CoV2D BrowserTM

CoV2D project home | Random page
Parikh vectors
1YZF_1 3PUP_1 3BZN_1 Letter Amino acid
13 22 25 D Aspartic acid
0 9 6 C Cysteine
17 19 25 E Glutamic acid
12 23 14 K Lycine
19 29 19 V Valine
5 18 32 Q Glutamine
6 18 15 F Phenylalanine
10 31 20 P Proline
10 30 25 T Threonine
17 34 46 A Alanine
11 27 34 R Arginine
6 17 15 N Asparagine
3 7 11 H Histidine
15 20 18 I Isoleucine
15 22 22 G Glycine
20 37 57 L Leucine
5 5 7 M Methionine
6 32 22 S Serine
0 2 11 W Tryptophan
5 18 7 Y Tyrosine 

1YZF_1|Chain A|lipase/acylhydrolase|Enterococcus faecalis (226185)
>3PUP_1|Chains A, B|Glycogen synthase kinase-3 beta|Homo sapiens (9606)
>3BZN_1|Chain A|Menaquinone-specific isochorismate synthase|Escherichia coli (562)
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 \(w=f(c)\)
1YZF , Knot 92 195 0.83 36 138 191 
MRKIVLFGDSITAGYLDEAVSPVLVDLVKRDIAAMGLEEVAVINAGMPGDTTEDGLKRLNKEVLIEKPDEVVIFFGANDASLDRNITVATFRENLETMIHEIGSEKVILITPPYADSGRRPERPQTRIKELVKVAQEVGAAHNLPVIDLYKAMTVYPGTDEFLQADGLHFSQVGYELLGALIVREIKGRLKPKQA
3PUP , Knot 175 420 0.84 40 230 394 
MSGRPRTTSFAESCKPVQQPSAFGSMKVSRDKDGSKVTTVVATPGQGPDRPQEVSYTDTKVIGNGSFGVVYQAKLCDSGELVAIKKVLQDKRFKNRELQIMRKLDHCNIVRLRYFFYSSGEKKDEVYLNLVLDYVPETVYRVARHYSRAKQTLPVIYVKLYMYQLFRSLAYIHSFGICHRDIKPQNLLLDPDTAVLKLCDFGSAKQLVRGEPNVSYICSRYYRAPELIFGATDYTSSIDVWSAGCVLAELLLGQPIFPGDSGVDQLVEIIKVLGTPTREQIREMNPNYTEFKFPQIKAHPWTKVFRPRTPPEAIALCSRLLEYTPTARLTPLEACAHSFFDELRDPNVKLPNGRDTPALFNFTTQELSSNPPLATILIPPHARIQAAASTPTNATAASDANTGDRGQTNNAASASASNST
3BZN , Knot 180 431 0.84 40 219 405 
MQSLTTALENLLRHLSQEIPATPGIRVIDIPFPLKDAFDALSWLASQQTYPQFYWQQRNGDEEAVVLGAITRFTSLDQAQRFLRQHPEHADLRIWGLNAFDPSQGNLLLPRLEWRRCGGKATLRLTLFSESSLQHDAIQAKEFIATLVSIKPLPGLHLTTTREQHWPDKTGWTQLIELATKTIAEGELDKVVLARATDLHFASPVNAAAMMAASRRLNLNCYHFYMAFDGENAFLGSSPERLWRRRDKALRTEALAGTVANNPDDKQAQQLGEWLMADDKNQRENMLVVEDICQRLQADTQTLDVLPPQVLRLRKVQHLRRCIWTSLNKADDVICLHQLQPTAAVAGLPRDLARQFIARHEPFTREWYAGSAGYLSLQQSEFCVSLRSAKISGNVVRLYAGAGIVRGSDPEQEWQEIDNKAAGLRTLLQME

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 \(c\).

\(|P_{f(1YZF_1)}(2) \setminus P_{f(3PUP_1)}(2)|=44\), \(|P_{f(3PUP_1)}(2) \setminus P_{f(1YZF_1)}(2)|=136\). 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 1:100111110010110100110111101100011111100111101111100000110010001110010011111110010100010110100010011001100011110110100100100100010011011001111001111010011010110001101011010011001111111001010101001
Pair \(Z_2\) Length of longest common subsequence
1YZF_1,3PUP_1 180 4
1YZF_1,3BZN_1 155 4
3PUP_1,3BZN_1 169 4

Newick tree

 
[
	3PUP_1:90.32,
	[
		1YZF_1:77.5,3BZN_1:77.5
	]:12.82
]

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 \((0.85)(0.8)(\frac{615 }{\log_{20} 615}-\frac{195}{\log_{20}195})=119.\)
Status Protein1 Protein2 d d1/2
Query variables 1YZF_1 3PUP_1 150 108.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]