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Parikh vectors
6JDZ_1 7TFQ_1 3QXF_1 Letter Amino acid
19 16 22 D Aspartic acid
4 1 2 C Cysteine
14 14 18 Q Glutamine
26 34 26 G Glycine
6 9 9 M Methionine
9 5 16 W Tryptophan
17 7 12 Y Tyrosine
3 13 21 R Arginine
13 17 8 I Isoleucine
13 19 20 P Proline
21 12 23 S Serine
25 16 18 T Threonine
24 20 16 V Valine
42 26 32 A Alanine
20 14 15 N Asparagine
8 15 20 E Glutamic acid
5 10 8 H Histidine
22 23 31 L Leucine
18 8 22 K Lycine
10 13 16 F Phenylalanine 

6JDZ_1|Chains A, B|Beta-xylanase|Aspergillus fumigatus Z5 (1437362)
>7TFQ_1|Chain A|Pirin family protein Yhak|Yersinia pestis CO92 (214092)
>3QXF_1|Chains A, B, C, D|Endoglucanase|Escherichia coli K-12 (83333)
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 \(w=f(c)\)
6JDZ , Knot 138 319 0.83 40 188 300 
AGLNTAAKAKGLKYFGSATDNPELTDSAYVAQLSNTDDFGQITPGNSMKWDATEPSQNSFSFANGDAVVNLANKNGQLMRCHTLVWHSQLPNWVSSGSWTNATLLAAMKNHITNVVTHYKGKCYAWDVVNEALNEDGTFRNSVFYQIIGPAYIPIAFATAAAADPDVKLYYNDYNIEYSGAKATAAQNIVKMIKAYGAKIDGVGLQAHFIVGSTPSQSDLTTVLKGYTALGVEVAYTELDIRMQLPSTAAKLAQQSTDFQGVAAACVSTTGCVGVTIWDWTDKYSWVPSVFQGYGAPLPWDENYVKKPAYDGLMAGLGA
7TFQ , Knot 127 292 0.82 40 184 271 
SNAMKKVQGIYRAPRQHWVGDGFPVRSMFSYQSHGKQLSPFLLLDYAGPMDFTPTTQRRGVGQHPHRGFETVTIVYHGEVEHRDSTGNGGIIGPGDVQWMTAGAGILHEEFHSDAFAQKGGPFEMVQLWVNLPAKDKMTAPGYQAIRREAIPQVNLPDDAGNLRVIAGEYAGNIGPAKTFSPLNVWDIRLTQGKSCEFSLPAGWNTALIVLHGTLLVNGDAIAREAEMVLLDPTGTHLSIEANNDTVLLLLSGEPIDEPIVGYGPFVMNTQAQIAEAIADFNGGRFGNMDVA
3QXF , Knot 155 355 0.85 40 220 339 
ACTWPAWEQFKKDYISQEGRVIDPSDARKITTSEGQSYGMFSALAANDRAAFDNILDWTQNNLAQGSLKERLPAWLWGKKENSKWEVLDSNSASDGDVWMAWSLLEAGRLWKEQRYTDIGSALLKRIAREEVVTVPGLGSMLLPGKVGFAEDNSWRFNPSYLPPTLAQYFTRFGAPWTTLRETNQRLLLETAPKGFSPDWVRYEKDKGWQLKAEKTLISSYDAIRVYMWVGMMPDSDPQKARMLNRFKPMATFTEKNGYPPEKVDVATGKAQGKGPVGFSAAMLPFLQNRDAQAVQRQRVADNFPGSDAYYNYVLTLFGQGWDQHRFRFSTKGELLPDWGQECANSHLEHHHHHH

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 \(c\).

\(|P_{f(6JDZ_1)}(2) \setminus P_{f(7TFQ_1)}(2)|=89\), \(|P_{f(7TFQ_1)}(2) \setminus P_{f(6JDZ_1)}(2)|=85\). 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 1:1110011010110011010001010001011010000011010110010101001000010110101110110001011000011100011011001010010111110001001100001000110110011000101000110011111011111101111010101000000100011010110011011010110101111010111100100001001101001111011000101010110011011000001011111010001011101101000001110110101111110000100110011111111
Pair \(Z_2\) Length of longest common subsequence
6JDZ_1,7TFQ_1 174 4
6JDZ_1,3QXF_1 174 3
7TFQ_1,3QXF_1 170 4

Newick tree

 
[
	6JDZ_1:87.65,
	[
		7TFQ_1:85,3QXF_1:85
	]:2.65
]

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 \((0.85)(0.8)(\frac{611 }{\log_{20} 611}-\frac{292}{\log_{20}292})=89.2\)
Status Protein1 Protein2 d d1/2
Query variables 6JDZ_1 7TFQ_1 112 107
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]