# Measuring Similarity among Protein Sequences Using a New Descriptor

Authors: Mervat M. Abo-Elkhier; Marwa A. Abd Elwahaab; Moheb I. Abo El Maaty
Journal: BioMed Research International
 (2019)

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## Abstract

The comparison of protein sequences according to similarity is a fundamental aspect of today’s biomedical research. With the developments of sequencing technologies, a large number of protein sequences increase exponentially in the public databases. Famous sequences’ comparison methods are alignment based. They generally give excellent results when the sequences under study are closely related and they are time consuming. Herein, a new alignment-free method is introduced. Our technique depends on a new graphical representation and descriptor. The graphical representation of protein sequence is a simple way to visualize protein sequences. The descriptor compresses the primary sequence into a single vector composed of only two values. Our approach gives good results with both short and long sequences within a little computation time. It is applied on nine beta globin, nine ND5 (NADH dehydrogenase subunit 5), and 24 spike protein sequences. Correlation and significance analyses are also introduced to compare our similarity/dissimilarity results with others’ approaches, results, and sequence homology.


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## Body

## 1. Introduction

Information encoded in the genome of any organism plays a central role in defining the life of that organism. The nucleotide sequence that forms any gene is translated into its corresponding amino acid sequence. This sequence of amino acids becomes functional only when it adopts its tertiary structure. Experimental methods such as X-ray diffraction and nuclear magnetic resonance are considered authoritative ways for obtaining proteins’ structure and function. These experimental methods are very expensive and time consuming. Therefore, computational methods for predicting protein structure have become very useful. Proteins with similar sequences are usually homologous, typically displaying similar 3D structure and function.Sequence alignment is the first step of 3D structure prediction for protein sequences. Alignment approaches are classified into alignment-based and alignment-free methods. BLAST (basic local alignment search tool) and ClustalW are the most widely used computer programs for alignment-based approaches [1–3]. Results of these programs provide an approximate solution to the protein alignment problem. On the other hand, many alignment-free approaches are proposed for sequence comparison. Most biological sequence analysis methods still have weaknesses, including having low precision and being time consuming [4, 5].Similarity/dissimilarity analysis of biological sequences is used to extract information stored in the protein sequence. Many mathematical schemes have been proposed to this end. Graphical representations of biological sequences identify the information content of any sequence to help biologists choose another complex theoretical or experimental method. Graphical representation provides not only visual qualitative inspection of gene data but also mathematical characterizations through objects such as matrices.Some 2D and 3D graphical representations are created by selecting a geometrical object that is used to describe nucleic acid bases or residues [6–10]. Others are based on assigning vectors of two or three components to nucleic acid bases or amino acids [11–17]. Adjacency matrices are also introduced in some articles [18–21], where an exact solution is obtained to the protein alignment problem. Additional methods use discrete Fourier transform (DFT) in which DNA sequences are mapped into four binary indicator sequences, followed by the application of DFT on these indicator sequences to transform them into a frequency domain [22, 23]. Dynamic representation is used to remove degeneracies in the previously mentioned approaches [24–31]. Another method is based on the simplified pulse-coupled neural network (S-PCNN) and Huffman coding where the triplet code was used as a code bit to transform DNA sequence into numerical sequence [32].In this study, we introduce a new alignment-free method for protein sequences. Each amino acid in the protein sequence is represented by a number, and a new 2D graphical representation is suggested. A new descriptor is introduced, comprising a vector composed of the mean and standard deviation of the total numbers of each protein sequence (A¯t, SAt). Our graphical representation eliminates degeneracy and has no loss of information. It is suitable for both short and long sequences. As a proof of concept, our approach is applied on nine beta globin protein sequences and nine ND5 (NADH dehydrogenase subunit 5) protein sequences. It can be applied on any sequence length with the same efficiency. Correlation and significance analyses are introduced among our results, along with PID% [15] and ClustalW [33] to demonstrate the utility of our approach.


