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Parikh vectors
7MRX_1 1ORP_1 6IYA_1 Letter Amino acid
7 0 1 Y Tyrosine
4 0 4 V Valine
2 2 0 C Cysteine
5 0 2 Q Glutamine
9 0 3 I Isoleucine
4 0 0 F Phenylalanine
7 0 5 L Leucine
11 0 4 S Serine
9 1 2 T Threonine
6 0 0 N Asparagine
9 0 2 D Aspartic acid
4 0 10 E Glutamic acid
8 0 8 H Histidine
8 5 7 A Alanine
8 0 5 K Lycine
3 0 1 W Tryptophan
7 0 8 R Arginine
12 3 0 G Glycine
1 0 3 M Methionine
4 0 1 P Proline 

7MRX_1|Chains A, C, E|Ribonuclease|Bacillus amyloliquefaciens (1390)
>1ORP_1|Chain A[auth B]|5'-D(*AP*AP*GP*AP*CP*AP*TP*GP*GP*AP*C)-3'|
>6IYA_1|Chains A, B, C, D, E, F|Transcriptional regulator CopG family|Shewanella oneidensis (211586)
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 \(w=f(c)\)
7MRX , Knot 65 128 0.82 40 98 120 
MGSSHHHHHHSQAPIEGRAQVINTFDGVADYLQTYHKLPDNYITKSEAQALGWVASKGNLCDVAPGKSIGGDIFSNREGKLPGKSGRTWREADINYTCGFRNSDRILYSSDWLIYKTTDHYQTFTKIR
1ORP , Knot 6 11 0.43 8 8 8 
AAGACATGGAC
6IYA , Knot 36 66 0.76 32 50 59 
MSTIKPVSVKLDADIKARVEHLAETRKRSSHWMMREAIREYVEREEKREALQQEALRALEHHHHHH

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 \(c\).

\(|P_{f(7MRX_1)}(2) \setminus P_{f(1ORP_1)}(2)|=97\), \(|P_{f(1ORP_1)}(2) \setminus P_{f(7MRX_1)}(2)|=7\). 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 1:11000000000011101010110010111001000001100010000101111110010100111100111011000010111001001001010000110000011000011100000000010010
Pair \(Z_2\) Length of longest common subsequence
7MRX_1,1ORP_1 104 2
7MRX_1,6IYA_1 124 6
1ORP_1,6IYA_1 58 1

Newick tree

 
[
	7MRX_1:63.91,
	[
		1ORP_1:29,6IYA_1:29
	]:34.91
]

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 \((0.85)(0.8)(\frac{139 }{\log_{20} 139}-\frac{11}{\log_{20}11})=48.0\)
Status Protein1 Protein2 d d1/2
Query variables 7MRX_1 1ORP_1 60 32
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]