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Parikh vectors
7KPI_1 2XDC_1 7KFV_1 Letter Amino acid
11 0 7 E Glutamic acid
9 1 18 G Glycine
0 0 1 H Histidine
3 0 0 M Methionine
4 0 13 P Proline
6 2 12 A Alanine
7 0 11 R Arginine
4 0 9 C Cysteine
4 0 15 Y Tyrosine
6 0 21 N Asparagine
16 0 12 K Lycine
4 0 13 T Threonine
13 0 19 S Serine
10 4 20 V Valine
9 0 9 D Aspartic acid
4 0 9 I Isoleucine
15 4 14 L Leucine
3 0 7 Q Glutamine
11 0 16 F Phenylalanine
3 4 2 W Tryptophan 

7KPI_1|Chain A|Speckle-type POZ protein|Homo sapiens (9606)
>2XDC_1|Chains A, B, C, D, E, F|GRAMICIDIN A|BREVIBACILLUS BREVIS (1393)
>7KFV_1|Chains A, B, E|Spike glycoprotein|Severe acute respiratory syndrome coronavirus 2 (2697049)
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 \(w=f(c)\)
7KPI , Knot 70 142 0.81 38 106 137 
GPGKVVKFSYMWTINNFSFCREEMGEVIKSSTFSSGANDKLKWCLRVNPKGLDEESKDYLSLYLLLVSCPKSEVRAKFKFSILNAKGEETKAMESQRAYRFVQGKDWGFKKFIRRDFLLDEANGLLPDDKLTLFCEVSVVQD
2XDC , Knot 8 16 0.46 12 10 11 
VGALAVVVWLWLWLWX
7KFV , Knot 103 228 0.81 38 155 218 
GSGSGRVQPTESIVRFPNITNLCPFGEVFNATRFASVYAWNRKRISNCVADYSVLYNSASFSTFKCYGVSPTKLNDLCFTNVYADSFVIRGDEVRQIAPGQTGKIADYNYKLPDDFTGCVIAWNSNNLDSKVGGNYNYLYRLFRKSNLKPFERDISTEIYQAGSTPCNGVEGFNCYFPLQSYGFQPTNGVGYQPYRVVVLSFELLHAPATVCGPKKSTNLVKNKCVNF

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 \(c\).

\(|P_{f(7KPI_1)}(2) \setminus P_{f(2XDC_1)}(2)|=104\), \(|P_{f(2XDC_1)}(2) \setminus P_{f(7KPI_1)}(2)|=8\). 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 1:1110110100110100101000011011000010011000101010101011000000010101111001000101010101101010000110000100110100111001100011100101111000101100101100
Pair \(Z_2\) Length of longest common subsequence
7KPI_1,2XDC_1 112 2
7KPI_1,7KFV_1 147 4
2XDC_1,7KFV_1 161 3

Newick tree

 
[
	7KFV_1:82.92,
	[
		7KPI_1:56,2XDC_1:56
	]:26.92
]

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 \((0.85)(0.8)(\frac{158 }{\log_{20} 158}-\frac{16}{\log_{20}16})=51.8\)
Status Protein1 Protein2 d d1/2
Query variables 7KPI_1 2XDC_1 67 36.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]