Tutorial for Dev: Spectral Libraries#

This notebook introduces functionalities for spectral libraries to developers.

[1]:

# One or two methods are renamed and only available in v1.0.1 (main branch),
# please install alphabase from github:

# %pip install git+https://github.com/mannlabs/alphabase

[2]:

import alphabase
# the version must be 1.0.1
alphabase.__version__

[2]:

'1.0.1'

The Base Library Class#

alphabase.spectral_library.base.SpecLibBase is the base class for spectral libraries. See https://alphabase.readthedocs.io/en/latest/ for details. We recommend users to access spectral library functionalities via alphabase.protein.fasta.SpecLibFasta.

SpecLibFasta#

Almost all DataFrame functionalities to process proteins and peptides have been integrated into alphabase.protein.fasta.SpecLibFasta.

[3]:

from alphabase.protein.fasta import SpecLibFasta

fasta_lib = SpecLibFasta(
    charged_frag_types=['b_z1','y_z1'],
    protease='trypsin',
    fix_mods=['Carbamidomethyl@C'],
    var_mods=['Acetyl@Protein N-term','Oxidation@M'],
    decoy=None,
)

Start from fasta/proteins#

The SpecLibFasta will do following for us:

  • Load fasta files into a protein_dict

  • Digest proteins into peptide sequences

  • Append decoy peptide sequences if self.decoy is not None

  • Add fixed and variable modifications

  • [Add special modifications]

  • [Add peptide labeling]

  • Add charge states to peptides

Load fasta files into a protein_dict#

[4]:

# from alphabase.protein.fasta import load_all_proteins
# protein_dict = load_all_proteins(fasta_files)

# For example, the protein_dict is:
protein_dict = {
    'yy': {
        'protein_id': 'yy',
        'full_name': 'yy_yy',
        'gene_name': 'y_y',
        'sequence': 'FGHIKLMNPQR'
    },
    'xx': {
        'protein_id': 'xx',
        'full_name': 'xx_xx',
        'gene_name': 'x_x',
        'sequence': 'MACDESTYKxKFGHIKLMNPQRST'
    },
}

Digest proteins into peptide sequences#

[5]:

fasta_lib.get_peptides_from_protein_dict(protein_dict)
fasta_lib.precursor_df

[5]:
sequence protein_idxes miss_cleavage is_prot_nterm is_prot_cterm mods mod_sites nAA
0 xKFGHIK 1 1 False False 7
1 LMNPQRST 1 1 False True 8
2 ACDESTYK 1 0 True False 8
3 MACDESTYK 1 0 True False 9
4 ACDESTYKxK 1 1 True False 10
5 FGHIKLMNPQR 0;1 1 True True 11
6 MACDESTYKxK 1 1 True False 11
7 xKFGHIKLMNPQR 1 2 False False 13
8 FGHIKLMNPQRST 1 2 False True 13
9 ACDESTYKxKFGHIK 1 2 True False 15
10 MACDESTYKxKFGHIK 1 2 True False 16 
[6]:

fasta_lib.protein_df

[6]:
protein_id full_name gene_name sequence
0 yy yy_yy y_y FGHIKLMNPQR
1 xx xx_xx x_x MACDESTYKxKFGHIKLMNPQRST

Append decoy sequences#

This depends on self.decoy:str, its value can be

  • protein_reverse: Reverse on target protein sequences

  • pseudo_reverse: Pseudo-reverse on target peptide sequences

  • diann: DiaNN-like decoy

  • None: no decoy.

Let’s take protein_reverse as an example:

[7]:

fasta_lib.decoy = 'protein_reverse'
fasta_lib.append_decoy_sequence()
fasta_lib.precursor_df.sample(5, random_state=0)

[7]:
sequence protein_idxes miss_cleavage is_prot_nterm is_prot_cterm mods mod_sites nAA decoy
20 ACDESTYKxKFGHIK 1 2 True False 15 0
10 QPNMLKIHGF 2 1 False True 10 1
14 FGHIKLMNPQR 0;1 1 True True 11 0
13 MACDESTYKxK 1 1 True False 11 0
1 IHGFKxK 3 1 False False 7 1

As protein_reverse is a protein-level decoy, the protein_df is changed too:

[8]:

fasta_lib.protein_df

[8]:
protein_id full_name gene_name sequence decoy
0 yy yy_yy y_y FGHIKLMNPQR 0
1 xx xx_xx x_x MACDESTYKxKFGHIKLMNPQRST 0
2 REV_yy REV_yy_yy REV_y_y RQPNMLKIHGF 1
3 REV_xx REV_xx_xx REV_x_x TSRQPNMLKIHGFKxKYTSEDCAM 1

Add modifications#

add_modifications() will add fixed and variable modifications.

