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Parikh vectors
7FCF_1 3EYA_1 3PPW_1 Letter Amino acid
12 36 16 E Glutamic acid
6 18 8 H Histidine
12 29 11 I Isoleucine
2 19 6 M Methionine
11 32 13 S Serine
7 22 6 T Threonine
18 64 10 A Alanine
9 27 11 D Aspartic acid
3 10 2 C Cysteine
5 52 17 L Leucine
16 28 5 K Lycine
5 27 11 P Proline
3 22 13 R Arginine
7 20 12 Q Glutamine
15 46 16 G Glycine
5 14 6 Y Tyrosine
4 16 8 N Asparagine
6 20 6 F Phenylalanine
2 4 1 W Tryptophan
6 43 18 V Valine 

7FCF_1|Chain A|Fimbrial protein|Chromobacterium haemolyticum (394935)
>3EYA_1|Chains A, B, C, D, E, F, G, H, I, J, K, L|Pyruvate dehydrogenase [cytochrome]|Escherichia coli (562)
>3PPW_1|Chain A|von Willebrand factor|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 \(w=f(c)\)
7FCF , Knot 77 154 0.84 40 117 148 
AFDAFLKIDGIPGESSDDKHKDWIEIQSFAHKLEQPAQATASSAGGATAERVNHAAYEITHFLDKASPKIYEACCKGQHIKEITIELCRAGGDKVKYMEIKMEQVLIAKVEPHGSANDNGFPSEKVSFTYGKIKWTYTQQKRADGAGGGNVSSG
3EYA , Knot 221 549 0.84 40 267 511 
MKQTVAAYIAKTLESAGVKRIWGVTGDSLNGLSDSLNRMGTIEWMSTRHEEVAAFAAGAEAQLSGELAVCAGSCGPGNLHLINGLFDCHRNHVPVLAIAAHIPSSEIGSGYFQETHPQELFRECSHYCELVSSPEQIPQVLAIAMRKAVLNRGVSVVVLPGDVALKPAPEGATMHWYHAPQPVVTPEEEELRKLAQLLRYSSNIALMCGSGCAGAHKELVEFAGKIKAPIVHALRGKEHVEYDNPYDVGMTGLIGFSSGFHTMMNADTLVLLGTQFPYRAFYPTDAKIIQIDINPASIGAHSKVDMALVGDIKSTLRALLPLVEEKADRKFLDKALEDYRDARKGLDDLAKPSEKAIHPQYLAQQISHFAADDAIFTCDVGTPTVWAARYLKMNGKRRLLGSFNHGSMANAMPQALGAQATEPERQVVAMCGDGGFSMLMGDFLSVVQMKLPVKIVVFNNSVLGFVAMEMKAGGYLTDGTELHDTNFARIAEACGITGIRVEKASEVDEALQRAFSIDGPVLVDVVVAKEELAIPPQIKLEQAKGFSLY
3PPW , Knot 90 196 0.80 40 136 183 
MLGPKRCSMVLDVAFVLEGSDKIGEADFNRSKEFMEEVIQRMDVGQDSIHVTVLQYSYMVTVEYPFSEAQSKGDILQRVREIRYQGGNRTNTGLALRYLSDHSFLVSQGAREQAPNLVYMVTGNPASDEIKRLPGDIQVVPIGVGPNANVQELERIGWPNAPILIQDFETLPREAPDLVLQRCSSGEGLEHHHHHH

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 \(c\).

\(|P_{f(7FCF_1)}(2) \setminus P_{f(3EYA_1)}(2)|=27\), \(|P_{f(3EYA_1)}(2) \setminus P_{f(7FCF_1)}(2)|=177\). 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 1:1101110101111000000000110100110010011010100111101001001100100110010101001000100100101010011100100101010011110101010100011100010100101010000000101111101001
Pair \(Z_2\) Length of longest common subsequence
7FCF_1,3EYA_1 204 5
7FCF_1,3PPW_1 161 3
3EYA_1,3PPW_1 191 4

Newick tree

 
[
	3EYA_1:10.19,
	[
		7FCF_1:80.5,3PPW_1:80.5
	]:23.69
]

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 \((0.85)(0.8)(\frac{703 }{\log_{20} 703}-\frac{154}{\log_{20}154})=156.\)
Status Protein1 Protein2 d d1/2
Query variables 7FCF_1 3EYA_1 196 122.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]