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Parikh vectors
8ONJ_1 2MMW_1 3ZVY_1 Letter Amino acid
6 0 2 Q Glutamine
25 1 4 E Glutamic acid
7 0 2 M Methionine
16 2 6 P Proline
16 1 5 R Arginine
31 0 5 L Leucine
9 2 2 Y Tyrosine
23 5 3 G Glycine
9 1 3 H Histidine
14 0 4 K Lycine
19 1 0 T Threonine
1 0 1 W Tryptophan
13 1 3 A Alanine
6 0 2 N Asparagine
8 1 9 D Aspartic acid
4 0 11 C Cysteine
25 1 1 I Isoleucine
10 2 1 F Phenylalanine
19 1 5 S Serine
16 2 3 V Valine 

8ONJ_1|Chains A, B|Aminotransferase class IV|Aminobacterium colombiense (81468)
>2MMW_1|Chain A|Microcin J25|Escherichia coli (562)
>3ZVY_1|Chains A, B|E3 UBIQUITIN-PROTEIN LIGASE UHRF1|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 \(w=f(c)\)
8ONJ , Knot 125 277 0.84 40 174 267 
GHMNLCYIDGKFLPLEEAKLPVTDLIIQRGVGVFETISTHSRRPLMLTPHLKRLEGSATASSIVMPATLDEMARIIREGIKKMGCETMVLPYITGGDSFGKDHLFSSSRYFVIFEEIRKPDPILYEKGVALHPINAERYLPSTKSINYMLSFTGQRDSKGAYEILYCPEGEIVEGSHSTFFLIKNGHLITAPTSRALSGTTRQIVLELARRGNIQVEERCPLLTELPEAEEAFITGTVKELLPVVRIGDQIIGNGVPGKLTKHLHQVYLSSIVEWLE
2MMW , Knot 15 21 0.72 26 20 19 
GGAGHVPEYFVRGDTPISFYG
3ZVY , Knot 38 72 0.75 38 62 70 
RKSGPSCKHCKDDVNRLCRVCACHLCGGRQDPDKQLMCDECDMAFHIYCLDPPLSSVPSEDEWYCPECRNDA

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 \(c\).

\(|P_{f(8ONJ_1)}(2) \setminus P_{f(2MMW_1)}(2)|=160\), \(|P_{f(2MMW_1)}(2) \setminus P_{f(8ONJ_1)}(2)|=6\). 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 1:1010100101011110010111001110011111001000000111101010010101010011111010011011001100110001111010110011000110000011110010010111000111101101000110000100110101000001100110010101101000011110010110110001101000011101100101010000111001101001110101001111101100111011110100010010100110110
Pair \(Z_2\) Length of longest common subsequence
8ONJ_1,2MMW_1 166 3
8ONJ_1,3ZVY_1 184 4
2MMW_1,3ZVY_1 76 2

Newick tree

 
[
	8ONJ_1:98.76,
	[
		2MMW_1:38,3ZVY_1:38
	]:60.76
]

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 \((0.85)(0.8)(\frac{298 }{\log_{20} 298}-\frac{21}{\log_{20}21})=92.5\)
Status Protein1 Protein2 d d1/2
Query variables 8ONJ_1 2MMW_1 115 61.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]