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Parikh vectors
5CFF_1 2HHQ_1 7DUZ_1 Letter Amino acid
0 0 3 W Tryptophan
3 0 9 Y Tyrosine
4 0 23 V Valine
7 0 11 R Arginine
4 0 7 N Asparagine
10 0 15 E Glutamic acid
1 0 5 F Phenylalanine
0 3 1 C Cysteine
0 0 9 H Histidine
1 0 13 P Proline
4 0 13 D Aspartic acid
12 0 6 Q Glutamine
3 0 4 K Lycine
1 0 0 M Methionine
10 0 17 S Serine
6 2 15 T Threonine
10 3 25 A Alanine
3 5 22 G Glycine
1 0 12 I Isoleucine
15 0 21 L Leucine 

5CFF_1|Chains A, B, C, D|Miranda|Drosophila melanogaster (7227)
>2HHQ_1|Chain A[auth B]|5'-D(*CP*AP*TP*(6OG)P*CP*GP*AP*GP*TP*CP*AP*GP*G)-3'|null
>7DUZ_1|Chains A, B|Beta-lactamase class B VIM-2|Pseudomonas aeruginosa (287)
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 \(w=f(c)\)
5CFF , Knot 46 95 0.73 34 67 92 
GPGSEFELRRQASNYQLTLTNTRATVNILMERLKKSDADVEQYRAELESVQLAKGALEQSYLVLQADAEQLRQQLTESQDALNALRSSSQTLQSE
2HHQ , Knot 8 13 0.52 8 10 11 
CATGCGAGTCAGG
7DUZ , Knot 104 231 0.81 38 148 225 
EYPTVSEIPVGEVRLYQIADGVWSHIATQSFDGAVYPSNGLIVRDGDELLLIDTAWGAKNTAALLAEIEKQIGLPVTRAVSTHFHDDRVGGVDVLRAAGVATYASPSTRRLAEVEGNEIPTHSLEGLSSSGDAVRFGPVELFYPGAAHSTDNLVVYVPSASVLYGGCAIYELSRTSAGNVADADLAEWPTSIERIQQHYPEAQFVIPGHGLPGGLDLLKHTTNVVKAHTNR

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 \(c\).

\(|P_{f(5CFF_1)}(2) \setminus P_{f(2HHQ_1)}(2)|=65\), \(|P_{f(2HHQ_1)}(2) \setminus P_{f(5CFF_1)}(2)|=8\). 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 1:11100101000100001010000101011100100001010000101001011011100001110101001000100000110110000001000
Pair \(Z_2\) Length of longest common subsequence
5CFF_1,2HHQ_1 73 2
5CFF_1,7DUZ_1 147 3
2HHQ_1,7DUZ_1 146 2

Newick tree

 
[
	7DUZ_1:81.91,
	[
		5CFF_1:36.5,2HHQ_1:36.5
	]:45.41
]

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 \((0.85)(0.8)(\frac{108 }{\log_{20} 108}-\frac{13}{\log_{20}13})=36.6\)
Status Protein1 Protein2 d d1/2
Query variables 5CFF_1 2HHQ_1 44 24.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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