# Topography Prediction of Helical Transmembrane Proteins by a New Modification of the Sliding Window Method

Authors: Maria N. Simakova; Nikolai N. Simakov
Journal: BioMed Research International
 (2014)

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## Abstract

Protein functions are specified by its three-dimensional structure, which is usually obtained by X-ray crystallography. Due to difficulty of handling membrane proteins experimentally to date the structure has only been determined for a very limited part of membrane proteins (<4%). Nevertheless, investigation of structure and functions of membrane proteins is important for medicine and pharmacology and, therefore, is of significant interest. Methods of computer modeling based on the data on the primary protein structure or the symbolic amino acid sequence have become an actual alternative to the experimental method of X-ray crystallography for investigating the structure of membrane proteins. Here we presented the results of the study of 35 transmembrane proteins, mainly GPCRs, using the novel method of cascade averaging of hydrophobicity function within the limits of a sliding window. The proposed method allowed revealing 139 transmembrane domains out of 140 (or 99.3%) identified by other methods. Also 236 transmembrane domain boundary positions out of 280 (or 84%) were predicted correctly by the proposed method with deviation from the predictions made by other methods that does not exceed the detection error of this method.


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## Body

## 1. Introduction

Problem and relevance of the study of membrane proteins, including GPCRs, are as follows. Membrane proteins are responsible for many cellular functions and processes, in particular ensuring the selective exchange of substances between the cell and its environment, maintaining the electric potential inside and outside the cell, and providing the transfer of electric signals into and out of the cell. They participate in nearly all energy transduction processes in the organism.Protein functions are specified by its three-dimensional structure, which is usually obtained by X-ray crystallography [1, 2]. This method is directly applied to protein crystals, which must be produced beforehand using a very complex and laborious technique. The difficulty of handling membrane proteins during their production, purification, and crystallization due to protein instability, unfolding, aggregation, and heterogeneity has made it hard to solve their structures experimentally and to date the structure has only been determined for a very limited part of membrane proteins (<4%).It is supposed that all information about the ultimate structure of a protein is contained in its amino acid sequence. Therefore, methods of computer modeling based on the data on the primary protein structure or the symbolic amino acid sequence have become an actual alternative to the experimental method of X-ray crystallography for studying the structure of membrane proteins [3].From the variety of membrane proteins, the group of integral polytopic proteins (transmembrane proteins, TMPs) with multiple hydrophobic sites, domains permeating the membrane, is of considerable interest. Many of these proteins function as gateways or “loading docks” to transport specific substances and relay signals across the biological membrane.The apparent feature and the inherent property ofα-helical membrane proteins are the (possibly periodical) repetition of transmembrane domains consisting of hydrophobic amino acids (15–30 aa in length) [4]. If the mentioned repetition is periodic, it can be detected using the known method of Fourier transform, applied to a digital image of a symbolic sequence of amino acids in a protein, as was done in our previous works [4, 5].If the repetition of transmembrane regions is aperiodic, it can be revealed by another method, that is, the method of the reiterated (four to five times) averaging of the protein hydrophobicity function in a window within the limits of 9–11 amino acids that moves along the sequence. This method is a novel advanced version of the known method of sliding window, which has been proposed and used in our previous work [4] to investigate the secondary structure of different membrane proteins.The aim of the present work is to apply this method for the prediction of the characteristics of unknown secondary structures of TMPs, mainly of GPCRs; these characteristics specify the functional properties of the proteins.G protein-coupled receptors (GPCRs), also known as seven-transmembrane domain receptors, comprise the largest family of membrane proteins in the human genome and the richest source of targets for the pharmaceutical industry [6].Over 800 unique GPCRs have been revealed from human genome sequence analysis, approximately 460 of which are predicted to be olfactory receptors [7, 8]. The physiologic function of a large fraction of these 800 GPCRs is unknown. There are many obstacles to obtaining structures of GPCRs by X-ray crystallography; the major difficulties include poor protein stability and absence of homogeneity during crystallization due to inherent properties of these receptors [6, 9, 10].Therefore, it is necessary to develop novel approaches in structurally resolving aspects of their biology [11–13]. One of such useful approaches is to screen these proteins with help of structural bioinformatics and methods of computer modeling to identify those of them with the best characteristics for structural studies and for crystallography trials.


