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Parikh vectors
4QVB_1 3IAD_1 2RVD_1 Letter Amino acid
13 15 0 R Arginine
0 3 0 C Cysteine
9 22 0 I Isoleucine
2 15 0 F Phenylalanine
2 5 1 W Tryptophan
11 27 0 V Valine
15 30 1 D Aspartic acid
15 42 0 L Leucine
4 16 0 K Lycine
2 12 0 M Methionine
8 22 0 S Serine
7 22 2 T Threonine
17 22 0 A Alanine
6 21 0 Q Glutamine
4 26 1 E Glutamic acid
9 11 1 G Glycine
5 9 3 Y Tyrosine
4 21 0 N Asparagine
4 22 0 H Histidine
10 14 1 P Proline 

4QVB_1|Chains A, B|Rv1155 protein|Mycobacterium tuberculosis (1138877)
>3IAD_1|Chains A, B, C, D|cAMP-specific 3',5'-cyclic phosphodiesterase 4D|Homo sapiens (9606)
>2RVD_1|Chain A|CLN025|synthetic construct (32630)
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 \(w=f(c)\)
4QVB , Knot 72 147 0.81 38 112 142 
GARQVFDDKLLAVISGNSIGVLATIKHDGRPQLSNVQYHFDPRKLLIQVSIAEPRAKTRNLRRDPRASILVDADDGWSYAVAEGTAQLTPPAAAPDDDTVEALIALYRNIAGEHSDWDDYRQAMVTDRRVLLTLPISHVYGLPPGMR
3IAD , Knot 163 377 0.85 40 211 353 
MSIPRFGVKTEQEDVLAKELEDVNKWGLHVFRIAELSGNRPLTVIMHTIFQERDLLKTFKIPVDTLITYLMTLEDHYHADVAYHNNIHAADVVQSTHVLLSTPALEAVFTDLEILAAIFASAIHDVDHPGVSNQFLINTNSELALMYNDSSVLENHHLAVGFKLLQEENCDIFQNLTKKQRQSLRKMVIDIVLATDMSKHMNLLADLKTMVETKKVTSSGVLLLDNYSDRIQVLQNMVHCADLSNPTKPLQLYRQWTDRIMEEFFRQGDRERERGMEISPMCDKHNASVEKSQVGFIDYIVHPLWETWADLVHPDAQDILDTLEDNREWYQSTIPQAPAPPLDEQNRDSQGNQVSEFISNTFLDENLYFQGHHHHHH
2RVD , Knot 8 10 0.61 14 9 8 
YYDPETGTWY

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 \(c\).

\(|P_{f(4QVB_1)}(2) \setminus P_{f(3IAD_1)}(2)|=38\), \(|P_{f(3IAD_1)}(2) \setminus P_{f(4QVB_1)}(2)|=137\). 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 1:110011000111110100111110100010101001000101001110101101010000100010101110100110011101010101111110000101111100011100001000001110000111011100101111110
Pair \(Z_2\) Length of longest common subsequence
4QVB_1,3IAD_1 175 4
4QVB_1,2RVD_1 117 2
3IAD_1,2RVD_1 214 2

Newick tree

 
[
	3IAD_1:10.68,
	[
		4QVB_1:58.5,2RVD_1:58.5
	]:49.18
]

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 \((0.85)(0.8)(\frac{524 }{\log_{20} 524}-\frac{147}{\log_{20}147})=110.\)
Status Protein1 Protein2 d d1/2
Query variables 4QVB_1 3IAD_1 139 96
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]