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Parikh vectors
6VVU_1 2KOP_1 1DCR_1 Letter Amino acid
21 9 3 A Alanine
15 12 0 D Aspartic acid
9 8 0 E Glutamic acid
23 3 4 G Glycine
12 1 0 H Histidine
4 2 0 F Phenylalanine
8 0 2 C Cysteine
5 1 0 M Methionine
26 2 0 P Proline
11 3 0 S Serine
27 12 0 V Valine
15 2 0 Q Glutamine
11 4 0 T Threonine
9 0 0 W Tryptophan
14 1 0 R Arginine
7 2 0 N Asparagine
11 6 0 I Isoleucine
28 6 0 L Leucine
8 6 0 K Lycine
11 1 0 Y Tyrosine 

6VVU_1|Chains A, B, C, D|Tryptase alpha/beta-1|Homo sapiens (9606)
>2KOP_1|Chain A|Acyl carrier protein|Streptomyces coelicolor (1902)
>1DCR_1|Chains A, B|5'-D(*CP*CP*GP*AP*AP*(BRU)P*GP*AP*GP*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 \(w=f(c)\)
6VVU , Knot 120 275 0.81 40 186 268 
MLNLLLLALPVLASRAYAAPAPGQALQRVGIVGGQEAPRSKWPWQVSLRVHGPYWMHFCGGSLIHPQWVLTAAHCVGPDVKDLAALRVQLREQHLYYQDQLLPVSRIIVHPQFYTAQIGADIALLELEEPVNVSSHVHTVTLPPASETFPPGMPCWVTGWGDVDNDERLPPPFPLKQVKVPIMENHICDAKYHLGAYTGDDVRIVRDDMLCAGNTRRDSCQGDSGGPLVCKVNGTWLQAGVVSWGEGCAQPNRPGIYTRVTYYLDWIHHYVPKKP
2KOP , Knot 41 81 0.74 36 59 76 
AATQEEIVAGLAEIVNEIAGIPVEDVKLDKSFTDDLDVDSLSMVEVVVAAEERFDVKIPDDDVKNLKTVGDATKYILDHQA
1DCR , Knot 6 10 0.46 8 8 8 
CCGAAUGAGG

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 \(c\).

\(|P_{f(6VVU_1)}(2) \setminus P_{f(2KOP_1)}(2)|=157\), \(|P_{f(2KOP_1)}(2) \setminus P_{f(6VVU_1)}(2)|=30\). 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 1:11011111111110010111111011001111110011000111010101011011010110110101110110011101001111010100001000001111001110101001011101111010011010001001011110001111110110111010000011111110010111100010010001110010010110001101100000000100111110010101101111011010101001110001000101100011001
Pair \(Z_2\) Length of longest common subsequence
6VVU_1,2KOP_1 187 3
6VVU_1,1DCR_1 184 2
2KOP_1,1DCR_1 63 2

Newick tree

 
[
	6VVU_1:10.54,
	[
		1DCR_1:31.5,2KOP_1:31.5
	]:74.04
]

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 \((0.85)(0.8)(\frac{356 }{\log_{20} 356}-\frac{81}{\log_{20}81})=85.8\)
Status Protein1 Protein2 d d1/2
Query variables 6VVU_1 2KOP_1 113 71.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]