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Parikh vectors
4GAL_1 1MXX_1 7HWC_1 Letter Amino acid
6 3 5 Q Glutamine
14 25 14 G Glycine
5 16 5 I Isoleucine
8 7 3 F Phenylalanine
10 17 14 S Serine
2 17 6 T Threonine
15 18 14 V Valine
7 19 10 A Alanine
13 10 9 R Arginine
7 13 9 D Aspartic acid
12 20 12 L Leucine
1 4 6 C Cysteine
0 10 2 M Methionine
10 7 4 P Proline
1 4 3 W Tryptophan
1 13 8 Y Tyrosine
5 10 5 N Asparagine
9 20 7 E Glutamic acid
6 2 6 H Histidine
3 28 2 K Lycine 

4GAL_1|Chains A, B|GALECTIN-7|Homo sapiens (9606)
>1MXX_1|Chains A, B, C|GLUTAMATE RECEPTOR 2|Rattus norvegicus (10116)
>7HWC_1|Chains A, B[auth C]|Protease 2A|Coxsackievirus A16 (31704)
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 \(w=f(c)\)
4GAL , Knot 69 135 0.83 38 105 131 
SNVPHKSSLPEGIRPGTVLRIRGLVPPNASRFHVNLLCGEEQGSDAALHFNPRLDTSEVVFNSKEQGSWGREERGPGVPFQRGQPFEVLIIASDDGFKAVVGDAQYHHFRHRLPLARVRLVEVGGDVQLDSVRIF
1MXX , Knot 122 263 0.86 40 173 253 
GANKTVVVTTILESPYVMMKKNHEMLEGNERYEGYCVDLAAEIAKHCGFKYKLTIVGDGKYGARDADTKIWNGMVGELVYGKADIAIAPLTITLVREEVIDFSKPFMSLGISIMIKKGTPIESAEDLSKQTEIAYGTLDSGSTKEFFRRSKIAVFDKMWTYMRSAEPSVFVRTTAEGVARVRKSKGKYAYLLESTMNEYIEQRKPCDTMKVGGNLDSKGYGIATPKGSSLGNAVNLAVLKLNEQGLLDKLKNKWWYDKGECGS
7HWC , Knot 70 144 0.80 40 112 139 
SGAIYVGNYRVVNRHLATHNDWANLVWEDSSRDLLVSSTTAQGCDTIARCDCQTGVYYCSSRRKHYPVSFSKPSLIFVEASEYYPARYQSHLMLAVGHSEPGDCGGILRCQHGVVGIVSTGGNGLVGFADVRDLLWLDEEAMEQ

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 \(c\).

\(|P_{f(4GAL_1)}(2) \setminus P_{f(1MXX_1)}(2)|=54\), \(|P_{f(1MXX_1)}(2) \setminus P_{f(4GAL_1)}(2)|=122\). 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 1:001100001101101101101011111010010101101000100111010101000011100000101100001111110010110111110001101111010000100011110101101110101001011
Pair \(Z_2\) Length of longest common subsequence
4GAL_1,1MXX_1 176 4
4GAL_1,7HWC_1 139 3
1MXX_1,7HWC_1 163 4

Newick tree

 
[
	1MXX_1:89.33,
	[
		4GAL_1:69.5,7HWC_1:69.5
	]:19.83
]

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 \((0.85)(0.8)(\frac{398 }{\log_{20} 398}-\frac{135}{\log_{20}135})=79.3\)
Status Protein1 Protein2 d d1/2
Query variables 4GAL_1 1MXX_1 103 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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]