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Parikh vectors
2IMU_1 6XAL_1 4RAI_1 Letter Amino acid
4 48 13 L Leucine
0 5 0 W Tryptophan
8 49 3 A Alanine
3 36 2 R Arginine
0 3 2 N Asparagine
3 21 3 D Aspartic acid
1 4 3 Y Tyrosine
4 31 7 G Glycine
1 15 1 H Histidine
5 8 11 I Isoleucine
1 4 4 K Lycine
1 24 5 S Serine
4 30 10 V Valine
0 6 0 C Cysteine
1 9 3 Q Glutamine
2 35 3 E Glutamic acid
0 6 1 M Methionine
3 17 9 F Phenylalanine
4 27 6 P Proline
1 23 10 T Threonine 

2IMU_1|Chain A|Structural polyprotein (PP) p1|null
>6XAL_1|Chain A|NzeB|Streptomyces sp. NRRL F-5053 (1463854)
>4RAI_1|Chains A, B|Potassium channel protein|Bacillus cereus ATCC 14579 (226900)
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 \(w=f(c)\)
2IMU , Knot 29 46 0.80 32 43 44 
FGFKDIIRAIRRIAVPVVSTLFPPAAPLAHAIGEGVDYLLGDEAQA
6XAL , Knot 162 401 0.80 40 192 372 
VTTTATLTYPFHDWSQELSPRYAQLRASDAPVCPVVSEGTGDPLWLVTRYATAVKLLEDSRFSSEAAQASGAPRQEPVELRAPGTRGDAIAMLREAGLRSVLADGLGPRAVRRHQGWINDLAETLMSELASREGTFDLAADFVEPLSSALVSRTLLGELSADERDLLAHCADTGLRFCGVTHEEQVHAFTQMHEFFLEHARRLAGTPGEHLLKLIAEAPVDQGPLSDEALAEAGSLLVVAGFPTSSGFLCGALLTLLRHPDAVQELHAHPERVPSAVEELLRYTPLSTGSVKRMATEDLEIDGVRIKAGEVVMVSLEAVNHDPDAFEDPDVFRPGREGPMHFGFGRGRHFCPGNRLARCVIEATVRAVARRPGLRLAVAPEEISWHEGLFFRRPRAIPATW
4RAI , Knot 52 96 0.82 36 77 93 
MAKDKEFQVLFVLTILTLISGTIFYSTVEGLRPIDALYFSVVTLTTVGETPPPQTDFGKIFTILYIFIGIGLVFGFIHKLAVNVQLPSILSNLVPR

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 \(c\).

\(|P_{f(2IMU_1)}(2) \setminus P_{f(6XAL_1)}(2)|=9\), \(|P_{f(6XAL_1)}(2) \setminus P_{f(2IMU_1)}(2)|=158\). 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 1:1110011011001111110011111111101110110011100101
Pair \(Z_2\) Length of longest common subsequence
2IMU_1,6XAL_1 167 4
2IMU_1,4RAI_1 92 3
6XAL_1,4RAI_1 177 3

Newick tree

 
[
	6XAL_1:95.73,
	[
		2IMU_1:46,4RAI_1:46
	]:49.73
]

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 \((0.85)(0.8)(\frac{447 }{\log_{20} 447}-\frac{46}{\log_{20}46})=124.\)
Status Protein1 Protein2 d d1/2
Query variables 2IMU_1 6XAL_1 148 82
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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