[9]:

fasta_lib.add_modifications()
fasta_lib.precursor_df.sample(5, random_state=0)

[9]:
sequence protein_idxes miss_cleavage is_prot_nterm is_prot_cterm mods mod_sites nAA decoy
35 MACDESTYKxK 1 1 True False Carbamidomethyl@C;Acetyl@Protein N-term 3;0 11 0
34 MACDESTYKxK 1 1 True False Carbamidomethyl@C;Acetyl@Protein N-term;Oxidat... 3;0;1 11 0
42 xKFGHIKLMNPQR 1 2 False False Oxidation@M 9 13 0
27 QPNMLKIHGFK 3 1 False False 11 1
11 YTSEDCAM 3 0 False True Carbamidomethyl@C 6 8 1

Add special modifications#

Special modifications here refer to some PTMs we want to have more controls on:

  1. We only needs peptides without unmodified forms

  2. GlyGly@K cannot occur on peptide C-term because trypsin cannot cleave Lys with GlyGly

  3. For some special modifications like Phospho@S and HexNAc@S, we would like to limit the number of peptidome forms to control the memory usage.

[10]:

fasta_lib.special_mods = ['GlyGly@K']
fasta_lib.special_mods_cannot_modify_pep_c_term = True
fasta_lib.min_special_mod_num = 1 # exclude the unmodified forms
fasta_lib.max_special_mod_num = 1 # limit the number of
fasta_lib.add_special_modifications()
fasta_lib.precursor_df.sample(10, random_state=0)

[10]:
sequence protein_idxes miss_cleavage is_prot_nterm is_prot_cterm mods mod_sites nAA decoy
28 QPNMLKIHGFKxK 3 2 False False Oxidation@M;GlyGly@K 4;6 13 1
37 IHGFKxKYTSEDCAM 3 2 False True Carbamidomethyl@C;Oxidation@M;GlyGly@K 13;15;7 15 1
11 RQPNMLKIHGF 2 2 True True GlyGly@K 7 11 1
34 TSRQPNMLKIHGFK 3 2 True False Acetyl@Protein N-term;Oxidation@M;GlyGly@K 0;7;9 14 1
2 ACDESTYKxK 1 1 True False Carbamidomethyl@C;GlyGly@K 2;8 10 0
30 QPNMLKIHGFKxK 3 2 False False GlyGly@K 6 13 1
40 ACDESTYKxKFGHIK 1 2 True False Carbamidomethyl@C;GlyGly@K 2;8 15 0
32 TSRQPNMLKIHGFK 3 2 True False Oxidation@M;GlyGly@K 7;9 14 1
26 xKFGHIKLMNPQR 1 2 False False GlyGly@K 2 13 0
4 xKYTSEDCAM 3 1 False True Carbamidomethyl@C;Oxidation@M;GlyGly@K 8;10;2 10 1

Add peptide labeling#

For example Dimethyl:

[11]:

fasta_lib.labeling_channels = {
    0: ['Dimethyl@K', 'Dimethyl@Any N-term'],
    4: ['Dimethyl:2H(4)@K', 'Dimethyl:2H(4)@Any N-term'],
}
fasta_lib.add_peptide_labeling()
fasta_lib.precursor_df.sample(10, random_state=0)

