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Parikh vectors
8WRV_1 5QBW_1 1ERF_1 Letter Amino acid
0 8 0 P Proline
9 8 0 C Cysteine
0 12 0 N Asparagine
0 11 0 D Aspartic acid
0 8 0 Q Glutamine
0 17 0 K Lycine
0 18 2 S Serine
11 8 1 T Threonine
0 4 0 W Tryptophan
10 16 5 A Alanine
0 17 1 V Valine
14 26 6 G Glycine
0 3 1 M Methionine
0 7 2 F Phenylalanine
0 16 0 Y Tyrosine
0 7 1 R Arginine
0 4 0 H Histidine
0 7 1 I Isoleucine
0 14 3 L Leucine
0 12 0 E Glutamic acid 

8WRV_1|Chain A[auth C]|TS|unclassified sequences (12908)
>5QBW_1|Chain A|Cathepsin S|Homo sapiens (9606)
>1ERF_1|Chain A|TRANSMEMBRANE GLYCOPROTEIN|null
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 \(w=f(c)\)
8WRV , Knot 17 44 0.48 8 15 33 
CAAGCCGTCTAGCGGTGAGGTTCTCTGATGGAAGCATATCGTAG
5QBW , Knot 103 223 0.83 40 149 215 
ILPDSVDWREKGCVTEVKYQGSCGASWAFSAVGALEAQLKLKTGKLVSLSAQNLVDCSTEKYGNKGCNGGFMTTAFQYIIDNKGIDSDASYPYKAMDQKCQYDSKYRAATCSKYTELPYGREDVLKEAVANKGPVSVGVDARHPSFFLYRSGVYYEPSCTQNVNHGVLVVGYGDLNGKEYWLVKNSWGHNFGEEGYIRMARNKGNHCGIASFPSYPEILQGGG
1ERF , Knot 15 24 0.66 22 19 21 
AVGIGALFLGFLGAAGSTMGARSX

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 \(c\).

\(|P_{f(8WRV_1)}(2) \setminus P_{f(5QBW_1)}(2)|=4\), \(|P_{f(5QBW_1)}(2) \setminus P_{f(8WRV_1)}(2)|=138\). 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 1:01110010001101101111000000110111110101001011
Pair \(Z_2\) Length of longest common subsequence
8WRV_1,5QBW_1 142 3
8WRV_1,1ERF_1 28 4
5QBW_1,1ERF_1 144 3

Newick tree

 
[
	5QBW_1:82.16,
	[
		8WRV_1:14,1ERF_1:14
	]:68.16
]

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 \((0.85)(0.8)(\frac{267 }{\log_{20} 267}-\frac{44}{\log_{20}44})=73.6\)
Status Protein1 Protein2 d d1/2
Query variables 8WRV_1 5QBW_1 100 57.5
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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