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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
7ZTS_1
3LCX_1
8AVA_1
Letter
Amino acid
45
22
38
V
Valine
38
6
21
N
Asparagine
13
18
22
H
Histidine
29
16
40
K
Lycine
28
9
11
M
Methionine
36
13
23
R
Arginine
7
5
11
C
Cysteine
43
14
40
T
Threonine
48
15
34
D
Aspartic acid
42
20
31
I
Isoleucine
27
9
27
F
Phenylalanine
39
11
35
P
Proline
60
35
69
L
Leucine
51
17
45
S
Serine
7
1
13
W
Tryptophan
36
12
22
Y
Tyrosine
57
27
38
A
Alanine
18
21
26
Q
Glutamine
37
17
41
E
Glutamic acid
36
31
30
G
Glycine
Select a full-length spike protein
6VXX_1, 6X6P_1, 7BYR_1
6X6P_1, 7BYR_1, 7C2L_1
7BYR_1, 7C2L_1, 6Z97_1
7ZTS_1|Chains AA[auth AB], AB[auth AC], AC[auth AD], AD[auth AE], A[auth AA], BA[auth AG], BB[auth AH], BC[auth AI], BD[auth AJ], B[auth AF], CA[auth AL], CB[auth AM], CC[auth AN], CD[auth AO], C[auth AK], DA[auth AQ], DB[auth AR], DC[auth AS], DD[auth AT], D[auth AP], EA[auth AV], EB[auth AW], EC[auth AX], ED[auth AY], E[auth AU], FA[auth BA], FB[auth BB], FC[auth BC], FD[auth BD], F[auth AZ], GA[auth BF], GB[auth BG], GC[auth BH], G[auth BE], HA[auth BJ], HB[auth BK], HC[auth BL], H[auth BI], IA[auth BN], IB[auth BO], IC[auth BP], I[auth BM], JA[auth BR], JB[auth BS], JC[auth BT], J[auth BQ], KA[auth BV], KB[auth BW], KC[auth BX], K[auth BU], LA[auth BZ], LB[auth CA], LC[auth CB], L[auth BY], MA[auth CD], MB[auth CE], MC[auth CF], M[auth CC], NA[auth CH], NB[auth CI], NC[auth CJ], N[auth CG], OA[auth CL], OB[auth CM], OC[auth CN], O[auth CK], PA[auth CP], PB[auth CQ], PC[auth CR], P[auth CO], QA[auth CT], QB[auth CU], QC[auth CV], Q[auth CS], RA[auth CX], RB[auth CY], RC[auth CZ], R[auth CW], SA[auth DB], SB[auth DC], SC[auth DD], S[auth DA], TA[auth DF], TB[auth DG], TC[auth DH], T[auth DE], UA[auth DJ], UB[auth DK], UC[auth DL], U[auth DI], VA[auth DN], VB[auth DO], VC[auth DP], V[auth DM], WA[auth DR], WB[auth DS], WC[auth DT], W[auth DQ], XA[auth DV], XB[auth DW], XC[auth DX], X[auth DU], YA[auth DZ], YB[auth EA], YC[auth EB], Y[auth DY], ZA[auth ED], ZB[auth EE], ZC[auth EF], Z[auth EC]|Major capsid protein|Saccharomyces cerevisiae BY4741 (1247190)
>3LCX_1|Chains A, B, C, D|N-acetylneuraminate lyase|Escherichia coli (83333)
>8AVA_1|Chain A|Leukotriene A-4 hydrolase|Homo sapiens (9606)
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 \(w=f(c)\)
7ZTS
, Knot
269
697
0.84
40
291
650
M SSLLNSLLPEYFKPKTNLNINSSRVQYG FNA RID MQYEDDSG T RK GS RPNAFMSN TVAFI GNYEGII VDDIPILDGL RADIFDTHGDLDMGLVEDAL SKSTMIRRNV PTYTAYA S ELLYKRNLTS LFYNMLRLYYIKKWGSIKYEKDA I FYDNGHACLLNRQL FPKS RDASL ESSL S LPEAEIA MLDPGLEFPEEDVPAILWHGRV SSRATCILGQACSEFAPLAPFS IAHYSPQLTRKLFV NA PAGIEPSSGRYTHEDVKDAI TIL VSANQAYTDFEAAYLM LAQT L VSPVPRTAEASA WFI NAGMVNMPTL SCANG YYPALTNVNPY HRLDTWKDTLNHWVAYPDML FYHSVAMIESCYVELGNVARVSDSD AINKYTFTELS VQGRPVMNRGIIVDLTL VAMRTGREISL PYPV SCGLTRTDALLQGTEIHVPVVVKDID MPQYYNAIDKDVIEG QETVIKVKQLPPAMYPI YTYGINTT EFYSD HFEDQVQVEMAPIDNGKAVF NDARKFSKFMSIMRMMGNDVTATDLVTGRKVSNWADNSSGRFLYTDVKYEGQTAFLVDMDTVK ARDHCWVSIVDPNGTMNLSYKMTNFRAA MFSRNKPLYMTGGSVRTIATGNYRDAAERLRAMDETLRLKPFKITEKLDFRVAAYAIPSLSGSNMPSLHHQEQLQISEVDAEPINPIGEDELPPDIE
