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Parikh vectors
6WWR_1 8AJQ_1 7HHL_1 Letter Amino acid
36 14 9 G Glycine
19 2 12 K Lycine
29 4 2 T Threonine
20 7 12 P Proline
23 9 3 S Serine
36 11 7 A Alanine
21 15 2 R Arginine
16 0 5 N Asparagine
37 12 3 E Glutamic acid
13 6 4 H Histidine
10 1 2 M Methionine
34 7 2 V Valine
12 7 0 C Cysteine
27 3 4 I Isoleucine
32 10 4 L Leucine
4 2 2 W Tryptophan
19 4 5 Y Tyrosine
27 8 7 D Aspartic acid
16 2 1 Q Glutamine
20 8 8 F Phenylalanine 

6WWR_1|Chain A|Tubulin alpha-1B chain|Sus scrofa (9823)
>8AJQ_1|Chains A, B, C, D, E, F, G, H|CENP-V/GFA domain-containing protein|Pseudomonas aeruginosa PAO1 (208964)
>7HHL_1|Chains A, B, C|Hepatoma-derived growth factor-related protein 2|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 \(w=f(c)\)
6WWR , Knot 192 451 0.86 40 258 426 
MRECISIHVGQAGVQIGNACWELYCLEHGIQPDGQMPSDKTIGGGDDSFNTFFSETGAGKHVPRAVFVDLEPTVIDEVRTGTYRQLFHPEQLITGKEDAANNYARGHYTIGKEIIDLVLDRIRKLADQCTGLQGFLVFHSFGGGTGSGFTSLLMERLSVDYGKKSKLEFSIYPAPQVSTAVVEPYNSILTTHTTLEHSDCAFMVDNEAIYDICRRNLDIERPTYTNLNRLISQIVSSITASLRFDGALNVDLTEFQTNLVPYPRIHFPLATYAPVISAEKAYHEQLSVAEITNACFEPANQMVKCDPRHGKYMACCLLYRGDVVPKDVNAAIATIKTKRSIQFVDWCPTGFKVGINYQPPTVVPGGDLAKVQRAVCMLSNTTAIAEAWARLDHKFDLMYAKRAFVHWYVGEGMEEGEFSEAREDMAALEKDYEEVGVDSVEGEGEEEGEEY
8AJQ , Knot 69 132 0.85 38 106 127 
GHMDRFTGGCLCGKVRLVASGRPYRVGLCHCLDCRKHHGALFHASAIFPEEAVSIEGETRDYAGRFFCPQCGSSVFSRSADEIEVSLGALDAPDRFQPTYELWTVRREGWLPAFPLARHYERDREGDGRSEE
7HHL , Knot 51 94 0.82 38 77 90 
GMPHAFKPGDLVFAKMKGYPHWPARIDDIADGAVKPPPNKYPIFFFGTHETAFLGPKDLFPYDKSKDKYGKPNKRKGFNEGLWEIQNNPHASYS

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 \(c\).

\(|P_{f(6WWR_1)}(2) \setminus P_{f(8AJQ_1)}(2)|=174\), \(|P_{f(8AJQ_1)}(2) \setminus P_{f(6WWR_1)}(2)|=22\). 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 1:1000101011011101101010100100110101011000011110001001100011100110111101010110010010000110100110100011000101000110011011100100110000110111110011110101100111001010010000101010111010011101000110000010000011110001100100001010010000100110011001010101011101010010001110101011110011110100100001011010010101100110001001001100110010111001011110100000101101010110111000110111110110100110110000111011101000101101001110101101100101001000111100000011100101010001000
Pair \(Z_2\) Length of longest common subsequence
6WWR_1,8AJQ_1 196 4
6WWR_1,7HHL_1 221 3
8AJQ_1,7HHL_1 133 3

Newick tree

 
[
	6WWR_1:11.31,
	[
		8AJQ_1:66.5,7HHL_1:66.5
	]:47.81
]

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 \((0.85)(0.8)(\frac{583 }{\log_{20} 583}-\frac{132}{\log_{20}132})=131.\)
Status Protein1 Protein2 d d1/2
Query variables 6WWR_1 8AJQ_1 169 107
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]