## 2. Materials and Methods

We used the method of reiterated averaging hydrophobicity function within a sliding window over the amino acid sequence. Since TM domains (TMDs) consist predominantly of hydrophobic amino acids, it is evident that the average hydrophobicity for this region, as specified in the protein sequence by a functionf
(
k
)
=
H
N
[
i
(
k
)
] of amino acid number k in the sequence, must be higher than that for both hydrophilic topological domains (TPDs) adjacent to it. Furthermore, this local property does not depend on the periodicity of the arrangement of characteristic TMDs and TPDs in the amino acid sequence. Here, i
(
k
)
=
1,2
,
…
,
20 is the number of amino acids of the 20 known (Table 1), which is located at position k in the protein sequence.Table 1
Hydrophobicity scalesH
N
(
i
).
i
Code
Abbreviation
Name
H
1
(
i
),  [14]
H
2
(
i
), [19]
H
3
(
i
),  [19]
H
4
(
i
),  [17, 19]
H
5
(
i
), [18]
H
6
(
i
), [16]
H
7
(
i
) [20]
1
A
Ala
Alanine
1.8
0
0
0.74
0.62
1.60
−0.17
2
C
Cys
Cysteine
2.5
1
1
0.91
0.29
2.00
0.24
3
D
Asp
Aspartic acid
−3.5
0
−1
0.62
−0.90
−9.20
−1.23
4
E
Glu
Glutamic acid
−3.5
0
−1
0.62
−0.74
−8.20
−2.02
5
F
Phe
Phenylalanine
2.8
1
1
0.88
1.19
3.70
1.13
6
G
Gly
Glycine
−0.4
0
−1
0.72
0.48
1.00
−0.01
7
H
His
Histidine
−3.2
0
0
0.78
−0.40
−3.00
−0.96
8
I
Ile
Isoleucine
4.5
1
1
0.88
1.38
3.10
0.31
9
K
Lys
Lysine
−3.9
0
−1
0.52
−1.50
−8.80
−0.99
10
L
Leu
Leucine
3.8
1
1
0.85
1.06
2.80
0.56
11
M
Met
Methionine
1.9
1
1
0.85
0.64
3.40
0.23
12
N
Asp
Asparagine
−3.5
0
−1
0.63
−0.78
−4.80
−1.23
13
P
Pro
Proline
−1.6
0
−1
0.64
0.12
−0.20
−0.45
14
Q
Gln
Glutamine
−3.5
0
−1
0.62
−0.85
−4.10
−0.58
15
R
Arg
Arginine
−4.5
0
−1
0.64
−2.53
−12.3
−0.81
16
S
Ser
Serine
−0.8
0
−1
0.66
−0.18
0.60
−0.13
17
T
Thr
Threonine
−0.7
0
−1
0.70
−0.05
1.20
−0.14
18
V
Val
Valine
4.2
1
1
0.86
1.08
2.60
−0.07
19
W
Trp
Tryptophan
−0.9
1
1
0.85
0.81
1.90
1.85
20
Y
Tyr
Tyrosine
−1.3
0
0
0.76
0.26
−0.70
0.94For the first time, this idea was realized in [14], where averaging of the function f
(
k
) within the limits of a segment, or window of width d
=
5
,
7
,
9
,
11, or 13 amino acids, moving along the amino acid sequence, was used. The result of averaging was assigned to a member of a new numerical sequence f
1
(
k
) with number k corresponding to the current position of the average segment point.The scale of hydrophobicityH
N
(
i
) used in this method can be specified in different ways (Table 1) depending on the physically measured value that characterizes this property [14–20]. In [14–16], the change of value of free energy of amino acid side groups upon their transfer into water from a hydrophobic medium was used as a measure of hydrophobicity. In [17, 19], the measure (scale) of amino acid hydrophobicity was defined as the function H
4
(
i
)
=
1
-
〈
A
〉
/
A
0 (Table 1) based on the values of the amino acid surface area A
0
(
i
), which is available to solvent in the standard state, and the mean solvent accessible surface area 〈
A
(
i
)
〉 in a folded protein conformation. In [17], the correlation between the free energy value and the surface area available to solvent was established.The set of 20 amino acids can be divided into a few characteristic groups based on their degree of hydrophobicity by different ways. Thus, according to [19], we used the division of 20 amino acids into three groups by the degree of hydrophobicity, including hydrophobic (C, F, I, L, M, V, and W, seven in total), hydrophilic (D, E, G, K, N, P, Q, R, S, and T, ten in total), and neutral (A, H, and Y, three in total). The hydrophobic amino acids were assigned a value of +1, the hydrophilic amino acids were assigned a value of −1, and the neutral amino acids were assigned a value of 0. Thus, we obtained the crude scale H
3
(
i
) in Table 1. On another crude scale H
2
(
i
) the hydrophobic amino acids were assigned a value of +1, and the remaining amino acids were assigned a value of 0.In our previous work [4], we proposed the procedure, different from that used in [14], for averaging the function f
(
k
) on the scale H
N
(
i
). The averaging was carried out not once, but repeatedly, using the algorithm
(1)
f
n
(
k
)
=
1
2
n
+
1
∑
k
=
-
n
n
f
n
-
1
(
k
)
,
n
=
1
,
2
,
…
,
5
,
f
0
(
k
)
=
f
(
k
)
,
where every new averaging was performed on the previous function f
n
-
1
(
k
) over a window with a greater width d
=
2
n
+
1; thus, the first averaging was over three elements, the second one was over five elements, and so on. In our opinion, the best result was obtained at n
=
4 and the averaging over the window of width d
=
9 amino acids (sometimes at n
=
5 and d
=
11 amino acids).It is interesting to compare the values ​​of the functionsf
n
(
k
) with the characteristic value of the initial hydrophobicity function f
0
(
k
)
=
f
(
k
), its arithmetic mean, calculated for the entire length L of the protein chain
(2)
u
=
〈
f
(
k
)
〉
=
1
L
∑
k
=
1
L
f
(
k
)
.For the major part of each hydrophobic region, in particular TMD, the correlationf
n
(
k
)
>
u must be performed, and in the hydrophilic region (TPD), a different correlation f
n
(
k
)
<
u must be performed.The scale and function of hydrophobicity can be specified in different ways (there are more than 30 known ones). A comparison of different scales and functions of hydrophobicity carried out in our previous work [4] showed that the numbers and arrangements of transmembrane regions obtained upon their usage were often almost identical, even for very simple (rough) scales, for example, H
2
(
i
) and H
3
(
i
) (see Table 1). However, sometimes a particular scale can be preferable for a given protein due to the better resolution of closely spaced TMDs.


