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Parikh vectors
3NBD_1 5IUH_1 2AIH_1 Letter Amino acid
16 15 4 T Threonine
10 17 4 A Alanine
13 12 2 N Asparagine
6 16 6 D Aspartic acid
9 12 3 Q Glutamine
5 24 3 E Glutamic acid
3 6 3 H Histidine
2 14 1 F Phenylalanine
4 19 3 R Arginine
11 24 1 G Glycine
10 22 1 I Isoleucine
14 30 1 L Leucine
5 12 3 Y Tyrosine
13 22 6 S Serine
0 10 14 C Cysteine
2 13 4 K Lycine
1 12 0 M Methionine
10 26 4 P Proline
2 4 0 W Tryptophan
12 17 4 V Valine 

3NBD_1|Chains A, B|Ricin B-like lectin|Clitocybe nebularis (117024)
>5IUH_1|Chain A|ALK tyrosine kinase receptor|Homo sapiens (9606)
>2AIH_1|Chain A|Bowman-Birk type protease inhibitor, LCTI|Lens culinaris (3864)
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 \(w=f(c)\)
3NBD , Knot 72 148 0.81 38 113 146 
SITPGTYNITNVAYTNRLIDLTGSNPAENTLIIGHHLNKTPSGYGNQQWTLVQLPHTTIYTMQAVNPQSYVRVRDDNLVDGAALVGSQQPTPVSIESAGNSGQFRIKIPNLGLALTLPSDANSTPIVLGEVDETSTNQLWAFESVSAV
5IUH , Knot 138 327 0.81 40 205 314 
RTSTIMTDYNPNYSFAGKTSSISDLKEVPRKNITLIRGLGHGAFGEVYEGQVSGMPNDPSPLQVAVKTLPEVCSEQDELDFLMEALIISKFNHQNIVRCIGVSLQSLPRFILLELMAGGDLKSFLRETRPRPSQPSSLAMLDLLHVARDIACGCQYLEENHFIHRDIAARNCLLTCPGPGRVAKIGDFGMARDIYRASYYRKGGCAMLPVKWMPPEAFMEGIFTSKTDTWSFGVLLWEIFSLGYMPYPSKSNQEVLEFVTSGGRMDPPKNCPGPVYRIMTQCWQHQPEDRPNFAIILERIEYCTQDPDVINTALPIEYGPLVEEEEK
2AIH , Knot 36 67 0.75 36 54 64 
GDDVKSACCDTCLCTRSQPPTCRCVDVRESCHSACDKCVCAYSNPPQCQCYDTHKFCYKACHNSEIE

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 \(c\).

\(|P_{f(3NBD_1)}(2) \setminus P_{f(5IUH_1)}(2)|=52\), \(|P_{f(5IUH_1)}(2) \setminus P_{f(3NBD_1)}(2)|=144\). 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 1:0101100010011000011010100110001111001000101010001011011000100101101000101000011011111100010110100110010101011011111011001000111110100000001111001011
Pair \(Z_2\) Length of longest common subsequence
3NBD_1,5IUH_1 196 3
3NBD_1,2AIH_1 139 3
5IUH_1,2AIH_1 205 3

Newick tree

 
[
	5IUH_1:10.61,
	[
		3NBD_1:69.5,2AIH_1:69.5
	]:39.11
]

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 \((0.85)(0.8)(\frac{475 }{\log_{20} 475}-\frac{148}{\log_{20}148})=96.6\)
Status Protein1 Protein2 d d1/2
Query variables 3NBD_1 5IUH_1 125 90
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]