## 2. Dataset, Technology, and Tools

All the protein sequences used in this study were downloaded from The National Center for Biotechnology Information (NCBI) “https://www.ncbi.nlm.nih.gov” as FASTA files. These FASTA files are imported into Wolfram Mathematica 8 where all the results and figures are produced. They are nine beta globin, nine ND5 (NADH dehydrogenase subunit 5), and 24 coronaviruses protein sequences as illustrated in Tables 1–3, respectively. These datasets are selected to be different in length.Table 1
Nine beta globin protein sequences.
No.
Species
ID
Length
1
Gorilla
CAA43421
121
2
Chimp
CAA26204
125
3
Human
AAA16334
147
4
Rat
CAA29887
147
5
Mouse
CAA24101
147
6
Gutta
ACH46399
147
7
Duck
CAA33756
147
8
Gallus
CAA23700
147
9
Opossum
AAA30976
147Table 2
Nine ND5 protein sequences.
No.
Species
ID
Length
1
Human
AP_000649
603
2
Gorilla
NP_008222
603
3
Common chimpanzee
NP_008196
603
4
Pygmy chimpanzee
NP_008209
603
5
Fin whale
NP_006899
606
6
Blue whale
NP_007066
606
7
Rat
AP_004902
610
8
Mouse
NP_904338
607
9
Opossum
NP_007105
602Table 3
The 24 coronaviruses protein sequences.
No.
Access no.
Abbreviation
Length
Class
1
CAB91145
TGEVG
1447
I
2
NP058424
TGEV
1447
I
3
AAK38656
PEDVC
1383
I
4
NP598310
PEDV
1383
I
5
NP937950
HCoVOC43
1361
II
6
AAK83356
BCoVE
1363
II
7
AAL57308
BCoVL
1363
II
8
AAA66399
BCoVM
1363
II
9
AAL40400
BCoVQ
1363
II
10
AAS00080
IBVC
1169
III
11
NP 040831
IBV
1162
III
12
AAS10463
GD03T0013
1255
SARS-CoV
13
AAU93318
PC4127
1255
SARS-CoV
14
AAV49720
PC4137
1255
SARS-CoV
15
AAU93319
PC4205
1255
SARS-CoV
16
AAU04646
civet007
1255
SARS-CoV
17
AAU04649
civet010
1255
SARS-CoV
18
AAV91631
A022
1255
SARS-CoV
19
AAP51227
GD01
1255
SARS-CoV
20
AAS00003
GZ02
1255
SARS-CoV
21
AAP30030
BJ01
1255
SARS-CoV
22
AAP50485
FRA
1255
SARS-CoV
23
AAP41037
TOR2
1255
SARS-CoV
24
AAQ01597
TaiwanTC1
1255
SARS-CoV