[11]:
sequence protein_idxes miss_cleavage is_prot_nterm is_prot_cterm mods mod_sites nAA decoy labeling_channel
26 xKFGHIKLMNPQR 1 2 False False GlyGly@K;Dimethyl@Any N-term;Dimethyl@K;Dimeth... 2;0;2;7 13 0 0
61 QPNMLKIHGFK 3 1 False False GlyGly@K;Dimethyl:2H(4)@Any N-term;Dimethyl:2H... 6;0;6;11 11 1 4
2 ACDESTYKxK 1 1 True False Carbamidomethyl@C;GlyGly@K;Dimethyl@Any N-term... 2;8;0;8;10 10 0 0
62 RQPNMLKIHGF 2 2 True True Oxidation@M;GlyGly@K;Dimethyl:2H(4)@Any N-term... 5;7;0;7 11 1 4
85 TSRQPNMLKIHGFK 3 2 True False GlyGly@K;Dimethyl:2H(4)@Any N-term;Dimethyl:2H... 9;0;9;14 14 1 4
48 MACDESTYKxKFGHIK 1 2 True False Carbamidomethyl@C;Acetyl@Protein N-term;Oxidat... 3;0;1;9;9;11;16 16 0 0
16 MACDESTYKxK 1 1 True False Carbamidomethyl@C;Acetyl@Protein N-term;Oxidat... 3;0;1;9;9;11 11 0 0
99 MACDESTYKxKFGHIK 1 2 True False Carbamidomethyl@C;GlyGly@K;Dimethyl:2H(4)@Any ... 3;11;0;9;11;16 16 0 4
56 xKYTSEDCAM 3 1 False True Carbamidomethyl@C;Oxidation@M;GlyGly@K;Dimethy... 8;10;2;0;2 10 1 4
45 MACDESTYKxKFGHIK 1 2 True False Carbamidomethyl@C;Oxidation@M;GlyGly@K;Dimethy... 3;1;11;0;9;11;16 16 0 0

Add charge states#

[12]:

fasta_lib.add_charge()
fasta_lib.precursor_df.sample(5, random_state=0)

[12]:
sequence protein_idxes miss_cleavage is_prot_nterm is_prot_cterm mods mod_sites nAA decoy labeling_channel charge
65 FGHIKLMNPQR 0;1 1 True True Acetyl@Protein N-term;GlyGly@K;Dimethyl@K 0;5;5 11 0 0 4
225 FGHIKLMNPQRST 1 2 False True GlyGly@K;Dimethyl:2H(4)@Any N-term;Dimethyl:2H... 5;0;5 13 0 4 2
188 RQPNMLKIHGF 2 2 True True Oxidation@M;GlyGly@K;Dimethyl:2H(4)@Any N-term... 5;7;0;7 11 1 4 4
200 MACDESTYKxK 1 1 True False Carbamidomethyl@C;Oxidation@M;GlyGly@K;Dimethy... 3;1;9;0;9;11 11 0 4 4
108 IHGFKxKYTSEDCAM 3 2 False True Carbamidomethyl@C;Oxidation@M;GlyGly@K;Dimethy... 13;15;5;0;5;7 15 1 0 2

import_and_process_protein_dict() combines all steps#

Or import_and_process_fasta() for fasta files.

[13]:

fasta_lib.special_mods = []
fasta_lib.labeling_channels = None
fasta_lib.import_and_process_protein_dict(protein_dict)
fasta_lib.protein_df

[13]:
protein_id full_name gene_name sequence decoy
0 yy yy_yy y_y FGHIKLMNPQR 0
1 xx xx_xx x_x MACDESTYKxKFGHIKLMNPQRST 0
2 REV_yy REV_yy_yy REV_y_y RQPNMLKIHGF 1
3 REV_xx REV_xx_xx REV_x_x TSRQPNMLKIHGFKxKYTSEDCAM 1 
[14]:

fasta_lib.precursor_df

[14]:
sequence protein_idxes miss_cleavage is_prot_nterm is_prot_cterm mods mod_sites nAA decoy charge
0 xKFGHIK 1 1 False False 7 0 2
1 xKFGHIK 1 1 False False 7 0 3
2 xKFGHIK 1 1 False False 7 0 4
3 IHGFKxK 3 1 False False 7 1 2
4 IHGFKxK 3 1 False False 7 1 3
... ... ... ... ... ... ... ... ... ... ...
169 MACDESTYKxKFGHIK 1 2 True False Carbamidomethyl@C;Acetyl@Protein N-term;Oxidat... 3;0;1 16 0 3
170 MACDESTYKxKFGHIK 1 2 True False Carbamidomethyl@C;Acetyl@Protein N-term;Oxidat... 3;0;1 16 0 4
171 MACDESTYKxKFGHIK 1 2 True False Carbamidomethyl@C;Acetyl@Protein N-term 3;0 16 0 2
172 MACDESTYKxKFGHIK 1 2 True False Carbamidomethyl@C;Acetyl@Protein N-term 3;0 16 0 3
173 MACDESTYKxKFGHIK 1 2 True False Carbamidomethyl@C;Acetyl@Protein N-term 3;0 16 0 4

174 rows × 10 columns

Start from peptides instead of proteins#

The modularity design of SpecLibFasta allows us to starts from arbitrary types of peptide inputs, meaning that fasta files or protein_dict is not necessary.

