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Parikh vectors
4AGK_1 7UVY_1 6PEX_1 Letter Amino acid
5 1 15 N Asparagine
10 3 23 E Glutamic acid
6 1 12 H Histidine
4 3 7 M Methionine
13 5 15 T Threonine
17 2 21 A Alanine
19 2 27 G Glycine
8 2 23 S Serine
4 2 6 Y Tyrosine
11 2 31 V Valine
1 1 3 Q Glutamine
8 2 16 D Aspartic acid
15 10 17 K Lycine
8 3 12 F Phenylalanine
3 0 2 W Tryptophan
4 4 19 R Arginine
7 5 20 I Isoleucine
8 1 37 L Leucine
7 2 17 P Proline
0 0 6 C Cysteine 

4AGK_1|Chain A|CAPSID PROTEIN|AURA VIRUS (44158)
>7UVY_1|Chain A[auth 0]|50S ribosomal protein L33|Acinetobacter baumannii AB0057 (480119)
>6PEX_1|Chains A, B, C, D|aldo keto reductase|Vitis vinifera (29760)
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 \(w=f(c)\)
4AGK , Knot 76 158 0.81 38 115 153 
ALKFEADRTFAVKNEDGKIMGYAVAMEGKVIKPLHVKGTIDHPALAKLKFTKSSSYDMEFAKLPTEMKSDAFGYTTEHPEGFYNWHHGAVQFSGGRFTIPTGAGGPGDSGRPILDNSGKVVAIVLGGANEGARTALSVVTWNKKGAAIKTTHEDTVEW
7UVY , Knot 31 51 0.79 36 45 48 
MRDKIRLVSSAGTGYFYTTTKNKRTMPEKMEIKKFDPKIRQHVIFKEAKIK
6PEX , Knot 139 329 0.81 40 198 312 
HHHHHSSGLVPRGSHMMESIGVLLTCPMNPYLEQELDKRFKLFRFWDFPSANDLFREHSNSIRAVVGNSFIGADAQMIEALPKMEIVSSFSVGLDKIDLVRCKEKGIRVTNTPDVLTEDVADLALALILATLRRICESDRYVRSGSWKKGDFKLTTKFTGKSVGIIGLGRIGSAIAKRAEGFSCPISYHSRTEKPGTNYKYYPSVVELASNCQILVVACALTPETRHIINREVINALGPKGVVINIGRGLHVDEPELVSALVEGRLGGAGLDVFENEPNVPEELLAMDNVVLLPHVGSGTVETRKDMADLVLGNLEAHFLNKPLLTPVV

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 \(c\).

\(|P_{f(4AGK_1)}(2) \setminus P_{f(7UVY_1)}(2)|=93\), \(|P_{f(7UVY_1)}(2) \setminus P_{f(4AGK_1)}(2)|=23\). 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 1:11010100011100001011101111010110110101010011110101000000010110110010001110000010110010011101011010110111111001011100010111111111001100110110100011110000000101
Pair \(Z_2\) Length of longest common subsequence
4AGK_1,7UVY_1 116 3
4AGK_1,6PEX_1 173 4
7UVY_1,6PEX_1 183 4

Newick tree

 
[
	6PEX_1:97.20,
	[
		4AGK_1:58,7UVY_1:58
	]:39.20
]

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 \((0.85)(0.8)(\frac{209 }{\log_{20} 209}-\frac{51}{\log_{20}51})=53.2\)
Status Protein1 Protein2 d d1/2
Query variables 4AGK_1 7UVY_1 66 42
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]