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Parikh vectors
9DWJ_1 7KCC_1 8CNM_1 Letter Amino acid
7 24 21 E Glutamic acid
7 36 25 G Glycine
7 23 11 I Isoleucine
13 27 14 K Lycine
6 21 14 S Serine
4 30 19 D Aspartic acid
0 6 5 C Cysteine
8 18 7 Q Glutamine
2 13 9 H Histidine
0 4 5 W Tryptophan
6 35 20 V Valine
19 32 21 A Alanine
12 33 36 L Leucine
4 12 9 F Phenylalanine
6 15 23 P Proline
10 19 21 T Threonine
1 7 6 N Asparagine
2 6 6 M Methionine
3 15 2 Y Tyrosine
18 20 28 R Arginine 

9DWJ_1|Chains A, E|Histone H3.2|Homo sapiens (9606)
>7KCC_1|Chain A|S-adenosylmethionine synthase isoform type-2|Homo sapiens (9606)
>8CNM_1|Chains A, B|NAD-dependent protein deacetylase sirtuin-6|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 \(w=f(c)\)
9DWJ , Knot 65 135 0.78 36 102 127 
ARTKQTARKSTGGKAPRKQLATKAARKSAPATGGVKKPHRYRPGTVALREIRRYQKSTELLIRKLPFQRLVREIAQDFKTDLRFQSSAVMALQEASEAYLVGLFEDTNLAAIHAKRVTIMPKDIQLARRIRGERA
7KCC , Knot 171 396 0.86 40 224 386 
SMNGQLNGFHEAFIEEGTFLFTSESVGEGHPDKICDQISDAVLDAHLQQDPDAKVACETVAKTGMILLAGEITSRAAVDYQKVVREAVKHIGYDDSSKGFDYKTCNVLVALEQQSPDIAQGVHLDRNEEDIGAGDQGLMFGYATDETEECMPLTIVLAHKLNAKLAELRRNGTLPWLRPDSKTQVTVQYMQDRGAVLPIRVHTIVISVQHDEEVCLDEMRDALKEKVIKAVVPAKYLDEDTIYHLQPSGRFVIGGPQGDAGLTGRKIIVDTYGGWGAHGGGAFSGKDYTKVDRSAAYAARWVAKSLVKGGLCRRVLVQVSYAIGVSHPLSISIFHYGTSQKSERELLEIVKKNFDLRPGVIVRDLDLKKPIYQRTAAYGHFGRDSFPWEVPKKLKY
8CNM , Knot 131 302 0.82 40 182 293 
GIDPFTADKGKCGLPEIFDPPEELERKVWELARLVWQSSSVVFHTGAGISTASGIPDFRGPHGVWTMEERGLAPKFDTTFESARPTQTHMALVQLERVGLLRFLVSQNVDGLHVRSGFPRDKLAELHGNMFVEECAKCKTQYVRDTVVGTMGLKATGRLCTVAKARGLRACRGELRDTILDWEDSLPDRDLALADEASRNADLSITLGTSLQIRPSGNLPLATKRRGGRLVIVNLQPTKHDRHADLRIHGYVDEVMTRLMKHLGLEIPAWDGPRVLERALPPLPRPPTPKLEPKEESPTRIN

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 \(c\).

\(|P_{f(9DWJ_1)}(2) \setminus P_{f(7KCC_1)}(2)|=28\), \(|P_{f(7KCC_1)}(2) \setminus P_{f(9DWJ_1)}(2)|=150\). 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 1:100000100001101100011001100011101110010000110111001000000001110011100110011001000101000111110010010111110000111101001011100101100101001
Pair \(Z_2\) Length of longest common subsequence
9DWJ_1,7KCC_1 178 3
9DWJ_1,8CNM_1 154 4
7KCC_1,8CNM_1 164 5

Newick tree

 
[
	7KCC_1:88.24,
	[
		9DWJ_1:77,8CNM_1:77
	]:11.24
]

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 \((0.85)(0.8)(\frac{531 }{\log_{20} 531}-\frac{135}{\log_{20}135})=116.\)
Status Protein1 Protein2 d d1/2
Query variables 9DWJ_1 7KCC_1 148 96.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]