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Parikh vectors
6GVE_1 4ZPY_1 9KBQ_1 Letter Amino acid
3 37 17 L Leucine
4 32 5 S Serine
8 29 7 D Aspartic acid
3 41 15 G Glycine
3 21 4 I Isoleucine
1 13 2 M Methionine
0 37 10 V Valine
1 15 2 W Tryptophan
13 38 12 A Alanine
3 22 6 R Arginine
4 6 1 C Cysteine
9 28 6 Q Glutamine
3 20 18 K Lycine
1 20 7 F Phenylalanine
3 55 12 T Threonine
2 23 5 Y Tyrosine
2 39 12 N Asparagine
10 21 7 E Glutamic acid
3 14 0 H Histidine
1 38 1 P Proline 

6GVE_1|Chains A[auth C], N[auth H], O[auth M], P|CP12 polypeptide|Thermosynechococcus elongatus (strain BP-1) (197221)
>4ZPY_1|Chain A|VP1 protein|Murine minute virus strain MVM prototype (648235)
>9KBQ_1|Chains A, B|Lysozyme|Acinetobacter baumannii (470)
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 \(w=f(c)\)
6GVE , Knot 42 77 0.79 38 59 75 
GSMSNLEKQIEQAREEAHKICDTEGATSGQCAAAWDALEELQAEAAHQRAEQQDHKTSFQQYCDDNPDAAECRIYDD
4ZPY , Knot 222 549 0.85 40 278 529 
GVGVSTGSYDNQTHYRFLGDGWVEITALATRLVHLNMPKSENYCRIRVHNTTDTSVKGNMAKDDAHEQIWTPWSLVDANAWGVWLQPSDWQYICNTMSQLNLVSLDQEIFNVVLKTVTEQDLGGQAIKIYNADLTACMMVAVDSNNILPYTPAANSMETLGFYPWKPTIASPYRYYFCVDRDLSVTYENQEGTVEHNVMGTPKGMNSQFFTIENTQQITLLRTGDEFATGTYYFDTNPVKLTHTWQTNRQLGQPPLLSTFPEADTDAGTLTAQGSRHGTTQMGVNWVSEAIRTRPAQVGFCQPHNDFEASRAGPFAAPKVPADITQGVDKEANGSVRYSYGKQHGENWASHGPAPERYTWDETSFGSGRDTKDGFIQSAPLVVPPPLNGILTNANPIGTKNDIHFSNVFNSYGPLTAFSHPSPVYPQGQIWDKELDLEHKPRLHITAPFVCKNNAPGQMLVRLGPNLTDQYDPNGATLSRIVTYGTFFWKGKLTMRAKLRANTTWNPVYQVSAEDNGNSYMSVTKWLPTATGNMQSVPLITRPVARNTY
9KBQ , Knot 74 149 0.82 38 108 145 
MSKTTSNAGLNLIKGFEGKRLNAYDDGVGVWTIGFGTIKYPNGVRVKKGDTCTEQQAETYLKNDLTKFEVAINKLVKVSLTQNQFDALASFTYNLGETNLANSTLLKKLNKGDYQGAADQFLVWNKAGGKVMKGLVRRREAERALFLKK

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 \(c\).

\(|P_{f(6GVE_1)}(2) \setminus P_{f(4ZPY_1)}(2)|=12\), \(|P_{f(4ZPY_1)}(2) \setminus P_{f(6GVE_1)}(2)|=231\). 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 1:10100100010010001001000011001001111011001010110001000000001000000010110001000
Pair \(Z_2\) Length of longest common subsequence
6GVE_1,4ZPY_1 243 3
6GVE_1,9KBQ_1 123 3
4ZPY_1,9KBQ_1 210 4

Newick tree

 
[
	4ZPY_1:12.21,
	[
		6GVE_1:61.5,9KBQ_1:61.5
	]:64.71
]

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 \((0.85)(0.8)(\frac{626 }{\log_{20} 626}-\frac{77}{\log_{20}77})=161.\)
Status Protein1 Protein2 d d1/2
Query variables 6GVE_1 4ZPY_1 209 118
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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