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Parikh vectors
6TBE_1 4RQN_1 2VGC_1 Letter Amino acid
9 7 0 K Lycine
4 1 0 Y Tyrosine
8 5 0 D Aspartic acid
3 3 0 N Asparagine
1 0 1 C Cysteine
10 5 1 Q Glutamine
8 5 0 E Glutamic acid
9 12 2 L Leucine
4 1 0 M Methionine
7 5 0 F Phenylalanine
9 3 0 R Arginine
0 0 0 W Tryptophan
7 6 1 S Serine
4 6 0 T Threonine
10 1 2 V Valine
5 2 1 A Alanine
3 0 0 H Histidine
8 3 1 I Isoleucine
7 1 2 P Proline
3 5 2 G Glycine 

6TBE_1|Chain A|Microtubule-associated proteins 1A/1B light chain 3A|Homo sapiens (9606)
>4RQN_1|Chains A, B, C|Protein bicaudal C homolog 1|Homo sapiens (9606)
>2VGC_1|Chain A|GAMMA CHYMOTRYPSIN|Bos taurus (9913)
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 \(w=f(c)\)
6TBE , Knot 63 119 0.84 38 98 117 
GAMDRPFKQRRSFADRCKEVQQIRDQHPSKIPVIIERYKGEKQLPVLDKTKFLVPDHVNMSELVKIIRRRLQLNPTQAFFLLVNQHSMVSVSTPIADIYEQEKDEDGFLYMVYASQETF
4RQN , Knot 40 71 0.80 34 60 69 
SNSSFKGSDLPELFSKLGLGKYTDVFQQQEIDLQTFLTLTDQDLKELGITTFGAREKMLLAISELNKNRRK
2VGC , Knot 11 13 0.72 18 12 11 
CGVPAIQPVLSGL

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 \(c\).

\(|P_{f(6TBE_1)}(2) \setminus P_{f(4RQN_1)}(2)|=79\), \(|P_{f(4RQN_1)}(2) \setminus P_{f(6TBE_1)}(2)|=41\). 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 1:11100110000011000001001000010011111000010001111000011110010100110110001010100111111000011010011101000000001110110100001
Pair \(Z_2\) Length of longest common subsequence
6TBE_1,4RQN_1 120 3
6TBE_1,2VGC_1 104 3
4RQN_1,2VGC_1 68 2

Newick tree

 
[
	6TBE_1:61.78,
	[
		2VGC_1:34,4RQN_1:34
	]:27.78
]

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 \((0.85)(0.8)(\frac{190 }{\log_{20} 190}-\frac{71}{\log_{20}71})=39.8\)
Status Protein1 Protein2 d d1/2
Query variables 6TBE_1 4RQN_1 49 39
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]