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Parikh vectors
7RWX_1 1JFN_1 6YKR_1 Letter Amino acid
3 6 3 C Cysteine
5 9 6 H Histidine
10 0 17 K Lycine
4 8 8 P Proline
3 6 16 V Valine
6 5 9 N Asparagine
2 8 6 R Arginine
5 7 6 Q Glutamine
8 7 22 E Glutamic acid
4 3 22 I Isoleucine
9 3 28 L Leucine
20 5 27 A Alanine
3 2 11 M Methionine
2 1 14 F Phenylalanine
4 14 13 T Threonine
2 4 2 W Tryptophan
9 4 10 D Aspartic acid
3 12 13 S Serine
1 7 4 Y Tyrosine
3 8 21 G Glycine 

7RWX_1|Chains A, B|Soluble cytochrome b562|Escherichia coli (562)
>1JFN_1|Chain A|APOLIPOPROTEIN A, KIV-T6|Homo sapiens (9606)
>6YKR_1|Chains A, B, C, D, E|Chemotaxis protein MotA, putative|Campylobacter jejuni subsp. jejuni serotype O:23/36 (strain 81-176) (354242)
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 \(w=f(c)\)
7RWX , Knot 54 106 0.79 40 84 100 
ADLEDNMETLNDNLKVIEKADNAAQVKDALTKMAAAAADAWSATPPKLEDKSPDSPEMHDFRHGFWILIGQIHAALHLANEGKVKEAQAAAEQLKCTCNACHQKYR
1JFN , Knot 61 119 0.81 38 96 114 
ARIHHHHHHIEGRAPTEQSPGVQDCYHGDGQSYRGSFSTTVTGRTCQSWSSMTPHWHQRTTEYYPNGGLTRNYCRNPDAEISPWCYTMDPNVRWEYCNLTQCPVTESSVLATSTAVSEQ
6YKR , Knot 114 258 0.81 40 161 252 
MDLSTILGMVLAVTSISVGDILEGGNPLHVIHLSSFLIVMPTAAFCAMTSTHKKIVKAAYKELKVVFKGSGVNLPERIAQLIEFAIIARRDGLLALESRTNEIENEFLKNAMMMLVDGKSFEEIHESMEIQTEQLEEHYKECAEYWIVFGETCPTMGLVGAVFGLILALKLLDNPQAMAAGISGAFTATVTGIFGAYALFAPWGKKLKANGMDLVKEQIVITEAIKGIAEGANPRDLEAKLFNFLSHDDPRISQFDKG

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 \(c\).

\(|P_{f(7RWX_1)}(2) \setminus P_{f(1JFN_1)}(2)|=64\), \(|P_{f(1JFN_1)}(2) \setminus P_{f(7RWX_1)}(2)|=76\). 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 1:1010001001000101100100110100110011111101101011010000100101001001111111010111011001010010111001000001000000
Pair \(Z_2\) Length of longest common subsequence
7RWX_1,1JFN_1 140 2
7RWX_1,6YKR_1 161 3
1JFN_1,6YKR_1 167 4

Newick tree

 
[
	6YKR_1:85.64,
	[
		7RWX_1:70,1JFN_1:70
	]:15.64
]

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 \((0.85)(0.8)(\frac{225 }{\log_{20} 225}-\frac{106}{\log_{20}106})=38.3\)
Status Protein1 Protein2 d d1/2
Query variables 7RWX_1 1JFN_1 51 47.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]