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Parikh vectors
5BQA_1 2BRA_1 2DVS_1 Letter Amino acid
1 30 4 R Arginine
1 30 10 Q Glutamine
10 40 3 G Glycine
6 23 5 F Phenylalanine
1 13 6 Y Tyrosine
10 55 7 A Alanine
1 8 2 C Cysteine
9 14 7 I Isoleucine
0 8 3 W Tryptophan
1 19 6 D Aspartic acid
1 24 6 E Glutamic acid
0 12 3 H Histidine
12 61 10 L Leucine
3 7 7 M Methionine
2 22 7 P Proline
2 15 7 N Asparagine
2 23 11 K Lycine
5 23 2 S Serine
3 22 7 T Threonine
6 35 9 V Valine 

5BQA_1|Chains A, B, C, D, E, F[auth K], G[auth L], H[auth M], I[auth N], J[auth O]|ATP synthase subunit 9, mitochondrial|Saccharomyces cerevisiae (4932)
>2BRA_1|Chains A, B|NEDD9 INTERACTING PROTEIN WITH CALPONIN HOMOLOGY AND LIM DOMAINS|MUS MUSCULUS (10090)
>2DVS_1|Chains A, B, C|bromodomain-containing protein 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 \(w=f(c)\)
5BQA , Knot 40 76 0.76 36 57 72 
MQLVLAAKYIGAGISTIGLLGAGIGIAIVFAALINGVSRNPSIKDTVFPMAILGFALSEATGLFCLMVSFLLLFGV
2BRA , Knot 192 484 0.81 40 231 436 
MASPASTNPAHDHFETFVQAQLCQDVLSSFQGLCRALGVESGGGLSQYHKIKAQLNYWSAKSLWAKLDKRASQPVYQQGQACTNTKCLVVGAGPCGLRAAVELALLGARVVLVEKRIKFSRHNVLHLWPFTIHDLRALGAAAFYGRFCTGTLDHISIRQLQLLLLKVALLLGVEIHWGVKFTGLQPPPRKGSGWRAQLQPNPPAQLASYEFDVLISAAGGKFVPEGFTIREMRGKLAIGITANFVNGRTVEETQVPEISGVARIYNQKFFQSLLKATGIDLENIVYYKDETHYFVMTAKKQCLLRLGVLRQDLSETDQLLGKANVVPEALQRFARAAADFATHGKLGKLEFAQDARGRPDVAAFDFTSMMRAESSARVQEKHGARLLLGLVGDCLVEPFWPLGTGVARGFLAAFDAAWMVKRWAEGAGPLEVLAERESLYQLLSQTSPENMHRNVAQYGLDPATRYPNLNLRAVTPNQVQDLYD
2DVS , Knot 63 122 0.82 40 108 120 
GRVTNQLQYLHKVVMKALWKHQFAWPFRQPVDAVKLGLPDYHKIIKQPMDMGTIKRRLENNYYWAASECMQDFNTMFTNCYIYNKPTDDIVLMAQTLEKIFLQKVASMPQEEQELVVTIPKN

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 \(c\).

\(|P_{f(5BQA_1)}(2) \setminus P_{f(2BRA_1)}(2)|=15\), \(|P_{f(2BRA_1)}(2) \setminus P_{f(5BQA_1)}(2)|=189\). 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 1:1011111001111100111111111111111111011000101000111111111110010111011101111111
Pair \(Z_2\) Length of longest common subsequence
5BQA_1,2BRA_1 204 4
5BQA_1,2DVS_1 129 2
2BRA_1,2DVS_1 199 4

Newick tree

 
[
	2BRA_1:11.22,
	[
		5BQA_1:64.5,2DVS_1:64.5
	]:45.72
]

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 \((0.85)(0.8)(\frac{560 }{\log_{20} 560}-\frac{76}{\log_{20}76})=144.\)
Status Protein1 Protein2 d d1/2
Query variables 5BQA_1 2BRA_1 177 101.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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