## 3. Results and Discussion

### 3.1. Testing of the Improved Method of a Sliding Window on Proteins with Known Structure

The improved method of a sliding window proposed in [4] by algorithm (1) was applied in this work to the group of membrane proteins, such as GPCRs, and to some other transmembrane α-helical proteins.To further test the predictions of our method, first it was used to examine 5 proteins with already known structure (Table2).Table 2
Comparison of TMD boundaries calculated upon processing of hydrophobicity functionsf
n
(
k
) at n
=
3
,
4
,
5 on H
N
(
i
) (N
=
3 and 5) scales for GPCRs with known data from [21].
Protein name, code, length
Data source
Number and boundaries of transmembrane domains
Scale level
1
2
3
4
5
6
7
GLR_HUMAN P47871477 aa
[21, 22]
137–161
174–198
226–249
264–285
304–326
351–369
382–402
H
5
(
i
)
,
n
=
4
u
=
0.266
143–166
180–192
218–257
261–288
303–327
353–368
384–401
CRFR1_HUMAN P34998444 aa
[21, 23]
112–142
179–203
219–247
255–282
299–324
336–360
368–397
H
3
(
i
)
,
n
=
5
〈
u
〉
=
-
0.052
116–146
178–204
217–247
255–280
302–325
344–362
370–397
ADRB1_MELGA P07700483 aa
[21, 24]
39–67
77–103
116–137
156–179
206–231
286–315
321–343
H
3
(
i
)
,
n
=
4,
u
=
0.1
44–64
81–99
108–138
160–181
214–229
293–314
320–331
5HT1B_HUMAN P28222 390 aa
[21, 25]
50–75
85–110
124–145
166–187
206–228
316–336
350–371
H
5
(
i
)
,
n
=
4
u
=
0.243
46–72
86–109
119–145
168–185
205–230
316–340
343–369
H
5
(
i
)
,
n
=
3
〈
u
〉
=
0.182
45–73
85–110
118–145
168–185
205–229
316–340
344–370
5HT2B_HUMAN P41595481 aa
[21, 26]
57–79
91–113
130–151
172–192
217–239
325–345
361–382
H
5
(
i
)
,
n
=
5
〈
u
〉
=
0.164
54–81
89–
89–109
−151
131–151
173–194
215–243
325–352
356–381Figure1 shows the results of averaging the hydrophobicity function for the protein sequence P47871 on the scale H
5
(
i
) in Table 1. Obviously, a hydrophobic segment in the form of a narrow peak relating to the signal peptide (SP) is present on the left edge of the graph of the function f
4
(
k
). If this peak is excluded, the remaining seven wide peaks that exceed the mean level u = const = 0.27 will just correspond to 7 TMDs in the resolved structure of this protein [21, 22]. In the graph of the function f
2
(
k
) the 2nd, the 3rd, the 5th, and the 7th TMDs have not been resolved yet, and there are several narrow peaks in their places.Figure 1
Hydrophobicity functionsf
n
(
k
) for the protein P47871 in Table 2 after averaging at n
=
2 and n
=
4 on the scale H
5
(
i
) in Table 1; dotted line shows the level u = const = 0.266.Figure2 shows the results obtained for the protein sequence P34998 using the relatively rough hydrophobicity scale H
3
(
i
) in Table 1. Apparently, a hydrophobic segment relating to the SP is revealed on the left edge of the graph of the function f
5
(
k
) above the mean level u
=
〈
f
(
k
)
〉
=
-
0.05, and also, in contrast to the function f
2
(
k
), all 7 TMDs known for the protein structure P34998 [21, 23] are resolved.Figure 2
Hydrophobicity functionsf
n
(
k
) for the protein P34998 in Table 2 after averaging at n
=
2 and n
=
5 on the scale H
3
(
i
) in Table 1; dotted line shows the level u = const = 〈
f
(
k
)
〉
=
-
0.052.The boundaries of TMDs of different proteins were determined by the intersection of the graph of the functionf
n
(
k
) with the straight line of some level u = const (e.g., the mean level u
=
〈
f
(
k
)
〉 for the whole protein sequence). They are summarized in Table 2 for 5 known proteins.The TMD boundaries from [21] are also shown for comparison in Table 2.Taking into account the errorsΔ
k
b
≈
d
/
2
≈
5
⋯
6 of the TMD boundary k
b detection, good agreement of the results of the TMD boundary position calculations with the data from [21] can be obtained. Indeed, according to Table 2, 34 TMDs out of 35 were resolved (or 97%); the obtained TMD boundary positions do not exceed the detection errors (
Δ
k
b
≤
6
) for 62 out of 70 boundaries (or 89%).Remark 1.
In the protein with a code P41595, the 2nd and the 3rd domains not resolved in calculating can be resolved using the outer boundaries of the combined segment of 89–151 aa by adding to the left borderk
b
=
89 and subtracting from the right border k
b
=
151 the estimated average length of a domain 20 aa, as shown in Table 2 in a bold font.In [21], a signal peptide (SP) consisting of 1–25 aa of a protein sequence is indicated in the structure of the protein P47871. In this part of the protein chain, the hydrophobic region of 11–23 aa was detected by the proposed method. Similarly, the sequence of the protein P34998 [21] contains a signal peptide consisting of 1–23 amino acid residues. The proposed method was helpful to reveal here the hydrophobic region of 9–19 aa.It is worth noting that processing with reiterated (four to five times) averaging of the hydrophobicity functionf
n
(
k
) on different scales (the rough scales H
2
(
i
) and H
3
(
i
) or the more precise scales H
4
(
i
)
–
H
7
(
i
)) produces different values for the TMD boundaries. Sometimes these differences are minor, but sometimes they are significant [4].


