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Parikh vectors
9LOT_1 1CVB_1 4AYF_1 Letter Amino acid
20 22 17 G Glycine
14 12 1 H Histidine
14 17 18 P Proline
19 18 14 S Serine
21 19 17 D Aspartic acid
4 1 2 C Cysteine
14 8 6 Y Tyrosine
25 18 17 V Valine
13 10 14 N Asparagine
2 7 5 W Tryptophan
31 26 18 L Leucine
10 1 2 M Methionine
12 12 11 F Phenylalanine
14 11 8 T Threonine
21 13 12 E Glutamic acid
17 9 18 I Isoleucine
19 11 10 Q Glutamine
24 24 21 K Lycine
30 13 15 A Alanine
16 7 9 R Arginine 

9LOT_1|Chains A, B|Tryptophan--tRNA ligase|Escherichia coli (562)
>1CVB_1|Chain A|CARBONIC ANHYDRASE II|Homo sapiens (9606)
>4AYF_1|Chain A|CHAPERONE PROTEIN CAF1M|YERSINIA PESTIS (632)
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 \(w=f(c)\)
9LOT , Knot 152 340 0.86 40 211 325 
MTKPIVFSGAQPSGELTIGNYMGALRQWVNMQDDYHCIYCIVDQHAITVRQDAQKLRKATLDTLALYLACGIDPEKSTIFVQSHVPEHAQLGWALNCYTYFGELSRMTQFKDKSARYAENINAGLFDYPVLMAADILLYQTNLVPVGEDQKQHLELSRDIAQRFNALYGEIFKVPEPFIPKSGARVMSLLEPTKKMSKSDDNRNNVIGLLEDPKSVVKKIKRAVTDSDEPPVVRYDVQNKAGVSNLLDILSAVTGQSIPELEKQFEGKMYGHLKGEVADAVSGMLTELQERYHRFRNDEAFLQQVMKDGAEKASAHASRTLKAVYEAIGFVAKRHHHHHH
1CVB , Knot 111 259 0.79 40 173 248 
SHHWGYGKHNGPEHWHKDFPIAKGERQSPVDIDTHTAKYDPSLKPLSVSYDQATSLRILNNGHAFNVEFDDSQDKAVLKGGPLDGTYRLIQFHFHWGSLDGQGSEHTVDKKKYAAELHLVHWNTKYGDFGKAVQQPDGLAVLGIFLKVGSAKPGLQKVVDVLDSIKTKGKSADFTNFDPRGLLPESLDYWTYPGSLVTPPLLECVTWIVLKEPISVSSEQVLKFRKLNFNGEGEPEELMVDNWRPAQPLKNRQIKASFK
4AYF , Knot 107 235 0.82 40 155 222 
AQPDIKFASKEYGVTIGESRIIYPLDAAGVMVSVKNTQDAPVLIQSRIYDENKEKESEDPFVVTPPLFRLDAKQQNSLRIAQAGGVFPRDKESLKWLCVKGIPPKDEDIWVDDATNKQKFNPDKDVGVFVQFAINNCIKLLVRPNELKGTPIQFAENLSWKVDGGKLIAENPSPFYMNIGELTFGGKSIPSHYIPPKSTWAFDLPKGLAGARNVSWRIINDQGGLDRLYSKNVTL

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 \(c\).

\(|P_{f(9LOT_1)}(2) \setminus P_{f(1CVB_1)}(2)|=108\), \(|P_{f(1CVB_1)}(2) \setminus P_{f(9LOT_1)}(2)|=70\). 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 1:1001111011010101011001111001101000000100110001101000100100101001110110110100001110001100101111100000110100100100001001001011110011111101110000111110000001010001100101101011011011110011011011010001000000000111110010011001001100000111100010001110011011011010011010001010101010101101101110010000001000011100110011001010100010110011111100000000
Pair \(Z_2\) Length of longest common subsequence
9LOT_1,1CVB_1 178 3
9LOT_1,4AYF_1 152 4
1CVB_1,4AYF_1 148 5

Newick tree

 
[
	9LOT_1:85.47,
	[
		4AYF_1:74,1CVB_1:74
	]:11.47
]

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 \((0.85)(0.8)(\frac{599 }{\log_{20} 599}-\frac{259}{\log_{20}259})=95.8\)
Status Protein1 Protein2 d d1/2
Query variables 9LOT_1 1CVB_1 123 108
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]