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Parikh vectors
5XDT_1 7OZL_1 8EHN_1 Letter Amino acid
19 21 16 L Leucine
9 15 3 F Phenylalanine
7 19 20 P Proline
0 11 6 Y Tyrosine
38 26 25 A Alanine
18 5 12 D Aspartic acid
23 16 7 E Glutamic acid
17 25 16 S Serine
9 16 12 R Arginine
13 9 5 Q Glutamine
15 13 9 K Lycine
13 9 3 M Methionine
17 32 9 T Threonine
16 25 6 N Asparagine
37 12 15 G Glycine
2 4 8 H Histidine
25 20 7 I Isoleucine
0 3 4 W Tryptophan
30 20 13 V Valine
0 4 8 C Cysteine 

5XDT_1|Chain A|Cell division protein FtsZ|Staphylococcus aureus (strain MRSA252) (282458)
>7OZL_1|Chain A|Capsid protein VP1|Human enterovirus 70 (strain J670/71) (31915)
>8EHN_1|Chain A|Papain-like protease 2|Porcine reproductive and respiratory syndrome virus (28344)
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 \(w=f(c)\)
5XDT , Knot 134 308 0.83 34 174 291 
GHMATLKVIGVGGGGNNAVNRMIDHGMNNVEFIAINTDGQALNLSKAESKIQIGEKLTRGLGAGANPEIGKKAAEESREQIEDAIQGADMVFVTSGMGGGTGTGAAPVVAKIAKEMGALTVGVVTRPFSFEGRKRQTQAAAGVEAMKAAVDTLIVIPNDRLLDIVDKSTPMMEAFKEADNVLRQGVQGISDLIAVSGEVNLDFADVKTIMSNQGSALMGIGVSSGENRAVEAAKKAISSPLLETSIVGAQGVLMNITGGESLSLFEAQEAADIVQDAADEDVNMIFGTVINPELQDEIVVTVIATGFD
7OZL , Knot 132 305 0.82 40 187 292 
ATTQIGEIVKTVANTVESEIKAELGVIPSLNAVETGATSNTEPEEAIQTRTVINMHGTAECLVENFLGRSALVCMRSFEYKNHSTSTSSIQKNFFIWTLNTRELVQIRRKMELFTYLRFDTEITIVPTLRLFSSSNVSFSGLPNLTLQAMYVPTGARKPSSQDSFEWQSACNPSVFFKINDPPARLTIPFMSINSAYANFYDGFAGFEKKATVLYGINPANTMGNLCLRVVNSYQPVQYTLTVRVYMKPKHIKAWAPRAPRTMPYTNILNNNYAGRSAAPNAPTAIVSHRSTIKTMPNDINLTTA
8EHN , Knot 93 204 0.80 40 142 194 
GAAGKRARAKRATKSGKDSALAPKIAPPVPTCGITTYSPPTDGSCGWHVLAAIVNRMINGDFTSPLPQYNRPEDDWASDYDLAQAIQCLQLPATVVRNRACPNAKYLIKLNGVHWEVEVRSGMAPRSLSRECVVGVCSEGCVAPPYPADGLPKRALEALASAYRLPSDCVSSGIADFLADPPPQEFWTLDKMLTGSSGHHHHHH

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 \(c\).

\(|P_{f(5XDT_1)}(2) \setminus P_{f(7OZL_1)}(2)|=71\), \(|P_{f(7OZL_1)}(2) \setminus P_{f(5XDT_1)}(2)|=84\). 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 1:10110101111111100110011001100101111000101101001000101100100111111010110011000000100110110111100111110101111111011001111011110011010100000011111011011100111110001101100001110110010011001101100111101010101101001100010111111100100011011001100111000111101111010110010110100110110011000101111011010100011101110110
Pair \(Z_2\) Length of longest common subsequence
5XDT_1,7OZL_1 155 4
5XDT_1,8EHN_1 164 5
7OZL_1,8EHN_1 183 3

Newick tree

 
[
	8EHN_1:89.78,
	[
		5XDT_1:77.5,7OZL_1:77.5
	]:12.28
]

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 \((0.85)(0.8)(\frac{613 }{\log_{20} 613}-\frac{305}{\log_{20}305})=85.9\)
Status Protein1 Protein2 d d1/2
Query variables 5XDT_1 7OZL_1 109 108
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]