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Parikh vectors
7HZP_1 7YUF_1 8YQL_1 Letter Amino acid
14 22 3 G Glycine
5 5 12 I Isoleucine
14 39 7 S Serine
3 7 0 W Tryptophan
8 16 3 Y Tyrosine
9 5 2 R Arginine
7 7 9 E Glutamic acid
2 2 2 M Methionine
3 6 9 F Phenylalanine
4 11 5 P Proline
6 19 11 T Threonine
6 5 1 C Cysteine
5 9 2 Q Glutamine
14 21 5 V Valine
5 8 6 N Asparagine
2 12 11 K Lycine
6 11 0 H Histidine
12 17 13 L Leucine
10 17 5 A Alanine
9 7 3 D Aspartic acid 

7HZP_1|Chain A|Protease 2A|Coxsackievirus A16 (31704)
>7YUF_1|Chain A[auth H]|NbFab H-chain|synthetic construct (32630)
>8YQL_1|Chains A, B, C|Roadblock domain in P31|Candidatus Prometheoarchaeum syntrophicum (2594042)
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 \(w=f(c)\)
7HZP , Knot 70 144 0.80 40 112 139 
SGAIYVGNYRVVNRHLATHNDWANLVWEDSSRDLLVSSTTAQGCDTIARCDCQTGVYYCSSRRKHYPVSFSKPSLIFVEASEYYPARYQSHLMLAVGHSEPGDCGGILRCQHGVVGIVSTGGNGLVGFADVRDLLWLDEEAMEQ
7YUF , Knot 105 246 0.78 40 148 230 
MEISEVQLVESGGGLVQPGGSLRLSCAASGFNFSYYSIHWVRQAPGKGLEWVAYISSSSSYTSYADSVKGRFTISADTSKNTAYLQMNSLRAEDTAVYYCARGYQYWQYHASWYWNGGLDYWGQGTLVTVSSASTKGPSVFPLAPSSKSTSGGTAALGCLVKDYFPEPVTVSWNSGALTSGVHTFPAVLQSSGLYSLSSVVTVPSSSLGTQTYICNVNHKPSNTKVDKKVEPKSCDKTHTHHHHHH
8YQL , Knot 54 109 0.77 36 85 106 
GPIIENCAAFIEKTMSKYAITLSDGTILKSTIKNETLKKTFPILKNLLKDQIPTGSSFFKLPVVFFRVTDNVIVILLTNEKENIILSMFELFSTQFAEKLALEYPRTYE

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 \(c\).

\(|P_{f(7HZP_1)}(2) \setminus P_{f(7YUF_1)}(2)|=64\), \(|P_{f(7YUF_1)}(2) \setminus P_{f(7HZP_1)}(2)|=100\). 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 1:011101100011000110000110111000000111000010100011000000110000000000110100101111010000110000011111100011001111000011111100110111111010011110001100
Pair \(Z_2\) Length of longest common subsequence
7HZP_1,7YUF_1 164 4
7HZP_1,8YQL_1 159 2
7YUF_1,8YQL_1 169 3

Newick tree

 
[
	7YUF_1:84.47,
	[
		7HZP_1:79.5,8YQL_1:79.5
	]:4.97
]

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 \((0.85)(0.8)(\frac{390 }{\log_{20} 390}-\frac{144}{\log_{20}144})=74.1\)
Status Protein1 Protein2 d d1/2
Query variables 7HZP_1 7YUF_1 91 73
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]