1
L
−
4
θ
(
R
i
R
i
+
1
,
R
i
+
3
R
i
+
3
)
(
λ
<
L
)
…
θ
λ
=
1
L
−
1
−
λ
∑
i
=
1
L
−
1
−
λ
θ
(
R
i
R
i
+
1
,
R
i
+
λ
R
i
+
λ
+
1
)
The correlation function is given as follows:
θ
(
R
i
R
i
+
1
,
R
j
+
1
R
j
+
1
)
=
1
μ
∑
u
=
1
μ
[
P
μ
(
R
i
R
i
+
1
)
−
P
μ
(
R
j
R
j
+
1
]
2
where physicochemical indices are represented by μ,
P
μ
(
R
i
R
i
+
1
)
measures are the numerical values of the u-th (u = 1, 2, …, μ) physicochemical index of the dinucleotide
R
i
R
i
+
1
at position
i
and
P
μ
(
R
j
R
j
+
1
)
represents the corresponding value of the dinucleotide
R
j
R
j
+
1
at position
j
.Pseudo k-tupler composition (PseKNC).
PseKNC encoding uses a k-tuple nucleotide composition defined as
D
=
[
d
1
,
d
2
,
…
,
d
4
k
,
d
4
k
+
1
,
…
,
d
4
k
+
λ
]
T
Whereas:
{
f
u
∑
i
=
1
4
k
f
i
+
w
∑
j
=
1
λ
θ
j
,
(
1
≤
u
≤
4
)
w
θ
u
−
4
k
∑
i
=
1
4
k
f
i
+
w
∑
j
=
1
λ
θ
j
,
(
4
k
≤
u
≤
4
k
+
λ
)
where
λ
is the total number of ranks of correlations along a nucleotide sequence,
f
u
(
u
=
1
,
2
,
…
,
4
k
)
is the frequency ofoligonucleotides normalized to
∑
i
=
1
4
k
f
i
=
1
, w is the factor, and
θ
j
is defined as follows:
θ
j
=
1
L
−
j
−
1
∑
i
=
1
L
−
j
−
1
Θ
(
R
i
R
i
+
1
,
R
i
+
j
R
i
+
j
+
1
)
,
(
j
=
1
,,,;
2
,,,;
…
,,,;
λ
,,,;
λ
<
L
)
The correlation function is defined as:
Θ
(
R
i
R
i
+
1
,
R
i
+
j
R
i
+
j
+
1
)
=
1
μ
∑
v
=
1
μ
[
P
v
(
R
i
R
i
+
1
)
−
P
v
(
R
i
+
j
R
i
+
j
+
1
)
]
2
where
μ
represents the physicochemical index.
P
v
(
R
i
R
i
+
1
)
is a numerical value v-th (v = 1, 2, …, μ). The physicochemical index of dinucleotide
(
R
i
R
i
+
1
)
at position i and
P
v
(
R
i
+
j
R
i
+
j
+
1
)
represents the corresponding value of dinucleotide
(
R
i
+
j
R
i
+
j
+
1
)
at position i + j.
Electron-ion interaction pseudopotentials of trinucleotide
The values of nucleotides A, G, C, and T electron-ion interaction pseudopotentials (EIIP) were determined as previously described using Nair (Lavigne et al., 2004; A: 0.1260, C: 0.1340, G: 0.0806, T: 0.1335). Nucleotides in the DNA sequence are directly represented by EIIP using the EIIP value. EIIPA, EIIPT, EIIPG, and EIIPC represent the EIIP values of nucleotides A, T, G, and C, respectively, in PseEIIP encoding. A feature vector is created using the mean EIIP value of the trinucleotides in each sample, as follows:
V
=
[
E
I
I
P
A
A
A
·
f
A
A
A
,
E
I
I
P
A
A
C
·
f
A
A
C
,
…
,
E
I
I
P
T
T
T
·
f
T
T
T
]
Parallel correlation pseudo dinucleotide composition
Similar to PseDNC, PCPseDNC encoding differs in that it uses 38 default physiochemical indices for DNA instead of the six indices used in PseDNC encoding. Supplementary Table S2 in Supplementary file presents a list of 38 physicochemical indices.
Parallel correlation pseudo trinucleotide composition
PCPseTNC encoding is described as:
S
=
[
s
1
,
s
2
,
…
,
s
64
,
s
64
+
1
,
…
,s
64
+
λ
]
T
Whereas:
s
k
=
{
f
k
∑
i
=
1
64
f
i
+
w
∑
j
=
1
λ
θ
j
,
(
1
≤
k
≤
64
)
w
θ
k
−
64
∑
i
=
1
64
f
i
+
w
∑
j
=
1
λ
θ
j
,
(
65
≤
k
≤
64
+
λ
)
where
f
k
(k = 1, 2,…, 64) is the normalized frequency of dinucleotide occurrence in the nucleotide sequence,
λ
represents the highest counted rank (or tie) of the correlation along the nucleotide sequence, w is the weight factor ranging from 0 to 1, and
θ
j
(j = 1,2,…,
λ
) is the jth correlation factor and is defined as:
{
θ
1
=
1
L
−
3
∑
i
=
1
L
−
3
Θ
(
R
i
R
i
+
1
R
i
+
2
,
R
i
+
1
R
i
+
2
R
i
+
3
)
θ
2
=
1
L
−
4
∑
i
=
1
L
−
4
Θ
(
R
i
R
i
+
1
R
i
+
2
,
R
i
+
2
R
i
+
3
R
i
+
4
)
θ
3
=
1
L
−
5
∑
i
=
1
L
−
5
Θ
(
R
i
R
i
+
1
R
i
+
2
,
R
i
+
3
R
i
+
4
R
i
+
5
)
(
λ
<
L
)
θ
λ
=
1
L
−
2
−
λ
∑
i
=
1
L
−
2
−
λ
Θ
(
R
i
R
i
+
1
R
i
+
2
,
R
i
+
λ
R
i
+
λ
+
1
R
i
+
λ
+
2
)
The correlation function is defined as:
Θ
(
R
i
R
i
+
1
R
i
+
2
,
R
j
+
1
R
j
+
1
R
j
+
2
)
=
1
μ
∑
u
=
1
μ
[
P
u
(
R
i
R
i
+
1
R
i
+
2
)
−
P
u
(
R
j
R
j
+
1
R
j
+
2
)
]
2
where physicochemical indices are represented by μ,
P
μ
(
R
i
R
i
+
1
R
i
+
2
)
measures are the numerical values of the u-th (u = 1, 2, …, μ) physicochemical index of the dinucleotide
R
i
R
i
+
1
R
i
+
2
at position
i
and
P
μ
(
R
j
R
j
+
1
R
j
+
2
)
represents the corresponding value of the dinucleotide
R
j
R
j
+
1
R
j
+
2
at position
j
.
Moran correlation
The distribution of amino acid characteristics along the sequence is used to create autocorrelation descriptors (Horne, 1988; Feng and Zhang, 2000; Sokal and Thomson, 2006). The amino acid properties used here are different types of amino acid indices retrieved from the AAindex Database (Kawashima et al., 2008) available at http://www.genome.jp/dbget/aaindex.html.
kmer
DNA sequences are represented as the occurrence frequencies of k adjacent nucleic acids in the kmer descriptor, which has been effectively used for human gene regulatory sequence prediction. The kmer descriptor (k = 3) is calculated as follows:
f
(
t
)
=
N
(
t
)
N
,
t
ε
{
A
A
A
,
A
A
C
,
A
A
G
,
…
,
T
T
T
}
where
N
(
t
)
represents the number of kmer types (t) and N is the length of the sequence.