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Parikh vectors
2KLV_1 7CSB_1 1PVA_1 Letter Amino acid
0 9 2 H Histidine
6 18 5 I Isoleucine
2 22 17 K Lycine
5 30 6 V Valine
7 24 19 A Alanine
1 15 1 R Arginine
3 16 14 D Aspartic acid
1 27 9 E Glutamic acid
0 1 0 W Tryptophan
4 29 10 L Leucine
0 14 9 F Phenylalanine
0 14 0 P Proline
3 13 4 S Serine
1 12 0 Q Glutamine
2 9 1 M Methionine
2 12 0 Y Tyrosine
0 11 2 N Asparagine
0 3 0 C Cysteine
7 23 7 G Glycine
2 15 3 T Threonine 

2KLV_1|Chain A|Capsid protein G8P|Pseudomonas phage Pf1 (2011081)
>7CSB_1|Chains A, B, C, D|Pinoresinol reductase 1|Arabidopsis thaliana (3702)
>1PVA_1|Chains A, B|PARVALBUMIN|Esox lucius (8010)
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 \(w=f(c)\)
2KLV , Knot 26 46 0.72 28 40 44 
GVIDTSAVESAITDGQGDMKAIGGYIVGALVILAVAGLIYSMLRKA
7CSB , Knot 141 317 0.85 40 185 298 
MGESKRTEKTRVLVVGATGYIGKRIVRACLAEGHETYVLQRPEIGLEIEKVQLFLSFKKLGARIVEGSFSDHQSLVSAVKLVDVVVSAMSGVHFRSHNILVQLKLVEAIKEAGNVKRFLPSEFGMDPPRMGHALPPGRETFDQKMEVRQAIEAAGIPYTYVVGACFAAYFAGNLSQMVTLLPPKEKVNIYGDGNVKVVFADEDDIAKYTAKTLNDPRTLNKTVNIRPPDNVLTQLELVQIWEKLTGKELEKTNIAAQDFLANIEQMEIPHQAGIGHFYHIFYEGCLTDHEVGEDEEASSLYPDVKYKRMDDYLRMFL
1PVA , Knot 52 110 0.74 32 74 104 
XAAKDLLKADDIKKALDAVKAEGSFNHKKFFALVGLKAMSANDVKKVFKAIDADASGFIEEEELKFVLKSFAADGRDLTDAETKAFLKAADKDGDGKIGIDEFETLVHEA

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 \(c\).

\(|P_{f(2KLV_1)}(2) \setminus P_{f(7CSB_1)}(2)|=17\), \(|P_{f(7CSB_1)}(2) \setminus P_{f(2KLV_1)}(2)|=162\). 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 1:1110001100110010101011110111111111111110011001
Pair \(Z_2\) Length of longest common subsequence
2KLV_1,7CSB_1 179 3
2KLV_1,1PVA_1 88 3
7CSB_1,1PVA_1 155 4

Newick tree

 
[
	7CSB_1:93.26,
	[
		2KLV_1:44,1PVA_1:44
	]:49.26
]

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 \((0.85)(0.8)(\frac{363 }{\log_{20} 363}-\frac{46}{\log_{20}46})=100.\)
Status Protein1 Protein2 d d1/2
Query variables 2KLV_1 7CSB_1 128 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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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