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Parikh vectors
2EVN_1 8OXK_1 5XHU_1 Letter Amino acid
2 4 2 W Tryptophan
6 4 8 H Histidine
7 2 24 K Lycine
3 0 9 M Methionine
13 7 14 S Serine
3 5 9 Y Tyrosine
3 13 18 D Aspartic acid
4 2 9 N Asparagine
2 4 3 C Cysteine
0 8 7 Q Glutamine
4 10 37 G Glycine
7 1 23 I Isoleucine
4 7 20 T Threonine
5 6 16 R Arginine
8 4 30 E Glutamic acid
6 4 26 L Leucine
6 7 14 F Phenylalanine
7 1 11 P Proline
7 7 26 V Valine
6 3 23 A Alanine 

2EVN_1|Chain A|Protein At1g77540|Arabidopsis thaliana (3702)
>8OXK_1|Chain A|CSEP0141 putative effector protein|Blumeria hordei (2867405)
>5XHU_1|Chain A|Ferredoxin--NADP reductase|Bacillus subtilis (1423)
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 \(w=f(c)\)
2EVN , Knot 56 103 0.84 38 85 101 
MATEPPKIVWNEGKRRFETEDHEAFIEYKMRNNGKVMDLVHTYVPSFKRGLGLASHLCVAAFEHASSHSISIIPSCSYVSDTFLPRNPSWKPLIHSEVFKSSI
8OXK , Knot 51 99 0.79 38 81 95 
GSDGWTCAGSDFDGDQVRGQARHWVDQQKTKFSDFQTHDGVQLCHFELGEGNQLTQSFTGFRAYCDEPGDVYNVRYWDVSSRTWVLCTHYDIDFESDYR
5XHU , Knot 140 329 0.82 40 193 311 
EVYDVTIIGGGPIGLFTAFYCGMRELKTKVIEFLPKLGGKVSLFFPEKIIRDIGGIPGIAGKQLIEQLKEQAATFDPDIVLNQRVTGFERLDDGTIVLTGSEGKKHYTRTVILACGMGTLEVNEFDSEDAARYAGKNLHYGVEKLDAFKGKRVVISGGGDTAVDWANELEPIAASVTVVHRREEFGGMESSVTKMKQSSVRVLTPYRLEQLNGDEEGIKSVTVCHTESGQRKDIEIDELIINHGFKIDLGPMMEWGLEIEEGRVKADRHMRTNLPGVFVAGDAAFYESKLRLIAGGFTEGPTAVNSAKAYLDPKAENMAMYSTHHKKLV

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 \(c\).

\(|P_{f(2EVN_1)}(2) \setminus P_{f(8OXK_1)}(2)|=75\), \(|P_{f(8OXK_1)}(2) \setminus P_{f(2EVN_1)}(2)|=71\). 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 1:1100110111001000100000011100010001011011000110100111110010111100100001011100001000111001010111000110001
Pair \(Z_2\) Length of longest common subsequence
2EVN_1,8OXK_1 146 2
2EVN_1,5XHU_1 188 3
8OXK_1,5XHU_1 184 3

Newick tree

 
[
	5XHU_1:98.77,
	[
		2EVN_1:73,8OXK_1:73
	]:25.77
]

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 \((0.85)(0.8)(\frac{202 }{\log_{20} 202}-\frac{99}{\log_{20}99})=33.6\)
Status Protein1 Protein2 d d1/2
Query variables 2EVN_1 8OXK_1 45 44
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]