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Parikh vectors
2EOF_1 6QGK_1 6FCD_1 Letter Amino acid
0 5 4 W Tryptophan
1 7 15 Y Tyrosine
1 17 33 A Alanine
2 1 6 C Cysteine
0 5 23 I Isoleucine
1 11 33 L Leucine
8 11 20 S Serine
3 9 7 N Asparagine
0 11 30 D Aspartic acid
2 2 15 P Proline
2 8 18 Q Glutamine
4 15 24 E Glutamic acid
3 3 27 K Lycine
1 6 6 M Methionine
1 14 35 V Valine
1 12 19 R Arginine
7 13 36 G Glycine
2 10 13 H Histidine
1 9 12 F Phenylalanine
4 8 19 T Threonine 

2EOF_1|Chain A|Zinc finger protein 268|Homo sapiens (9606)
>6QGK_1|Chain A|Apoptosis regulator Bcl-2,Bcl-2-like protein 1,Apoptosis regulator Bcl-2,Bcl-2-like protein 1|Homo sapiens (9606)
>6FCD_1|Chain A|S-adenosylmethionine synthase isoform type-2|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 \(w=f(c)\)
2EOF , Knot 24 44 0.68 34 34 38 
GSSGSSGTGEKPYECNECQKAFNTKSNLMVHQRTHTGESGPSSG
6QGK , Knot 86 177 0.83 40 133 169 
MSQDNREIVMKYISYKLSQRGYEWDAGDVEENRTEAPEGTESEVVHQTLRQAGDDFSLRYRRDFAQMSSQLHLTPGTAYASFATVVAELFRDGVNWGRIVAFFEFGGVMCVESVNRAMSVLVDNIAAWMATYLNDHLHTWIQDNGGWDAFVELYGNNAAAESRKGQERFLEHHHHHH
6FCD , Knot 171 395 0.86 40 222 385 
MNGQLNGFHEAFIEEGTFLFTSESVGEGHPDKICDQISDAVLDAHLQQDPDAKVACETVAKTGMILLAGEITSRAAVDYQKVVREAVKHIGYDDSSKGFDYKTCNVLVALEQQSPDIAQGVHLDRNEEDIGAGDQGLMFGYATDETEECMPLTIVLAHKLNAKLAELRRNGTLPWLRPDSKTQVTVQYMQDRGAVLPIRVHTIVISVQHDEEVCLDEMRDALKEKVIKAVVPAKYLDEDTIYHLQPSGRFVIGGPQGDAGLTGAKIIVDTYGGWGAHGGGAFSGKDYTKVDRSAAYAARWVAKSLVKGGLCRRVLVQVSYAIGVSHPLSISIFHYGTSQKSERELLEIVKKNFDLRPGVIVRDLDLKKPIYQRTAAYGHFGRDSFPWEVPKKLKY

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 \(c\).

\(|P_{f(2EOF_1)}(2) \setminus P_{f(6QGK_1)}(2)|=24\), \(|P_{f(6QGK_1)}(2) \setminus P_{f(2EOF_1)}(2)|=123\). 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 1:10010010100100000000110000011100000010011001
Pair \(Z_2\) Length of longest common subsequence
2EOF_1,6QGK_1 147 3
2EOF_1,6FCD_1 210 3
6QGK_1,6FCD_1 195 3

Newick tree

 
[
	6FCD_1:10.02,
	[
		2EOF_1:73.5,6QGK_1:73.5
	]:35.52
]

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 \((0.85)(0.8)(\frac{221 }{\log_{20} 221}-\frac{44}{\log_{20}44})=59.7\)
Status Protein1 Protein2 d d1/2
Query variables 2EOF_1 6QGK_1 75 46
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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