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Parikh vectors
2YOF_1 3QMS_1 8UBA_1 Letter Amino acid
5 3 10 Q Glutamine
10 21 20 G Glycine
16 22 16 I Isoleucine
9 6 13 T Threonine
13 3 14 Y Tyrosine
14 17 17 V Valine
17 7 9 N Asparagine
11 18 18 D Aspartic acid
2 3 5 C Cysteine
6 10 12 P Proline
13 10 15 S Serine
7 26 30 A Alanine
5 10 4 M Methionine
8 10 15 F Phenylalanine
5 0 8 W Tryptophan
6 20 30 R Arginine
19 16 19 E Glutamic acid
6 2 15 H Histidine
16 17 38 L Leucine
22 7 20 K Lycine 

2YOF_1|Chains A, B, C|THYMIDYLATE KINASE|PLASMODIUM FALCIPARUM (36329)
>3QMS_1|Chains A, B|Orotidine 5'-phosphate decarboxylase|Methanothermobacter thermautotrophicus str. Delta H (187420)
>8UBA_1|Chain A|Reverse transcriptase|Bordetella phage BPP-1 (2885909)
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 \(w=f(c)\)
2YOF , Knot 97 210 0.82 40 150 204 
MTDDKKKGKFIVFEGLDRSGKSTQSKLLVEYLKNNNVEVKHLYFPNRETGIGQIISKYLKMENSMSNETIHLLFSANRWEHMNEIKSLLLKGIWVVCDRYAYSGVAYSSGALNLNKTWCMNPDQGLIKPDVVFYLNVPPNYAQNRSDYGEEIYEKVETQKKIYETYKHFAHEDYWINIDATRKIEDIHNDIVKEVTKIKVEPEEFNFLWS
3QMS , Knot 97 228 0.77 38 142 212 
MRSRRVDVMDVMNRLILAMDLMNRDDALRVTGEVREYIDTVKIGYPLVLSEGMDIIAEFRKRFGCRIIADFKVADIPETNEKICRATFKAGADAIIVHGFPGADSVRACLNVAEEMGREVFLLTEMSHPGAEMFIQGAADEIARMGVDLGVKNYVGPSVRPERLSRLREIIGQDSFLISPGAGAQGGDPGETLRFADAIIVGRSIFLADNPAAAAAGIIESIKDLLNP
8UBA , Knot 140 328 0.82 40 206 312 
MGKRHRNLIDQITTWENLLDAYRKTSHGKRRTWGYLEFKEYDLANLLALQAELKAGNYERGPYREFLVYEPKPRLISALEFKDRLVQHALCNIVAPIFEAGLLPYTYACRPDKGTHAGVCHVQAELRRTRATHFLKSDFSKFFPSIDRAALYAMIDKKIHCAATRRLLRVVLPDEGVGIPIGSLTSQLFANVYGGAVDRLLHDELKQRHWARYMDDIVVLGDDPEELRAVFYRLRDFASERLGLKISHWQVAPVSRGINFLGYRIWPTHKLLRKSSVKRAKRKVANFIKHGEDESLQRFLASWSGHAQWADTHNLFTWMEEQYGIACH

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 \(c\).

\(|P_{f(2YOF_1)}(2) \setminus P_{f(3QMS_1)}(2)|=95\), \(|P_{f(3QMS_1)}(2) \setminus P_{f(2YOF_1)}(2)|=87\). 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 1:100000010111101100010000001110010000101001011000011101100010100010000101110100100100100111011111000010011100011101000101010011101011101011100100000010010001000001000000110000110101000100100011001001010100101110
Pair \(Z_2\) Length of longest common subsequence
2YOF_1,3QMS_1 182 3
2YOF_1,8UBA_1 174 3
3QMS_1,8UBA_1 176 3

Newick tree

 
[
	3QMS_1:90.33,
	[
		2YOF_1:87,8UBA_1:87
	]:3.33
]

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 \((0.85)(0.8)(\frac{438 }{\log_{20} 438}-\frac{210}{\log_{20}210})=66.6\)
Status Protein1 Protein2 d d1/2
Query variables 2YOF_1 3QMS_1 85 83
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]