CoV2D BrowserTM

CoV2D project home | Random page
Parikh vectors
1JKM_1 8OTH_1 1DUZ_1 Letter Amino acid
4 6 5 M Methionine
46 34 24 A Alanine
11 12 13 H Histidine
13 15 4 I Isoleucine
35 21 17 L Leucine
22 43 11 P Proline
20 35 23 T Threonine
9 5 14 Y Tyrosine
30 29 18 D Aspartic acid
2 2 4 C Cysteine
2 19 17 Q Glutamine
37 49 20 G Glycine
1 44 10 K Lycine
6 0 10 W Tryptophan
27 14 23 R Arginine
8 11 2 N Asparagine
22 27 22 E Glutamic acid
12 3 8 F Phenylalanine
18 45 14 S Serine
36 27 16 V Valine 

1JKM_1|Chains A, B|BREFELDIN A ESTERASE|Bacillus subtilis (1423)
>8OTH_1|Chains A, B, C, D, E|Microtubule-associated protein tau|Homo sapiens (9606)
>1DUZ_1|Chains A, D|HLA-A*0201|Homo sapiens (9606)
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 \(w=f(c)\)
1JKM , Knot 149 361 0.81 40 180 338 
YTPPGRLGDESSGPRTDPRFSPAMVEALATFGLDAVAAAPPVSASDDLPTVLAAVGASHDGFQAVYDSIALDLPTDRDDVETSTETILGVDGNEITLHVFRPAGVEGVLPGLVYTHGGGMTILTTDNRVHRRWCTDLAAAGSVVVMVDFRNAWTAEGHHPFPSGVEDCLAAVLWVDEHRESLGLSGVVVQGESGGGNLAIATTLLAKRRGRLDAIDGVYASIPYISGGYAWDHERRLTELPSLVENDGYFIENGGMALLVRAYDPTGEHAEDPIAWPYFASEDELRGLPPFVVAVNELDPLRDEGIAFARRLARAGVDVAARVNIGLVHGADVIFRHWLPAALESTVRDVAGFAADRARLR
8OTH , Knot 167 441 0.76 38 190 383 
MAEPRQEFEVMEDHAGTYGLGDRKDQGGYTMHQDQEGDTDAGLKESPLQTPTEDGSEEPGSETSDAKSTPTAEDVTAPLVDEGAPGKQAAAQPHTEIPEGTTAEEAGIGDTPSLEDEAAGHVTQARMVSKSKDGTGSDDKKAKGADGKTKIATPRGAAPPGQKGQANATRIPAKTPPAPKTPPSSGEPPKSGDRSGYSSPGSPGTPGSRSRTPSLPTPPTREPKKVAVVRTPPKSPSSAKSRLQTAPVPMPDLKNVKSKIGSTENLKHQPGGGKVQIINKKLDLSNVQSKCGSKDNIKHVPGGGSVQIVYKPVDLSKVTSKCGSLGNIHHKPGGGQVEVKSEKLDFKDRVQSKIGSLDNITHVPGGGNKKIETHKLTFRENAKAKTDHGAEIVYKSPVVSGDTSPRHLSNVSSTGSIDMVDSPQLATLADEVSASLAKQGL
1DUZ , Knot 122 275 0.83 40 182 263 
GSHSMRYFFTSVSRPGRGEPRFIAVGYVDDTQFVRFDSDAASQRMEPRAPWIEQEGPEYWDGETRKVKAHSQTHRVDLGTLRGYYNQSEAGSHTVQRMYGCDVGSDWRFLRGYHQYAYDGKDYIALKEDLRSWTAADMAAQTTKHKWEAAHVAEQLRAYLEGTCVEWLRRYLENGKETLQRTDAPKTHMTHHAVSDHEATLRCWALSFYPAEITLTWQRDGEDQTQDTELVETRPAGDGTFQKWAAVVVPSGQEQRYTCHVQHEGLPKPLTLRWE

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 \(c\).

\(|P_{f(1JKM_1)}(2) \setminus P_{f(8OTH_1)}(2)|=72\), \(|P_{f(8OTH_1)}(2) \setminus P_{f(1JKM_1)}(2)|=82\). 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 1:0011101100001100010101111011101110111111110100011011111110001101100011101100000100000011110100101011011110111111100011110110000010001000111110111110100110101001110110001111111000000111011110100111011110011100010101101101011010110110000010011011000101100111111101001010010011111011000010111111111001011000111110011011101110101111011011100111111000100111111001010
Pair \(Z_2\) Length of longest common subsequence
1JKM_1,8OTH_1 154 4
1JKM_1,1DUZ_1 170 4
8OTH_1,1DUZ_1 160 4

Newick tree

 
[
	1DUZ_1:84.30,
	[
		1JKM_1:77,8OTH_1:77
	]:7.30
]

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 \((0.85)(0.8)(\frac{802 }{\log_{20} 802}-\frac{361}{\log_{20}361})=119.\)
Status Protein1 Protein2 d d1/2
Query variables 1JKM_1 8OTH_1 143 131.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]