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Parikh vectors
7GBU_1 7QWH_1 6AXS_1 Letter Amino acid
7 4 6 H Histidine
11 3 16 I Isoleucine
13 4 17 P Proline
3 0 5 W Tryptophan
11 6 4 Y Tyrosine
17 12 21 A Alanine
11 4 11 R Arginine
12 8 2 C Cysteine
21 10 10 N Asparagine
17 5 7 D Aspartic acid
26 3 18 G Glycine
11 10 11 K Lycine
16 15 9 S Serine
24 10 15 T Threonine
27 9 14 V Valine
14 7 15 Q Glutamine
9 5 17 E Glutamic acid
29 2 18 L Leucine
10 4 11 M Methionine
17 3 4 F Phenylalanine 

7GBU_1|Chain A|3C-like proteinase|Severe acute respiratory syndrome coronavirus 2 (2697049)
>7QWH_1|Chains A[auth AAA], B[auth BBB]|Ribonuclease pancreatic|Bos taurus (9913)
>6AXS_1|Chain A|HIV-1 capsid protein|Human immunodeficiency virus 1 (11676)
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 \(w=f(c)\)
7GBU , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ
7QWH , Knot 64 124 0.83 38 107 121 
KETAAAKFERQHMDSSTSAASSSNYCNQMMKSRNLTKDRCKPVNTFVHESLADVQAVCSQKNVACKNGQTNCYQSYSTMSITDCRETGSSKYPNCAYKTTQANKHIIVACEGNPYVPVHFDASV
6AXS , Knot 103 231 0.81 40 158 221 
PIVQNLQGQMIHQAISPRTLNAWVKVVEEKAFSPEVIPMFSALSEGATPQDLNTMLNAVGGHQAAMQMLKETINEEAAEWDRLHPVHAGPIAPGQMREPRGSDIAGTTSTLQEQIGWMTHNAPIPVGEIYKRWIILGLNKIVRMYSPTSILDIRQGPKEPFRDYVDRFYKTLRAEQASQEVKNWMTETLLVQNANPDCKTILKALGPGATLEEMMTACQGVGGPGHKARVL

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 \(c\).

\(|P_{f(7GBU_1)}(2) \setminus P_{f(7QWH_1)}(2)|=141\), \(|P_{f(7QWH_1)}(2) \setminus P_{f(7GBU_1)}(2)|=52\). 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 1:011001111010101011010010001011110011001001100000110100001110000001110110101011100100011010100101001000110101100101110001010110001101010101011010010111010000101001001011011011001010101111000010111000010101111101111010011100100010010111100000110000101111101001111101010100110011010011101110001011011000011010
Pair \(Z_2\) Length of longest common subsequence
7GBU_1,7QWH_1 193 3
7GBU_1,6AXS_1 186 4
7QWH_1,6AXS_1 185 3

Newick tree

 
[
	7GBU_1:95.50,
	[
		6AXS_1:92.5,7QWH_1:92.5
	]:3.00
]

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 \((0.85)(0.8)(\frac{430 }{\log_{20} 430}-\frac{124}{\log_{20}124})=92.0\)
Status Protein1 Protein2 d d1/2
Query variables 7GBU_1 7QWH_1 120 83.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]