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Parikh vectors
6AFL_1 2VGH_1 7ICJ_1 Letter Amino acid
9 4 0 P Proline
8 3 2 T Threonine
6 3 0 N Asparagine
4 4 0 Q Glutamine
15 4 0 E Glutamic acid
16 5 0 K Lycine
5 0 0 M Methionine
3 1 0 F Phenylalanine
3 0 0 Y Tyrosine
19 1 0 V Valine
7 9 0 R Arginine
3 1 0 H Histidine
24 2 1 A Alanine
18 3 0 L Leucine
9 3 0 S Serine
0 0 0 W Tryptophan
9 3 0 D Aspartic acid
3 8 2 C Cysteine
18 1 1 G Glycine
10 0 0 I Isoleucine 

6AFL_1|Chain A|Protein/nucleic acid deglycase DJ-1|Homo sapiens (9606)
>2VGH_1|Chain A|VASCULAR ENDOTHELIAL GROWTH FACTOR-165|Homo sapiens (9606)
>7ICJ_1|Chain A[auth T]|DNA (5'-D(*CP*AP*TP*CP*TP*G)-3')|
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 \(w=f(c)\)
6AFL , Knot 86 189 0.79 38 124 182 
MASKRALVILAKGAEEMETVIPVDVMRRAGIKVTVAGLAGKDPVQCSRDVVICPDASLEDAKKEGPYDVVVLPGGNLGAQNLSESAAVKEILKEQENRKGLIAAICAGPTALLAHEIGFGSKVTTHPLAKDKMMNGGHYTYSENRVEKDGLILTSRGPGTSFEFALAIVEALNGKEVAAQVKAPLVLKD
2VGH , Knot 32 55 0.77 32 44 52 
ARQENPCGPCSERRKHLFVQDPQTCKCSCKNTDSRCKARQLELNERTCRCDKPRR
7ICJ , Knot 5 6 0.49 8 5 4 
CATCTG

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 \(c\).

\(|P_{f(6AFL_1)}(2) \setminus P_{f(2VGH_1)}(2)|=110\), \(|P_{f(2VGH_1)}(2) \setminus P_{f(6AFL_1)}(2)|=30\). 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 1:110001111110110010011110110011101011111100110000011101010100100011001111111011100100011100110000000111111011101111001111001000111000110110000000010001111000111001011111101101001110101111100
Pair \(Z_2\) Length of longest common subsequence
6AFL_1,2VGH_1 140 3
6AFL_1,7ICJ_1 127 2
2VGH_1,7ICJ_1 47 2

Newick tree

 
[
	6AFL_1:75.96,
	[
		7ICJ_1:23.5,2VGH_1:23.5
	]:52.46
]

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 \((0.85)(0.8)(\frac{244 }{\log_{20} 244}-\frac{55}{\log_{20}55})=62.4\)
Status Protein1 Protein2 d d1/2
Query variables 6AFL_1 2VGH_1 78 51
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]