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Parikh vectors
6EAI_1 7ZRN_1 7BRE_1 Letter Amino acid
9 20 4 H Histidine
57 29 13 L Leucine
53 15 18 S Serine
20 14 13 Y Tyrosine
19 29 9 R Arginine
17 8 2 C Cysteine
21 7 6 Q Glutamine
28 22 6 E Glutamic acid
44 6 13 K Lycine
45 23 11 V Valine
28 37 9 A Alanine
21 24 11 D Aspartic acid
30 15 20 G Glycine
37 16 10 I Isoleucine
43 13 5 N Asparagine
20 16 9 F Phenylalanine
9 8 4 M Methionine
18 19 11 P Proline
44 14 7 T Threonine
5 8 3 W Tryptophan 

6EAI_1|Chains A, B, C|Fusion glycoprotein F0|Human respiratory syncytial virus (11250)
>7ZRN_1|Chains A, B|10-epi-cubebol synthase|Sorangium cellulosum (56)
>7BRE_1|Chains A, D|Set1/Ash2 histone methyltransferase complex subunit ASH2|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 \(w=f(c)\)
6EAI , Knot 226 568 0.84 40 254 527 
MELLILKANAITTILTAVTFCFASGQNITEEFYQSTCSAVSKGYLSALRTGWYTSVITIELSNIKENKCNGTDAKVKLIKQELDKYKNAVTELQLLMQSTPATNNRARRELPRFMNYTLNNAKKTNVTLSKKRKRRFLGFLLGVGSAIASGVAVCKVLHLEGEVNKIKSALLSTNKAVVSLSNGVSVLTFKVLDLKNYIDKQLLPILNKQSCSISNIETVIEFQQKNNRLLEITREFSVNAGVTTPVSTYMLTNSELLSLINDMPITNDQKKLMSNNVQIVRQQSYSIMCIIKEEVLAYVVQLPLYGVIDTPCWKLHTSPLCTTNTKEGSNICLTRTDRGWYCDNAGSVSFFPQAETCKVQSNRVFCDTMNSLTLPSEVNLCNVDIFNPKYDCKIMTLKTDVSSSVITSLGAIVSCYGKTKCTASNKNRGIIKTFSNGCDYVSNKGVDTVSVGNTLYYVNKQEGKSLYVKGEPIINFYDPLVFPSDEFDASISQVNEKINQSLAFIRKSDELLSAIGGYIPEAPRDGQAYVRKDGEWVLLSTFLGGLVPRGSHHHHHHSAWSHPQFEK
7ZRN , Knot 151 343 0.85 40 213 330 
MKHHHHHHPMSDYDIPTTENLYFQGAMAMHRALLCPFPATTPHPQAAQLANDCLEWTRKCGLLPDESPRTLDKVRSYSALAAHCYPDAHFERLRAICDYYSWLFFFDDVCENTSLNGAEPKVVSSLLFDVYGVLRGPTAAVGHAPFAQALADIWRRIGDGCPGFWRRRLIRHVENYIDGCVWEAQNRQLDRVPSRAVFEGMRMHTSTMYEFWDFIEYAGDLFLPDEVVEHPLVAEVRRAGNAIASFANDIYSLRKETSNRDVHNLVVVLMHEERIELEAAYARAAGIHDAQVEHFLDLVKHLPTFSATIDRNLARYVEGIRIWIRANHDWSIVTPRYNEPDAR
7BRE , Knot 89 184 0.84 40 141 181 
SRVLLALHDRAPQLKISDDRLTVVGEKGYSMVRASHGVRKGAWYFEITVDEMPPDTAARLGWSQPLGNLQAPLGYDKFSYSWRSKKGTKFHQSIGKHYSSGYGQGDVLGFYINLPEDTISGRGSSEIIFYKNGVNQGVAYKDIFEGVYFPAISLYKSCTVSINFGPCFKYPPKDLTYRPMSDMG

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 \(c\).

\(|P_{f(6EAI_1)}(2) \setminus P_{f(7ZRN_1)}(2)|=111\), \(|P_{f(7ZRN_1)}(2) \setminus P_{f(6EAI_1)}(2)|=70\). 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 1:1011110101100110110101101001000100000011001010110011000110101001000000100101011000100000110010111000110000100011011000100100001010000000111111111011101111001101010100100111000011101001101101011010001000111110000001001001101000000110100010101110011000110000110110011100000011000101100000011011000111011011101110010101000110000000100101000001100001101011101000010000110001001011001010010110100000110100010001100111110001000001000001110010010001000110010110010010000100101010111010011111000101010010001000111100000110111101101100101010001011110011111110100000000110010100
Pair \(Z_2\) Length of longest common subsequence
6EAI_1,7ZRN_1 181 6
6EAI_1,7BRE_1 177 3
7ZRN_1,7BRE_1 208 4

Newick tree

 
[
	7ZRN_1:10.29,
	[
		6EAI_1:88.5,7BRE_1:88.5
	]:11.79
]

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 \((0.85)(0.8)(\frac{911 }{\log_{20} 911}-\frac{343}{\log_{20}343})=152.\)
Status Protein1 Protein2 d d1/2
Query variables 6EAI_1 7ZRN_1 196 157.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]