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Parikh vectors
7RHD_1 4PPU_1 4XZH_1 Letter Amino acid
2 2 6 W Tryptophan
2 4 7 C Cysteine
10 14 19 I Isoleucine
18 24 25 K Lycine
10 15 17 S Serine
8 8 15 N Asparagine
21 26 23 E Glutamic acid
5 6 9 H Histidine
23 18 25 V Valine
8 18 19 A Alanine
29 18 16 G Glycine
16 12 15 T Threonine
12 13 11 Y Tyrosine
10 10 6 M Methionine
10 11 11 F Phenylalanine
12 14 20 P Proline
11 12 11 R Arginine
11 21 15 D Aspartic acid
7 7 13 Q Glutamine
12 25 33 L Leucine 

7RHD_1|Chain A|darkmRuby M94T/F96Y mutant|Entacmaea quadricolor (6118)
>4PPU_1|Chain A|Chorismate mutase 1, chloroplastic|Arabidopsis thaliana (3702)
>4XZH_1|Chains A, B|Aldose reductase|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 \(w=f(c)\)
7RHD , Knot 110 237 0.84 40 168 230 
MVSKGEELIKEEMPMKVVLEGTVNGHQFKCTGEGEGRPYEGVQTMRIKVIEGGPLPFAFDILATSFMYGSRTFVKHPKGIPDYFKQSFPEGFTWERVTRYEDGGVVTVTQDTSLQDGVLIYNAKVRGVNFPSNGPVMQKKTKGWEPNTEMIYPADGGLRGYTDMALKVDGGGHLHCSFVTEYRSKKTVGNIKMPGVYAIDHRLERIEESDNETYVVQREVAVAKYSNLGGGMDELYK
4PPU , Knot 125 278 0.84 40 184 264 
GSHAVMTLAGSLTGKKRVDESESLTLEGIRNSLIRQEDSIIFGLLERAKYCYNADTYDPTAFDMDGFNGSLVEYMVKGTEKLHAKVGRFKSPDEHPFFPDDLPEPMLPPLQYPKVLHFAADSININKKIWNMYFRDLVPRLVKKGDDGNYGSTAVCDAICLQCLSKRIHYGKFVAEAKFQASPEAYESAIKAQDKDALMDMLTFPTVEDAIKKRVEMKTRTYGQEVKVGMEEKEEEEEEGNESHVYKISPILVGDLYGDWIMPLTKEVQVEYLLRRLD
4XZH , Knot 141 316 0.85 40 209 304 
MASRILLNNGAKMPILGLGTWKSPPGQVTEAVKVAIDVGYRHIDCAHVYQNENEVGVAIQEKLREQVVKREELFIVSKLWCTYHEKGLVKGACQKTLSDLKLDYLDLYLIHWPTGFKPGKEFFPLDESGNVVPSDTNILDTWAAMEELVDEGLVKAIGISNFNHLQVEMILNKPGLKYKPAVNQIECHPYLTQEKLIQYCQSKGIVVTAYSPLGSPDRPWAKPEDPSLLEDPRIKAIAAKHNKTTAQVLIRFPMQRNLVVIPKSVTPERIAENFKVFDFELSSQDMTTLLSYNRNWRVCALLSCTSHKDYPFHEEF

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 \(c\).

\(|P_{f(7RHD_1)}(2) \setminus P_{f(4PPU_1)}(2)|=76\), \(|P_{f(4PPU_1)}(2) \setminus P_{f(7RHD_1)}(2)|=92\). 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 1:110010011000111011101010100100010101010011001010110111111110111001101000110010111001000110110100100000111101000001001111001010110110011110000011010001101101110100011101011101000110000000011010111101100010010000000011000111100001111100100
Pair \(Z_2\) Length of longest common subsequence
7RHD_1,4PPU_1 168 3
7RHD_1,4XZH_1 171 3
4PPU_1,4XZH_1 171 3

Newick tree

 
[
	4XZH_1:85.99,
	[
		7RHD_1:84,4PPU_1:84
	]:1.99
]

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 \((0.85)(0.8)(\frac{515 }{\log_{20} 515}-\frac{237}{\log_{20}237})=79.7\)
Status Protein1 Protein2 d d1/2
Query variables 7RHD_1 4PPU_1 101 94.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]