### 3.2. Comparison of Protein Secondary Structure Predictions Made by the Proposed Method and Other Techniques

Secondary structure predictions of a set of 20 membrane proteins belonging to a class of GPCRs performed using the new proposed method were compared with the predictions made ​​by other methods (Table3).Table 3
Comparison of TMD boundaries calculated upon processing of hydrophobicity functionsf
n
(
k
) at n
=
4
,
5 on H
N
(
i
) (N
=
3
,
5
,
6) scales for GPCRs with known data from [21].
Protein name, code, length
Data source
Number and boundaries of transmembrane domains
Scale level
1
2
3
4
5
6
7
S1PR1_HUMAN P21453382 aa
[21], by similarity
47–71
79–107
122–140
160–185
202–222
256–277
294–314
H
5
(
i
)
,
n
=
5
u
=
0.25
48–69
83–107
122–142
160–195
199–223
255–281
293–310
ACM2_HUMAN P08172466 aa
[21],  by similarity
23–45
60–80
98–119
140–162
185–207
389–409
424–443
H
3
(
i
)
,
n
=
5
u
=
0.07
21–48
60–85
90–122
142–167
192–208
389–415
422–429
ACM3_RAT P08483589 aa
[21],  by similarity
67–90
104–124
142–163
184–206
229–251
492–512
527–546
H
5
(
i
)
,
n
=
5
u
=
0.30
62–92
105–128
137–161
187–208
221–249
492–515
526–541
CXCR1_HUMAN P25024350 aa
[21],  potential
40–66
76–96
112–133
155–174
200–220
243–264
286–308
H
3
(
i
)
,
n
=
4
u
=
-
0.05
39–67
76–96
102–141
152–175
199–230
241–267
291–308
CCR5_HUMAN P51681352 aa
[21], potential
31–58
69–89
103–124
142–166
199–218
236–260
278–301
H
5
(
i
)
,
n
=
5
u
=
0.25
33–56
68–93
100–136
141–164
196–218
238–264
288–299
HRH1_HUMAN P35367487 aa
[21], potential
30–49
64–83
102–123
146–165
190–210
419–438
451–470
H
5
(
i
)
,
n
=
5
u
=
0.17
25–50
63–93
96–122
147–167
188–212
418–442
449–469
OPRK_HUMAN P41145380 aa
[21], potential
59–85
96–117
133–154
174–196
223–247
276–299
312–333
H
6
(
i
)
,
n
=
4
u
=
0.50
56–83
99–122
143–151
180–195
227–248
277–300
302–320
OPRM_MOUSE P42866398 aa
[21], potential
65–94
104–121
144–163
194–209
235–257
281–303
312–328
H
3
(
i
)
,
n
=
4
u
=
-
0.02
68–95
105–114
136–162
187–205
229–262
280–306
317–325
OPRD_MOUSE P32300    372 aa
[21],  potential
46–75
85–102
125–144
175–190
216–238
262–284
294–310
H
5
(
i
)
,
n
=
5
u
=
0.213
44–74
85–102
112–142
167–187
211–236
263–286
296–319
OPRX_HUMAN P41146   370 aa
[21],  potential
51–77
88–109
125–146
166–188
212–236
265–288
301–322
H
3
(
i
)
,
n
=
5
u
=
0.011
42–79
90–107
112–130
172–186
212–241
263–284
301–335
NTR1_RAT P20789424 aa
[21],  potential
65–87
97–121
144–165
189–210
236–260
309–330
349–372
H
5
(
i
)
,
n
=
5
u
=
0.144
63–86
103–139
154–172
191–208
220–268
306–324
338–374
PAR1_HUMAN P25116425 aa
[21],  potential
103–128
138–157
177–198
219–239
269–288
312–334
351–374
H
3
(
i
)
,
n
=
4
u
=
0.100
101–133
136–158
175–208
221–238
270–296
313–338
350–371
O51E1_HUMAN Q8TCB6317 aa
[21], potential
28–48
57–77
102–122
142–162
199–219
239–259
275–295
H
5
(
i
)
,
n
=
5
〈
u
〉
=
0.300
12–49
60–77
80–120
146–166
198–227
243–260
276–292
SMO_HUMAN Q99835787 aa
[21],  potential
234–254
263–283
315–335
359–379
403–423
452–472
525–545
H
3
(
i
)
,
n
=
5
u
=
0.00
236–251
264–283
313–340
362–380
403–425
451–473
519–545
GP160_HUMAN Q9UJ42338 aa
[21], potential
24–44
59–79
94–114
137–157
178–198
245–265
269–289
H
5
(
i
)
,
n
=
5
u
=
0.420
26–40
59–81
97–118
139–157
182–202
244–271
274–292
HRH3_HUMAN Q9Y5N1445 aa
[21], potential
40–60
71–91
109–129
157–177
197–217
360–380
396–416
H
3
(
i
)
,
n
=
5
u
=
0.00
33–61
72–95
105–132
155–173
191–222
360–388
395–416
HRH4_HUMAN Q9H3N8390 aa
[21], potential
20–40
53–73
88–108
132–152
173–193
305–325
342–362
H
5
(
i
)
,
n
=
5
u
=
0.25
16–41
55–79
83–107
130–153
169–198
305–331
341–357
RAI3_HUMAN Q8NFJ5   357 aa
[21], potential
34–54
69–89
98–118
130–150
177–197
213–233
248–268
H
5
(
i
)
,
n
=
4
〈
u
〉
=
0.195
26–53
68–92
96–118
130–155
178–202
213–233
246–265
VN1R1_HUMAN Q9GZP7   353 aa
[21], potential
57–77
85–105
133–153
170–190
227–247
275–295
304–324
H
4
(
i
)
,
n
=
5
〈
u
〉
=
0.754
53–77
90–103
122–145
165–188
222–245
274–301
306–338
APJ_HUMAN P35414   380 aa
[21],  potential
27–51
67–91
101–125
145–166
201–221
245–271
285–308
H
3
(
i
)
,
n
=
5
u
=
-
0.090
30–52
67–85
98–135
147–167
208–228
246–
246–266
−312
292–312As can be seen from Table3, the proposed method allowed revealing 139 TMDs out of 140 (or 99.3%) identified by other methods. In the protein P35414 (the last one in Table 3) the 6th and the 7th domains “merged” into one long stretch of 246–312 aa. However, taking into account Remark 1, the boundaries of these two domains can be easily recovered using the outer boundaries of the combined segment by adding to the left border k
b
=
246 and subtracting from the right border k
b
=
312 the estimated average length of a domain 20 aa, as shown in Table 3 in a bold font.236 TMD boundary positions out of 280 (or 84%) were predicted correctly by the proposed method with deviation from the predictions made by other methods that does not exceed the detection error of this method(
Δ
k
b
≤
6
).In [21], a signal peptide (SP) consisting of 1–21 aa of a protein sequence is indicated in the structure of the protein P25116. In this part of the protein chain the hydrophobic region of 6–17 aa was detected by the proposed method. Similarly, the sequence of the protein Q99835 [21] contains a signal peptide consisting of 1–27 amino acid residues. The proposed method was helpful to reveal here the hydrophobic region of 13–23 aa.


