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Parikh vectors
2WAW_1 6ODH_1 2ZND_1 Letter Amino acid
3 5 14 F Phenylalanine
11 3 13 S Serine
11 4 9 T Threonine
7 1 3 P Proline
3 6 6 Y Tyrosine
15 5 13 R Arginine
4 1 6 K Lycine
3 2 3 M Methionine
9 5 13 I Isoleucine
4 1 5 W Tryptophan
21 4 12 V Valine
20 6 6 A Alanine
3 7 14 Q Glutamine
3 3 1 H Histidine
9 6 5 E Glutamic acid
24 8 11 G Glycine
28 10 11 L Leucine
1 4 8 N Asparagine
17 3 18 D Aspartic acid
3 0 1 C Cysteine 

2WAW_1|Chain A|MOBA RELATE PROTEIN|MYCOBACTERIUM SP. JC-1 (212194)
>6ODH_1|Chains A, B, C, D, E, F|Bcl-2 homologous antagonist/killer|Homo sapiens (9606)
>2ZND_1|Chain A|Programmed cell death protein 6|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 \(w=f(c)\)
2WAW , Knot 89 199 0.79 40 121 194 
MLRSRVTGVVLAAGYSRRLGTPKQLLPLGDTTLLGATLAMARRCPFDQLIVTLGGAADEVLEKVELDGLDIVLVDDAGLGCSSSLKSALTWVDPTAEGIVLMLGDQPGITASAVASLIAGGRGATIAVCEYANGIGHPFWVSRGVFGDLAELHGDKGVWRLIESGRHGVRRIRVDADVPLDVDTWDDYERLLASVVRLE
6ODH , Knot 45 84 0.79 38 74 82 
MGQVGRQLAIIGDDINRRYDSEFQTMLQHLQPTAENAYEYFTKIATSLFESGINWGRVVALLGFGYRLALHVYQHGLEENLYFQ
2ZND , Knot 83 172 0.82 40 131 166 
AALPDQSFLWNVFQRVDKDRSGVISDTELQQALSNGTWTPFNPVTVRSIISMFDRENKAGVNFSEFTGVWKYITDWQNVFRTYDRDNSGMIDKNELKQALSGFGYRLSDQFHDILIRKFDRQGRGQIAFDDFIQGCIVLQRLTDIFRRYDTDQDGWIQVSYEQYLSMVFSIV

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 \(c\).

\(|P_{f(2WAW_1)}(2) \setminus P_{f(6ODH_1)}(2)|=87\), \(|P_{f(6ODH_1)}(2) \setminus P_{f(2WAW_1)}(2)|=40\). 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 1:1100010111111100001101001111100011110111100011001110111110011001010110111100111100001001101101010111111100111010111011111011011100010111011110011110110101001110110010011001010101110100100000111011010
Pair \(Z_2\) Length of longest common subsequence
2WAW_1,6ODH_1 127 4
2WAW_1,2ZND_1 162 3
6ODH_1,2ZND_1 153 6

Newick tree

 
[
	2ZND_1:83.25,
	[
		2WAW_1:63.5,6ODH_1:63.5
	]:19.75
]

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 \((0.85)(0.8)(\frac{283 }{\log_{20} 283}-\frac{84}{\log_{20}84})=63.4\)
Status Protein1 Protein2 d d1/2
Query variables 2WAW_1 6ODH_1 77 54.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]