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Parikh vectors
7UTP_1 3ZRH_1 3ZRG_1 Letter Amino acid
39 23 3 G Glycine
28 19 0 F Phenylalanine
28 30 3 D Aspartic acid
26 24 0 Q Glutamine
54 23 6 T Threonine
14 14 0 W Tryptophan
22 15 3 Y Tyrosine
36 28 3 V Valine
21 30 2 R Arginine
4 10 0 C Cysteine
26 20 1 I Isoleucine
41 14 1 P Proline
27 29 1 S Serine
33 33 12 A Alanine
49 11 3 N Asparagine
23 32 4 E Glutamic acid
11 12 1 H Histidine
34 60 9 L Leucine
20 21 10 K Lycine
12 6 5 M Methionine 

7UTP_1|Chains A, D[auth B], E[auth C], F[auth D], G[auth E], H[auth F], I[auth G], J[auth I]|Capsid protein VP1|Canis lupus familiaris (9615)
>3ZRH_1|Chain A|UBIQUITIN THIOESTERASE ZRANB1|HOMO SAPIENS (9606)
>3ZRG_1|Chains A, B|PEXRD2 FAMILY SECRETED RXLR EFFECTOR PEPTIDE, PUTATIVE|PHYTOPHTHORA INFESTANS (4787)
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 \(w=f(c)\)
7UTP , Knot 224 548 0.86 40 271 527 
GVGISTGTFNNQTEFKFLENGWVEITANSSRLVHLNMPESENYRRVVVNNMDKTAVNGNMALDDIHAQIVTPWSLVDANAWGVWFNPGDWQLIVNTMSELHLVSFEQEIFNVVLKTVSESATQPPTKVYNNDLTASLMVALDSNNTMPFTPAAMRSETLGFYPWKPTIPTPWRYYFQWDRTLIPSHTGTSGTPTNIYHGTDPDDVQFYTIENSVPVHLLRTGDEFATGTFFFDCKPCRLTHTWQTNRALGLPPFLNSLPQSEGATNFGDIGVQQDKRRGVTQMGNTNYITEATIMRPAEVGYSAPYYSFEASTQGPFKTPIAAGRGGAQTDENQAADGNPRYAFGRQHGQKTTTTGETPERFTYIAHQDTGRYPEGDWIQNINFNLPVTNDNVLLPTDPIGGKTGINYTNIFNTYGPLTALNNVPPVYPNGQIWDKEFDTDLKPRLHVNAPFVCQNNCPGQLFVKVAPNLTNEYDPDASANMSRIVTYSDFWWKGKLVFKAKLRASHTWNPIQQMSINVDNQFNYVPSNIGGMKIVYEKSQLAPRKLY
3ZRH , Knot 184 454 0.82 40 233 417 
ALEVDFKKLKQIKNRMKKTDWLFLNACVGVVEGDLAAIEAYKSSGGDIARQLTADEVRLLNRPSAFDVGYTLVHLAIRFQRQDMLAILLTEVSQQAAKCIPAMVCPELTEQIRREIAASLHQRKGDFACYFLTDLVTFTLPADIEDLPPTVQEKLFDEVLDRDVQKELEEESPIINWSLELATRLDSRLYALWNRTAGDCLLDSVLQATWGIYDKDSVLRKALHDSLHDCSHWFYTRWKDWESWYSQSFGLHFSLREEQWQEDWAFILSLASQPGASLEQTHIFVLAHILRRPIIVYGVKYYKSFRGETLGYTRFQGVYLPLLWEQSFCWKSPIALGYTRGHFSALVAMENDGYGNRGAGANLNTDDDVTITFLPLVDSERKLLHVHFLSAQELGNEEQQEKLLREWLDCCVTEGGVLVAMQKSSRRRNHPLVTQMVEKWLDRYRQIRPCTSLS
3ZRG , Knot 37 67 0.77 32 54 63 
GPALNTEKMKTMLKAGMTVDDYAAKLKLTDKIAAAANSARAMEKLGETLKMKKLLRYLNYVAEHTAV

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 \(c\).

\(|P_{f(7UTP_1)}(2) \setminus P_{f(3ZRH_1)}(2)|=99\), \(|P_{f(3ZRH_1)}(2) \setminus P_{f(7UTP_1)}(2)|=61\). 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 1:11110010100000101100111010100001101011000000011100100011010111001010110110110101111110110101110010010110100011011100100010011001000010101111100000111011110000111011010110110001010001110001001010010010010010100100011101100100110101110001001000100001111111100110001100110111000000110011000010010110110110011000101000111001111101110000001101010011100010000001001001001100001001010110010101110000111100111100110000110001110110011110101011000100010101010111100000110111011101000001010101001100001110101110101010001011001010100010011001111011000001110010
Pair \(Z_2\) Length of longest common subsequence
7UTP_1,3ZRH_1 160 4
7UTP_1,3ZRG_1 235 3
3ZRH_1,3ZRG_1 209 4

Newick tree

 
[
	3ZRG_1:11.79,
	[
		7UTP_1:80,3ZRH_1:80
	]:39.79
]

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 \((0.85)(0.8)(\frac{1002 }{\log_{20} 1002}-\frac{454}{\log_{20}454})=144.\)
Status Protein1 Protein2 d d1/2
Query variables 7UTP_1 3ZRH_1 189 169.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]