For example, we have a list of sequences, and we what to add modifications using SpecLibFasta functionalities:

[15]:

import pandas as pd
pep_lib = SpecLibFasta(
    charged_frag_types=['b_z1','y_z1'],
    fix_mods=['Carbamidomethyl@C'],
    var_mods=['Acetyl@Protein N-term','Oxidation@M'],
    labeling_channels={
        0: ['Dimethyl@K', 'Dimethyl@Any N-term'],
        4: ['Dimethyl:2H(4)@K', 'Dimethyl:2H(4)@Any N-term'],
    },
    decoy=None,
)

pep_lib.precursor_df = pd.DataFrame({
    'sequence': ['ABCDEFG','HIJKLMN','OPQRST','UVWXYZ']
})
pep_lib.process_from_naked_peptide_seqs()
pep_lib.precursor_df

[15]:
sequence nAA is_prot_nterm is_prot_cterm mods mod_sites labeling_channel charge
0 OPQRST 6 False False Dimethyl@Any N-term 0 0 2
1 OPQRST 6 False False Dimethyl@Any N-term 0 0 3
2 OPQRST 6 False False Dimethyl@Any N-term 0 0 4
3 UVWXYZ 6 False False Dimethyl@Any N-term 0 0 2
4 UVWXYZ 6 False False Dimethyl@Any N-term 0 0 3
5 UVWXYZ 6 False False Dimethyl@Any N-term 0 0 4
6 ABCDEFG 7 False False Carbamidomethyl@C;Dimethyl@Any N-term 3;0 0 2
7 ABCDEFG 7 False False Carbamidomethyl@C;Dimethyl@Any N-term 3;0 0 3
8 ABCDEFG 7 False False Carbamidomethyl@C;Dimethyl@Any N-term 3;0 0 4
9 HIJKLMN 7 False False Oxidation@M;Dimethyl@Any N-term;Dimethyl@K 6;0;4 0 2
10 HIJKLMN 7 False False Oxidation@M;Dimethyl@Any N-term;Dimethyl@K 6;0;4 0 3
11 HIJKLMN 7 False False Oxidation@M;Dimethyl@Any N-term;Dimethyl@K 6;0;4 0 4
12 HIJKLMN 7 False False Dimethyl@Any N-term;Dimethyl@K 0;4 0 2
13 HIJKLMN 7 False False Dimethyl@Any N-term;Dimethyl@K 0;4 0 3
14 HIJKLMN 7 False False Dimethyl@Any N-term;Dimethyl@K 0;4 0 4
15 OPQRST 6 False False Dimethyl:2H(4)@Any N-term 0 4 2
16 OPQRST 6 False False Dimethyl:2H(4)@Any N-term 0 4 3
17 OPQRST 6 False False Dimethyl:2H(4)@Any N-term 0 4 4
18 UVWXYZ 6 False False Dimethyl:2H(4)@Any N-term 0 4 2
19 UVWXYZ 6 False False Dimethyl:2H(4)@Any N-term 0 4 3
20 UVWXYZ 6 False False Dimethyl:2H(4)@Any N-term 0 4 4
21 ABCDEFG 7 False False Carbamidomethyl@C;Dimethyl:2H(4)@Any N-term 3;0 4 2
22 ABCDEFG 7 False False Carbamidomethyl@C;Dimethyl:2H(4)@Any N-term 3;0 4 3
23 ABCDEFG 7 False False Carbamidomethyl@C;Dimethyl:2H(4)@Any N-term 3;0 4 4
24 HIJKLMN 7 False False Oxidation@M;Dimethyl:2H(4)@Any N-term;Dimethyl... 6;0;4 4 2
25 HIJKLMN 7 False False Oxidation@M;Dimethyl:2H(4)@Any N-term;Dimethyl... 6;0;4 4 3
26 HIJKLMN 7 False False Oxidation@M;Dimethyl:2H(4)@Any N-term;Dimethyl... 6;0;4 4 4
27 HIJKLMN 7 False False Dimethyl:2H(4)@Any N-term;Dimethyl:2H(4)@K 0;4 4 2
28 HIJKLMN 7 False False Dimethyl:2H(4)@Any N-term;Dimethyl:2H(4)@K 0;4 4 3
29 HIJKLMN 7 False False Dimethyl:2H(4)@Any N-term;Dimethyl:2H(4)@K 0;4 4 4

