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Parikh vectors
5OKR_1 4YGH_1 2MLT_1 Letter Amino acid
33 6 2 A Alanine
30 17 0 E Glutamic acid
19 0 0 H Histidine
21 12 2 T Threonine
29 3 0 Y Tyrosine
1 3 0 C Cysteine
17 4 2 Q Glutamine
17 3 1 W Tryptophan
40 8 3 G Glycine
23 7 3 I Isoleucine
19 7 1 S Serine
34 15 2 V Valine
30 4 2 R Arginine
25 7 0 N Asparagine
35 5 0 D Aspartic acid
34 10 4 L Leucine
20 14 3 K Lycine
11 3 0 M Methionine
22 6 0 F Phenylalanine
25 3 1 P Proline 

5OKR_1|Chains A, B|Putative 6-phospho-beta-galactobiosidase|Geobacillus stearothermophilus (1422)
>4YGH_1|Chain A|Cellular retinoic acid-binding protein 2|Homo sapiens (9606)
>2MLT_1|Chains A, B|MELITTIN|Apis mellifera (7460)
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 \(w=f(c)\)
5OKR , Knot 196 485 0.83 40 246 453 
MIHHHHHHEHRHLKPFPPEFLWGAASAAYQVEGAWNEDGKGLSVWDVFAKQPGRTFKGTNGDVAVDHYHRYQEDVALMAEMGLKAYRFSVSWSRVFPDGNGAVNEKGLDFYDRLIEELRNHGIEPIVTLYHWDVPQALMDAYGAWESRRIIDDFDRYAVTLFQRFGDRVKYWVTLNEQNIFISFGYRLGLHPPGVKDMKRMYEANHIANLANAKVIQSFRHYVPDGKIGPSFAYSPMYPYDSRPENVLAFENAEEFQNHWWMDVYAWGMYPQAAWNYLESQGLEPTVAPGDWELLQAAKPDFMGVNYYQTTTVEHNPPDGVGEGVMNTTGKKGTSTSSGIPGLFKTVRNPHVDTTNWDWAIDPVGLRIGLRRIANRYQLPILITENGLGEFDTLEPGDIVNDDYRIDYLRRHVQEIQRAITDGVDVLGYCAWSFTDLLSWLNGYQKRYGFVYVNRDDESEKDLRRIKKKSFYWYQRVIETNGAEL
4YGH , Knot 67 137 0.80 38 109 132 
PNFSGNWKIIRSENFEELLKVLGVNVMLRKIAVAAASKYAVEIKQEGDTFYIKVSTTVYTTEINFKVGEEFEEQTVDGRPCKSLVKWESENKMVCEQKLLKGEGPKTSWTKELTNDGELILTMTADDVVCTQVFVRE
2MLT , Knot 16 27 0.65 26 24 25 
GIGAVLKVLTTGLPALISWIKRKRQQX

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 \(c\).

\(|P_{f(5OKR_1)}(2) \setminus P_{f(4YGH_1)}(2)|=172\), \(|P_{f(4YGH_1)}(2) \setminus P_{f(5OKR_1)}(2)|=35\). 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 1:11000000000010111101111110110010111000101101101110011001010010111000000000111110111010010101001110101110001101000110010001101110100101101110101110000110010001101100110010011010000111011001110111100100100100110110101100100011010111011001101000010011110010010001110101111010111001000110101111010110110101111000000010001101110111000100100000111111001001010000101110111101110011000011111000111010010110110000010010001001001100110111001101001101101000001110100000000010010000101000110001101
Pair \(Z_2\) Length of longest common subsequence
5OKR_1,4YGH_1 207 3
5OKR_1,2MLT_1 236 3
4YGH_1,2MLT_1 113 4

Newick tree

 
[
	5OKR_1:12.93,
	[
		4YGH_1:56.5,2MLT_1:56.5
	]:67.43
]

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 \((0.85)(0.8)(\frac{622 }{\log_{20} 622}-\frac{137}{\log_{20}137})=140.\)
Status Protein1 Protein2 d d1/2
Query variables 5OKR_1 4YGH_1 177 112
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]