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Parikh vectors
6DQD_1 9CKP_1 2LXR_1 Letter Amino acid
28 35 4 V Valine
7 17 0 C Cysteine
21 42 3 G Glycine
13 25 6 I Isoleucine
11 23 1 T Threonine
12 21 0 Y Tyrosine
10 24 3 Q Glutamine
21 57 7 L Leucine
11 52 7 K Lycine
27 29 3 P Proline
23 29 7 F Phenylalanine
20 34 4 S Serine
9 5 1 W Tryptophan
19 24 5 A Alanine
11 29 3 D Aspartic acid
35 54 9 E Glutamic acid
10 20 1 H Histidine
16 37 5 R Arginine
15 28 4 N Asparagine
11 13 3 M Methionine 

6DQD_1|Chain A|Linked KDM5A Jmj Domain|Homo sapiens (9606)
>9CKP_1|Chain A|G protein-coupled receptor kinase 5|Homo sapiens (9606)
>2LXR_1|Chain A|NADH dehydrogenase I subunit E|Helicobacter pylori (85962)
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 \(w=f(c)\)
6DQD , Knot 144 330 0.84 40 208 319 
HNMAGVGPGGYAAEFVPPPECPVFEPSWEEFTDPLSFIGRIRPLAEKTGICKIRPPKDWQPPFACEVKSFRFTPRVQRLNELEAMTRVRPREAFGFEQAVREYTLQSFGEMADNFKSDYFNMPVHMVPTELVEKEFWRLVSSIEEDVIVEYGADISSKDFGSGFPVKDGRRKILPEEEEYALSGWNLNNMPVLEQSVLAHINVDISGMKVPWLYVGMCFSSFCWHIEDHWSYSINYLHWGEPKTWYGVPSHAAEQLEEVMRELAPELFESQPDLLHQLVTIMNPNVLMEHGVPVYRTNQCAGEFVVTFPRAYHSGFNQGYNFAEAVNFCT
9CKP , Knot 232 598 0.82 40 269 550 
MELENIVANTVLLKAREGGGGKRKGKSKKWKEILKFPHISQCEDLRRTIDRDYCSLCDKQPIGRLLFRQFCETRPGLECYIQFLDSVAEYEVTPDEKLGEKGKEIMTKYLTPKSPVFIAQVGQDLVSQTEEKLLQKPCKELFSACAQSVHEYLRGEPFHEYLDSMFFDRFLQWKWLERQPVTKNTFRQYRVLGKGGFGEVCACQVRATGKMYACKRLEKKRIKKRKGESMALNEKQILEKVNSQFVVNLAYAYETKDALCLVLTIMNGGDLKFHIYNMGNPGFEEERALFYAAEILCGLEDLHRENTVYRNLKPENILLDDYGHIRISDLGLAVKIPEGDLIRGRVGTVGYMAPEVLNNQRYGLSPDYWGLGCLIYEMIEGQSPFRGRKEKVKREEVDRRVLETEEVYSHKFSEEAKSICKMLLTKDAKQRLGCQEEGAAEVKRHPFFRNMNFKRLEAGMLDPPFVPDPRAVYCKDVLDIEQFSTVKGVNLDHTDDDFYSKFSTGSVSIPWQNEMIETECFKELNVFGPNGTLPPDLNRNHPPEPPKKGLLQRLFKRQHQNNSKSSPSSKTSFNHHINSNHVSSNSTGSSVDHHHHHH
2LXR , Knot 43 76 0.81 36 68 74 
MKRFDLRPLKAGIFERLEELIEKEMQPNEVAIFMFEVGDFSNIPKSAEFIQSKGHELLNSLRFNQADWTIVVRKKA

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 \(c\).

\(|P_{f(6DQD_1)}(2) \setminus P_{f(9CKP_1)}(2)|=55\), \(|P_{f(9CKP_1)}(2) \setminus P_{f(6DQD_1)}(2)|=116\). 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 1:001111111101101111100111010100100110111010111000110010110010111100100101010100100101100101001111001100001001101100100001011101110011000110110010001110011010000110111100100011100000110110100111100011101010101101111011101001010100010001001011010010111001100100110011101100010110011011010111001111000000110111011010001100100110110100
Pair \(Z_2\) Length of longest common subsequence
6DQD_1,9CKP_1 171 4
6DQD_1,2LXR_1 192 3
9CKP_1,2LXR_1 225 3

Newick tree

 
[
	2LXR_1:11.20,
	[
		6DQD_1:85.5,9CKP_1:85.5
	]:24.70
]

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 \((0.85)(0.8)(\frac{928 }{\log_{20} 928}-\frac{330}{\log_{20}330})=160.\)
Status Protein1 Protein2 d d1/2
Query variables 6DQD_1 9CKP_1 200 154
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]