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Parikh vectors
1XWG_1 7AIA_1 6EOI_1 Letter Amino acid
1 4 2 W Tryptophan
12 17 12 R Arginine
7 13 8 N Asparagine
1 4 2 C Cysteine
21 30 13 E Glutamic acid
15 15 11 I Isoleucine
12 15 19 S Serine
12 13 9 D Aspartic acid
10 7 8 F Phenylalanine
3 16 25 T Threonine
3 11 7 H Histidine
30 37 40 L Leucine
7 5 9 M Methionine
10 16 16 V Valine
16 12 48 A Alanine
5 11 10 Q Glutamine
10 10 34 G Glycine
24 20 6 K Lycine
12 13 11 P Proline
10 11 8 Y Tyrosine 

1XWG_1|Chains A, B|Glutathione S-transferase A1|Homo sapiens (9606)
>7AIA_1|Chains A[auth AAA], B[auth BBB]|Ganglioside-induced differentiation-associated protein 1|Homo sapiens (9606)
>6EOI_1|Chains A, B|Reductive Aminase|Aspergillus terreus (33178)
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 \(w=f(c)\)
1XWG , Knot 103 221 0.83 40 152 215 
AEKPKLHYFNARGRMESTRWLLAAAGVEFEEKFIKSAEDLDKLRNDGYLMFQQVPMVEIDGMKLVQERAILNYIASKYNLYGKDIKERALIDMYIEGIADLGEMILLLPVCPPEEKDAKLALIKEKIKNRYFPAFEKVLKSHGQDYLVGNKLSRADIHLVELLYYVEELDSSLISSFPLLKALKTRISNLPTVKKFLQPGSPRKPPMDEKSLEEARKIFRF
7AIA , Knot 123 280 0.82 40 183 269 
EVKLILYHWTHSFSSQKVRLVIAEKALKCEEHDVSLPLSEHNEPWFMRLNSTGEVPVLIHGENIICEATQIIDYLEQTFLDERTPRLMPDKESMYYPRVQHYRELLDSLPMDAYTHGCILHPELTVDSMIPAYATTRIRSQIGNTESELKKLAEENPDLQEAYIAKQKRLKSKLLDHDNVKYLKKILDELEKVLDQVETELQRRNEETPEEGQQPWLCGESFTLADVSLAVTLHRLKFLGFARRNWGNGKRPNLETYYERVLKRKTFNKVLGHVNNILIS
6EOI , Knot 124 298 0.79 40 167 275 
MATTTTTTKLTIFGLGAMGTAMATQFLKQGHTPTVWNRTAAKANPLVEQGAHLAATIPAAIAASPLLIFCLLDNAAVEQTLAAGPPSLAGKTILNLTNGTPSQARRLATLASARGARYFHGGIMATPDMIGAPHAVILYSGGGSAETYASVEGVLAVLGSGKYLGDDAGSASLHDLALLSGMYGLFAGFLHATALVRSEGEGVSATEFLGLLAPWLQAMTGYLGLLARQIDDGVYTAQTSNLEMQLVALENACAASREQGVSAEVMLPLKGLVERAVREGRGGHDISSLIDYFRNASV

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 \(c\).

\(|P_{f(1XWG_1)}(2) \setminus P_{f(7AIA_1)}(2)|=62\), \(|P_{f(7AIA_1)}(2) \setminus P_{f(1XWG_1)}(2)|=93\). 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 1:10010100101010100001111111101000110010010010001011100111101011011000111001100001010010001110101011101101111111011000010111100010000111100110001000111001001010110110010010001100111101100010011010011011010011100001001001101
Pair \(Z_2\) Length of longest common subsequence
1XWG_1,7AIA_1 155 4
1XWG_1,6EOI_1 161 4
7AIA_1,6EOI_1 174 3

Newick tree

 
[
	6EOI_1:85.81,
	[
		1XWG_1:77.5,7AIA_1:77.5
	]:8.31
]

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 \((0.85)(0.8)(\frac{501 }{\log_{20} 501}-\frac{221}{\log_{20}221})=80.7\)
Status Protein1 Protein2 d d1/2
Query variables 1XWG_1 7AIA_1 100 89.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]