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Parikh vectors
1DQF_1 6FXG_1 8YDB_1 Letter Amino acid
0 10 8 M Methionine
0 9 10 F Phenylalanine
0 11 11 V Valine
1 23 16 A Alanine
0 9 20 E Glutamic acid
0 23 18 K Lycine
0 1 10 R Arginine
0 14 26 I Isoleucine
0 17 12 S Serine
0 3 1 W Tryptophan
0 17 14 D Aspartic acid
0 13 27 L Leucine
0 6 8 P Proline
2 22 20 G Glycine
0 1 6 H Histidine
0 15 10 T Threonine
0 12 10 Y Tyrosine
0 11 15 N Asparagine
5 0 6 C Cysteine
0 10 7 Q Glutamine

1DQF_1|Chain A|RNA (5'-R(*GP*CP*CP*AP*CP*CP*CP*UP*G)-3')|
>6FXG_1|Chains A, B, C|Amino acid ABC transporter membrane protein PAAT family|Lactococcus lactis subsp. lactis (1360)
>8YDB_1|Chain A|Cas5f|Selenomonas sp. (2053611)
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 \(w=f(c)\)
1DQF , Knot 6 9 0.48 8 6 7
GCCACCCUG
6FXG , Knot 103 227 0.82 38 147 216
GMETTVKIASDSSYAPFEFQNGQKKWVGIDVDIMQEVAKINDWKLEMSYPGFDAALQNLKAGQVDGIIAGMTITDERKETFDFSNPYYTSALTIATTKDSKLSDYSDLKGKAVGAKNGTAAQTWLQENQKKYGYTIKTYSDGVHMFAALSSGNIAGAMDEVPVISYAMKQGQDLAMNFPSISLPGGYGFAVMKGKNSTLVDGFNKALAEMKSNGDYDKILKKYGITA
8YDB , Knot 116 255 0.84 40 179 247
MMKGYILLEKVNIENANAFNNIIVGIPAITSFLGFARALERKLNAKEIAIRINGVGLEFHEYELKGYKNKRGQYVTSCPLPGSIPGQNEKKLDAHIMNQAYIDLNMSFLLEVEGPHVDMSTCKSIKSTMETLRIAGGIIRNYKKIRLIDTLADIPYGYFLTLRQDNLNDAAGDDMLDKMIHALQQEDTLVPIAVGFKALSEVGHVEGQRDPEKDHCFVESIFSLGGFECSKILEDINSCLWRYKTEEGLYLCTII

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 \(c\).

\(|P_{f(1DQF_1)}(2) \setminus P_{f(6FXG_1)}(2)|=6\), \(|P_{f(6FXG_1)}(2) \setminus P_{f(1DQF_1)}(2)|=147\). 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 1:100100001
Pair \(Z_2\) Length of longest common subsequence
1DQF_1,6FXG_1 153 1
1DQF_1,8YDB_1 185 1
6FXG_1,8YDB_1 168 3

Newick tree

 
[
	8YDB_1:91.96,
	[
		1DQF_1:76.5,6FXG_1:76.5
	]:15.46
]

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 \((0.85)(0.8)(\frac{236 }{\log_{20} 236}-\frac{9}{\log_{20}9})=79.6\)
Status Protein1 Protein2 d d1/2
Query variables 1DQF_1 6FXG_1 101 53
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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