### 3.3.  Predictions of Unknown Secondary Structure of GPCRs and Other Membrane Proteins

Then the proposed method of multiple averaging of hydrophobicity function was used to predict the location of hydrophobic regions, including TMDs, in several GPCRs with unknown structure. The results are shown in Table4.Table 4
Prediction of TMD boundaries calculated upon processing of hydrophobicity functionsf
n
(
k
) at n
=
4
,
5 on H
N
(
i
) (N
=
3
,
4
,
5) scales for GPCRs.
Protein name,  code, length
Scale level
Number and boundaries of hydrophobic regions, including TMDs
1
2
3
4
5
6
7
A4D1U0_HUMAN A4D1U0299 aa
H
5
(
i
)
,
n
=
5
〈
u
〉
=
0.439
7–28
45–70
82–102
127–147
173–194
222–240
253–274
H
3
(
i
)
,
n
=
5
〈
u
〉
=
0.057
7–29
46–71
77–103
124–144
179–194
222–237
258–275
A5Z1T7_HUMAN A5Z1T7300 aa
H
4
(
i
)
,
n
=
5
〈
u
〉
=
0.755
7–27
43–57
75–100
121–146
185–210
225–240
263–274
H
3
(
i
)
,
n
=
5
〈
u
〉
=
-
0.043
7–26
41–64
75–97
123–144
185–209
225–238
264–274
B5B0C2_HUMAN B5B0C2337 aa
H
5
(
i
)
,
n
=
5
〈
u
〉
=
0.142
14–40
49–72
85–122
132–155
189–201
227–255
275–293
H
3
(
i
)
,
n
=
5
〈
u
〉
=
-
0.030
14–39
51–71
89–
89–109
−154
134–154
193–205
226–256
277–292
M9TID6_9BETA M9TID6347 aa
H
3
(
i
)
,
n
=
4
u
=
0.055
43–57
69–88
97–123
149–161
188–219
232–262
265–288
H
5
(
i
)
,
n
=
5
〈
u
〉
=
0.191
33–56
66–87
100–123
148–164
186–217
233–
233–253
−295
275–295
Q76L88_HUMAN Q76L88321 aa
H
5
(
i
)
,
n
=
5
〈
u
〉
=
0.201
11–40
54–78
93–116
156–178
196–223
251–270
H
3
(
i
)
,
n
=
5
〈
u
〉
=
-
0.050
13–37
55–78
90–117
153–174
198–225
248–282At least two hydrophobicity scalesH
N
(
i
) were applied to make predictions for each of the 5 proteins. Obviously, these predictions are consistent with each other for most of the domain boundaries considering the detection errors Δ
k
b
=
±
6.For the protein B5D0C2 the calculation on theH
5
(
i
) scale resolved the 3rd and the 4th domains, but the application of the H
3
(
i
) scale did not resolve these domains; they merged into a single domain. And it was vice versa for the protein M9TID6 with the 6th and the 7th TMDs. Taking into account Remark 1, the boundaries of unresolved domains can be restored, as shown in Table 4 in a bold font.Surprisingly, for the protein Q76L88 given thatf
n
(
k
) is higher than the mean level u
=
〈
f
(
k
)
〉, only 6 domains were surely detected instead of 7 as for other proteins in Table 4.The results of prediction of TMDs using the proposed method are shown in Table5 for 4 α-helical membrane proteins of unknown structure. The first two proteins (P71044 and P49785) belong to the group of channels: intercellular, the third one Q8TMG0 to the group of methyltransferases, and the fourth one P77335 to the group of adventitious membrane proteins: alpha-helical pore-forming toxins.Table 5
Prediction of hydrophobic regions and TMDs calculated upon processing of hydrophobicity functionsf
n
(
k
) at n
=
4
,
5 on H
N
(
i
) (N
=
3
,
4
,
5) scales for α-helical membrane proteins.
Protein name, code, length
Data source
Number and boundaries of hydrophobic regions, including TMDs
Scale level
1
2
3
4
5
6
7
SP2Q_BACSU P71044283 aa
[21], potential
22–42
H
5
(
i
)
,
n
=
5
〈
u
〉
=
-
0.127
20–47
70–94
107–124
130–175
207–229
H
4
(
i
)
,
n
=
5
〈
u
〉
=
0.696
16–48
70–94
109–121
132–174
197–225
SP3AH_BACSU P49785218 aa
[21],  potential
7–26
H
5
(
i
)
,
n
=
5
〈
u
〉
=
-
0.137
3–31
92–106
146–179
193–211
H
4
(
i
)
,
n
=
5
〈
u
〉
=
0.692
3–30
95–113
146–179
193–211
Q8TMG0_METAC Q8TMG0194 aa
H
5
(
i
)
,
n
=
5
〈
u
〉
=
0.232
7–20
49–67
76–93
130–162
H
3
(
i
)
,
n
=
5
〈
u
〉
=
0.041
0–22
45–62
77–91
127–163
HLYE_ECOLI P77335303 aa
[21], potential
183–203
H
3
(
i
)
,
n
=
5
〈
u
〉
=
-
0.248
0–17
24–38
82–103
114–123
180–209
242–247
264–280
H
5
(
i
)
,
n
=
4
〈
u
〉
=
0.029
5–26
32–40
81–102
115–123
179–208
242–253
267–275Here, as well as in Table4, the predictions were made on at least two hydrophobicity scales H
N
(
i
). Evidently, these predictions are consistent with each other for all domain boundaries considering the detection errors Δ
k
b
=
±
6. Individual single domains predicted earlier by other methods [21] were also identified by the proposed method.Table6 shows data comparison from [21] with prediction of TMDs made by the proposed method for the long (L
=
2424 aa) α-helical membrane protein from the group of adventitious membrane proteins: alpha-helical pore-forming toxins. Obviously, compliance between the predictions takes place for most of TMDs considering errors in determining their boundaries Δ
k
b
≤
6.Table 6
Prediction of TMDs calculated upon processing of hydrophobicity functionsf
n
(
k
) at n
=
5 on the scale H
5
(
i
) for the long α-helical membrane protein.
Protein name, code, length
Data source
Number and boundaries of transmembrane domains
Scale
1
2
3
4
5
6
CAC1A_RABIT P278842424 aa
[21], potential
99–117
136–155
168–185
191–209
229–248
336–360
H
5
,
u
=
0.305
101–116
141–158
172–185
210–249
302–317
336–358
Scale
7
8
9
10
11
12
[21], potential
488–506
522–541
550–568
579–597
617–636
690–714
H
5
,
u
=
0.305
491–507
518–537
554–577
609–638
654–665
685–714
Scale
13
14
15
16
17
18
[21], potential
1254–1272
1289–1308
1321–1339
1351–1369
1389–1408
1496–1520
H
5
,
u
=
0.305
1255–1270
1293–1312
1323–1339
1384–1408
1456–1467
1497–1522
Scale
19
20
21
22
23
24
[21], potential
1576–1604
1610–1629
1638–1656
1666–1684
1704–1723
1796–1820
H
5
,
u
=
0.305
1575–1599
1607–1633
1641–1660
1691–1725
—
1794–1820In the calculation using the proposed method of multiple averaging of hydrophobicity function over a sliding window, besides those domains indicated in Table6, a hydrophobic region of 16–28 aa was identified, which may belong to a signal peptide (SP) or may be the 1st one out of 24 TMDs of the present protein. Moreover, it is obvious that TMDs numbered in [21] as 5, 11, 17, and 23 and highlighted in Table 6 by a bold font in our prediction have the numbers, which are one less than in [21], but other domains that are not specified in [21] have the numbers, which are one more. Thus, two varied predictions in Table 6 have great similarities as well as notable differences.