## 3. 2D Graphical Representation

A new 2D graphical representation is introduced. Each amino acid in any protein sequence is represented by the suggested intensityYxi and intensity level Axi. The intensity Yxi of each amino in the sequence depends on its abundance and location in the different sequences. It is calculated using (1)Yxi=fxi,where fx is the frequency of amino acid x in the sequence, number of times of x/N. N is the protein sequence length, number of residues in protein sequence. i is the position of each amino acid x in a sequence.Then, the intensity levelAxi of each amino acid (x) in the sequence is calculated by using the natural logarithm function as in (2)Axi=10lnYxiN,if the elementxexists at positioni,0,if the elementxdoes not exist at positioni.Therefore, each amino acid has its own intensity level which is a vector ofN elements according to equation (2). Finally, the combined intensity level of the protein sequence Ati is obtained by the summation of the 20 intensity levels’ vectors Axi of the protein sequence by using equation (3). The combined intensity level Ati is also a vector of N elements:(3)Ati=∑x=120Axi.Each amino acid has its own graph. Now, twenty graphs are obtained for each sequence of the 20 different amino acids. The combined graph is obtained by combining these 20 graphs within a single graph. This combined intensity level is our new 2D graphical representation.Our approach is first applied on two short segments of protein from “yeastSaccharomyces cerevisiae”:Protein I: “WTFESRNDPAKDPVILWLNGGPGCS‐SLTGL”Protein II: “WFFESRNDPANDPIILWLNGGPGCS‐SFTGL”These two short proteins consist of 30 amino acids each. The two sequences are different in amino acids at positions 2, 11, 14, and 27. The valuesYxi and Axi for each amino acid in the two sequences are calculated. For protein I, the G amino acid is repeated four times in the protein sequence. These four repeats occur in positions 20, 21, 23, and 29. The frequency, fG, equals (4/30). By substituting in equations (1) and (2), the results of YGi and AGi are presented in Table 4.Table 4
The intensity and intensity level vectors of the two short segments of protein from “yeastSaccharomyces cerevisiae” protein sequences.
i
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Y
G
i
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
A
G
i
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
i
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Y
G
i
0
0
0
0
2.67
2.80
0
3.07
0
0
0
0
0
3.87
0
A
G
i
0
0
0
0
24.2
23.7
0
22.8
0
0
0
0
0
20.5
0By summing the values ofAxi for all amino acids in protein I, the total value of Ati is obtained, as shown in Figure 1(a). The position i of each amino acid is located on the x-axis, and the total intensity level Ati is located on the y-axis. Figures 1(a) and 1(b) show the intensity level of protein I and protein II, respectively. Of note, the two graphs have different Axi values at positions 2, 11, 14, and 27.Figure 1
2D graphical representation of the “combined intensity level” of two short segments of protein of “yeastSaccharomyces cerevisiae”. (a) Protein 1. (b) Protein 2.
(a)
(b)We next apply our approach on nine beta globin and nine ND5 (NADH dehydrogenase subunit 5) protein sequences, which are illustrated in Tables1 and 2. The 2D graphical representation for human, chimpanzee, and opossum beta globin protein sequences is illustrated in Figures 2(a)–2(c), respectively. The 2D graphical representations for fin whale and rat ND5 protein sequences are illustrated in Figures 3(a) and 3(b), respectively.Figure 2
2D graphical representation the “combined intensity level” of beta globin protein sequences. (a) Human, (b) chimpanzee, and (c) opossum.
(a)
(b)
(c)Figure 3
2D graphical representation of “combined intensity level” of ND5 protein sequences. (a) Fin whale and (b) rat.
(a)
(b)We finally apply our approach on 24 coronaviruses protein sequences which are illustrated in Table3. The 2D graphical representation of TGEVG from class I and GD03T0013 from SARS_CoV protein sequences is illustrated in Figures 4(a) and 4(b) respectively.Figure 4
2D graphical representation of “combined intensity level” of TGEVG and GD03T0013 coronaviruses protein sequences. (a) Fin whale and (b) rat.
(a)
(b)


