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Parikh vectors
6GEU_1 4TTB_1 1PAG_1 Letter Amino acid
39 16 14 A Alanine
3 6 5 M Methionine
8 20 20 K Lycine
16 14 20 T Threonine
7 5 2 W Tryptophan
7 7 10 Y Tyrosine
5 11 25 N Asparagine
11 13 11 D Aspartic acid
42 23 23 L Leucine
9 6 9 F Phenylalanine
16 12 19 S Serine
3 2 4 C Cysteine
14 26 14 E Glutamic acid
9 16 2 H Histidine
9 16 18 I Isoleucine
25 16 12 P Proline
22 22 20 V Valine
24 16 11 R Arginine
12 7 9 Q Glutamine
33 11 14 G Glycine 

6GEU_1|Chain A|Putative transferase CAF17, mitochondrial|Homo sapiens (9606)
>4TTB_1|Chains A, B|Iodotyrosine dehalogenase 1|Homo sapiens (9606)
>1PAG_1|Chains A, B|POKEWEED ANTIVIRAL PROTEIN|Phytolacca americana (3527)
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 \(w=f(c)\)
6GEU , Knot 133 314 0.81 40 171 289 
TAGAAWACFRLDGRTLLRVRGPDAAPFLLGLLTNELPLPSPAAAGAPPAARAGYAHFLNVQGRTLYDVILYGLQEHSEVSGFLLECDSSVQGALQKHLALYRIRRKVTVEPHPELRVWAVLPSSPEACGAASLQERAGAAAILIRDPRTARMGWRLLTQDEGPALVPGGRLGDLWDYHQHRYLQGVPEGVRDLPPGVALPLESNLAFMNGVSFTKGAYIGQELTARTHHMGVIRKRLFPVRFLDPLPTSGITPGATVLTASGQTVGKFRAGQGNVGLALLWSEKIKGPLHIRASEGAQVALAASVPDWWPTVSK
4TTB , Knot 121 265 0.85 40 181 253 
SGEPRTRAEARPWVDEDLKDSSDLHQAEEDADEWQESEENVEHIPFSHNHYPEKEMVKRSQEFYELLNKRRSVRFISNEQVPMEVIDNVIRTAGTAPSGAHTEPWTFVVVKDPDVKHKIRKIIEEEEEINYMKRMGHRWVTDLKKLRTNWIKEYLDTAPILILIFKQVHGFAANGKKKVHYYNEISVSIACGILLAALQNAGLVTVTTTPLNCGPRLRVLLGRPAHEKLLMLLPVGYPSKEATVPDLKRKPLDQIMVTVHHHHHH
1PAG , Knot 119 262 0.84 40 169 255 
VNTIIYNVGSTTISKYATFLNDLRNEAKDPSLKCYGIPMLPNTNTNPKYVLVELQGSNKKTITLMLRRNNLYVMGYSDPFETNKCRYHIFNDISGTERQDVETTLCPNANSRVSKNINFDSRYPTLESKAGVKSRSQVQLGIQILDSNIGKISGVMSFTEKTEAEFLLVAIQMVSEAARFKYIENQVKTNFNRAFNPNPKVLNLQETWGKISTAIHDAKNGVLPKPLELVDASGAKWIVLRVDEIKPDVALLNYVGGSCQTT

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 \(c\).

\(|P_{f(6GEU_1)}(2) \setminus P_{f(4TTB_1)}(2)|=78\), \(|P_{f(4TTB_1)}(2) \setminus P_{f(6GEU_1)}(2)|=88\). 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 1:01111110101010011010110111111111000111101111111111011010110101001001110110000010111100000101110001110010001010101010111111001010111010001111111100100101110110000111111110110110000000101110110011111111100011110110100110110010100001111000111101101110011011101101010011010110101111111000101110101001101111101101110100
Pair \(Z_2\) Length of longest common subsequence
6GEU_1,4TTB_1 166 3
6GEU_1,1PAG_1 174 3
4TTB_1,1PAG_1 166 3

Newick tree

 
[
	1PAG_1:85.68,
	[
		6GEU_1:83,4TTB_1:83
	]:2.68
]

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 \((0.85)(0.8)(\frac{579 }{\log_{20} 579}-\frac{265}{\log_{20}265})=88.6\)
Status Protein1 Protein2 d d1/2
Query variables 6GEU_1 4TTB_1 109 101.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]