## 3.1. Testing of the Improved Method of a Sliding Window on Proteins with Known Structure

The improved method of a sliding window proposed in [4] by algorithm (1) was applied in this work to the group of membrane proteins, such as GPCRs, and to some other transmembrane α-helical proteins.To further test the predictions of our method, first it was used to examine 5 proteins with already known structure (Table2).Table 2
Comparison of TMD boundaries calculated upon processing of hydrophobicity functionsf
n
(
k
) at n
=
3
,
4
,
5 on H
N
(
i
) (N
=
3 and 5) scales for GPCRs with known data from [21].
Protein name, code, length
Data source
Number and boundaries of transmembrane domains
Scale level
1
2
3
4
5
6
7
GLR_HUMAN P47871477 aa
[21, 22]
137–161
174–198
226–249
264–285
304–326
351–369
382–402
H
5
(
i
)
,
n
=
4
u
=
0.266
143–166
180–192
218–257
261–288
303–327
353–368
384–401
CRFR1_HUMAN P34998444 aa
[21, 23]
112–142
179–203
219–247
255–282
299–324
336–360
368–397
H
3
(
i
)
,
n
=
5
〈
u
〉
=
-
0.052
116–146
178–204
217–247
255–280
302–325
344–362
370–397
ADRB1_MELGA P07700483 aa
[21, 24]
39–67
77–103
116–137
156–179
206–231
286–315
321–343
H
3
(
i
)
,
n
=
4,
u
=
0.1
44–64
81–99
108–138
160–181
214–229
293–314
320–331
5HT1B_HUMAN P28222 390 aa
[21, 25]
50–75
85–110
124–145
166–187
206–228
316–336
350–371
H
5
(
i
)
,
n
=
4
u
=
0.243
46–72
86–109
119–145
168–185
205–230
316–340
343–369
H
5
(
i
)
,
n
=
3
〈
u
〉
=
0.182
45–73
85–110
118–145
168–185
205–229
316–340
344–370
5HT2B_HUMAN P41595481 aa
[21, 26]
57–79
91–113
130–151
172–192
217–239
325–345
361–382
H
5
(
i
)
,
n
=
5
〈
u
〉
=
0.164
54–81
89–
89–109
−151
131–151
173–194
215–243
325–352
356–381Figure1 shows the results of averaging the hydrophobicity function for the protein sequence P47871 on the scale H
5
(
i
) in Table 1. Obviously, a hydrophobic segment in the form of a narrow peak relating to the signal peptide (SP) is present on the left edge of the graph of the function f
4
(
k
). If this peak is excluded, the remaining seven wide peaks that exceed the mean level u = const = 0.27 will just correspond to 7 TMDs in the resolved structure of this protein [21, 22]. In the graph of the function f
2
(
k
) the 2nd, the 3rd, the 5th, and the 7th TMDs have not been resolved yet, and there are several narrow peaks in their places.Figure 1
Hydrophobicity functionsf
n
(
k
) for the protein P47871 in Table 2 after averaging at n
=
2 and n
=
4 on the scale H
5
(
i
) in Table 1; dotted line shows the level u = const = 0.266.Figure2 shows the results obtained for the protein sequence P34998 using the relatively rough hydrophobicity scale H
3
(
i
) in Table 1. Apparently, a hydrophobic segment relating to the SP is revealed on the left edge of the graph of the function f
5
(
k
) above the mean level u
=
〈
f
(
k
)
〉
=
-
0.05, and also, in contrast to the function f
2
(
k
), all 7 TMDs known for the protein structure P34998 [21, 23] are resolved.Figure 2
Hydrophobicity functionsf
n
(
k
) for the protein P34998 in Table 2 after averaging at n
=
2 and n
=
5 on the scale H
3
(
i
) in Table 1; dotted line shows the level u = const = 〈
f
(
k
)
〉
=
-
0.052.The boundaries of TMDs of different proteins were determined by the intersection of the graph of the functionf
n
(
k
) with the straight line of some level u = const (e.g., the mean level u
=
〈
f
(
k
)
〉 for the whole protein sequence). They are summarized in Table 2 for 5 known proteins.The TMD boundaries from [21] are also shown for comparison in Table 2.Taking into account the errorsΔ
k
b
≈
d
/
2
≈
5
⋯
6 of the TMD boundary k
b detection, good agreement of the results of the TMD boundary position calculations with the data from [21] can be obtained. Indeed, according to Table 2, 34 TMDs out of 35 were resolved (or 97%); the obtained TMD boundary positions do not exceed the detection errors (
Δ
k
b
≤
6
) for 62 out of 70 boundaries (or 89%).Remark 1.
In the protein with a code P41595, the 2nd and the 3rd domains not resolved in calculating can be resolved using the outer boundaries of the combined segment of 89–151 aa by adding to the left borderk
b
=
89 and subtracting from the right border k
b
=
151 the estimated average length of a domain 20 aa, as shown in Table 2 in a bold font.In [21], a signal peptide (SP) consisting of 1–25 aa of a protein sequence is indicated in the structure of the protein P47871. In this part of the protein chain, the hydrophobic region of 11–23 aa was detected by the proposed method. Similarly, the sequence of the protein P34998 [21] contains a signal peptide consisting of 1–23 amino acid residues. The proposed method was helpful to reveal here the hydrophobic region of 9–19 aa.It is worth noting that processing with reiterated (four to five times) averaging of the hydrophobicity functionf
n
(
k
) on different scales (the rough scales H
2
(
i
) and H
3
(
i
) or the more precise scales H
4
(
i
)
–
H
7
(
i
)) produces different values for the TMD boundaries. Sometimes these differences are minor, but sometimes they are significant [4].