## 4. Protein Sequence Descriptor

Mathematical descriptors help in recognizing major differences among similar protein sequences quantitatively. A new descriptor for protein sequences is suggested, which is a vector composed of the arithmetic meanA¯t and standard deviation SAt of the combined intensity level value Ati of the protein sequence. They are evaluated according to the following equations:(4)At¯=1N∑i=1i=NAti,SAt=1N−1Ati−At¯2.This descriptor compresses the information from primary protein sequences into a single vector composed of only two values. The beta globin, ND5, and coronaviruses protein sequence descriptors are illustrated in Tables5–7, respectively.Table 5
Mean and standard deviation descriptor of beta globin protein sequences.
No.
Species
A
¯
t
SA
t
1
Gorilla
36.803
11.744
2
Chimp
36.912
11.586
3
Human
37.145
11.505
4
Rat
37.721
11.399
5
Mouse
37.695
11.727
6
Gutta
38.046
11.537
7
Duck
38.244
11.399
8
Gallus
38.349
11.169
9
Opossum
38.418
10.944Table 6
Mean and standard deviation descriptor of ND5 protein sequences.
No.
Species
A
¯
t
SA
t
1
Human
37.300
12.267
2
Gorilla
37.338
12.223
3
Pigmy chimpanzee
37.249
12.091
4
Common chimpanzee
37.251
12.277
5
Fin whale
37.540
11.961
6
Blue whale
37.534
12.027
7
Rat
37.385
11.621
8
Mouse
37.328
11.562
9
Opossum
37.558
11.419Table 7
Mean and standard deviation descriptor of the coronaviruses protein sequences.
Abb.
Class no.
Mean
Standard deviation
1
TGEVG
I
38.643
10.9412
2
TGEV
I
38.643
10.9412
3
PEDVC
I
38.452
11.1723
4
PEDV
I
38.452
11.1723
5
HCoVOC43
II
38.703
10.7564
6
BCoVE
II
38.668
10.6803
7
BCoVL
II
38.678
10.6846
8
BCoVM
II
38.698
10.7755
9
BCoVQ
II
38.714
10.7656
10
IBVC
III
38.601
10.6271
11
IBV
III
38.654
10.6458
12
GD03T0013
SARS-CoV
38.833
10.5783
13
PC4127
SARS-CoV
38.838
10.5744
14
PC4137
SARS-CoV
38.832
10.5785
15
PC4205
SARS-CoV
38.838
10.5733
16
civet007
SARS-CoV
38.831
10.587
17
civet010
SARS-CoV
38.833
10.5829
18
A022
SARS-CoV
38.829
10.5892
19
GD01
SARS-CoV
38.821
10.5946
20
GZ02
SARS-CoV
38.824
10.5867
21
BJ01
SARS-CoV
38.816
10.5912
22
FRA
SARS-CoV
38.8189
10.5875
23
TOR2
SARS-CoV
38.8186
10.5932
24
TaiwanTC1
SARS-CoV
38.8176
10.5928Table7 shows that the mean of all 24 coronaviruses is around 38.7 and with a range from 38.601 to 38.838 while their standard deviation varies according to their class. They are divided into four classes. The first four viruses belong to class I. The fifth to the ninth coronaviruses belong to class II. Class III contains the tenth and eleventh viruses. The rest viruses from the 12th to the 24th belong to SARS-CoV. According to our approach, the standard deviation of class I ranges from 10.94 to 11.17. Class II’s standard deviation ranges from 10.68 to 10.77. Class III’s standard deviation has values from 10.6271 to 10.6458. SARS-CoV’s standard deviation almost equals 10.58. The resulting standard deviation values of the 24 coronaviruses classify them correctly to the four classes. The coronaviruses classes’ ranges according to our approach are shown in Figure 5.Figure 5
The four classes of the 24 coronaviruses protein sequences based on their standard deviation of the combined intensity level.


## 5. Similarity/Dissimilarity Analysis

To compare the species’ protein sequences, the Euclidean distance among species’ descriptors is evaluated. For example, the human beta globin protein sequence’s descriptor is (37.145, 11.505) and the chimpanzee beta globin protein sequence’s descriptor is (36.912, 11.586). To measure the degree of similarity between human and chimpanzee, the Euclidean distance between these vectors is evaluated. The similarity/dissimilarity matrices of beta globin and ND5 protein sequences are illustrated in Tables8 and 9, respectively. Table 8 results show that human and chimpanzee sequences are similar. There is also striking similarity between mouse and rat sequences, while human and opossum sequences are obviously dissimilar. Table 9 results show that pigmy chimpanzee, common chimpanzee, human, and gorilla ND5 protein sequences are similar, while the blue whale is similar to the fin whale, and mouse is similar to rat. Similar to the other sequence, human and opossum are still dissimilar. However, our algorithm cannot measure the degree of similarity very well for pigmy chimpanzee. The distance between human and pigmy chimpanzee is 0.1826, while the distance between human and gorilla is 0.0575, as shown in Table 9. The results of both Tables 8 and 9 are approximately comparable to previous reports [13, 15, 21, 33–39].Table 8
Similarity/dissimilarity analysis among nine beta globin protein sequences.
Human
Gorilla
Chimp
Lemur
Mouse
Rat
Opossum
Duck
Gallus
Human
0
0.417
0.246
0.461
0.593
0.586
1.391
1.104
1.25
Gorilla
0
0.192
0.104
0.892
0.980
1.802
1.481
1.649
Chimp
0
0.270
0.795
0.829
1.637
1.344
1.496
Lemur
0
0.870
0.993
1.823
1.479
1.660
Mouse
0
0.329
1.066
0.639
0.860
Rat
0
0.833
0.523
0.669
Opossum
0
0.488
0.236
Duck
0
0.253
Gallus
0Table 9
Similarity/dissimilarity analysis among nine ND5 protein sequences.
Human
Gorilla
P. chimp
C. chimp
F. whale
B. whale
Rat
Mouse
Opossum
Human
0
0.0575
0.1826
0.0503
0.3885
0.3349
0.6509
0.7054
0.8853
Gorilla
0
0.1590
0.1021
0.3311
0.2775
0.6039
0.6617
0.8332
P. chimp
0
0.1855
0.3184
0.2918
0.4890
0.5351
0.7389
C. chimp
0
0.4281
0.3776
0.6689
0.7189
0.9102
F. whale
0
0.0663
0.3737
0.4524
0.5417
B. whale
0
0.4325
0.5092
0.6079
Rat
0
0.0826
0.2656
Mouse
0
0.2705
Opossum
0


## 6. The Phylogenetic Tree of the Protein Sequences Based on Our Method

We got the phylogenetic trees of beta globin and ND5 protein sequences by applying the UPGMA (Unweighted Pair Group Method with Arithmetic Mean). The phylogenetic tree based on Tables8 and 9 of our method is presented in Figures 6 and 7, respectively. Figure 6 proves the utility of our similarity/dissimilarity analysis for beta globin protein sequences. Figure 7 shows our analysis of similarity/dissimilarity of ND5. It is mentioned that our algorithm cannot measure the degree of similarity very well for pigmy chimpanzee with human. This appears of course in Figure 7. The P. chimp branch should be close to C. chimp. Despite this error, the tree shows that human, common chimpanzee, pigmy chimpanzee, and gorilla belong to the same cluster. To check the effect of this error on our algorithm, the results of our algorithm are compared to sequence homology. A correlation and significance analysis is also provided.Figure 6
The phylogenetic tree of the nine beta globin protein sequences based on our method.Figure 7
The phylogenetic tree of the nine ND5 protein sequences based on our method.


## 7. Our Method Compared to PID% and ClustalW Results

The results of our algorithm are compared to the sequence homology by two methods. First, we use the Smith Waterman algorithm to calculate the number of identical residues in each pair of protein sequences [15]. The results of the PID% of nine beta globin sequences are illustrated as a similarity/dissimilarity matrix in Table 10. The larger PID% represents the more similar protein sequences. A correlation and significance analysis is provided to compare our approach in Table 8 with PID% in Table 10. The correlation of the two sets of data is sufficiently strong when the correlation coefficient (r) is greater than 0.7. The negative sign of (r) indicates that when the first data set increases, the second data set decreases. We then assess statistical significance for correlation coefficient values greater than 0.7 to ensure that they likely do not occur by chance. Our sample set is composed of nine protein sequences. Therefore, we use 7 degrees of freedom. A t-value of 2.385 or greater indicates that a less than 0.05 chance of the results occurred by coincidence. The results for correlation coefficients and t-values for our approach are illustrated in Table 11.Table 10
The similarity distance for nine different species of beta globin proteins calculated by the PID%.
Human
Gorilla
Chimp
Lemur
Mouse
Rat
Opossum
Duck
Gallus
Human
100
98.347
93.6
66.667
60.544
59.184
44.898
39.456
38.776
Gorilla
100
95.041
66.942
58.678
55.372
46.281
39.669
38.843
Chimp
100
61.6
55.2
52.
40.
36.8
36.
Lemur
100
53.061
48.979
40.136
31.973
31.293
Mouse
100
78.231
39.456
35.374
35.374
Rat
100
33.333
36.054
34.014
Opossum
100
40.136
39.456
Duck
100
94.5578
Gallus
100Table 11
The correlation and significance analysis between our similarity analysis results of beta globin protein sequences in Table8 and PID% similarity matrix in Table 10.
Correlation coeff. (r) of our approach
t-value of our approach
Human
−0.8974
5.3806
Gorilla
−0.8715
4.7015
Chimp
−0.9105
5.8266
Lemur
−0.9151
6.0024
Mouse
−0.8489
4.2505
Rat
−0.7248
2.7830
Opossum
−0.5318
—
Duck
−0.7169
2.7209
Gallus
−0.6960
