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Parikh vectors
2DVV_1 8YGX_1 5QYM_1 Letter Amino acid
6 13 11 R Arginine
3 20 23 I Isoleucine
6 14 10 P Proline
1 11 21 T Threonine
9 27 29 L Leucine
11 20 19 K Lycine
6 10 8 M Methionine
1 6 5 W Tryptophan
7 14 7 Y Tyrosine
11 11 18 A Alanine
4 11 14 N Asparagine
11 17 14 D Aspartic acid
3 4 9 Q Glutamine
5 24 15 E Glutamic acid
3 14 7 G Glycine
7 5 5 H Histidine
5 14 18 S Serine
6 22 14 V Valine
2 9 1 C Cysteine
5 11 10 F Phenylalanine 

2DVV_1|Chain A|Bromodomain-containing protein 2|Homo sapiens (9606)
>8YGX_1|Chain A|Protein-tyrosine kinase 2-beta|Homo sapiens (9606)
>5QYM_1|Chain A|Pre-mRNA-splicing factor 8|Saccharomyces cerevisiae (strain ATCC 204508 / S288c) (559292)
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 \(w=f(c)\)
2DVV , Knot 58 112 0.81 40 92 110 
GSHMEQLKHCNGILKELLSKKHAAYAWPFYKPVDASALGLHDYHDIIKHPMDLSTVKRKMENRDYRDAQEFAADVRLMFSNCYKYNPPDHDVVAMARKLQDVFEFRYAKMPD
8YGX , Knot 127 277 0.86 40 180 265 
PQYGIAREDVVLNRILGEGFFGEVYEGVYTNHKGEKINVAVKTCKKDCTLDNKEKFMSEAVIMKNLDHPHIVKLIGIIEEEPTWIIMELYPYGELGHYLERNKNSLKVLTLVLYSLQICKAMAYLESINCVHRDIAVRNILVASPECVKLGDFGLSRYIEDEDYYKASVTRLPIKWMSPESINFRRFTTASDVWMFAVCMWEILSFGKQPFFWLENKDVIGVLEKGDRLPKPDLCPPVLYTLMTRCWDYDPSDRPRFTELVCSLSDVYQMEKDIAME
5QYM , Knot 117 258 0.84 40 175 251 
GAMNSSNYAELFNNDIKLFVDDTNVYRVTVHKTFEGNVATKAINGCIFTLNPKTGHLFLKIIHTSVWAGQKRLSQLAKWKTAEEVSALVRSLPKEEQPKQIIVTRKAMLDPLEVHMLDFPNIAIRPTELRLPFSAAMSIDKLSDVVMKATEPQMVLFNIYDDWLDRISSYTAFSRLTLLLRALKTNEESAKMILLSDPTITIKSYHLWPSFTDEQWITIESQMRDLILTEYGRKYNVNISALTQTEIKDIILGQNIKA

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 \(c\).

\(|P_{f(2DVV_1)}(2) \setminus P_{f(8YGX_1)}(2)|=47\), \(|P_{f(8YGX_1)}(2) \setminus P_{f(2DVV_1)}(2)|=135\). 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 1:1001001000011100110000110111100110101111000001100110100100010000000100111010111000000011000111110010011010010110
Pair \(Z_2\) Length of longest common subsequence
2DVV_1,8YGX_1 182 3
2DVV_1,5QYM_1 181 3
8YGX_1,5QYM_1 187 4

Newick tree

 
[
	8YGX_1:92.83,
	[
		2DVV_1:90.5,5QYM_1:90.5
	]:2.33
]

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 \((0.85)(0.8)(\frac{389 }{\log_{20} 389}-\frac{112}{\log_{20}112})=84.5\)
Status Protein1 Protein2 d d1/2
Query variables 2DVV_1 8YGX_1 110 76
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]