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Parikh vectors
2QOC_1 7YIY_1 5JJO_1 Letter Amino acid
10 18 7 M Methionine
28 29 8 S Serine
20 27 9 T Threonine
22 45 34 A Alanine
20 43 9 E Glutamic acid
28 51 29 L Leucine
14 21 22 P Proline
13 23 10 N Asparagine
6 12 2 C Cysteine
5 13 7 H Histidine
25 39 11 V Valine
22 22 27 D Aspartic acid
11 21 7 F Phenylalanine
7 4 6 W Tryptophan
26 33 7 I Isoleucine
22 28 17 K Lycine
12 29 19 Y Tyrosine
19 39 12 R Arginine
10 14 10 Q Glutamine
24 51 20 G Glycine 

2QOC_1|Chain A|Ephrin receptor|Homo sapiens (9606)
>7YIY_1|Chain A[auth B]|Serine palmitoyltransferase 2|Homo sapiens (9606)
>5JJO_1|Chain A|Uncharacterized protein|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 \(w=f(c)\)
2QOC , Knot 152 344 0.86 40 215 335 
GSTQTVHEFAKELDATNISIDKVVGAGEFGEVCSGRLKLPSKKEISVAIKTLKVGYTEKQRRDFLGEASIMGQFDHPNIIRLEGVVTKSKPVMIVTEYMENGSLDSFLRKHDAQFTVIQLVGMLRGIASGMKYLSDMGYVHRDLAARNILINSNLVCKVSDFGLSRVLEDDPEAAYTTRGGKIPIRWTSPEAIAYRKFTSASDVWSYGIVLWEVMSYGERPYWEMSNQDVIKAVDEGYRLPPPMDCPAALYQLMLDCWQKDRNNRPKFEQIVSILDKLIRNPGSLKIITSAAARPSNLLLDQSNVDITTFRTTGDWLNGVWTAHCKEIFTGVEYSSCDTIAKIS
7YIY , Knot 223 562 0.83 40 266 527 
MRPEPGGCCCRRTVRANGCVANGEVRNGYVRSSAAAAAAAAAGQIHHVTQNGGLYKRPFNEAFEETPMLVAVLTYVGYGVLTLFGYLRDFLRYWRIEKCHHATEREEQKDFVSLYQDFENFYTRNLYMRIRDNWNRPICSVPGARVDIMERQSHDYNWSFKYTGNIIKGVINMGSYNYLGFARNTGSCQEAAAKVLEEYGAGVCSTRQEIGNLDKHEELEELVARFLGVEAAMAYGMGFATNSMNIPALVGKGCLILSDELNHASLVLGARLSGATIRIFKHNNMQSLEKLLKDAIVYGQPRTRRPWKKILILVEGIYSMEGSIVRLPEVIALKKKYKAYLYLDEAHSIGALGPTGRGVVEYFGLDPEDVDVMMGTFTKSFGASGGYIGGKKELIDYLRTHSHSAVYATSLSPPVVEQIITSMKCIMGQDGTSLGKECVQQLAENTRYFRRRLKEMGFIIYGNEDSPVVPLMLYMPAKIGAFGREMLKRNIGVVVVGFPATPIIESRARFCLSAAHTKEILDTALKEIDEVGDLLQLKYSRHRLVPLLDRPFDETTYEETED
5JJO , Knot 121 273 0.82 40 162 258 
SAELRPFICVNEKDHLPSLDPQADAWYREAVALAKPDTLRPWDRIVDLYSKAVERGHWKAMHNLASLYRTGWPGGVEKDTQKALDLYQKMIDLKVPQGFYDMAAMIGNRAGVKNPATDGLTFLDKAASLGNPPALTELGRLYIYVAGQDELGLKYTNCAAGQGYAPANYELAMYYRLVAHNYPKAAGYYLLAASQGNDDAAFFMSGVFDKTSPDVDRMWYAPDEKLHKLYDGIYDQLAADPDLRFPNLIKDHPLPPHPTQGYDADRPDWKPGQ

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 \(c\).

\(|P_{f(2QOC_1)}(2) \setminus P_{f(7YIY_1)}(2)|=45\), \(|P_{f(7YIY_1)}(2) \setminus P_{f(2QOC_1)}(2)|=96\). 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 1:10000100110010100101001111101101001010110000101110010110000000011101011101001011010111000011111000100101001100001010110111110111011001001101000111001110001100100111001100010110000110111010010111000100100110011111011001001010100001101100100111110011110011100100000001010011011001100110101100111010011100001010010001011011101000011011000000011010
Pair \(Z_2\) Length of longest common subsequence
2QOC_1,7YIY_1 141 4
2QOC_1,5JJO_1 189 3
7YIY_1,5JJO_1 208 4

Newick tree

 
[
	5JJO_1:10.27,
	[
		2QOC_1:70.5,7YIY_1:70.5
	]:36.77
]

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 \((0.85)(0.8)(\frac{906 }{\log_{20} 906}-\frac{344}{\log_{20}344})=151.\)
Status Protein1 Protein2 d d1/2
Query variables 2QOC_1 7YIY_1 191 152.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]