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Parikh vectors
3VHI_1 8XZR_1 5DAS_1 Letter Amino acid
5 0 11 E Glutamic acid
1 0 6 H Histidine
2 0 5 M Methionine
9 0 15 S Serine
7 0 15 R Arginine
3 0 8 Q Glutamine
4 0 4 W Tryptophan
1 0 8 Y Tyrosine
5 0 13 D Aspartic acid
2 16 1 C Cysteine
7 0 7 F Phenylalanine
11 17 16 G Glycine
7 0 22 L Leucine
8 0 7 I Isoleucine
8 0 4 K Lycine
2 0 10 P Proline
19 0 12 T Threonine
7 0 16 V Valine
4 8 19 A Alanine
10 0 2 N Asparagine 

3VHI_1|Chains A, B, C, D|Avidin|Gallus gallus (9031)
>8XZR_1|Chain A|RNA (53-MER)|unidentified eubacterium clone A70 (41312)
>5DAS_1|Chains A, B, C, D|Nicotinate-nucleotide adenylyltransferase|Mycobacterium tuberculosis (83332)
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 \(w=f(c)\)
3VHI , Knot 63 122 0.82 40 98 119 
RKCSLTGKWTNDLGSNMTIGAVNSRGEFTGTYITAVTATSNEIKESPLHGTQNTINKRTQPTFGFTVNWKFSESTTVFTGQCFIDRNGKEVLKTMWLLRSSVNDIGDDWKATRVGINIFTRL
8XZR , Knot 19 53 0.47 8 15 38 
GGGUGUGUACCGUUCAACUCGUCCCAGCUUCGACUGGGACUACGGGAGCGCCU
5DAS , Knot 92 201 0.81 40 145 192 
GAMGRRLGVMGGTFDPIHYGHLVAASEVADLFDLDEVVFVPSGQPWQKGRQVSAAEHRYLMTVIATASNPRFSVSRVDIDRGGPTYTKDTLADLHALHPDSELYFTTGADALASIMSWQGWEELFELARFVGVSRPGYELRNEHITSLLGQLAKDALTLVEIPALAISSTDCRQRAEQSRPLWYLMPDGVVQYVSKRRLYT

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 \(c\).

\(|P_{f(3VHI_1)}(2) \setminus P_{f(8XZR_1)}(2)|=97\), \(|P_{f(8XZR_1)}(2) \setminus P_{f(3VHI_1)}(2)|=14\). 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 1:00001010100011001011110001010100101101000010001101000010000010111010101000001101001100010011001111000100110010100111011001
Pair \(Z_2\) Length of longest common subsequence
3VHI_1,8XZR_1 111 2
3VHI_1,5DAS_1 155 3
8XZR_1,5DAS_1 154 2

Newick tree

 
[
	5DAS_1:83.24,
	[
		3VHI_1:55.5,8XZR_1:55.5
	]:27.74
]

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 \((0.85)(0.8)(\frac{175 }{\log_{20} 175}-\frac{53}{\log_{20}53})=41.8\)
Status Protein1 Protein2 d d1/2
Query variables 3VHI_1 8XZR_1 60 38.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]