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Parikh vectors
5XDI_1 7UAA_1 7EEO_1 Letter Amino acid
8 7 6 C Cysteine
0 13 0 H Histidine
0 32 0 I Isoleucine
2 18 0 F Phenylalanine
2 19 0 P Proline
1 26 0 T Threonine
0 17 0 D Aspartic acid
8 23 9 G Glycine
2 7 0 Y Tyrosine
0 33 0 V Valine
0 21 0 E Glutamic acid
1 42 0 L Leucine
1 10 0 N Asparagine
6 11 0 Q Glutamine
0 15 0 K Lycine
0 11 0 M Methionine
4 28 0 S Serine
0 5 0 W Tryptophan
3 26 6 A Alanine
2 26 0 R Arginine 

5XDI_1|Chain A|Vaccatide, vH1|Vaccaria hispanica (39387)
>7UAA_1|Chains A, B, C, D|ATP-sensitive inward rectifier potassium channel 11|Rattus norvegicus (10116)
>7EEO_1|Chains A, B|DNA/RNA (27-MER)|synthetic construct (32630)
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 \(w=f(c)\)
5XDI , Knot 23 40 0.70 24 30 37 
FQCGRQAGGARCSNGLCCSQFGYCGSTPPYCGAGQCQSQC
7UAA , Knot 166 390 0.84 40 218 379 
MLSRKGIIPEEYVLTRLAEDPTEPRYRTRERRARFVSKKGNCNVAHKNIREQGRFLQDVFTTLVDLKWPHTLLIFTMSFLCSWLLFAMVWWLIAFAHGDLAPGEGTNVPCVTSIHSFSSAFLFSIEVQVTIGFGGRMVTEECPLAILILIVQNIVGLMINAIMLGCIFMKTAQAHRRAETLIFSKHAVITLRHGRLCFMLRVGDLRKSMIISATIHMQVVRKTTSPEGEVVPLHQVDIPMENGVGGNSIFLVAPLIIYHVIDSNSPLYDLAPSDLHHHQDLEIIVILEGVVETTGITTQARTSYLADEILWGQRFVPIVAEEDGRYSVDYSKFGNTVKVPTPLCTARQLDEDRSLLDALTLASSRGPLRKRSVAVAKAKPKFSISPDSLS
7EEO , Knot 12 27 0.48 10 13 21 
XXCUCCUAGUACGAGAGGACCGGAGUG

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 \(c\).

\(|P_{f(5XDI_1)}(2) \setminus P_{f(7UAA_1)}(2)|=17\), \(|P_{f(7UAA_1)}(2) \setminus P_{f(5XDI_1)}(2)|=205\). 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 1:1001001111000011000011001001100111000000
Pair \(Z_2\) Length of longest common subsequence
5XDI_1,7UAA_1 222 2
5XDI_1,7EEO_1 33 4
7UAA_1,7EEO_1 229 2

Newick tree

 
[
	7UAA_1:12.85,
	[
		5XDI_1:16.5,7EEO_1:16.5
	]:11.35
]

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 \((0.85)(0.8)(\frac{430 }{\log_{20} 430}-\frac{40}{\log_{20}40})=122.\)
Status Protein1 Protein2 d d1/2
Query variables 5XDI_1 7UAA_1 160 87
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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