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Parikh vectors
1IDB_1 5JWS_1 1JWM_1 Letter Amino acid
9 9 17 V Valine
2 5 3 Q Glutamine
6 8 19 E Glutamic acid
6 13 9 K Lycine
2 5 3 M Methionine
7 12 12 T Threonine
0 1 6 H Histidine
9 15 15 L Leucine
3 5 15 F Phenylalanine
5 3 13 P Proline
4 6 6 S Serine
5 17 9 A Alanine
3 13 8 R Arginine
8 12 9 N Asparagine
4 10 12 D Aspartic acid
11 11 7 G Glycine
0 0 2 C Cysteine
11 10 9 I Isoleucine
1 3 4 W Tryptophan
3 6 4 Y Tyrosine 

1IDB_1|Chains A, B|Protease|Human immunodeficiency virus 2 (11709)
>5JWS_1|Chain A|Endolysin|Enterobacteria phage T4 sensu lato (2681598)
>1JWM_1|Chain A|HLA class II histocompatibility antigen, DR alpha chain|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 \(w=f(c)\)
1IDB , Knot 52 99 0.80 36 81 96 
PQFSLWKRPVVTAYIEGQPVEVLLDTGADDSIVAGIELGNNYSPKIVGGIGGFINTKEYKNVEIEVLNKKVRATIMTGDTPINIFGRNILTALGMSLNL
5JWS , Knot 77 164 0.79 38 116 157 
MNIFEMLRIDEGLRLKIYKDTEGYYTIGIGHLLTKSPSLNAAKSELDKAIGRNTNGVITKDEAEKLFNQDVDAAVRGILRNAKLKPVYDSLDAVRRAAAINMVFQMGETGVAGFTNSLRMLQQKRWDEAAVNLAKSRWYNQTPNRAKRVITTFRTGTWDAYKNL
1JWM , Knot 86 182 0.82 40 141 178 
IKEEHVIIQAEFYLNPDQSGEFMFDFDGDEIFHVDMAKKETVWRLEEFGRFASFEAQGALANIAVDKANLEIMTKRSNYTPITNVPPEVTVLTNSPVELREPNVLICFIDKFTPPVVNVTWLRNGKPVTTGVSETVFLPREDHLFRKFHYLPFLPSTEDVYDCRVEHWGLDEPLLKHWEFDA

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 \(c\).

\(|P_{f(1IDB_1)}(2) \setminus P_{f(5JWS_1)}(2)|=46\), \(|P_{f(5JWS_1)}(2) \setminus P_{f(1IDB_1)}(2)|=81\). 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 1:101011001110101010110111001100011111011000010111111111000000010101100010101101001101110011011110101
Pair \(Z_2\) Length of longest common subsequence
1IDB_1,5JWS_1 127 3
1IDB_1,1JWM_1 154 3
5JWS_1,1JWM_1 141 3

Newick tree

 
[
	1JWM_1:76.95,
	[
		1IDB_1:63.5,5JWS_1:63.5
	]:13.45
]

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 \((0.85)(0.8)(\frac{263 }{\log_{20} 263}-\frac{99}{\log_{20}99})=52.2\)
Status Protein1 Protein2 d d1/2
Query variables 1IDB_1 5JWS_1 66 51
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]