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Parikh vectors
2XBI_1 3OLJ_1 7RKE_1 Letter Amino acid
6 12 10 G Glycine
1 7 13 H Histidine
3 10 9 P Proline
10 18 13 V Valine
2 7 9 Q Glutamine
3 11 15 M Methionine
6 25 7 F Phenylalanine
9 24 48 L Leucine
15 17 11 K Lycine
2 8 4 Y Tyrosine
8 20 15 A Alanine
1 16 11 R Arginine
3 9 8 N Asparagine
2 5 4 C Cysteine
4 8 11 T Threonine
1 6 3 W Tryptophan
8 13 13 D Aspartic acid
9 33 15 E Glutamic acid
9 22 12 I Isoleucine
6 15 19 S Serine 

2XBI_1|Chain A|THIOREDOXIN|SCHISTOSOMA MANSONI (6183)
>3OLJ_1|Chains A, B, C, D|Ribonucleoside-diphosphate reductase subunit M2|Homo sapiens (9606)
>7RKE_1|Chains A, B|Estrogen receptor|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 \(w=f(c)\)
2XBI , Knot 56 108 0.81 40 85 106 
GSMSKLIELKQDGDLESLLEQHKNKLVVVDFFATWCGPCKTIAPLFKELSEKYDAIFVKVDVDKLEETARKYNISAMPTFIAIKNGEKVGDVVGASIAKVEDMIKKFI
3OLJ , Knot 128 286 0.84 40 192 277 
MGVEDEPLLRENPRRFVIFPIEYHDIWQMYKKAEASFWTAEEVDLSKDIQHWESLKPEERYFISHVLAFFAASDGIVNENLVERFSQEVQITEARCFYGFQIAMENIHSEMYSLLIDTYIKDPKEREFLFNAIETMPCVKKKADWALRWIGDKEATYGERVVAFAAVEGIFFSGSFASIFWLKKRGLMPGLTFSNELISRDEGLHCDFACLMFKHLVHKPSEERVREIIINAVRIEQEFLTEALPVKLIGMNCTLMKQYIEFVADRLMLELGFSKVFRVENPFDFM
7RKE , Knot 114 250 0.84 40 162 239 
SLALSLTADQMVSALLDAEPPILYSEYDPTRPFSEASMMGLLTNLADRELVHMINWAKRVPGFVDLTLHDQVHLLECAWLEILMIGLVWRSMEHPGKLLFAPNLLLDRNQGKCVEGMVEIFDMLLATSSRFRMMNLQGEEFVCLKSIILLNSGVYTFLSSTLKSLEEKDHIHRVLDKITDTLIHLMAKAGLTLQQQHQRLAQLLLILSHIRHMSNKGMEHLYSMKCKNVVPLSDLLLEMLDAHRLHAPTS

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 \(c\).

\(|P_{f(2XBI_1)}(2) \setminus P_{f(3OLJ_1)}(2)|=29\), \(|P_{f(3OLJ_1)}(2) \setminus P_{f(2XBI_1)}(2)|=136\). 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 1:101001101000101001100000011110111010110001111100100000111101010010001000010111011110010011011110110100110011
Pair \(Z_2\) Length of longest common subsequence
2XBI_1,3OLJ_1 165 3
2XBI_1,7RKE_1 163 3
3OLJ_1,7RKE_1 174 3

Newick tree

 
[
	3OLJ_1:85.84,
	[
		2XBI_1:81.5,7RKE_1:81.5
	]:4.34
]

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 \((0.85)(0.8)(\frac{394 }{\log_{20} 394}-\frac{108}{\log_{20}108})=87.3\)
Status Protein1 Protein2 d d1/2
Query variables 2XBI_1 3OLJ_1 112 76
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]