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Parikh vectors
8ACB_1 7JIN_1 5FLK_1 Letter Amino acid
15 0 18 R Arginine
16 0 9 N Asparagine
11 0 4 Q Glutamine
11 0 6 M Methionine
7 0 10 S Serine
17 6 21 A Alanine
9 0 19 I Isoleucine
12 0 19 D Aspartic acid
1 3 4 C Cysteine
14 0 24 E Glutamic acid
7 0 17 H Histidine
8 0 14 F Phenylalanine
9 0 31 P Proline
3 0 9 W Tryptophan
9 0 8 Y Tyrosine
14 3 20 G Glycine
16 0 29 L Leucine
9 0 8 K Lycine
19 0 9 T Threonine
13 0 21 V Valine 

8ACB_1|Chain A|Genome polyprotein|Sweet potato feathery mottle virus (12844)
>7JIN_1|Chain A|DNA (5'-D(*GP*AP*AP*CP*GP*AP*CP*AP*CP*AP*GP*A)-3')|synthetic construct (32630)
>5FLK_1|Chain A|DHAA101|RHODOCOCCUS RHODOCHROUS (1829)
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 \(w=f(c)\)
8ACB , Knot 103 220 0.84 40 160 214 
VPRVKMNANKKRQPMVNGRAIINFQHLSTYEPEQFEVANTRSTQEQFQAWYEGVKGDYGVDDTGMGILLNGLMVWCIENGTSPNINGVWTMMDGDEQVTYPIKPLLDHAVPTFRQIMTHFSDVAEAYIEMRNRTKAYMPRYGLQRNLTDMSLARYAFDFYELHSTTPARAKEAHLQMKAAALKNARNRLFGLDGNVSTQEEDTERHTTTDVTRNIHNLLG
7JIN , Knot 6 12 0.41 6 6 9 
GAACGACACAGA
5FLK , Knot 131 300 0.83 40 184 282 
MSEIGTGFPFDPHYVEVLGSRMHYVDVGPRDGTPVLFLHGNPTSSYLWRNIIPHVAPSHRCIAPDLIGMGKSDKPDLDYRFDDHVRYLDAFIEALGLEEVVLVIHDWGSALGFHWAKRNPERVKGIACMEFIRPIPTWDEWPEFARETFQAFRTPDVGRELIIDQNAFIEGALPKCVVRPLTEVEMDHYREPFLKPVDREPLWRFPNELPIAGEPANIVALVEAYMNWLHQSPVPKLLFWGTPGVLIPPAEAARLAESLPNCKTVDIGPGLHYLQEDNPDLIGSEIARWLPALEHHHHHH

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 \(c\).

\(|P_{f(8ACB_1)}(2) \setminus P_{f(7JIN_1)}(2)|=159\), \(|P_{f(7JIN_1)}(2) \setminus P_{f(8ACB_1)}(2)|=5\). 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 1:1101010100000111010111010010000100101100000000101100110100110001111110111110100100101011101101000100110111001110100110010011010101000001011001100010010110011010010000110100101010111100100011110101000000000000001000100111
Pair \(Z_2\) Length of longest common subsequence
8ACB_1,7JIN_1 164 2
8ACB_1,5FLK_1 180 3
7JIN_1,5FLK_1 182 2

Newick tree

 
[
	5FLK_1:93.16,
	[
		8ACB_1:82,7JIN_1:82
	]:11.16
]

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 \((0.85)(0.8)(\frac{232 }{\log_{20} 232}-\frac{12}{\log_{20}12})=76.9\)
Status Protein1 Protein2 d d1/2
Query variables 8ACB_1 7JIN_1 100 52.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]