Calculate masses#

Calculate precursor m/z#

[16]:

fasta_lib.calc_precursor_mz()
# fasta_lib.calc_precursor_isotope()
fasta_lib.precursor_df

[16]:
sequence protein_idxes miss_cleavage is_prot_nterm is_prot_cterm mods mod_sites nAA decoy charge precursor_mz
0 RQPNMLK 2 1 True False Oxidation@M 5 7 1 2 451.747462
1 RQPNMLK 2 1 True False 7 1 2 443.750005
2 RQPNMLK 2 1 True False Acetyl@Protein N-term;Oxidation@M 0;5 7 1 2 472.752744
3 RQPNMLK 2 1 True False Acetyl@Protein N-term 0 7 1 2 464.755287
4 LMNPQRST 1 1 False True Oxidation@M 2 8 0 2 481.739834
5 LMNPQRST 1 1 False True 8 0 2 473.742377
6 ACDESTYK 1 0 True False Carbamidomethyl@C 2 8 0 2 487.200207
7 ACDESTYK 1 0 True False Carbamidomethyl@C;Acetyl@Protein N-term 2;0 8 0 2 508.205490
8 YTSEDCAM 3 0 False True Carbamidomethyl@C;Oxidation@M 6;8 8 1 2 496.670426
9 YTSEDCAM 3 0 False True Carbamidomethyl@C 6 8 1 2 488.672968
10 MACDESTYK 1 0 True False Carbamidomethyl@C;Oxidation@M 3;1 9 0 2 560.717907
11 MACDESTYK 1 0 True False Carbamidomethyl@C 3 9 0 2 552.720450
12 MACDESTYK 1 0 True False Carbamidomethyl@C;Acetyl@Protein N-term;Oxidat... 3;0;1 9 0 2 581.723190
13 MACDESTYK 1 0 True False Carbamidomethyl@C;Acetyl@Protein N-term 3;0 9 0 2 573.725732
14 TSRQPNMLK 3 1 True False Oxidation@M 7 9 1 2 545.787316
15 TSRQPNMLK 3 1 True False 9 1 2 537.789858
16 TSRQPNMLK 3 1 True False Acetyl@Protein N-term;Oxidation@M 0;7 9 1 2 566.792598
17 TSRQPNMLK 3 1 True False Acetyl@Protein N-term 0 9 1 2 558.795141
18 QPNMLKIHGF 2 1 False True Oxidation@M 4 10 1 2 600.813333
19 QPNMLKIHGF 2 1 False True Oxidation@M 4 10 1 3 400.877981
20 QPNMLKIHGF 2 1 False True 10 1 2 592.815876
21 QPNMLKIHGFK 3 1 False False Oxidation@M 4 11 1 2 664.860815
22 QPNMLKIHGFK 3 1 False False Oxidation@M 4 11 1 3 443.576302
23 QPNMLKIHGFK 3 1 False False 11 1 2 656.863357
24 QPNMLKIHGFK 3 1 False False 11 1 3 438.244664
25 RQPNMLKIHGF 2 2 True True Oxidation@M 5 11 1 2 678.863889
26 RQPNMLKIHGF 2 2 True True Oxidation@M 5 11 1 3 452.911685
27 RQPNMLKIHGF 2 2 True True 11 1 2 670.866431
28 RQPNMLKIHGF 2 2 True True 11 1 3 447.580046
29 RQPNMLKIHGF 2 2 True True Acetyl@Protein N-term;Oxidation@M 0;5 11 1 2 699.869171
30 RQPNMLKIHGF 2 2 True True Acetyl@Protein N-term;Oxidation@M 0;5 11 1 3 466.915206
31 RQPNMLKIHGF 2 2 True True Acetyl@Protein N-term 0 11 1 2 691.871714
32 RQPNMLKIHGF 2 2 True True Acetyl@Protein N-term 0 11 1 3 461.583568
33 FGHIKLMNPQR 0;1 1 True True Oxidation@M 7 11 0 2 678.863889
34 FGHIKLMNPQR 0;1 1 True True Oxidation@M 7 11 0 3 452.911685
35 FGHIKLMNPQR 0;1 1 True True 11 0 2 670.866431
36 FGHIKLMNPQR 0;1 1 True True 11 0 3 447.580046
37 FGHIKLMNPQR 0;1 1 True True Acetyl@Protein N-term;Oxidation@M 0;7 11 0 2 699.869171
38 FGHIKLMNPQR 0;1 1 True True Acetyl@Protein N-term;Oxidation@M 0;7 11 0 3 466.915206
39 FGHIKLMNPQR 0;1 1 True True Acetyl@Protein N-term 0 11 0 2 691.871714
40 FGHIKLMNPQR 0;1 1 True True Acetyl@Protein N-term 0 11 0 3 461.583568
41 FGHIKLMNPQRST 1 2 False True Oxidation@M 7 13 0 2 772.903742
42 FGHIKLMNPQRST 1 2 False True Oxidation@M 7 13 0 3 515.604920
43 FGHIKLMNPQRST 1 2 False True 13 0 2 764.906285
44 FGHIKLMNPQRST 1 2 False True 13 0 3 510.273282
45 TSRQPNMLKIHGFK 3 2 True False Oxidation@M 7 14 1 2 836.951224
46 TSRQPNMLKIHGFK 3 2 True False Oxidation@M 7 14 1 3 558.303241
47 TSRQPNMLKIHGFK 3 2 True False Oxidation@M 7 14 1 4 418.979250
48 TSRQPNMLKIHGFK 3 2 True False 14 1 2 828.953766
49 TSRQPNMLKIHGFK 3 2 True False 14 1 3 552.971603
50 TSRQPNMLKIHGFK 3 2 True False 14 1 4 414.980521
51 TSRQPNMLKIHGFK 3 2 True False Acetyl@Protein N-term;Oxidation@M 0;7 14 1 2 857.956506
52 TSRQPNMLKIHGFK 3 2 True False Acetyl@Protein N-term;Oxidation@M 0;7 14 1 3 572.306763
53 TSRQPNMLKIHGFK 3 2 True False Acetyl@Protein N-term;Oxidation@M 0;7 14 1 4 429.481891
54 TSRQPNMLKIHGFK 3 2 True False Acetyl@Protein N-term 0 14 1 2 849.959049
55 TSRQPNMLKIHGFK 3 2 True False Acetyl@Protein N-term 0 14 1 3 566.975125
56 TSRQPNMLKIHGFK 3 2 True False Acetyl@Protein N-term 0 14 1 4 425.483163

