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Parikh vectors
1VTW_1 5WNF_1 7GEB_1 Letter Amino acid
0 15 11 I Isoleucine
0 16 13 P Proline
1 16 24 T Threonine
1 22 17 A Alanine
0 23 21 N Asparagine
0 41 17 D Aspartic acid
0 6 14 Q Glutamine
0 25 17 F Phenylalanine
0 7 3 W Tryptophan
2 5 12 C Cysteine
0 7 7 H Histidine
0 38 29 L Leucine
0 17 10 M Methionine
0 30 27 V Valine
0 24 11 R Arginine
0 26 9 E Glutamic acid
2 24 26 G Glycine
0 28 11 K Lycine
0 26 16 S Serine
0 19 11 Y Tyrosine 

1VTW_1|Chains A, B|DNA (5'-D(*(CH3)CP*GP*TP*AP*(CH3)CP*G)-3')|
>5WNF_1|Chains A, B, C, D|Rho-associated protein kinase 1|Homo sapiens (9606)
>7GEB_1|Chain A|3C-like proteinase|Severe acute respiratory syndrome coronavirus 2 (2697049)
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 \(w=f(c)\)
1VTW , Knot 5 6 0.49 8 4 4 
CGTACG
5WNF , Knot 173 415 0.83 40 225 399 
GSLHMSFETRFEKMDNLLRDPKSEVNSDCLLDGLDALVYDLDFPALRKNKNIDNFLSRYKDTINKIRDLRMKAEDYEVVKVIGRGAFGEVQLVRHKSTRKVYAMKLLSKFEMIKRSDSAFFWEERDIMAFANSPWVVQLFYAFQDDRYLYMVMEYMPGGDLVNLMSNYDVPEKWARFYTAEVVLALDAIHSMGFIHRDVKPDNMLLDKSGHLKLADFGTCMKMNKEGMVRCDTAVGTPDYISPEVLKSQGGDGYYGRECDWWSVGVFLYEMLVGDTPFYADSLVGTYSKIMNHKNSLTFPDDNDISKEAKNLICAFLTDREVRLGRNGVEEIKRHLFFKNDQWAWETLRDTVAPVVPDLSSDIDTSNFDDLEEDKGEEETFPIPKAFVGNQLPFVGFTYYSNRRYLSSANPNDNR
7GEB , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ

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 \(c\).

\(|P_{f(1VTW_1)}(2) \setminus P_{f(5WNF_1)}(2)|=2\), \(|P_{f(5WNF_1)}(2) \setminus P_{f(1VTW_1)}(2)|=223\). 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 1:010101
Pair \(Z_2\) Length of longest common subsequence
1VTW_1,5WNF_1 225 2
1VTW_1,7GEB_1 192 3
5WNF_1,7GEB_1 177 3

Newick tree

 
[
	1VTW_1:10.41,
	[
		7GEB_1:88.5,5WNF_1:88.5
	]:20.91
]

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 \((0.85)(0.8)(\frac{421 }{\log_{20} 421}-\frac{6}{\log_{20}6})=135.\)
Status Protein1 Protein2 d d1/2
Query variables 1VTW_1 5WNF_1 171 87
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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