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Parikh vectors
7TOF_1 2EQQ_1 8GRQ_1 Letter Amino acid
13 0 2 H Histidine
46 1 11 L Leucine
30 1 7 I Isoleucine
14 1 2 M Methionine
24 1 5 S Serine
24 2 4 P Proline
22 3 5 T Threonine
25 1 1 N Asparagine
29 1 4 D Aspartic acid
8 2 0 C Cysteine
23 1 6 Q Glutamine
33 4 3 G Glycine
29 1 6 K Lycine
35 1 5 V Valine
32 1 9 A Alanine
34 2 14 R Arginine
38 1 7 E Glutamic acid
28 2 4 F Phenylalanine
7 0 0 W Tryptophan
21 2 3 Y Tyrosine 

7TOF_1|Chains A, B|Glucose-6-phosphate 1-dehydrogenase|Homo sapiens (9606)
>2EQQ_1|Chain A|Growth-blocking peptide, long form|Mythimna separata (271217)
>8GRQ_1|Chains A, E|Histone H3|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 \(w=f(c)\)
7TOF , Knot 215 515 0.87 40 263 491 
MAEQVALSRTQVCGILREELFQGDAFHQSDTHIFIIMGASGDLAKKKIYPTIWWLFRDGLLPENTFIVGYARSRLTVADIRKQSEPFFKATPEEKLKLEDFFARNSYVAGQYDDAASYQRLNSHMNALHLGSQANRLFYLALPPTVYEAVTKNIHESCMSQIGWNRIIVEKPFGRDLQSSDRLSNHISSLFREDQIYRIDHYLGKEMVQNLMVLRFANRIFGPIWNRDNIACVILTFKEPFGTEGRGGYFDEFGIIRDVMQNHLLQMLCLVAMEKPASTNSDDVRDEKVKVLKCISEVQANNVVLGQYVGNPDGEGEATKGYLDDPTVPRGSTTATFAAVVLYVENERWDGVPFILRCGKALNERKAEVRLQFHDVAGDIFHQQCKRNELVIRVQPNEAVYTKMMTKKPGMFFNPEESELDLTYGNRYKNVKLPDAYERLILDVFCGSQMHFVRSDELREAWRIFTPLLHQIELEKPKPIPYIYGSRGPTEADELMKRVGFQYEGTYKWVNPHKL
2EQQ , Knot 22 28 0.87 36 27 26 
ENFSGGCVAGYMRTPDGRCKPTFYQLIT
8GRQ , Knot 52 98 0.81 36 85 95 
KPHRYRPGTVALREIRRYQKSTELLIRKLPFQRLVREIAQDFKTDLRFQSSAVMALQEASEAYLVGLFEDTNLSAIHAKRVTIMPKDIQLARRIRGER

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 \(c\).

\(|P_{f(7TOF_1)}(2) \setminus P_{f(2EQQ_1)}(2)|=243\), \(|P_{f(2EQQ_1)}(2) \setminus P_{f(7TOF_1)}(2)|=7\). 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 1:11001110000101110001101011000000111111101011000101011111001111000111101000101101000001110101000101001110000111000011000010001011011001001101111101001100010000100111001110011100100000100010011000010010001100110011110110011111100001101110100111001011010011110011000110110111100110000001000010110010010100111100110101010100101001011010001011111101000010111111001011000010101010011101100000000111010100110001100011111010000101001000001011010001110110100101100001001101101110010100101110101001100100110011100010001101001
Pair \(Z_2\) Length of longest common subsequence
7TOF_1,2EQQ_1 250 3
7TOF_1,8GRQ_1 216 3
2EQQ_1,8GRQ_1 102 2

Newick tree

 
[
	7TOF_1:13.62,
	[
		8GRQ_1:51,2EQQ_1:51
	]:80.62
]

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 \((0.85)(0.8)(\frac{543 }{\log_{20} 543}-\frac{28}{\log_{20}28})=158.\)
Status Protein1 Protein2 d d1/2
Query variables 7TOF_1 2EQQ_1 204 106.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]