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Parikh vectors
2NTB_1 5JOP_1 3UFD_1 Letter Amino acid
2 5 0 C Cysteine
9 9 1 Q Glutamine
18 11 8 I Isoleucine
22 11 9 K Lycine
39 28 9 S Serine
5 3 0 W Tryptophan
15 12 2 Y Tyrosine
27 13 4 D Aspartic acid
20 11 5 V Valine
16 11 4 R Arginine
20 9 3 N Asparagine
3 3 2 H Histidine
32 7 1 A Alanine
18 18 11 L Leucine
16 9 4 F Phenylalanine
11 11 0 P Proline
29 17 4 G Glycine
2 2 4 M Methionine
32 19 3 T Threonine
6 10 8 E Glutamic acid 

2NTB_1|Chains A, B|Pectinesterase A|Erwinia chrysanthemi (198628)
>5JOP_1|Chains A[auth D], C[auth L]|Fab 14.22 light chain|Mus musculus (10090)
>3UFD_1|Chains A, B, E, F|Regulatory protein|Enterobacter sp. RFL1396 (211595)
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 \(w=f(c)\)
2NTB , Knot 145 342 0.82 40 186 321 
ATTYNAVVSKSSSDGKTFKTIADAIASAPAGSTPFVILIKNGVYNERLTITRNNLHLKGESRNGAVIAAATAAGTLKSDGSKWGTAGSSTITISAKDFSAQSLTIRNDFDFPANQAKSDSDSSKIKDTQAVALYVTKSGDRAYFKDVSLVGYQDTLYVSGGRSFFSDCRISGTVDFIFGDGTALFNNCDLVSRYRADVKSGNVSGYLTAPSTNINQKYGLVITNSRVIRESDSVPAKSYGLGRPWHPTTTFSDGRYADPNAIGQTVFLNTSMDNHIYGWDKMSGKDKNGNTIWFNPEDSRFFEYKSYGAGATVSKDRRQLTDAQAAEYTQSKVLGDWTPTLP
5JOP , Knot 102 219 0.83 40 163 214 
DVLLTQTPLSLPVNLGDQASISCRSSQTILHSDGYTYLEWYLQRPGQSPKLLIYRVYKRFSGIPDRFRGSGSGMDFTLTISGVEAEDLGIYYCFQGSYVPRTFGGGTKLEIKRADAAPTVSIFPPSSEQLTSGGASVVCFLNNFYPKDINVKWKIDGSERQNGVLNSWTDQDSKDSTYSMSSTLTLTKDEYERHNSYTCEATHKTSTSPIVKSFNRNEC
3UFD , Knot 44 82 0.78 34 70 80 
GSHMESFLLSKVSFVIKKIRLEKGMTQEDLAYKSNLDRTYISGIERNSRNLTIKSLELIMKGLEVSDVVFFEMLIKEILKHD

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 \(c\).

\(|P_{f(2NTB_1)}(2) \setminus P_{f(5JOP_1)}(2)|=85\), \(|P_{f(5JOP_1)}(2) \setminus P_{f(2NTB_1)}(2)|=62\). 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 1:100001110000001001001101110111100111111001100001010000101010000111111101110100010011011000101010010100101000101110010000000010000111101000100101001011100001010110011000010101011110101110000110000101001010101011000100001111000011000001110001110110100010010010101110011100010001011001010000100111010000110000011110100000010010110000001110101011
Pair \(Z_2\) Length of longest common subsequence
2NTB_1,5JOP_1 147 3
2NTB_1,3UFD_1 172 3
5JOP_1,3UFD_1 163 3

Newick tree

 
[
	3UFD_1:86.93,
	[
		2NTB_1:73.5,5JOP_1:73.5
	]:13.43
]

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 \((0.85)(0.8)(\frac{561 }{\log_{20} 561}-\frac{219}{\log_{20}219})=97.7\)
Status Protein1 Protein2 d d1/2
Query variables 2NTB_1 5JOP_1 121 99.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]