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Parikh vectors
2RLL_1 9KHW_1 1ETA_1 Letter Amino acid
0 0 4 R Arginine
0 0 0 Q Glutamine
0 0 12 E Glutamic acid
2 0 5 I Isoleucine
0 0 7 L Leucine
0 0 5 F Phenylalanine
1 0 8 P Proline
0 2 12 A Alanine
1 0 5 D Aspartic acid
0 8 1 C Cysteine
0 0 2 W Tryptophan
3 0 5 Y Tyrosine
1 0 3 N Asparagine
0 0 2 M Methionine
0 6 10 G Glycine
0 0 4 H Histidine
0 0 8 K Lycine
1 0 11 S Serine
0 0 12 T Threonine
0 0 11 V Valine 

2RLL_1|Chain A|9-mer from C-C chemokine receptor type 5|null
>9KHW_1|Chains A, B|DNA (5'-D(*CP*CP*GP*CP*GP*CP*GP*CP*GP*CP*CP*GP*CP*GP*AP*A)-3')|synthetic construct (32630)
>1ETA_1|Chains A[auth 1], B[auth 2]|TRANSTHYRETIN|Homo sapiens (9606)
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 \(w=f(c)\)
2RLL , Knot 7 9 0.57 12 8 7 
SPIYDINYY
9KHW , Knot 5 16 0.28 6 5 6 
CCGCGCGCGCCGCGAA
1ETA , Knot 65 127 0.82 38 102 125 
GPTGTGESKCPLMVKVLDAVRGSPAINVAMHVFRKAADDTWEPFASGKTSESGELHGLTTEEEFVEGIYKVEIDTKSYWKALGISPFHEHAEVVFTANDSGPRRYTIAALLSPYSYSTTAVVTNPKE

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 \(c\).

\(|P_{f(2RLL_1)}(2) \setminus P_{f(9KHW_1)}(2)|=8\), \(|P_{f(9KHW_1)}(2) \setminus P_{f(2RLL_1)}(2)|=5\). 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 1:011001000
Pair \(Z_2\) Length of longest common subsequence
2RLL_1,9KHW_1 13 0
2RLL_1,1ETA_1 104 2
9KHW_1,1ETA_1 105 2

Newick tree

 
[
	1ETA_1:60.21,
	[
		2RLL_1:6.5,9KHW_1:6.5
	]:53.71
]

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 \((0.85)(0.8)(\frac{25 }{\log_{20} 25}-\frac{9}{\log_{20}9})=7.47\)
Status Protein1 Protein2 d d1/2
Query variables 2RLL_1 9KHW_1 6 5.5
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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