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Parikh vectors
2XFX_1 1JMQ_1 3LXJ_1 Letter Amino acid
22 2 2 G Glycine
24 2 14 L Leucine
19 3 9 A Alanine
28 2 9 R Arginine
9 1 6 N Asparagine
4 0 3 C Cysteine
14 4 1 Q Glutamine
15 3 5 S Serine
12 1 5 V Valine
29 2 14 E Glutamic acid
7 1 3 H Histidine
4 2 13 I Isoleucine
17 4 8 T Threonine
9 2 0 W Tryptophan
15 1 3 Y Tyrosine
17 4 15 D Aspartic acid
7 3 14 K Lycine
4 3 2 M Methionine
7 2 5 F Phenylalanine
14 4 5 P Proline 

2XFX_1|Chain A|MHC CLASS 1|BOS TAURUS (9913)
>1JMQ_1|Chain A|65 KDA YES-ASSOCIATED PROTEIN|Homo sapiens (9606)
>3LXJ_1|Chains A, B, C, D|ATPase family AAA domain-containing protein 2B|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 \(w=f(c)\)
2XFX , Knot 125 277 0.84 40 179 262 
GSHSLRYFHTAVSRPGLREPLFITVGYVDDTQFVRFDSDARDPRTEPRQPWMEKEGPEYWDRETQISKENALWYREALNNLRGYYNQSEAGSHTLQEMYGCDVGSDGRLRRGYEQYGYDGRDYLALNEDLRSWTAADTAAQISKRKMEAAGAAERFRNYLEGTCVEWLRRYLENGKDTLLRADPPKAHVTRHPSSEHEVTLRCWALGFYPEEISLTWQRNGEDQTQDMELVETRPSGDGNFQKWAALVVPSGEEQRYTCRVQHEGLQEPLTLRWEPG
1JMQ , Knot 30 46 0.83 38 44 44 
FEIPDDVPLPAGWEMAKTSSGQRYFKNHIDQTTTWQDPRKAMLSQM
3LXJ , Knot 68 136 0.81 38 102 132 
SMEDQEENTLRELRLFLRDVTKRLATDKRFNIFSKPVDIEEVSDYLEVIKEPMDLSTVITKIDKHNYLTAKDFLKDIDLICSNALEYNPDKDPGDKIIRHRACTLKDTAHAIIAAELDPEFNKLCEEIKEARIKRG

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 \(c\).

\(|P_{f(2XFX_1)}(2) \setminus P_{f(1JMQ_1)}(2)|=157\), \(|P_{f(1JMQ_1)}(2) \setminus P_{f(2XFX_1)}(2)|=22\). 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 1:1000100100110011100111101101000011010001001000100111000110010000010000111000110010100000011000100101001100101001000010010001110001001011001101000010111110010001010010110001001000110101101010001000001010011111010010101000100000010110001010101001111111010000000010001100110101011
Pair \(Z_2\) Length of longest common subsequence
2XFX_1,1JMQ_1 179 3
2XFX_1,3LXJ_1 175 3
1JMQ_1,3LXJ_1 130 2

Newick tree

 
[
	2XFX_1:95.05,
	[
		3LXJ_1:65,1JMQ_1:65
	]:30.05
]

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 \((0.85)(0.8)(\frac{323 }{\log_{20} 323}-\frac{46}{\log_{20}46})=89.4\)
Status Protein1 Protein2 d d1/2
Query variables 2XFX_1 1JMQ_1 113 65
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]