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Parikh vectors
9ONN_1 7VIO_1 7GSB_1 Letter Amino acid
7 10 19 R Arginine
0 3 4 C Cysteine
15 15 30 E Glutamic acid
3 3 11 M Methionine
6 8 14 F Phenylalanine
21 15 13 A Alanine
5 11 14 Q Glutamine
7 9 23 K Lycine
7 10 25 S Serine
1 1 6 W Tryptophan
3 8 17 V Valine
7 12 18 D Aspartic acid
5 7 11 H Histidine
3 4 18 I Isoleucine
7 6 9 Y Tyrosine
13 11 14 G Glycine
11 27 29 L Leucine
3 2 22 P Proline
10 6 13 T Threonine
6 6 11 N Asparagine 

9ONN_1|Chains A, B, C, D, E, F|Rubrerythrin|Burkholderia pseudomallei (28450)
>7VIO_1|Chain A|Ferritin light chain|Equus caballus (9796)
>7GSB_1|Chain A|Tyrosine-protein phosphatase non-receptor type 1|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 \(w=f(c)\)
9ONN , Knot 67 140 0.78 38 102 135 
MAQLKGSKTEENLKYAFAGESQANRRYLYFASKADVEGQNDIAALFRSTAEGETGHAHGHLEYLEAVGDPATGLPFGTSRQNLQSAIAGETHEYTDMYPGMAKTARDEGFEEIANWFETLAKAERSHANRYTKALDGLVD
7VIO , Knot 84 174 0.83 40 130 171 
SSQIRQNYSTEVEAAVNRLVNLYLRASYTYLSLGFYFDRDDVALEGVCHFFRELAEEKREGAERLLKMQNQRGGRALFQDLQKPSQDEWGTTLDAMKAAIVLEKSLNQALLDLHALGSAQADPHLCDFLESHFLDEEVKLIKKMGDHLTNIQRLVGSQAGLGEYLFEHCTLKHD
7GSB , Knot 141 321 0.84 40 205 309 
MEMEKEFEQIDKSGSWAAIYQDIRHEASDFPSRVAKLPKNKNRNRYRDVSPFDHSRIKLHQEDNDYINASLIKMEEAQRSYILTQGPLPNTVGHFWEMVWEQKSRGVVMLNRVMEKGSLKCAQYWPQKEEKEMIFEDTNLKLTLISEDIKSYYTVRQLELENLTTQETREILHFHYTTWPDFGVPESPASFLNFLFKVRESGSLSPEHGPVVVHCSAGIGRSGTFCLADTCLLLMDKRKDPSSVDIKKVLLEMRKFRMGLIQTADQLRFSYLAVIEGAKFIMGDSSVQDQWKELSHEDLEPPPEHIPPPPRPPKRILEPHN

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 \(c\).

\(|P_{f(9ONN_1)}(2) \setminus P_{f(7VIO_1)}(2)|=48\), \(|P_{f(7VIO_1)}(2) \setminus P_{f(9ONN_1)}(2)|=76\). 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 1:11010100000010011110001000010110010101000111110001010010101010010111011011111000001001111000000010111100100011001101100110100001000001101110
Pair \(Z_2\) Length of longest common subsequence
9ONN_1,7VIO_1 124 3
9ONN_1,7GSB_1 201 3
7VIO_1,7GSB_1 181 3

Newick tree

 
[
	7GSB_1:10.46,
	[
		9ONN_1:62,7VIO_1:62
	]:42.46
]

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 \((0.85)(0.8)(\frac{314 }{\log_{20} 314}-\frac{140}{\log_{20}140})=53.5\)
Status Protein1 Protein2 d d1/2
Query variables 9ONN_1 7VIO_1 68 58.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]