After calc_precursor_mz(), all sequences containing x are removed because x’s mass is very large which is out of the range of fasta_lib.min_precursor_mz and fasta_lib.max_precursor_mz.

[17]:

from alphabase.constants.aa import AA_ASCII_MASS
(
    fasta_lib.min_precursor_mz, fasta_lib.max_precursor_mz,
    f"mass of 'x' is {AA_ASCII_MASS[ord('x')]}"
)

[17]:

(400.0, 2000.0, "mass of 'x' is 100000000.0")

Calculate fragment m/z#

[18]:

fasta_lib.calc_fragment_mz_df()
fasta_lib.fragment_mz_df

[18]:
b_z1 y_z1
0 157.108387 746.386537
1 285.166965 618.327959
2 382.219729 521.275195
3 496.262656 407.232268
4 643.298056 260.196868
... ... ...
556 1098.572440 601.345658
557 1211.656504 488.261594
558 1348.715416 351.202682
559 1405.736879 294.181218
560 1552.805293 147.112804

561 rows × 2 columns

Use frag_start_idx and frag_stop_idx in precursor_df to locate the corresponding fragments

[19]:

ith_pep = 5
frag_start, frag_stop = fasta_lib.precursor_df.loc[ith_pep,['frag_start_idx','frag_stop_idx']].values
fasta_lib.fragment_mz_df.iloc[frag_start:frag_stop]

[19]:
b_z1 y_z1
31 114.091340 833.393413
32 245.131826 702.352928
33 359.174753 588.310000
34 456.227517 491.257237
35 584.286094 363.198659
36 740.387205 207.097548
37 827.419234 120.065520 
[ ]: