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Parikh vectors
5RXQ_1 7DXP_1 3RSK_1 Letter Amino acid
23 22 7 Q Glutamine
37 37 5 E Glutamic acid
29 48 3 G Glycine
17 13 4 H Histidine
24 17 3 F Phenylalanine
8 6 0 W Tryptophan
17 25 10 N Asparagine
16 55 3 R Arginine
43 31 2 L Leucine
7 26 4 M Methionine
38 43 15 S Serine
39 25 10 T Threonine
16 13 6 Y Tyrosine
17 37 15 A Alanine
6 6 8 C Cysteine
31 30 3 I Isoleucine
32 16 8 K Lycine
20 15 4 P Proline
22 21 9 V Valine
21 21 5 D Aspartic acid

5RXQ_1|Chain A|Phosphatidylinositol 3,4,5-trisphosphate 5-phosphatase 1|Homo sapiens (9606)
>7DXP_1|Chains A, B|Nucleoprotein|Influenza A virus (A/Hong Kong/483/1997(H5N1)) (88104)
>3RSK_1|Chain A|RIBONUCLEASE A|Bos taurus (9913)
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 \(w=f(c)\)
5RXQ , Knot 195 463 0.86 40 252 447
SMEQPEPDMITIFIGTWNMGNAPPPKKITSWFLSKGQGKTRDDSADYIPHDIYVIGTQEDPLSEKEWLEILKHSLQEITSVTFKTVAIHTLWNIRIVVLAKPEHENRISHICTDNVKTGIANTLGNKGAVGVSFMFNGTSLGFVNSHLTSGSEKKLRRNQNYMNILRFLALGDKKLSPFNITHRFTHLFWFGDLNYRVDLPTWEAETIIQKIKQQQYADLLSHDQLLTERREQKVFLHFEEEEITFAPTYRFERLTRDKYAYTKQKATGMKYNLPSWCDRVLWKSYPLVHVVCQSYGSTSDIMTSDHSPVFATFEAGVTSQFVSKNGPGTVDSQGQIEFLRCYATLKTKSQTKFYLEFHSSCLESFVKSQEGENEEGSEGELVVKFGETLPKLKPIISDPEYLLDQHILISIKSSDSDESYGEGCIALRLEATETQLPIYTPLTHHGELTGHFQGEIKLQTSQ
7DXP , Knot 201 507 0.82 40 245 468
MGSSHHHHHHSSGLVPRGSHMASMTGGQQMGRGSEFMASQGTKRSYEQMETGGERQNATEIRASVGRMVGGIGRFYIQMCTELKLSDQEGRLIQNSITIERMVLSAFDERRNRYLEEHPSAGKDPKKTGGPIYRRRDGKWVRELILYDKEEIRRIWRQANNGEDATAGLTHMMIWHSNLNDATYQRTRALVRTGMDPRMCSLMQGSTLPRRSGAAGAAIKGVGTMVMELIRMIKRGINDRNFWRGENGRRTRIAYERMCNILKGKFQTAAQKAMMDQVRESRNPGNAEIEDLIFLARSALILRGSIAHKSCLPACVYGLAVASGYDFEREGYSLVGIDPFRLLQNSQVFSLIRPNENPAHKSQLVWMACHSAAFEDLRVSSFIRGTRVIPRGQLSTRGVQIASNENVEAMDSSTLELRSRYWAIRTRSGGNTNQQRAFKGNTEGRTSDMRTEIIRMMESARPEDVSFQGRGVFELSDEKATNPIVPSFDMSNEGSYFFGDNAEEYDN
3RSK , Knot 64 124 0.83 38 106 120
KETAAAAFEAQHMDSSTSAASSSNYCNQMMKSRNLTKDRCKPVNTFVHESLADVQAVCSQKNVACANGQTNCYQSYSTMSITDCRETGSSKYPNCAYKTTQANKHIIVACEGNPYVPVHFDASV

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 \(c\).

\(|P_{f(5RXQ_1)}(2) \setminus P_{f(7DXP_1)}(2)|=92\), \(|P_{f(7DXP_1)}(2) \setminus P_{f(5RXQ_1)}(2)|=85\). 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 1:0100101011011110101101111001001110010100000010011001011100001100001101100010010010100111001101011111010000010010000100111001100111110111010011110001001000010000001011011111000101101000100111110100010110101001100100000101100001100000001110100001011100010010000010000010110001101000111000111011000010000110000011110101110001100011101000101011000101000000010101000010011000010000100101110110011010111001001100011101000000000101011101010000111001100010101010101010000
Pair \(Z_2\) Length of longest common subsequence
5RXQ_1,7DXP_1 177 3
5RXQ_1,3RSK_1 222 3
7DXP_1,3RSK_1 211 5

Newick tree

 
[
	3RSK_1:11.12,
	[
		5RXQ_1:88.5,7DXP_1:88.5
	]:25.62
]

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 \((0.85)(0.8)(\frac{970 }{\log_{20} 970}-\frac{463}{\log_{20}463})=133.\)
Status Protein1 Protein2 d d1/2
Query variables 5RXQ_1 7DXP_1 169 164
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]