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Parikh vectors
7XDV_1 5TTC_1 9DSY_1 Letter Amino acid
13 2 14 D Aspartic acid
12 0 23 Q Glutamine
9 0 8 M Methionine
4 1 5 W Tryptophan
22 0 30 K Lycine
13 0 13 F Phenylalanine
20 3 14 S Serine
12 0 7 Y Tyrosine
18 2 26 A Alanine
23 0 27 E Glutamic acid
25 1 21 G Glycine
18 0 13 T Threonine
20 2 25 V Valine
15 1 11 R Arginine
8 0 14 N Asparagine
8 0 0 C Cysteine
18 1 5 H Histidine
14 5 15 I Isoleucine
30 6 26 L Leucine
11 1 14 P Proline 

7XDV_1|Chains A, B|Receptor-like protein kinase FERONIA|Arabidopsis thaliana (3702)
>5TTC_1|Chain A|Matrix protein 2|Influenza A virus (A/Hickox/1940(H1N1)) (383543)
>9DSY_1|Chain A|C4-dicarboxylate-binding periplasmic protein DctP|Pseudomonas aeruginosa PAO1 (208964)
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 \(w=f(c)\)
7XDV , Knot 138 313 0.84 40 201 301 
MGSSHHHHHHSQGSSNLCRHFSFAEIKAATKNFDESRVLGVGGFGKVYRGEIDGGTTKVAIRRGNPMSEQGVHEFQTEIEMLSKLRHRHLVSLIGYCEENCEMILVYDYMAHGTMREHLYKTQNPSLPWKQRLEICIGAARGLHYLHTGAKHTIIHRDVKTTNILLDEKWVAKVSDFGLSKTGPTLDHTHVSTVVKGSFGYLDPEYFRRQQLTEKSDVYSFGVVLFEALCARPALNPTLAKEQVSLAEWAPYCYKKGMLDQIVDPYLKGKITPECFKKFAETAMKCVLDQGIERPSMGDVLWNLEFALQLQES
5TTC , Knot 17 27 0.69 24 24 25 
XSSDPLVVAASIIGILHLILWILDRLX
9DSY , Knot 137 311 0.84 38 195 298 
SNAADPIVIKFSHVVAEHTPKGQGALLFKKLVEERLPGKVKVEVYPNSSLFGDGKEMEALLLGDVQIIAPSLAKFEQYTKKLQIFDLPFLFDNIQAVDRFQQSPQGKELLTSMQDKGITGLGYWHNGMKQLSANKPLREPKDARGLKFRVQASKVLEEQFKAVRANPRKMSFAEVYQGLQTGVVNGTENPWSNIYSQKMHEVQKYITESDHGVLDYMVITNTKFWNGLPEDVRGVLAKTMDEVTVEVNKQAEALNQGDKQRIVEAKTSEIIELTPEQRAEWRKAMQPVWKKFEGEIGADLIKAAEAANQAQ

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 \(c\).

\(|P_{f(7XDV_1)}(2) \setminus P_{f(5TTC_1)}(2)|=184\), \(|P_{f(5TTC_1)}(2) \setminus P_{f(7XDV_1)}(2)|=7\). 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 1:1100000000001000100010110101100010000111111110100101011000111001011000110010001011001000011011100000001111000110101000100000101110001010111101100100110001100010000111000111010011100011010000100110101101010010000100000100111111011010111010110001011011100000111001101010101010010011001100110011001011011101011101000
Pair \(Z_2\) Length of longest common subsequence
7XDV_1,5TTC_1 191 2
7XDV_1,9DSY_1 158 4
5TTC_1,9DSY_1 187 3

Newick tree

 
[
	5TTC_1:99.13,
	[
		7XDV_1:79,9DSY_1:79
	]:20.13
]

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 \((0.85)(0.8)(\frac{340 }{\log_{20} 340}-\frac{27}{\log_{20}27})=102.\)
Status Protein1 Protein2 d d1/2
Query variables 7XDV_1 5TTC_1 130 70
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]