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Parikh vectors
8EHR_1 2GGC_1 1KJL_1 Letter Amino acid
7 11 12 P Proline
15 16 5 T Threonine
4 8 4 Y Tyrosine
1 13 9 R Arginine
0 7 1 C Cysteine
8 18 8 K Lycine
2 6 8 F Phenylalanine
18 24 13 V Valine
19 14 8 A Alanine
6 8 14 N Asparagine
1 9 4 H Histidine
5 26 10 I Isoleucine
6 17 7 D Aspartic acid
6 5 4 Q Glutamine
10 22 11 G Glycine
12 16 13 L Leucine
5 22 6 E Glutamic acid
3 8 2 M Methionine
17 12 6 S Serine
1 1 1 W Tryptophan 

8EHR_1|Chains A, B, C, D, E, F, G|CFA/I fimbrial subunit B|Escherichia coli (562)
>2GGC_1|Chain A|Methionine aminopeptidase|Escherichia coli K12 (83333)
>1KJL_1|Chain A|Galectin-3|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 \(w=f(c)\)
8EHR , Knot 71 146 0.80 38 105 139 
VEKNITVTASVDPAIDLLQADGNALPSAVKLAYSPASKTFESYRVMTQVHTNDATKKVIVKLADTPQLTDVLNSTVQMPISVSWGGQVLSTTAKEFEAAALGYSASGVNGVSSSQELVISAAPKTAGTAPTAGNYSGVVSLVMTLG
2GGC , Knot 121 263 0.85 40 181 251 
AISIKTPEDIEKMRVAGRLAAEVLEMIEPYVKPGVSTGELDRICNDYIVNEQHAVSACLGYHGYPKSVCISINEVVCHGIPDDAKLLKDGDIVNIDVTVIKDGFHGDTSKMFIVGKPTIMGERLCRITQESLYLALRMVKPGINLREIGAAIQKFVEAEGFSVVREYCGHGIGRGFHEEPQVLHYDSRETNVVLKPGMTFTIEPMVNAGKKEIRTMKDGWTVKTKDRSLSAQYEHTIVVTDNGCEILTLRKDDTIPAIISHDE
1KJL , Knot 71 146 0.80 40 118 144 
GPYGAPAGPLIVPYNLPLPGGVVPRMLITILGTVKPNANRIALDFQRGNDVAFHFNPRFNENNRRVIVCNTKLDNNWGREERQSVFPFESGKPFKIQVLVEPDHFKVAVNDAHLLQYNHRVKKLNEISKLGISGDIDLTSASYTMI

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 \(c\).

\(|P_{f(8EHR_1)}(2) \setminus P_{f(2GGC_1)}(2)|=42\), \(|P_{f(2GGC_1)}(2) \setminus P_{f(8EHR_1)}(2)|=118\). 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 1:10001010101011101101010111011011001100010000110010000100011101100101001100010111010111011000100101111100101101100000111011100110110110001110111011
Pair \(Z_2\) Length of longest common subsequence
8EHR_1,2GGC_1 160 3
8EHR_1,1KJL_1 129 3
2GGC_1,1KJL_1 169 3

Newick tree

 
[
	2GGC_1:87.40,
	[
		8EHR_1:64.5,1KJL_1:64.5
	]:22.90
]

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 \((0.85)(0.8)(\frac{409 }{\log_{20} 409}-\frac{146}{\log_{20}146})=78.8\)
Status Protein1 Protein2 d d1/2
Query variables 8EHR_1 2GGC_1 100 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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]