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Parikh vectors
1YEV_1 8IZK_1 6MQW_1 Letter Amino acid
3 2 4 R Arginine
1 10 4 Q Glutamine
10 3 0 H Histidine
18 14 9 L Leucine
21 14 6 A Alanine
4 16 7 N Asparagine
1 12 3 C Cysteine
0 15 7 I Isoleucine
2 2 3 M Methionine
13 17 15 V Valine
4 4 18 E Glutamic acid
11 14 14 K Lycine
7 8 3 P Proline
11 34 7 S Serine
9 10 12 T Threonine
3 10 3 Y Tyrosine
8 6 5 D Aspartic acid
7 25 8 G Glycine
7 3 6 F Phenylalanine
1 4 3 W Tryptophan 

1YEV_1|Chains A, C|Hemoglobin alpha chain|Homo sapiens (9606)
>8IZK_1|Chain A|Cationic trypsin|Bos taurus (9913)
>6MQW_1|Chain A|Cellular retinoic acid-binding 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 \(w=f(c)\)
1YEV , Knot 69 141 0.80 38 99 137 
VLSPADKTNVKAAWGKVGAHAGEYGAEALERMFLSFPTTKTYFPHFDLSHGSAQVKGHGKKVADALTNAVAHVDDMPNALSALSDLHAHKLRVDPVNFKLLSHCLLVTLAAHLPAEFTPAVHASLDKFLASVSTVLTSKYR
8IZK , Knot 101 223 0.81 40 140 216 
IVGGYTCGANTVPYQVSLNSGYHFCGGSLINSQWVVSAAHCYKSGIQVRLGEDNINVVEGNEQFISASKSIVHPSYNSNTLNNDIMLIKLKSAASLNSRVASISLPTSCASAGTQCLISGWGNTKSSGTSYPDVLKCLKAPILSDSSCKSAYPGQITSNMFCAGYLEGGKDSCQGDSGGPVVCSGKLQGIVSWGSGCAQKNKPGVYTKVCNYVSWIKQTIASN
6MQW , Knot 67 137 0.80 38 110 132 
PNFSGNWKIIRSENFEELLKVLGVNVMLRKIAVAAASKYAVEIKQEGDTFYIKVSTTVYTTEINFKVGEEFEEQTVDGRPCKSLVKWESENKMVCEQKLLKGEGPKTSWTKELTNDGELIETMTADDVVCTQVFVRE

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 \(c\).

\(|P_{f(1YEV_1)}(2) \setminus P_{f(8IZK_1)}(2)|=61\), \(|P_{f(8IZK_1)}(2) \setminus P_{f(1YEV_1)}(2)|=102\). 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 1:110110000101111011101100110110011101100000110101001010101010011011001110100110110110010100101011010110001110111011101011101010011101001100000
Pair \(Z_2\) Length of longest common subsequence
1YEV_1,8IZK_1 163 3
1YEV_1,6MQW_1 137 3
8IZK_1,6MQW_1 158 3

Newick tree

 
[
	8IZK_1:83.81,
	[
		1YEV_1:68.5,6MQW_1:68.5
	]:15.31
]

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 \((0.85)(0.8)(\frac{364 }{\log_{20} 364}-\frac{141}{\log_{20}141})=67.6\)
Status Protein1 Protein2 d d1/2
Query variables 1YEV_1 8IZK_1 85 70
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]