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Parikh vectors
2NAR_1 9NCM_1 8CLE_1 Letter Amino acid
4 0 30 E Glutamic acid
2 0 20 P Proline
6 0 23 S Serine
3 0 20 F Phenylalanine
14 1 36 A Alanine
3 0 21 R Arginine
0 3 12 C Cysteine
5 0 16 Q Glutamine
3 0 27 I Isoleucine
13 0 32 L Leucine
9 0 16 N Asparagine
2 0 13 H Histidine
9 0 19 K Lycine
4 0 10 M Methionine
5 2 29 T Threonine
2 0 4 W Tryptophan
6 0 27 D Aspartic acid
4 2 33 G Glycine
5 0 18 Y Tyrosine
3 0 34 V Valine 

2NAR_1|Chain A|Effector protein Avr3a|Phytophthora infestans (4787)
>9NCM_1|Chain A|DNA (5'-D(*GP*CP*AP*CP*CP*TP*GP*T)-3')|synthetic construct (32630)
>8CLE_1|Chains A, B[auth C]|Tubulin alpha-1B chain|Bos taurus (9913)
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 \(w=f(c)\)
2NAR , Knot 50 102 0.75 38 77 93 
PNFNLASLNEEMFNVAALTKRADAKKLAKQLMGNDKLADAAYIWWQHNRVTLDQIDTFLKLASRKTQGAKYNQIYNSYMMHLGLTGYEPNSSSVDKLAAALE
9NCM , Knot 6 8 0.52 8 7 6 
GCACCTGT
8CLE , Knot 190 440 0.87 40 257 421 
MRECISIHVGQAGVQIGNACWELYCLEHGIQPDGQMPSDKTIGGGDDSFNTFFSETGAGKHVPRAVFVDLEPTVIDEVRTGTYRQLFHPEQLITGKEDAANNYARGHYTIGKEIIDLVLDRIRKLADQCTGLQGFLVFHSFGGGTGSGFTSLLMERLSVDYGKKSKLEFSIYPAPQVSTAVVEPYNSILTTHTTLEHSDCAFMVDNEAIYDICRRNLDIERPTYTNLNRLISQIVSSITASLRFDGALNVDLTEFQTNLVPYPRIHFPLATYAPVISAEKAYHEQLSVAEITNACFEPANQMVKCDPRHGKYMACCLLYRGDVVPKDVNAAIATIKTKRSIQFVDWCPTGFKVGINYQPPTVVPGGDLAKVQRAVCMLSNTTAIAEAWARLDHKFDLMYAKRAFVHWYVGEGMEEGEFSEAREDMAALEKDYEEVGVDSV

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 \(c\).

\(|P_{f(2NAR_1)}(2) \setminus P_{f(9NCM_1)}(2)|=76\), \(|P_{f(9NCM_1)}(2) \setminus P_{f(2NAR_1)}(2)|=6\). 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 1:101011010001101111000101001100111000110110111000010100100110110000011000010000110111010010000100111110
Pair \(Z_2\) Length of longest common subsequence
2NAR_1,9NCM_1 82 2
2NAR_1,8CLE_1 230 4
9NCM_1,8CLE_1 252 3

Newick tree

 
[
	8CLE_1:13.26,
	[
		2NAR_1:41,9NCM_1:41
	]:96.26
]

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 \((0.85)(0.8)(\frac{110 }{\log_{20} 110}-\frac{8}{\log_{20}8})=39.8\)
Status Protein1 Protein2 d d1/2
Query variables 2NAR_1 9NCM_1 49 26.5
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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