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Parikh vectors
4DYX_1 2ADB_1 5PQE_1 Letter Amino acid
14 0 11 A Alanine
7 0 7 G Glycine
6 0 6 F Phenylalanine
5 0 5 T Threonine
6 0 10 V Valine
11 0 4 N Asparagine
13 0 13 D Aspartic acid
21 0 18 L Leucine
12 0 6 K Lycine
4 0 7 M Methionine
9 0 5 Y Tyrosine
6 0 14 R Arginine
13 0 10 H Histidine
6 0 5 I Isoleucine
3 0 6 P Proline
0 3 1 C Cysteine
11 0 8 Q Glutamine
15 0 13 E Glutamic acid
9 0 7 S Serine
1 0 0 W Tryptophan 

4DYX_1|Chain A|Ferritin heavy chain|Homo sapiens (9606)
>2ADB_1|Chain A[auth B]|5'-R(*CP*UP*CP*UP*CP*U)-3'|null
>5PQE_1|Chains A, B|Bromodomain-containing protein 1|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 \(w=f(c)\)
4DYX , Knot 81 172 0.80 38 130 165 
TSQVRQNYHQDSEAAINRQINLELYASYVYLSMSYYFDRDDVALKNFAKYFHHQSHEEHEHAHKLMKLQNQRGGRIFLQDIQKPDEDDWESGLNAMEAALHLEKNVNQSLLELHKLATDKNDPHLADFIETHYLNEQVKAIKELGDHVTNLRKMGAPESGLAEYLFDKHTLG
2ADB , Knot 3 6 0.29 4 2 2 
CUCUCU
5PQE , Knot 74 156 0.79 38 120 151 
MHHHHHHSSGVDLGTENLYFQSMEQVAMELRLTELTRLLRSVLDQLQDKDPARIFAQPVSLKEVPDYLDHIKHPMDFATMRKRLEAQGYKNLHEFEEDFDLIIDNCMKYNARDTVFYRAAVRLRDQGGVVLRQARREVDSIGLEEASGMHLPERPA

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 \(c\).

\(|P_{f(4DYX_1)}(2) \setminus P_{f(2ADB_1)}(2)|=130\), \(|P_{f(2ADB_1)}(2) \setminus P_{f(4DYX_1)}(2)|=2\). 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 1:0001000000000111000101010100101010001000011100110010000000000100110100001101110010010000100110110111010001000110100110000010110110000100010110011001001001111001110011000011
Pair \(Z_2\) Length of longest common subsequence
4DYX_1,2ADB_1 132 0
4DYX_1,5PQE_1 140 3
2ADB_1,5PQE_1 122 1

Newick tree

 
[
	4DYX_1:70.21,
	[
		2ADB_1:61,5PQE_1:61
	]:9.21
]

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 \((0.85)(0.8)(\frac{178 }{\log_{20} 178}-\frac{6}{\log_{20}6})=63.1\)
Status Protein1 Protein2 d d1/2
Query variables 4DYX_1 2ADB_1 80 41
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]