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Parikh vectors
8WDI_1 7TGA_1 7OKU_1 Letter Amino acid
11 0 13 R Arginine
2 0 12 E Glutamic acid
6 0 2 K Lycine
2 0 1 M Methionine
2 0 9 P Proline
10 0 17 S Serine
12 5 10 A Alanine
14 0 6 N Asparagine
7 0 6 D Aspartic acid
12 6 13 G Glycine
1 0 8 H Histidine
7 5 16 T Threonine
6 0 3 W Tryptophan
8 5 3 C Cysteine
3 0 10 F Phenylalanine
6 0 13 V Valine
3 0 18 Q Glutamine
6 0 5 I Isoleucine
8 0 22 L Leucine
3 0 8 Y Tyrosine 

8WDI_1|Chain A|Lysozyme C|Gallus gallus (9031)
>7TGA_1|Chain A|DNA (5'-D(*GP*AP*GP*CP*AP*GP*CP*CP*TP*GP*TP*TP*TP*GP*GP*AP*CP*AP*TP*CP*A)-3')|synthetic construct (32630)
>7OKU_1|Chain A|Endothelial protein C receptor|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 \(w=f(c)\)
8WDI , Knot 66 129 0.82 40 104 127 
KVFGRCELAAAMKRHGLDNYRGYSLGNWVCAAKFESNFNTQATNRNTDGSTDYGILQINSRWWCNDGRTPGSRNLCNIPCSALLSSDITASVNCAKKIVSDGNGMNAWVAWRNRCKGTDVQAWIRGCRL
7TGA , Knot 10 21 0.48 8 13 18 
GAGCAGCCTGTTTGGACATCA
7OKU , Knot 93 195 0.83 40 143 192 
GPSQDASDGLQRLHMLQISYFRDPYHVWYQGNASLGGHLTHVLEGPDTNTTIIQLQPLQEPESWARTQSGLQSYLLQFHGLVRLVHQERTLAFPLTIRCFLGCELPPEGSRAHVFFEVAVNGSSFVSFRPERALWQADTQVTSGVVTFTLQQLNAYNRTRYELREFLEDTCVQYVQKHISAENTKGSQTSRSYTS

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 \(c\).

\(|P_{f(8WDI_1)}(2) \setminus P_{f(7TGA_1)}(2)|=100\), \(|P_{f(7TGA_1)}(2) \setminus P_{f(8WDI_1)}(2)|=9\). 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 1:011100011111000110000100110110110100010001000000100001110100011000100110001001100111000101010010011001011011111000001001011101001
Pair \(Z_2\) Length of longest common subsequence
8WDI_1,7TGA_1 109 2
8WDI_1,7OKU_1 169 3
7TGA_1,7OKU_1 148 2

Newick tree

 
[
	7OKU_1:86.14,
	[
		8WDI_1:54.5,7TGA_1:54.5
	]:31.64
]

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 \((0.85)(0.8)(\frac{150 }{\log_{20} 150}-\frac{21}{\log_{20}21})=46.9\)
Status Protein1 Protein2 d d1/2
Query variables 8WDI_1 7TGA_1 62 35.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]