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Parikh vectors
5FSK_1 6IMV_1 6WRC_1 Letter Amino acid
11 25 0 F Phenylalanine
2 6 8 C Cysteine
11 23 0 Q Glutamine
17 38 5 G Glycine
6 38 0 S Serine
8 38 1 T Threonine
12 25 0 D Aspartic acid
5 28 0 I Isoleucine
9 22 0 K Lycine
5 10 0 M Methionine
7 24 0 P Proline
4 16 0 W Tryptophan
4 37 7 A Alanine
8 14 0 R Arginine
16 30 0 L Leucine
4 23 0 Y Tyrosine
13 36 0 V Valine
1 31 0 N Asparagine
12 26 0 E Glutamic acid
4 15 0 H Histidine 

5FSK_1|Chain A|7,8-DIHYDRO-8-OXOGUANINE TRIPHOSPHATASE|HOMO SAPIENS (9606)
>6IMV_1|Chains A, B|Endo-beta-1,2-glucanase|Talaromyces funiculosus (28572)
>6WRC_1|Chain A|DNA (5'-D(*GP*AP*GP*CP*AP*GP*AP*CP*CP*AP*GP*AP*CP*GP*CP*CP*AP*CP*TP*CP*A)-3')|synthetic construct (32630)
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 \(w=f(c)\)
5FSK , Knot 75 159 0.79 40 122 154 
GSHMGASRLYTLVLVLQPQRVLLGMKKRGFGAGRWNGFGGKVQEGETIEDGARRELQEESGLTVDALHKVGQIVFEFVGEPELMDVHVFCTDSIQGTPVESDEMRPCWFQLDQIPFKDMWPDDSYWFPLLLQKKKFHGYFKFQGQDTILDYTLREVDTV
6IMV , Knot 206 505 0.84 40 268 476 
AGIHHHHHHSSEPSCRFAHQYTQEQVLQNPSKFINDVLFWEGKFHQNNISYNSGNGMSYDGTNIDWVTGEGTVKHPFSAASKESLQVMLYAHAIAGSADAARFLSPNNPSAAPGIAASIMDTKLQTYLRFNETYPGFGGFLPWFTSSSQDLTPTWDWNNRVPGLDNGELLWAVYAFIQAAENTSNKSFIDLAKKWQTWMDYTKTTAAHIFYQGEGKVCAVTDIKNQSLPVYHPEQTYACEGTSYLNDPYEGELFTWWLQFFGGLSDADIEALWEYKRPQLVSVDYHIGNVGPITVQKGYWFSSHETWKVLEMPYYDIDIIRRVFQNAERARTCNSVVTQVPGMFASINNVTDPATGDVVGYISNAGIPSIANQTIQELDVITPYSVFPTVLFDKGVGMAWWRNMAIGKKMQNIYGSTESTRRDGTGVSALLTWDSKVSTVNAILGGVSGLVSQKMKAENIYNTFVERIEAEYSRVFKNLKGEHVPFCLPQETVPDTGLVDFTTCN
6WRC , Knot 9 21 0.43 8 9 15 
GAGCAGACCAGACGCCACTCA

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 \(c\).

\(|P_{f(5FSK_1)}(2) \setminus P_{f(6IMV_1)}(2)|=37\), \(|P_{f(6IMV_1)}(2) \setminus P_{f(5FSK_1)}(2)|=183\). 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 1:100111001001111101001111100011111010111101001001001100010000110101100110111011101011010110000101011000010101101001110011100001111110000101010101000110001001001
Pair \(Z_2\) Length of longest common subsequence
5FSK_1,6IMV_1 220 4
5FSK_1,6WRC_1 125 3
6IMV_1,6WRC_1 269 2

Newick tree

 
[
	6IMV_1:13.20,
	[
		5FSK_1:62.5,6WRC_1:62.5
	]:74.70
]

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 \((0.85)(0.8)(\frac{664 }{\log_{20} 664}-\frac{159}{\log_{20}159})=144.\)
Status Protein1 Protein2 d d1/2
Query variables 5FSK_1 6IMV_1 187 121.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]