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6M3M
6VXX
7BWJ
6X6P
6VYB
6WZO
7C01
6VW1
6WPT
6WPS
6LXT
6WZQ
6XDC
7BYR
6W41
6WJI
6WKP
6YOR
6M0J
6Z97
6XC2
6XC4
6XC3
6XKL
6LZG
6XC7
7BV2
6WTT
7C2L
6WS6
6YM0
6M71
7C22
6YUN
6Y2G
6Y2E
6WIQ
6WQD
6W37
6ZCZ
6ZDH
6ZER
6YLA
6Y2F
7BW4
6WTC
6WX4
6ZGG
6M17
6M2N
6M2Q
6XDG
6X2A
6X2C
6X2B
6X29
6WUU
6W4H
6W75
6VWW
6WKQ
6WQF
6YZ5
6ZGE
6ZGI
6Z4U
6ZCO
6YI3
7C8V
7C8W
7CAN
6Z43
6ZFO
6XCN
6XCM
6XE1
7BQ7
5RGG
5RGI
5RGH
5RG3
5RG2
5RG1
5RGS
5RGR
5RGK
5RGJ
5RGM
5RGL
5RGO
5RGN
5RGQ
5RGP
6XCA
6W01
7BV1
6YYT
6M0K
6WKS
6LZE
6W6Y
7BUY
5R8T
5REA
5REC
5REB
5REE
5RED
5REG
5REF
5RE9
5RE8
5RE5
5RE4
5RE7
5RE6
5RFB
5RFA
5RFD
5RFC
5RFF
5RFE
5RFH
5RFG
5REY
5REX
5RF9
5REZ
5RF2
5REP
5RF1
5RES
5RF4
5RER
5RF3
5REU
5RF6
5RET
5RF5
5REW
5RF8
5REV
5RF7
5REI
5REH
5REK
5REJ
5REM
5REL
5REO
5RF0
5REN
5RFZ
5RFY
5RFR
5RFQ
5RFT
5RFS
5RFV
5RFU
5RFX
5RFW
5RFJ
5RFI
5RFL
5RFK
5RFN
5RFM
5RFP
5RFO
5RG0
5RHD
5RHC
5RGZ
5RHB
5RHA
5RH4
5RH3
5RGU
5RH6
5RGT
5RH5
5RGW
5RH8
5RGV
5RH7
5RGY
5RGX
5RH9
5RH0
5RH2
5RH1
6WNP
6Z2M
6YZ7
6YNQ
6YT8
6YVF
6X2G
6ZGH
6YHU
6WEY
6W7Y
6XOA
6Z2E
6YWM
6YWL
6YWK
6YZ1
5RHF
5RHE
6W9Q
6W9C
6WOJ
6WRH
6WTK
6WTM
6WTJ
6WXD
6WZU
6XB1
6XB0
6XB2
6XAA
6XDH
6XG3
6XIP
6XKF
6XKH
6M5I
6ZGF
7C2K
7BZF
6XKM
6M1D
6VSB
6M18
6YZ6
6XCH
6W02
6XMK
6W63
7C2I
7C2J
7C8T
7C8R
5R83
5R80
5R7Z
6VXS
6WCF
6WEN
6X1B
6X4I
6WXC
6XBI
6XBH
6XBG
6XFN
6XHU
6XA9
6W61
7BTF
6WJT
6WLC
6WQ3
6WRZ
6WVN
6LU7
6VYO
6YVA
6XA4
6ZCT
5R84
5R7Y
5R82
5R81
6YB7
6WAQ
6WAR
7BQY
6LVN
6Y84
6W4B
7BRR
7BRO
7BRP
6XHM
6M1V
7BZ5
6Y7M
7C8U
6M03
3R24
Parikh vectors
4XLQ_1
9LDT_1
1UYS_1
Letter
Amino acid
19
12
39
T
Threonine
26
36
52
V
Valine
22
20
52
A
Alanine
17
15
43
D
Aspartic acid
43
36
60
L
Leucine
4
8
17
M
Methionine
18
12
34
P
Proline
34
20
60
E
Glutamic acid
22
26
57
G
Glycine
6
12
9
H
Histidine
19
24
51
I
Isoleucine
16
23
39
S
Serine
21
11
49
R
Arginine
0
5
2
C
Cysteine
5
8
29
Q
Glutamine
5
7
25
Y
Tyrosine
9
17
33
N
Asparagine
17
26
40
K
Lycine
10
7
32
F
Phenylalanine
1
6
14
W
Tryptophan
Select a full-length spike protein
6VXX_1, 6X6P_1, 7BYR_1
6X6P_1, 7BYR_1, 7C2L_1
7BYR_1, 7C2L_1, 6Z97_1
4XLQ_1|Chains A, B, G, H|DNA-directed RNA polymerase subunit alpha|Thermus aquaticus (271)
>9LDT_1|Chains A, B|LACTATE DEHYDROGENASE|Sus scrofa (9823)
>1UYS_1|Chains A, B, C|ACETYL-COA CARBOXYLASE|SACCHAROMYCES CEREVISIAE (4932)
Protein code \(c\)
LZ-complexity \(\mathrm{LZ}(w)\)
Length \(n=|w|\)
\(\frac{\mathrm{LZ}(w)}{n /\log_{20} n}\)
\(p_w(1)\)
\(p_w(2)\)
\(p_w(3)\)
Sequence \(w=f(c)\)
4XLQ
, Knot
133
314
0.81
38
169
293
MLESK LKAPVFTATTQGDHYGEFVLEPLERGFGVTLGNPL RRIL LS SI PGTAV TSVYIEDVLHEFSTIPGVKE DVVEIILNLKELVVRFLDPKMASTTLILRAE GPKEVRAGDFTPSADVE IMN PDLHIA TLEEGGKLY MEVRVDRGVG YVPAERHGIKDRIN AIPVDAIFSPVRRVAFQVEDT RLG QRTDLDKL T LR IWTDG SVTPLEAL NQAVAIL KEHLNYFANPEASLLPTPEVSKGEK RESAEEDLDLPLEEL GLSTRVLHSLKEEGI ESVRA LL ALNLKDLRNIPGIGERSLEEI RQALAKKGFT LKE