—Second, ClustalW is a widely used system for aligning any number of homologous nucleotides or protein sequences [33]. The ClustalW program’s distance matrix of nine ND5 protein sequences is illustrated in Table 12. Correlation and significance analyses are also provided to compare our approach in Table 9 with ClustalW results in Table 12. The results of the correlation and significance analyses of our approach and other approaches [15, 33] are illustrated in Table 13. Our sample set of ND5 is also composed of nine protein sequences. Therefore, we use 7 degrees of freedom and a t-value of 2.385 or greater. Despite the unusual result for pigmy chimpanzee that appeared in Table 9, the correlation coefficient of pigmy chimpanzee in our similarity matrix and clustalW matrix is 0.8811. This value likely does not occur by chance, as the t-value equals 4.928, as illustrated in Table 13. The comparison between our results and both PID% and ClustalW and other approaches’ results indicate the utility of our approach.Table 12
The similarity distance for nine different species of ND5 proteins calculated by the ClustalW.
Human
Gorilla
P. chimp
C. chimp
F. whale
B. whale
Rat
Mouse
Opossum
Human
0
10.7
7.1
6.9
41
41.3
50.2
48.9
50.4
Gorilla
0
9.7
9.9
42.7
42.4
51.4
49.9
54
P. chimp
0
5.1
40.1
40.1
50.2
48.9
50.1
C. chimp
0
40.4
40.4
50.8
49.6
51.4
F. whale
0
3.5
45.3
46.8
52.7
B. whale
0
45
45.9
52.7
Rat
0
25.9
54
Mouse
0
50.8
Opossum
0Table 13
The correlation and significance analysis between our similarity analysis results of ND5 protein sequences in Tables9 and 7 in [33] and Table 3 in [15] and ClustalW similarity matrix in Table 12.
Correlation coeff. (r) of our approach
t-value of our approach
Correlation coeff. (r) of [33]
t-value of [33]
Correlation coeff. (r) of [15] (Table 3)
t-value of [15] (Table 3)
Human
0.9159
6.0389
0.7819
3.3181
0.9419
7.4169
Gorilla
0.9062
5.6692
0.7630
3.1229
0.9363
7.0524
P. chimp
0.8811
4.9288
0.7856
3.3588
0.8755
4.7944
C. chimp
0.9345
6.9482
0.7808
3.3069
0.9448
7.6311
F. whale
0.9674
10.109
0.8360
4.0314
0.8146
3.7160
B. whale
0.9239
6.3875
0.8430
4.1463
0.6593
—
Rat
0.8048
3.5871
0.9213
6.2663
0.6479
—
Mouse
0.8112
3.6699
0.6391
—
0.6308
—
Opossum
0.6378
—
0.4299
—
0.4772
—


## 8. Conclusions

A new graphical representation of protein sequences is introduced. It is the combined intensity level of the 20 amino acids composing any protein sequence. Each amino acid in a given protein sequence has its own intensity and intensity level. They are vectors of N elements as N is the protein sequence length. The combined intensity level is then computed and graphed to represent any protein sequence graphically. Our 2D graphical representation effectively displays differences between protein sequences without degeneracies. The graph does not overlap or intersect with itself. Our new descriptor suggested a vector of two elements, which are the mean and standard deviation of the combined intensity level (A¯t and SAt). A similarity/dissimilarity analysis is evaluated by computing Euclidean distance between each two species’ descriptors. Examination of similarity/dissimilarity among nine beta globin, nine ND5, and 24 coronaviruses protein sequences provided good results compared to previous approaches. The suggested approach is effective for both short and long sequences, and the computations are very simple. Furthermore, loss of sequence information is avoided. Correlation and significance analyses with PID% and ClustalW are also introduced to show the utility of our approach.



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*Source: 2796971-2019-11-22.xml*