## 3.2. Comparison of Protein Secondary Structure Predictions Made by the Proposed Method and Other Techniques

Secondary structure predictions of a set of 20 membrane proteins belonging to a class of GPCRs performed using the new proposed method were compared with the predictions made ​​by other methods (Table3).Table 3
Comparison of TMD boundaries calculated upon processing of hydrophobicity functionsf
n
(
k
) at n
=
4
,
5 on H
N
(
i
) (N
=
3
,
5
,
6) scales for GPCRs with known data from [21].
Protein name, code, length
Data source
Number and boundaries of transmembrane domains
Scale level
1
2
3
4
5
6
7
S1PR1_HUMAN P21453382 aa
[21], by similarity
47–71
79–107
122–140
160–185
202–222
256–277
294–314
H
5
(
i
)
,
n
=
5
u
=
0.25
48–69
83–107
122–142
160–195
199–223
255–281
293–310
ACM2_HUMAN P08172466 aa
[21],  by similarity
23–45
60–80
98–119
140–162
185–207
389–409
424–443
H
3
(
i
)
,
n
=
5
u
=
0.07
21–48
60–85
90–122
142–167
192–208
389–415
422–429
ACM3_RAT P08483589 aa
[21],  by similarity
67–90
104–124
142–163
184–206
229–251
492–512
527–546
H
5
(
i
)
,
n
=
5
u
=
0.30
62–92
105–128
137–161
187–208
221–249
492–515
526–541
CXCR1_HUMAN P25024350 aa
[21],  potential
40–66
76–96
112–133
155–174
200–220
243–264
286–308
H
3
(
i
)
,
n
=
4
u
=
-
0.05
39–67
76–96
102–141
152–175
199–230
241–267
291–308
CCR5_HUMAN P51681352 aa
[21], potential
31–58
69–89
103–124
142–166
199–218
236–260
278–301
H
5
(
i
)
,
n
=
5
u
=
0.25
33–56
68–93
100–136
141–164
196–218
238–264
288–299
HRH1_HUMAN P35367487 aa
[21], potential
30–49
64–83
102–123
146–165
190–210
419–438
451–470
H
5
(
i
)
,
n
=
5
u
=
0.17
25–50
63–93
96–122
147–167
188–212
418–442
449–469
OPRK_HUMAN P41145380 aa
[21], potential
59–85
96–117
133–154
174–196
223–247
276–299
312–333
H
6
(
i
)
,
n
=
4
u
=
0.50
56–83
99–122
143–151
180–195
227–248
277–300
302–320
OPRM_MOUSE P42866398 aa
[21], potential
65–94
104–121
144–163
194–209
235–257
281–303
312–328
H
3
(
i
)
,
n
=
4
u
=
-
0.02
68–95
105–114
136–162
187–205
229–262
280–306
317–325
OPRD_MOUSE P32300    372 aa
[21],  potential
46–75
85–102
125–144
175–190
216–238
262–284
294–310
H
5
(
i
)
,
n
=
5
u
=
0.213
44–74
85–102
112–142
167–187
211–236
263–286
296–319
OPRX_HUMAN P41146   370 aa
[21],  potential
51–77
88–109
125–146
166–188
212–236
265–288
301–322
H
3
(
i
)
,
n
=
5
u
=
0.011
42–79
90–107
112–130
172–186
212–241
263–284
301–335
NTR1_RAT P20789424 aa
[21],  potential
65–87
97–121
144–165
189–210
236–260
309–330
349–372
H
5
(
i
)
,
n
=
5
u
=
0.144
63–86
103–139
154–172
191–208
220–268
306–324
338–374
PAR1_HUMAN P25116425 aa
[21],  potential
103–128
138–157
177–198
219–239
269–288
312–334
351–374
H
3
(
i
)
,
n
=
4
u
=
0.100
101–133
136–158
175–208
221–238
270–296
313–338
350–371
O51E1_HUMAN Q8TCB6317 aa
[21], potential
28–48
57–77
102–122
142–162
199–219
239–259
275–295
H
5
(
i
)
,
n
=
5
〈
u
〉
=
0.300
12–49
60–77
80–120
146–166
198–227
243–260
276–292
SMO_HUMAN Q99835787 aa
[21],  potential
234–254
263–283
315–335
359–379
403–423
452–472
525–545
H
3
(
i
)
,
n
=
5
u
=
0.00
236–251
264–283
313–340
362–380
403–425
451–473
519–545
GP160_HUMAN Q9UJ42338 aa
[21], potential
24–44
59–79
94–114
137–157
178–198
245–265
269–289
H
5
(
i
)
,
n
=
5
u
=
0.420
26–40
59–81
97–118
139–157
182–202
244–271
274–292
HRH3_HUMAN Q9Y5N1445 aa
[21], potential
40–60
71–91
109–129
157–177
197–217
360–380
396–416
H
3
(
i
)
,
n
=
5
u
=
0.00
33–61
72–95
105–132
155–173
191–222
360–388
395–416
HRH4_HUMAN Q9H3N8390 aa
[21], potential
20–40
53–73
88–108
132–152
173–193
305–325
342–362
H
5
(
i
)
,
n
=
5
u
=
0.25
16–41
55–79
83–107
130–153
169–198
305–331
341–357
RAI3_HUMAN Q8NFJ5   357 aa
[21], potential
34–54
69–89
98–118
130–150
177–197
213–233
248–268
H
5
(
i
)
,
n
=
4
〈
u
〉
=
0.195
26–53
68–92
96–118
130–155
178–202
213–233
246–265
VN1R1_HUMAN Q9GZP7   353 aa
[21], potential
57–77
85–105
133–153
170–190
227–247
275–295
304–324
H
4
(
i
)
,
n
=
5
〈
u
〉
=
0.754
53–77
90–103
122–145
165–188
222–245
274–301
306–338
APJ_HUMAN P35414   380 aa
[21],  potential
27–51
67–91
101–125
145–166
201–221
245–271
285–308
H
3
(
i
)
,
n
=
5
u
=
-
0.090
30–52
67–85
98–135
147–167
208–228
246–
246–266
−312
292–312As can be seen from Table3, the proposed method allowed revealing 139 TMDs out of 140 (or 99.3%) identified by other methods. In the protein P35414 (the last one in Table 3) the 6th and the 7th domains “merged” into one long stretch of 246–312 aa. However, taking into account Remark 1, the boundaries of these two domains can be easily recovered using the outer boundaries of the combined segment by adding to the left border k
b
=
246 and subtracting from the right border k
b
=
312 the estimated average length of a domain 20 aa, as shown in Table 3 in a bold font.236 TMD boundary positions out of 280 (or 84%) were predicted correctly by the proposed method with deviation from the predictions made by other methods that does not exceed the detection error of this method(
Δ
k
b
≤
6
).In [21], a signal peptide (SP) consisting of 1–21 aa of a protein sequence is indicated in the structure of the protein P25116. In this part of the protein chain the hydrophobic region of 6–17 aa was detected by the proposed method. Similarly, the sequence of the protein Q99835 [21] contains a signal peptide consisting of 1–27 amino acid residues. The proposed method was helpful to reveal here the hydrophobic region of 13–23 aa.