9LDT
, Knot
143
332
0.83
42
198
319
XATLK DQLIHNL LKEEHVPH NKIT VVGVGAVGMACAIS IL MKEL ADEI ALVDV MEDKLKGEMMD LQHGSLFLRTPKIVSGKDYNVTANSRLVVITAGAR Q QEGE SRLNLVQRNVNIFKFIIPNIVKYSPNCK LLVVSNPVDILTYVAWKISGFPKNRVIGSGCNLDSARFRYLMGERLGVHPLSCHG WILGEHGDSSVPV WSG VNVAGVSL KNLHPEL GTDADKEHWKAVHKEVVDSAYEVIK LKGYT SWAIG LSVADLAESIMKNLRRVHP I STMIKGL YGIKENVFLSVPCILGQNGISDVVKVTLTPEEEAHL KKSADTLWGIQKELQF
1UYS
, Knot
289
737
0.86
40
287
676
PIATPYPVKEWL QPKRYKAH LMGT TYVYDFPELFRQAS SSQWKNFS ADVKLTDDFFISNELIED ENGELTEVE REPGANAIGMVAFKITVKTPEYPRGR Q FVVVANDITFKIGSFGPQEDE FFN KVTEYA RK RGIPRIY LAANSGARIG MAEEIVPLFQVAWN DAANPDKGFQYLYLTSEGMET LKKFDKENSVL T ER TV ING EERFVIKTIIGSEDGLGVECLRGSGLIAGATSRAYHDIFTITLVT CRSVG IGAYL VRLGQRAIQVEGQP I ILTGA PAINKMLGREVYTSNLQLGGTQI MYNNGVSHLT AVDDL AGVEKIVEWMSYVPAKRNMPVPILETKDTWDRPVDFTPTNDETYDVRWMIEGRETESGFEYGLFDKGSFFETLSGWAKGVVVGRARLGGIPLGVIGVETRTVENLIPADPANPNSAETLIQEPGQVWHPNSAFKTAQAINDFNNGEQLPMMILANWRGFSGGQRDMFNEVLKYGSFIVDALVDYKQPIIIYIPPTGELRGGSWVVVDPTINADQMEMYADVNARAGVLEPQGMVGIKFRREKLLDTMNRLDDKYRELRSQLSNKSLAPEVHQQISKQLADRERELLPIYGQISLQFADLHDRSSRMVAKGVISKELEWTEARRFFFWRLRRRLNEEYLIKRLSHQVGEASRLEKIARIRSWYPASVDHEDDRQVATWIEENYKTLDDKLKGLKLESFAQDLAKKIRSDHDNAIDGLSEVIK
Let \(P_w(n)\) be the set of distinct subwords (intervals) in a word \(w\).
Let \(p_w(n)\) be the cardinality of \(P_w(n)\).
Let \(f(c)\) be the sequence in FASTA with 4-symbol Protein Data Bank code \(c\).
\(|P_{f(4XLQ_1)}(2) \setminus P_{f(9LDT_1)}(2)|=65\),
\(|P_{f(9LDT_1)}(2) \setminus P_{f(4XLQ_1)}(2)|=94\).
Let
\(
Z_k(x,y)=|P_x(k)\setminus P_y(k)|+|P_y(k)\setminus P_x(k)|
\)
be a LZ76 style (set of subwords) Jaccard distance numerator for \(P(k)\).Hydrophobic-polar version of Sequence 1:11000101111010001000101110110011110110110011100111011001010011001001111000110111010011101101011000111010110010110101010101101010110100110101010100111011100011000101111011101100111010000110000100101011001010110110011111000100110101011101010010000010001011100111000110010001100101111101001001111100010010011100110100
Pair
\(Z_2\)
Length of longest common subsequence
4XLQ_1,9LDT_1
159
4
4XLQ_1,1UYS_1
162
5
9LDT_1,1UYS_1
175
5
Newick tree
[
1UYS_1:85.85,
[
4XLQ_1:79.5,9LDT_1:79.5
]:6.35
]
Let d be the
Otu--Sayood
distance d.
Let d1 be the Otu--Sayood distance d1 . (This makes the 4TYN sequence AAAAAA a close match...)
A roughly speaking expected distance is \((0.85)(0.8)(\frac{646
}{\log_{20}
646}-\frac{314}{\log_{20}314})=92.1\)
Status
Protein1
Protein2
d
d1 /2
Query variables
4XLQ_1
9LDT_1
114
110
Was not able to put for d Was not able to put for d1
In notation analogous to
[Theorem 16, Kjos-Hanssen, Niraula and Yoon (2022) ],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]