3LCX
, Knot
138
319
0.83
40
194
301
M GH H H H H HHHHHSSGHIEGRHMMAT NLRG VMA ALLTPFDQQQALDK AS LRRLVQFN IQQGI D GLYVGGSTGEAFVQ SL SERAQVLEIVAEEAKGKIKL I A HVGCVSTAESQQLAA S AK RHGFDAVS AVTPFYYPFSLEEHCDHYRAIIDSADGLPMVVYNIPAL SGV KLTLGQIYTL VTLPGVGA LKQTSGDLYQMEQI RREHPDLV L YNGYDEIFAS GLLAGADGGIGSTYNIMGWRY QGIV KA LKEGDIQTAQKLQTECNKVI DLL IKTGIFRG LKTVLHYM DVISVPLCRK PFGPV DEKCLPELKALAQQL MQERG
8AVA
, Knot
246
617
0.85
40
286
574
M HH H H H H PEIVDTCSLASPASVCRT KHLHLRCSVD FTRRTLTG T AALTVQSQEDNLRSLVLD TKDLTI EKVVINGQ EVKYALGERQSYKGSPMEISLPI A LSKNQEIV IEISFETS PK SSALQWLTPEQTSGKEHPYLFSQCQAIHCRA I LPCQDTPSVKLTYTAEV S VPKEL VALMS AIRDGETPDPEDPSRKIYKFI QKVPIPCYL IALVVGALES RQIGPRTLVWS EKEQVEKSAY EFSETESMLKIAEDLGGPYVWGQYDLLVL PPSFPYGG MENPCLTFVTPT L LAGDK SLSNV IA HEI SHSWTGNLVTNKTWDHFWLNEGHTVY LERHICGRLFGEKFRHFNAL GGWGELQNSVKTFGETHPFTKLVVD LTDIDPDVAYS SVPYEKGFALLFYLEQL LGGPEIFLGFL KAYV EKFSYKSITTDDWKDFLYSYFKDKVD VLNQVDWNAWLYSPG LPPIKPNYDMTLTNACI ALSQRWIT AKEDD LNSFNATDLKDLSSHQLNEF LAQTLQRAPLPLGHIKRMQEVYNFNAINNSEIRFRWLRLCIQSKWEDAIPLALKMATEQGRMK FTRPLFKDLAAFDKSHDQAVRTYQEHKA SMHPVTAMLVGKDLKVD
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 \(c\).
\(|P_{f(7ZTS_1)}(2) \setminus P_{f(3LCX_1)}(2)|=133\),
\(|P_{f(3LCX_1)}(2) \setminus P_{f(7ZTS_1)}(2)|=36\).
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 1:1001100111001010001010000100110101010000001000100101110001111100011110011110110101100010101111001100001100011000101001100001001100110100100110100000111000101011000111000010100010110101111011101100011111101010001001110100011111110110001010001110111110100100000010011011101001000101101111001101110010101111011110110100101001110010100010010001001110101110001111000010110110100001100001001010101110011110101111001001011011001100001110100101111100101100001100011010001101001111101100011000010000100010101111001011100100100110110111001010011010010011000010110001000100111101001010000110110101010100010010111100001101011010011010000110010110001010110100010101110111010100110100000101001010110111000111010
Pair
\(Z_2\)
Length of longest common subsequence
7ZTS_1,3LCX_1
169
3
7ZTS_1,8AVA_1
129
5
3LCX_1,8AVA_1
170
6
Newick tree
[
3LCX_1:90.49,
[
7ZTS_1:64.5,8AVA_1:64.5
]:25.99
]
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 \((0.85)(0.8)(\frac{1016
}{\log_{20}
1016}-\frac{319}{\log_{20}319})=186.\)
Status
Protein1
Protein2
d
d1 /2
Query variables
7ZTS_1
3LCX_1
236
169.5
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) ],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]