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Parikh vectors
1EDE_1 1JVZ_1 7XHU_1 Letter Amino acid
16 6 19 T Threonine
6 5 2 W Tryptophan
14 10 10 V Valine
28 10 14 L Leucine
12 2 14 K Lycine
23 4 6 F Phenylalanine
13 8 6 S Serine
5 4 3 H Histidine
11 1 3 M Methionine
23 13 1 P Proline
30 21 6 A Alanine
10 7 3 N Asparagine
26 9 11 D Aspartic acid
13 10 3 Q Glutamine
18 15 10 G Glycine
11 11 2 Y Tyrosine
15 9 4 R Arginine
4 0 1 C Cysteine
18 7 8 E Glutamic acid
14 6 7 I Isoleucine 

1EDE_1|Chain A|HALOALKANE DEHALOGENASE|Xanthobacter autotrophicus (280)
>1JVZ_1|Chain A|cephalosporin acylase alpha chain|Brevundimonas diminuta (293)
>7XHU_1|Chain A|Fatty acid-binding protein, heart|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 \(w=f(c)\)
1EDE , Knot 136 310 0.84 40 197 298 
MINAIRTPDQRFSNLDQYPFSPNYLDDLPGYPGLRAHYLDEGNSDAEDVFLCLHGEPTWSYLYRKMIPVFAESGARVIAPDFFGFGKSDKPVDEEDYTFEFHRNFLLALIERLDLRNITLVVQDWGGFLGLTLPMADPSRFKRLIIMNACLMTDPVTQPAFSAFVTQPADGFTAWKYDLVTPSDLRLDQFMKRWAPTLTEAEASAYAAPFPDTSYQAGVRKFPKMVAQRDQACIDISTEAISFWQNDWNGQTFMAIGMKDKLLGPDVMYPMKALINGCPEPLEIADAGHFVQEFGEQVAREALKHFAETE
1JVZ , Knot 77 158 0.82 38 123 150 
EPTSTPQAPIAAYKPRSNEILWDGYGVPHIYGVDAPSAFYGYGWAQARSHGDNILRLYGEARGKGAEYWGPDYEQTTVWLLTNGVPERAQQWYAQQSPDFRANLDAFAAGINAYAQQNPDDISPEVRQVLPVSGADVVAHAHRLMNFLYVASPGRTLG
7XHU , Knot 66 133 0.81 40 99 125 
MVDAFLGTWKLVDSKNFDDYMKSLGVGFATRQVASMTKPTTIIEKNGDILTLKTHSTFKNTEISFKLGVEFDETTADDRKVKSIVTLDGGKLVHLQKWDGQETTLVRELIDGKLILTLTHGTAVCTRTYEKEA

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 \(c\).

\(|P_{f(1EDE_1)}(2) \setminus P_{f(1JVZ_1)}(2)|=118\), \(|P_{f(1JVZ_1)}(2) \setminus P_{f(1EDE_1)}(2)|=44\). 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 1:1101100100010010001101001001110111010010010001001110101010100100011111100110111101111100001100000010100011111100101001011100111111101111010010011110101100110011101110011011011000110100101001100111010010101011111000001110011011100001010100011011000101001111110001111011011011101010110110110110011001100110011000
Pair \(Z_2\) Length of longest common subsequence
1EDE_1,1JVZ_1 162 3
1EDE_1,7XHU_1 180 3
1JVZ_1,7XHU_1 150 3

Newick tree

 
[
	1EDE_1:88.87,
	[
		1JVZ_1:75,7XHU_1:75
	]:13.87
]

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 \((0.85)(0.8)(\frac{468 }{\log_{20} 468}-\frac{158}{\log_{20}158})=91.4\)
Status Protein1 Protein2 d d1/2
Query variables 1EDE_1 1JVZ_1 121 88.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]