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Parikh vectors
7HUQ_1 6JSS_1 2RUT_1 Letter Amino acid
7 30 2 E Glutamic acid
14 32 3 G Glycine
5 20 2 I Isoleucine
2 14 5 K Lycine
3 2 0 W Tryptophan
8 11 1 Y Tyrosine
10 30 1 A Alanine
5 10 2 N Asparagine
5 10 1 Q Glutamine
12 24 2 L Leucine
14 6 5 S Serine
9 19 1 R Arginine
9 16 0 D Aspartic acid
2 13 0 M Methionine
3 17 3 F Phenylalanine
14 21 1 V Valine
6 4 2 C Cysteine
6 11 3 H Histidine
4 18 0 P Proline
6 22 2 T Threonine 

7HUQ_1|Chain A|Protease 2A|Coxsackievirus A16 (31704)
>6JSS_1|Chains A, B, C, D|Phosphotriesterase|Geobacillus kaustophilus (strain HTA426) (235909)
>2RUT_1|Chain A|Zinc finger protein ZFAT|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 \(w=f(c)\)
7HUQ , Knot 70 144 0.80 40 112 139 
SGAIYVGNYRVVNRHLATHNDWANLVWEDSSRDLLVSSTTAQGCDTIARCDCQTGVYYCSSRRKHYPVSFSKPSLIFVEASEYYPARYQSHLMLAVGHSEPGDCGGILRCQHGVVGIVSTGGNGLVGFADVRDLLWLDEEAMEQ
6JSS , Knot 143 330 0.83 40 206 315 
GSHNMAEMVETVCGPVPVEQLGKTLIHEHFLFGYPGFQGDVTRGTFREDESLRVAVEAAEKMKRHGIQTVVDPTPNDCGRNPAFLRRVAEETGLNIICATGYPYEGEGAPPYFQFRRLLGTAEDDIYDMFMAELTEGIADTGIKAGVIKLASSKGRITEYEKMFFRAAARAQKETGAVIITHTQEGTMGPEQAAYLLEHGADPKKIVIGHMCGNTDPDYHRKTLAYGVYIAFDRFGIQGMVGAPTDEERVRTLLALLRDGYEKQIMLSHDTVNVWLGRPFTLPEPFAEMMKNWHVEHLFVNIIPALKNEGIRDEVLEQMFIGNPAALFSA
2RUT , Knot 22 36 0.73 32 31 32 
GSSGSSGKIFTCEYCNKVFKFKHSLQAHLRIHTNEK

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 \(c\).

\(|P_{f(7HUQ_1)}(2) \setminus P_{f(6JSS_1)}(2)|=46\), \(|P_{f(6JSS_1)}(2) \setminus P_{f(7HUQ_1)}(2)|=140\). 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 1:011101100011000110000110111000000111000010100011000000110000000000110100101111010000110000011111100011001111000011111100110111111010011110001100
Pair \(Z_2\) Length of longest common subsequence
7HUQ_1,6JSS_1 186 3
7HUQ_1,2RUT_1 123 2
6JSS_1,2RUT_1 207 2

Newick tree

 
[
	6JSS_1:10.92,
	[
		7HUQ_1:61.5,2RUT_1:61.5
	]:46.42
]

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 \((0.85)(0.8)(\frac{474 }{\log_{20} 474}-\frac{144}{\log_{20}144})=97.6\)
Status Protein1 Protein2 d d1/2
Query variables 7HUQ_1 6JSS_1 127 90.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]