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Parikh vectors
7MSK_1 2AGH_1 6TOA_1 Letter Amino acid
31 0 9 D Aspartic acid
8 1 8 M Methionine
37 1 4 S Serine
18 1 17 R Arginine
13 0 2 H Histidine
34 4 1 K Lycine
13 0 12 P Proline
12 1 20 G Glycine
9 0 0 C Cysteine
15 2 3 Q Glutamine
31 5 10 E Glutamic acid
16 0 7 F Phenylalanine
5 0 5 W Tryptophan
23 0 3 Y Tyrosine
12 1 36 A Alanine
43 1 8 I Isoleucine
49 6 24 L Leucine
21 1 12 T Threonine
14 0 15 V Valine
26 1 1 N Asparagine 

7MSK_1|Chains A, B|Glyco_trans_2-like domain-containing protein|Bacillus thuringiensis serovar andalousiensis BGSC 4AW1 (527032)
>2AGH_1|Chain A|Myb proto-oncogene protein|Mus musculus (10090)
>6TOA_1|Chains A[auth C], D|Adaptor protein Rcc01688|Rhodobacter capsulatus DE442 (1415160)
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 \(w=f(c)\)
7MSK , Knot 181 430 0.85 40 226 404 
GSHMASMETLNDLVTRLEHSHPNSSLLKDLSLIQGNEQYNYIKWGDLSNSQNLNELVFQYEKAPYPSITCGILTYNEERCIKRCLDSLGSQFDEILVLDSHSTDNTTKIINRDFPMVKVIYEPWIDDFSFHRNKLISLTSSEWIYYIDADNYCVDSTNKFKRVAKLIQFLSIDCIISPMIKEHIGHVYTDNRKMFSVKKGIQFKGKVHEEPINADGSIPQNITVDIMICHDGYDPEVINLSEKNDRNIKLTRQMMEEEPSNPKWLYFYARELHYASEDTHIIETLLIKAIDLYKQSTYKRYQPEAILLLCSILFQKRQIRKLNEYLDLLEELQPLCSDVNYYRSLILFYDIRLKTGKLLDTLKSSELENNKYSFIDSSKDHIKALLIELYCSIDDWEGAFTLFDELQSTEARNKFLRRVKTINTHISKKI
2AGH , Knot 15 25 0.64 24 20 23 
KEKRIKELELLLMSTENELKGQQAL
6TOA , Knot 86 197 0.76 38 113 180 
MMLNEVTAVPGTALPVAEFRDHLRLGTGFADLGAEDAALLSYLRAAIAAIEGRTAKALISRGFRLALTAWRWGDMQTLPIAPVATVTALRLVDAAGVETPVAAGWRLVPDMARPRIEALGAMLPMIPTGGRVEIDFTAGFGASWSALPVDLAQAVFLLAAQYYELRHDGAAEGGAMPFGVMALIERWRTVRVLGGRP

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 \(c\).

\(|P_{f(7MSK_1)}(2) \setminus P_{f(2AGH_1)}(2)|=212\), \(|P_{f(2AGH_1)}(2) \setminus P_{f(7MSK_1)}(2)|=6\). 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 1:1001101001001100100001000110010110100000010110100000100111000011010100111000000010001001100100111100000000001100011110110011100101000011010000110010100001000001001101101101001101110001101000000110100110101010001101010110010101110001001011010000000101000110001001011010100100100000110011101101000000000010111110011100001001000101100101100010000011110010100101100100001000000110000001011110100010010111011001000010001100100100010001
Pair \(Z_2\) Length of longest common subsequence
7MSK_1,2AGH_1 218 3
7MSK_1,6TOA_1 219 3
2AGH_1,6TOA_1 121 2

Newick tree

 
[
	7MSK_1:12.21,
	[
		2AGH_1:60.5,6TOA_1:60.5
	]:60.71
]

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 \((0.85)(0.8)(\frac{455 }{\log_{20} 455}-\frac{25}{\log_{20}25})=135.\)
Status Protein1 Protein2 d d1/2
Query variables 7MSK_1 2AGH_1 171 90.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]