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Parikh vectors
9DBY_1 6YQQ_1 9CED_1 Letter Amino acid
2 8 7 H Histidine
13 7 11 K Lycine
3 3 11 Y Tyrosine
19 51 17 A Alanine
8 10 14 Q Glutamine
6 30 26 G Glycine
6 19 16 S Serine
6 27 27 V Valine
4 19 17 D Aspartic acid
1 3 12 C Cysteine
7 8 11 I Isoleucine
0 7 3 W Tryptophan
7 21 9 E Glutamic acid
12 35 29 L Leucine
10 19 24 T Threonine
4 17 17 F Phenylalanine
6 21 13 P Proline
18 27 11 R Arginine
1 6 21 N Asparagine
3 3 10 M Methionine 

9DBY_1|Chains A, E|Histone H3.2|Xenopus laevis (8355)
>6YQQ_1|Chain A|ForT-PRPP complex|Streptomyces kaniharaensis (212423)
>9CED_1|Chain A|3C-like proteinase nsp5|Severe acute respiratory syndrome coronavirus 2 (2697049)
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 \(w=f(c)\)
9DBY , Knot 65 136 0.78 38 102 127 
MARTKQTARKSTGGKAPRKQLATKAARKSAPATGGVKKPHRYRPGTVALREIRRYQKSTELLIRKLPFQRLVREIAQDFKTDLRFQSSAVMALQEASEAYLVALFEDTNLCAIHAKRVTIMPKDIQLARRIRGERA
6YQQ , Knot 140 341 0.79 40 180 320 
MALDRPDRSGAVRVSAPARLSFTLISLDGSSLRRNGIAAMAVDRPGLTAEVREAADGIVAVTGTAEETARELAAALEALRKLWDGPAARVDVLEALPQHSGFGSKTSTLLAVGHAYGRLCGVEPDLRELARTLGRGRTSGASTGLSAYGGFLVDGGHVNPPDFAEAPQKYLRPSRFAQQVAPPKPVVRLDFPDWPVLVLLTHGRHLGGQEELEWFHSVAPIPAEESWRTSHLVFMGLAPAVLEQDFDAFCAAVNEITFTGHFKQAQIAFQGDAVADVLEAGRAAPSVDAIALSVTGPACFAFTKRPEDAERWAWELKNRGLIRDFWFTRANNQGLATTVVS
9CED , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ

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 \(c\).

\(|P_{f(9DBY_1)}(2) \setminus P_{f(6YQQ_1)}(2)|=36\), \(|P_{f(6YQQ_1)}(2) \setminus P_{f(9DBY_1)}(2)|=114\). 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 1:1100000100001101100011001100011101110010000110111001000000001110011100110011001000101000111110010010111110000101101001011100101100101001
Pair \(Z_2\) Length of longest common subsequence
9DBY_1,6YQQ_1 150 4
9DBY_1,9CED_1 186 5
6YQQ_1,9CED_1 176 3

Newick tree

 
[
	9CED_1:95.15,
	[
		9DBY_1:75,6YQQ_1:75
	]:20.15
]

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 \((0.85)(0.8)(\frac{477 }{\log_{20} 477}-\frac{136}{\log_{20}136})=101.\)
Status Protein1 Protein2 d d1/2
Query variables 9DBY_1 6YQQ_1 122 84
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]