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Parikh vectors
9BNV_1 7NBR_1 1NLI_1 Letter Amino acid
24 24 16 T Threonine
28 27 15 V Valine
16 17 30 A Alanine
17 17 9 D Aspartic acid
12 12 0 C Cysteine
10 10 5 M Methionine
17 17 9 F Phenylalanine
3 3 1 W Tryptophan
11 11 13 R Arginine
7 7 1 H Histidine
29 29 25 L Leucine
11 11 10 K Lycine
13 13 8 P Proline
16 16 26 S Serine
11 11 13 Y Tyrosine
21 21 19 N Asparagine
14 14 10 Q Glutamine
9 9 8 E Glutamic acid
26 26 11 G Glycine
11 11 19 I Isoleucine 

9BNV_1|Chain A|3C-like proteinase nsp5|Severe acute respiratory syndrome coronavirus 2 (2697049)
>7NBR_1|Chain A[auth AAA]|3C-like proteinase|Severe acute respiratory syndrome coronavirus 2 (2697049)
>1NLI_1|Chain A|Ribosome-inactivating protein alpha-trichosanthin|Trichosanthes kirilowii (3677)
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 \(w=f(c)\)
9BNV , Knot 134 306 0.83 40 195 291 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHVGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ
7NBR , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ
1NLI , Knot 114 248 0.84 38 161 238 
MDVSFRLSGATSSSYGVFISNLRKALPNERKLYDIPLLRSSLPGSQRYALIHLTNYADETISVAIDVTNVYIMGYRAGDTSYFFNEASATEAAKYVFKDAMRKVTLPYSGNYERLQTAAGKIRENIPLGLPALDSAITTLFYYNANSAASALMVLIQSTSAAARYKFIEQQIGKRVDKTFLPSLAIISLANSWSALSKQIQIASTNNGQFESPVVLINAQNQRVTITNVDAGVVTSNIALLLNRNNMA

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 \(c\).

\(|P_{f(9BNV_1)}(2) \setminus P_{f(7NBR_1)}(2)|=0\), \(|P_{f(7NBR_1)}(2) \setminus P_{f(9BNV_1)}(2)|=1\). 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 1:011001111010101011010010001011110011001001100000110100001110000001110110101011100100011010100101001000110101100101110001010110001101010101011010010111010000101001001011011011001010101111000010111000010101111101111010011100100010010111100000110000101111101001111101010100110011010011101110001011011000011010
Pair \(Z_2\) Length of longest common subsequence
9BNV_1,7NBR_1 1 172
9BNV_1,1NLI_1 178 3
7NBR_1,1NLI_1 179 3

Newick tree

 
[
	1NLI_1:10.05,
	[
		9BNV_1:0.5,7NBR_1:0.5
	]:10.55
]

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 \((0.85)(0.8)(\frac{612 }{\log_{20} 612}-\frac{306}{\log_{20}306})=85.3\)
Status Protein1 Protein2 d d1/2
Query variables 9BNV_1 7NBR_1 2 2
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]