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Parikh vectors
6NJY_1 1DNA_1 6JBC_1 Letter Amino acid
8 13 14 R Arginine
13 13 31 E Glutamic acid
18 16 15 I Isoleucine
15 13 15 F Phenylalanine
19 14 15 P Proline
21 14 11 T Threonine
1 7 3 W Tryptophan
8 12 9 N Asparagine
7 20 11 D Aspartic acid
9 11 6 H Histidine
20 28 34 L Leucine
21 12 20 K Lycine
10 10 10 S Serine
17 9 8 Y Tyrosine
13 13 26 V Valine
8 16 4 Q Glutamine
15 13 28 A Alanine
2 5 0 C Cysteine
17 18 34 G Glycine
6 7 6 M Methionine 

6NJY_1|Chains A, B|Type IV CRISPR associated Cas6 RNA endonuclease|Mahella australiensis (strain DSM 15567 / CIP 107919 / 50-1 BON) (697281)
>1DNA_1|Chains A, B|THYMIDYLATE SYNTHASE|Escherichia coli (562)
>6JBC_1|Chain A|Pantoate kinase|Thermococcus kodakarensis (strain ATCC BAA-918 / JCM 12380 / KOD1) (69014)
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 \(w=f(c)\)
6NJY , Knot 106 248 0.78 40 157 237 
MKSSHHHHHHENLYFQSNAMTGYPYPRPQAVKIQVKGHVPYPKNALATVYDIFRDIETVNKAHEAKEAPPFAIKDFNMNGFAITSYLALPTDTVTERLKTKGFHTVGQPIYLPQNELPPLYGLKGVTIQFRTPTAFKYNTGYVPEFYGPVFIKSITESYRRIIPGCPEFSTSDILKYIRFTATDLQKGKYRLTEELMVTGFKGKVYLQFKLSTPPELKLLILYFLEAASICGVGMKKAWGMGDIYITI
1DNA , Knot 124 264 0.87 40 186 256 
MKQYLELMQKVLDEGTQKNDRTGTGTLSIFGHQMRFNLQDGFPLVTTKRCHLRSIIHELLWFLQGDTNIAYLHENNVTIWDEWADENGDLGPVYGKQWRAWPTPDGRHIDQITTVLNQLKNDPDSRRIIVSAWNVGELDKMALAPCHAFFQFYVADGKLSCQLYQRSCNVFLGLPFNIASYALLVHMMAQQCDLEVGDFVWTGGDTHLYSNHMDQTHLQLSREPRPLPKLIIKRKPESIFDYRFEDFEIEGYDPHPGIKAPVAI
6JBC , Knot 129 300 0.81 38 172 286 
MLIRAFIPAHITAFFVPVFHEEPLKAGSLGAGVNLSKGTNVFASIETGTLERHIHVAFNGEPVKREEAEITYYVAEKLVPKDFLGEVEVWQYFDFPNGYGFGNSAGGALGTALALSYAFGGTWLRAAQLAHEAEVKHKGGLGDVIGQLAGGIEVRIKPGGPGIGVTDNLFFEDYKVLVVPLGRLSTREVLDGDVVKAIEVEGRKALEELLKEPKPERMMVLARNFAEKTGLLPGELSEIARELDKVLKNPSSMIMLGKGLFALVRDEEAEKAKQLLSDMNLPYDIAEIYTERPKVGRWVG

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 \(c\).

\(|P_{f(6NJY_1)}(2) \setminus P_{f(1DNA_1)}(2)|=79\), \(|P_{f(1DNA_1)}(2) \setminus P_{f(6NJY_1)}(2)|=108\). 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 1:10000000000010100011010101010110101010110100111010011001001001001001111110010101111000111100010001000110011011011000111101101101010010110000101101011111001000000111101010000110010101001001000100011101101010101010011010111101101101011110011111010101
Pair \(Z_2\) Length of longest common subsequence
6NJY_1,1DNA_1 187 4
6NJY_1,6JBC_1 163 4
1DNA_1,6JBC_1 172 4

Newick tree

 
[
	1DNA_1:92.43,
	[
		6NJY_1:81.5,6JBC_1:81.5
	]:10.93
]

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 \((0.85)(0.8)(\frac{512 }{\log_{20} 512}-\frac{248}{\log_{20}248})=75.5\)
Status Protein1 Protein2 d d1/2
Query variables 6NJY_1 1DNA_1 100 94.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]