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Parikh vectors
7TIE_1 1STN_1 2EBO_1 Letter Amino acid
38 9 0 V Valine
40 14 5 A Alanine
16 8 6 D Aspartic acid
6 6 5 Q Glutamine
47 10 4 G Glycine
9 23 3 K Lycine
38 10 8 T Threonine
17 1 2 W Tryptophan
8 5 5 R Arginine
19 6 3 N Asparagine
9 12 3 E Glutamic acid
17 4 3 H Histidine
59 11 10 L Leucine
30 5 1 S Serine
1 0 2 C Cysteine
34 4 0 M Methionine
42 3 4 F Phenylalanine
37 5 8 I Isoleucine
28 6 2 P Proline
19 7 0 Y Tyrosine 

7TIE_1|Chains A, N|Cytochrome c oxidase subunit 1|Bos taurus (9913)
>1STN_1|Chain A|STAPHYLOCOCCAL NUCLEASE|Staphylococcus aureus (1280)
>2EBO_1|Chains A, B, C|EBOLA VIRUS ENVELOPE GLYCOPROTEIN|Zaire ebolavirus - Mayinga (Zaire, 1976) (128952)
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 \(w=f(c)\)
7TIE , Knot 204 514 0.82 40 236 478 
MFINRWLFSTNHKDIGTLYLLFGAWAGMVGTALSLLIRAELGQPGTLLGDDQIYNVVVTAHAFVMIFFMVMPIMIGGFGNWLVPLMIGAPDMAFPRMNNMSFWLLPPSFLLLLASSMVEAGAGTGWTVYPPLAGNLAHAGASVDLTIFSLHLAGVSSILGAINFITTIINMKPPAMSQYQTPLFVWSVMITAVLLLLSLPVLAAGITMLLTDRNLNTTFFDPAGGGDPILYQHLFWFFGHPEVYILILPGFGMISHIVTYYSGKKEPFGYMGMVWAMMSIGFLGFIVWAHHMFTVGMDVDTRAYFTSATMIIAIPTGVKVFSWLATLHGGNIKWSPAMMWALGFIFLFTVGGLTGIVLANSSLDIVLHDTYYVVAHFHYVLSMGAVFAIMGGFVHWFPLFSGYTLNDTWAKIHFAIMFVGVNMTFFPQHFLGLSGMPRRYSDYPDAYTMWNTISSMGSFISLTAVMLMVFIIWEAFASKREVLTVDLTTTNLEWLNGCPPPYHTFEEPTYVNLK
1STN , Knot 71 149 0.79 38 110 141 
ATSTKKLHKEPATLIKAIDGDTVKLMYKGQPMTFRLLLVDTPETKHPKKGVEKYGPEASAFTKKMVENAKKIEVEFDKGQRTDKYGRGLAYIYADGKMVNEALVRQGLAKVAYVYKPNNTHEQHLRKSEAQAKKEKLNIWSEDNADSGQ
2EBO , Knot 39 74 0.75 34 62 72 
GLRQLANETTQALQLFLRATTELRTFSILNRKAIDFLLQRWGGTCHILGPDCAIEPHDWTKNITDKIDQIIHDF

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 \(c\).

\(|P_{f(7TIE_1)}(2) \setminus P_{f(1STN_1)}(2)|=173\), \(|P_{f(1STN_1)}(2) \setminus P_{f(7TIE_1)}(2)|=47\). 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 1:1110011100000011010111111111110110111010110110111000100111010111111111111111111011111111110111101001011111101111110011011110110101111101101110101011010111100111110110011010111100000111110111011111101111111101110000100011011111011100011111101010111111111100110000100011101111111101111111111001101110100010100101111110110110111010110101011111111111110111101111100010111000001110100110111111111111011111010010001101011111111010111001111011100000010100110010011011010111111111101110000110101000010110101110001001001010
Pair \(Z_2\) Length of longest common subsequence
7TIE_1,1STN_1 220 3
7TIE_1,2EBO_1 228 3
1STN_1,2EBO_1 120 4

Newick tree

 
[
	7TIE_1:12.62,
	[
		1STN_1:60,2EBO_1:60
	]:64.62
]

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 \((0.85)(0.8)(\frac{663 }{\log_{20} 663}-\frac{149}{\log_{20}149})=147.\)
Status Protein1 Protein2 d d1/2
Query variables 7TIE_1 1STN_1 188 121
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]