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Parikh vectors
7JFT_1 5FDG_1 8XFH_1 Letter Amino acid
0 2 11 W Tryptophan
0 7 5 Y Tyrosine
0 8 36 V Valine
0 9 21 D Aspartic acid
0 3 16 Q Glutamine
4 9 32 G Glycine
0 14 26 K Lycine
0 11 23 F Phenylalanine
3 4 9 C Cysteine
0 14 26 I Isoleucine
0 5 29 P Proline
0 10 41 S Serine
1 14 23 T Threonine
0 22 30 E Glutamic acid
0 12 52 L Leucine
0 7 7 M Methionine
4 14 25 A Alanine
0 15 22 R Arginine
0 6 18 N Asparagine
0 5 10 H Histidine 

7JFT_1|Chain A|DNA (5'-D(*GP*AP*GP*CP*AP*GP*AP*CP*CP*TP*GP*A)-3')|synthetic construct (32630)
>5FDG_1|Chain A|Polymerase acidic protein|Influenza A virus (211044)
>8XFH_1|Chains A, B|UDP-glycosyltransferase 13|Mangifera indica (29780)
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 \(w=f(c)\)
7JFT , Knot 7 12 0.48 8 8 10 
GAGCAGACCTGA
5FDG , Knot 94 191 0.86 40 143 185 
GPLGSMEDFVRQCFNPMIVELAEKTMKEYGEDLKIETNKFAAICTHLEVCFMYSDASKHRFEIIEGRDRTMAWTVVNSICNTTGAEKPKFLPDLYDYKENRFIEIGVTRREVHIYYLEKANKIKSEKTHIHIFSFTGEEMATKADYTLDEESRARIKTRLFTIRQEMASRGLWDSFRQSERGAAELALVPR
8XFH , Knot 188 462 0.83 40 234 435 
SCPHVALLLSSGMGHLTPCLRFAATLVQHHCRVTIITNYPTVSVAESRAISLLLSDFPQITEKQFHLLPFDPSTANTTDPFFLRWEAIRRSAHLLNPLLSSISPPLSALVIDSPLVSSFVPVAANLDLPSYVLFTSSTRMCSLQETFPAFVASKTNFDSIQLDDVIEIPGFSPVPVSSVPPDFLNLNHLFTTMLIQNGQSFRKANGILINTFEALEGGILPGINDKRAADGLPPYCSVGPLLPCKFEKTECSAPVKWLDDQPEGSVVYVSFGSRFALSSEQIKELGDGLIRSGCRFLWVVKCKKVDQEDEESLDELLGRDVLEKIKKYGFVIKNWVNQQEILDHRAVGGFVTHGGWNSSMEAVWHGVPMLVWPQFGDQKINAEVIERSGLGMWVKRWGWGTQQLVKGEEIGERIKDLMGNNPLRVRAKTLREEARKAIEVGGSSEKTLKELIENWKKTSRKT

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 \(c\).

\(|P_{f(7JFT_1)}(2) \setminus P_{f(5FDG_1)}(2)|=5\), \(|P_{f(5FDG_1)}(2) \setminus P_{f(7JFT_1)}(2)|=140\). 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 1:111011100011
Pair \(Z_2\) Length of longest common subsequence
7JFT_1,5FDG_1 145 3
7JFT_1,8XFH_1 240 2
5FDG_1,8XFH_1 191 4

Newick tree

 
[
	8XFH_1:11.01,
	[
		7JFT_1:72.5,5FDG_1:72.5
	]:45.51
]

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 \((0.85)(0.8)(\frac{203 }{\log_{20} 203}-\frac{12}{\log_{20}12})=67.9\)
Status Protein1 Protein2 d d1/2
Query variables 7JFT_1 5FDG_1 91 47.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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