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Parikh vectors
6OKT_1 4EQU_1 7MSG_1 Letter Amino acid
81 23 3 K Lycine
1 4 2 C Cysteine
63 21 3 I Isoleucine
36 16 6 P Proline
70 14 15 S Serine
78 14 9 T Threonine
7 5 3 W Tryptophan
49 9 8 Y Tyrosine
5 8 11 H Histidine
75 8 2 N Asparagine
71 18 4 D Aspartic acid
58 31 10 E Glutamic acid
49 15 20 G Glycine
20 14 12 R Arginine
26 6 5 Q Glutamine
68 33 22 L Leucine
17 11 1 M Methionine
26 8 4 F Phenylalanine
39 19 15 V Valine
37 25 10 A Alanine 

6OKT_1|Chains A[auth H], B[auth I], C[auth J], D[auth K], E[auth L], F[auth M], G[auth N]|ADP-ribosyltransferase binding component|Clostridioides difficile (1496)
>4EQU_1|Chains A, B|Serine/threonine-protein kinase 10|Homo sapiens (9606)
>7MSG_1|Chains A, B, C|Tumor necrosis factor ligand superfamily member 14, membrane form|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 \(w=f(c)\)
6OKT , Knot 322 876 0.83 40 270 770 
MKIQMRNKKVLSFLTLTAIVSQALVYPVYAQTSTSNHSNKKKEIVNEDILPNNGLMGYYFTDEHFKDLKLMAPIKDGNLKFEEKKVDKLLDKDKSDVKSIRWTGRIIPSKDGEYTLSTDRDDVLMQVNTESTISNTLKVNMKKGKEYKVRIELQDKNLGSIDNLSSPNLYWELDGMKKIIPEENLFLRDYSNIEKDDPFIPNNNFFDPKLMSDWEDEDLDTDNDNIPDSYERNGYTIKDLIAVKWEDSFAEQGYKKYVSNYLESNTAGDPYTDYEKASGSFDKAIKTEARDPLVAAYPIVGVGMEKLIISTNEHASTDQGKTVSRATTNSKTESNTAGVSVNVGYQNGFTANVTTNYSHTTDNSTAVQDSNGESWNTGLSINKGESAYINANVRYYNTGTAPMYKVTPTTNLVLDGDTLSTIKAQENQIGNNLSPGDTYPKKGLSPLALNTMDQFSSRLIPINYDQLKKLDAGKQIKLETTQVSGNFGTKNSSGQIVTEGNSWSDYISQIDSISASIILDTENESYERRVTAKNLQDPEDKTPELTIGEAIEKAFGATKKDGLLYFNDIPIDESCVELIFDDNTANKIKDSLKTLSDKKIYNVKLERGMNILIKTPTYFTNFDDYNNYPSTWSNVNTTNQDGLQGSANKLNGETKIKIPMSELKPYKRYVFSGYSKDPLTSNSIIVKIKAKEEKTDYLVPEQGYTKFSYEFETTEKDSSNIEITLIGSGTTYLDNLSITELNSTPEILDEPEVKIPTDQEIMDAHKIYFADLNFNPSTGNTYINGMYFAPTQTNKEALDYIQKYRVEATLQYSGFKDIGTKDKEMRNYLGDPNQPKTNYVNLRSYFTGGENIMTYKKLRIYAITPDDRELLVLSVD
4EQU , Knot 137 302 0.86 40 189 292 
SMRKSREYEHVRRDLDPNEVWEIVGELGDGAFGKVYKAKNKETGALAAAKVIETKSEEELEDYIVEIEILATCDHPYIVKLLGAYYHDGKLWIMIEFCPGGAVDAIMLELDRGLTEPQIQVVCRQMLEALNFLHSKRIIHRDLKAGNVLMTLEGDIRLADFGVSAKNLKTLQKRDSFIGTPYWMAPEVVMCETMKDTPYDYKADIWSLGITLIEMAQIEPPHHELNPMRVLLKIAKSDPPTLLTPSKWSVEFRDFLKIALDKNPETRPSAAQLLEHPFVSSITSNKALRELVAEAKAEVMEE
7MSG , Knot 77 165 0.79 40 116 153 
HHHHHHGLIQERRSHEVNPAAHLTGANSSLTGSGGPLLWETQLGLAFLRGLSYHDGALVVTKAGYYYIYSKVQLGGVGCPLGLASTITHGLYKRTPRYPEELELLVSQQSPCGRATSSSRVWWDSSFLGGVVHLEAGEEVVVRVLDERLVRLRDGTRSYFGAFMV

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 \(c\).

\(|P_{f(6OKT_1)}(2) \setminus P_{f(4EQU_1)}(2)|=121\), \(|P_{f(4EQU_1)}(2) \setminus P_{f(6OKT_1)}(2)|=40\). 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 1:101010000110110101110011101101000000000000011000111001111001000010010111110010101000010011000000100101010111000100010000001110100000100010101001000010101000011010010010101010110011100011100000100001111000110101100100001000000110000001001001111010001100100001000100001101000000101010011000100111110111111100111000001000010010010000000000111010110001101010000000000001100001001001101001001010101000001011100101000111010010010100001100101100010011011110010010001111000010010110010100001010110000010110010010001001001010111000000000010100100100001010110110011110000111010011100001011100001001000100100001001010011011100100100100000010010010000001101010010100010111001010000110100001100001110101000000011100100010001000000000101011101000100101001000101100101011000011010010110101010010001011011100000011001000010101000110011000001000110100100001010001011001100001010110100001111010
Pair \(Z_2\) Length of longest common subsequence
6OKT_1,4EQU_1 161 4
6OKT_1,7MSG_1 206 4
4EQU_1,7MSG_1 169 4

Newick tree

 
[
	7MSG_1:98.35,
	[
		6OKT_1:80.5,4EQU_1:80.5
	]:17.85
]

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 \((0.85)(0.8)(\frac{1178 }{\log_{20} 1178}-\frac{302}{\log_{20}302})=231.\)
Status Protein1 Protein2 d d1/2
Query variables 6OKT_1 4EQU_1 291 195.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]