## 3.3.  Predictions of Unknown Secondary Structure of GPCRs and Other Membrane Proteins

Then the proposed method of multiple averaging of hydrophobicity function was used to predict the location of hydrophobic regions, including TMDs, in several GPCRs with unknown structure. The results are shown in Table4.Table 4
Prediction of TMD boundaries calculated upon processing of hydrophobicity functionsf
n
(
k
) at n
=
4
,
5 on H
N
(
i
) (N
=
3
,
4
,
5) scales for GPCRs.
Protein name,  code, length
Scale level
Number and boundaries of hydrophobic regions, including TMDs
1
2
3
4
5
6
7
A4D1U0_HUMAN A4D1U0299 aa
H
5
(
i
)
,
n
=
5
〈
u
〉
=
0.439
7–28
45–70
82–102
127–147
173–194
222–240
253–274
H
3
(
i
)
,
n
=
5
〈
u
〉
=
0.057
7–29
46–71
77–103
124–144
179–194
222–237
258–275
A5Z1T7_HUMAN A5Z1T7300 aa
H
4
(
i
)
,
n
=
5
〈
u
〉
=
0.755
7–27
43–57
75–100
121–146
185–210
225–240
263–274
H
3
(
i
)
,
n
=
5
〈
u
〉
=
-
0.043
7–26
41–64
75–97
123–144
185–209
225–238
264–274
B5B0C2_HUMAN B5B0C2337 aa
H
5
(
i
)
,
n
=
5
〈
u
〉
=
0.142
14–40
49–72
85–122
132–155
189–201
227–255
275–293
H
3
(
i
)
,
n
=
5
〈
u
〉
=
-
0.030
14–39
51–71
89–
89–109
−154
134–154
193–205
226–256
277–292
M9TID6_9BETA M9TID6347 aa
H
3
(
i
)
,
n
=
4
u
=
0.055
43–57
69–88
97–123
149–161
188–219
232–262
265–288
H
5
(
i
)
,
n
=
5
〈
u
〉
=
0.191
33–56
66–87
100–123
148–164
186–217
233–
233–253
−295
275–295
Q76L88_HUMAN Q76L88321 aa
H
5
(
i
)
,
n
=
5
〈
u
〉
=
0.201
11–40
54–78
93–116
156–178
196–223
251–270
H
3
(
i
)
,
n
=
5
〈
u
〉
=
-
0.050
13–37
55–78
90–117
153–174
198–225
248–282At least two hydrophobicity scalesH
N
(
i
) were applied to make predictions for each of the 5 proteins. Obviously, these predictions are consistent with each other for most of the domain boundaries considering the detection errors Δ
k
b
=
±
6.For the protein B5D0C2 the calculation on theH
5
(
i
) scale resolved the 3rd and the 4th domains, but the application of the H
3
(
i
) scale did not resolve these domains; they merged into a single domain. And it was vice versa for the protein M9TID6 with the 6th and the 7th TMDs. Taking into account Remark 1, the boundaries of unresolved domains can be restored, as shown in Table 4 in a bold font.Surprisingly, for the protein Q76L88 given thatf
n
(
k
) is higher than the mean level u
=
〈
f
(
k
)
〉, only 6 domains were surely detected instead of 7 as for other proteins in Table 4.The results of prediction of TMDs using the proposed method are shown in Table5 for 4 α-helical membrane proteins of unknown structure. The first two proteins (P71044 and P49785) belong to the group of channels: intercellular, the third one Q8TMG0 to the group of methyltransferases, and the fourth one P77335 to the group of adventitious membrane proteins: alpha-helical pore-forming toxins.Table 5
Prediction of hydrophobic regions and TMDs calculated upon processing of hydrophobicity functionsf
n
(
k
) at n
=
4
,
5 on H
N
(
i
) (N
=
3
,
4
,
5) scales for α-helical membrane proteins.
Protein name, code, length
Data source
Number and boundaries of hydrophobic regions, including TMDs
Scale level
1
2
3
4
5
6
7
SP2Q_BACSU P71044283 aa
[21], potential
22–42
H
5
(
i
)
,
n
=
5
〈
u
〉
=
-
0.127
20–47
70–94
107–124
130–175
207–229
H
4
(
i
)
,
n
=
5
〈
u
〉
=
0.696
16–48
70–94
109–121
132–174
197–225
SP3AH_BACSU P49785218 aa
[21],  potential
7–26
H
5
(
i
)
,
n
=
5
〈
u
〉
=
-
0.137
3–31
92–106
146–179
193–211
H
4
(
i
)
,
n
=
5
〈
u
〉
=
0.692
3–30
95–113
146–179
193–211
Q8TMG0_METAC Q8TMG0194 aa
H
5
(
i
)
,
n
=
5
〈
u
〉
=
0.232
7–20
49–67
76–93
130–162
H
3
(
i
)
,
n
=
5
〈
u
〉
=
0.041
0–22
45–62
77–91
127–163
HLYE_ECOLI P77335303 aa
[21], potential
183–203
H
3
(
i
)
,
n
=
5
〈
u
〉
=
-
0.248
0–17
24–38
82–103
114–123
180–209
242–247
264–280
H
5
(
i
)
,
n
=
4
〈
u
〉
=
0.029
5–26
32–40
81–102
115–123
179–208
242–253
267–275Here, as well as in Table4, the predictions were made on at least two hydrophobicity scales H
N
(
i
). Evidently, these predictions are consistent with each other for all domain boundaries considering the detection errors Δ
k
b
=
±
6. Individual single domains predicted earlier by other methods [21] were also identified by the proposed method.Table6 shows data comparison from [21] with prediction of TMDs made by the proposed method for the long (L
=
2424 aa) α-helical membrane protein from the group of adventitious membrane proteins: alpha-helical pore-forming toxins. Obviously, compliance between the predictions takes place for most of TMDs considering errors in determining their boundaries Δ
k
b
≤
6.Table 6
Prediction of TMDs calculated upon processing of hydrophobicity functionsf
n
(
k
) at n
=
5 on the scale H
5
(
i
) for the long α-helical membrane protein.
Protein name, code, length
Data source
Number and boundaries of transmembrane domains
Scale
1
2
3
4
5
6
CAC1A_RABIT P278842424 aa
[21], potential
99–117
136–155
168–185
191–209
229–248
336–360
H
5
,
u
=
0.305
101–116
141–158
172–185
210–249
302–317
336–358
Scale
7
8
9
10
11
12
[21], potential
488–506
522–541
550–568
579–597
617–636
690–714
H
5
,
u
=
0.305
491–507
518–537
554–577
609–638
654–665
685–714
Scale
13
14
15
16
17
18
[21], potential
1254–1272
1289–1308
1321–1339
1351–1369
1389–1408
1496–1520
H
5
,
u
=
0.305
1255–1270
1293–1312
1323–1339
1384–1408
1456–1467
1497–1522
Scale
19
20
21
22
23
24
[21], potential
1576–1604
1610–1629
1638–1656
1666–1684
1704–1723
1796–1820
H
5
,
u
=
0.305
1575–1599
1607–1633
1641–1660
1691–1725
—
1794–1820In the calculation using the proposed method of multiple averaging of hydrophobicity function over a sliding window, besides those domains indicated in Table6, a hydrophobic region of 16–28 aa was identified, which may belong to a signal peptide (SP) or may be the 1st one out of 24 TMDs of the present protein. Moreover, it is obvious that TMDs numbered in [21] as 5, 11, 17, and 23 and highlighted in Table 6 by a bold font in our prediction have the numbers, which are one less than in [21], but other domains that are not specified in [21] have the numbers, which are one more. Thus, two varied predictions in Table 6 have great similarities as well as notable differences.


## 4. Conclusions

The first membrane protein topology prediction algorithms were based solely on the hydrophobicity plots, for example, [14, 16, 18], and it seemed that the performance of these early methods was rather poor in practice. Hence, they soon were supplied by novel statistical, machine-learning methods, which use hundreds of free parameters extracted from databases of experimentally mapped topologies [13, 27]. However, as it is stated in [27], the translocons (cellular machineries) responsible for membrane-protein biogenesis do not have access to statistical data but rather exploit molecular interactions to ensure that membrane proteins attain their correct topology. Therefore, as it is concluded in [13], those methods which are based on the same physical properties that determine translocon-mediated membrane insertion, by using properly scaled hydrophobicity values, may access the same level of prediction accuracy as the best statistical methods.Thereby, here we presented the results of the study of 35 transmembrane proteins using cascade averaging of hydrophobicity function within the limits of a sliding window, as expressed in formula (1).In the work [4], the proposed method was successfully applied to predict the location of TMDs, secondary structure elements of a number of membrane proteins, in particular, bacteriorhodopsin, halorhodopsin, sensory rhodopsin 2, some connexins, and others.In the current work, this method was used to analyze the arrangement of the hydrophobic regions, including the transmembrane domains of another protein class, primarily GPCRs. At first, the method was tested on 5 known proteins of this class. Then an additional comparison of TMDs location predictions made by the proposed method and some other methods [21] was carried out on 20 proteins of the same class. These verifications confirmed the applicability of the proposed method for the stated purposes.Whereupon, this method was used to predict the TMDs in proteins with unknown structure, namely, 5 GPCRs and 5α-helical transmembrane proteins of other classes. For 9 out of 10 of these proteins (Tables 4 and 5) concordant predictions were made using at least two different hydrophobicity scales. The prediction made by the proposed method for a very long protein (Table 6) is consistent largely with the prediction made by another method [21].These facts indicate the applicability and usefulness of the new method presented in our work [4] and proposed here.



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*Source: 921218-2014-05-11.xml*