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Parikh vectors
5OGA_1 4BLX_1 7PCX_1 Letter Amino acid
0 7 10 H Histidine
0 9 8 K Lycine
10 19 12 T Threonine
0 37 18 A Alanine
0 9 17 R Arginine
0 15 3 Q Glutamine
4 30 23 G Glycine
0 30 29 P Proline
0 0 6 Y Tyrosine
0 22 23 V Valine
0 10 10 N Asparagine
6 8 2 C Cysteine
0 24 28 L Leucine
0 5 7 M Methionine
0 2 10 W Tryptophan
0 26 19 D Aspartic acid
0 20 20 I Isoleucine
0 24 8 S Serine
0 14 23 E Glutamic acid
0 21 17 F Phenylalanine 

5OGA_1|Chain A|DNA (5'-D(*TP*(DCP)P*GP*TP*TP*CP*(DCP)P*GP*TP*TP*TP*TP*TP*CP*GP*TP*TP*CP*CP*GP*T)-3')|synthetic construct (32630)
>4BLX_1|Chain A|VERSATILE PEROXIDASE I|PLEUROTUS OSTREATUS (5322)
>7PCX_1|Chains A, B, C, D, E, F|Haloalkane dehalogenase|Rhodococcus sp. (1831)
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 \(w=f(c)\)
5OGA , Knot 8 21 0.38 8 6 8 
XCGTTCCGTTTTTCGTTCCGT
4BLX , Knot 141 332 0.82 38 189 309 
MATCADGRTTANAACCVLFPILDDIQENLFDGAQCGEEVHESLRLTFHDAIGFSPTLGGGGADGSIITFDTIETNFPANAGIDEIVSAQKPFVAKHNISAGDFIQFAGAVGVSNCPGGVRIPFFLGRPDAVAASPDHLVPEPFDSVDTILARMGDAGFSAVEVVWLLASHSIAAADKVDPSIPGTPFDSTPGVFDSQFFIETQLKGRLFPGTPDNKGEVQSPLQGEIRLQSDHLLARDPQTACEWQSMVNNQPKIQNRFAGTMSKMALLGQDKSKLIDCSDIIPTPPALVGAAHLPAGFSLSDVEQACAETPFPALTADPGPVTSVPPVPGS
7PCX , Knot 128 293 0.82 40 180 281 
GIGTGFPFDPHYVEVLGERMHYVDVGPRDGTPVLFLHGNPTSSYVWRNIIPHVAPTHRCIAPDLIGMGKSDKPDLGYFFDDHVRFMDAFIEALGLEEVVLVIHDWGSALGFHWAKRNPERVKGIAFMEFIRPIPTWDEWPEFARETFQAFRTTDVGRKLIIDWNVFIEGTLPMGVVRPLTEVEMDHYREPFLNPVDREPLWRFPNELPIAGEPANIVALVEEYMDWLHQSPVPKLLFWGTPGVLIPPAEAARLAKSLPNCKAVDIGPGLNLLQEDNPDLIGSEIARWLSTLEI

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 \(c\).

\(|P_{f(5OGA_1)}(2) \setminus P_{f(4BLX_1)}(2)|=1\), \(|P_{f(4BLX_1)}(2) \setminus P_{f(5OGA_1)}(2)|=184\). 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 1:001000010000001000010
Pair \(Z_2\) Length of longest common subsequence
5OGA_1,4BLX_1 185 2
5OGA_1,7PCX_1 182 2
4BLX_1,7PCX_1 155 4

Newick tree

 
[
	5OGA_1:96.03,
	[
		7PCX_1:77.5,4BLX_1:77.5
	]:18.53
]

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 \((0.85)(0.8)(\frac{353 }{\log_{20} 353}-\frac{21}{\log_{20}21})=108.\)
Status Protein1 Protein2 d d1/2
Query variables 5OGA_1 4BLX_1 137 71
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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