CoV2D BrowserTM

CoV2D project home | Random page
Parikh vectors
8QTC_1 1BZJ_1 8VCH_1 Letter Amino acid
7 10 14 M Methionine
4 12 30 P Proline
18 24 43 S Serine
10 13 30 T Threonine
2 6 8 C Cysteine
7 14 40 F Phenylalanine
2 6 5 W Tryptophan
4 9 9 H Histidine
8 10 18 N Asparagine
17 18 24 D Aspartic acid
7 14 22 Q Glutamine
11 14 36 G Glycine
25 27 41 L Leucine
11 9 19 Y Tyrosine
15 17 28 R Arginine
26 27 44 E Glutamic acid
14 16 41 I Isoleucine
14 22 18 K Lycine
10 16 34 V Valine
28 13 32 A Alanine 

8QTC_1|Chains A, C[auth B]|14-3-3-like protein GF14 omega|Arabidopsis thaliana (3702)
>1BZJ_1|Chain A|PROTEIN (PROTEIN-TYROSINE-PHOSPHATASE)|Homo sapiens (9606)
>8VCH_1|Chains A, B, C, D|Potassium voltage-gated channel subfamily A member 2|Rattus norvegicus (10116)
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 \(w=f(c)\)
8QTC , Knot 108 240 0.82 40 158 232 
MASGREEFVYMAKLAEQAERYEEMVEFMEKVSAAVDGDELTVEERNLLSVAYKNVIGARRASWRIISSIEQKEESRGNDDHVTAIREYRSKIETELSGICDGILKLLDSRLIPAAASGDSKVFYLKMKGDYHRYLAEFKTGQERKDAAEHTLAAYKSAQDIANAELAPTHPIRLGLALNFSVFYYEILNSPDRACNLAKQAFDEAIAELDTLGEESYKDSTLIMQLLRDNLTLWTSDMQD
1BZJ , Knot 132 297 0.84 40 198 289 
EMEKEFEQIDKSGSWAAIYQDIRHEASDFPCRVAKLPKNKNRNRYRDVSPFDHSRIKLHQEDNDYINASLIKMEEAQRSYILTQGPLPNTCGHFWEMVWEQKSRGVVMLNRVMEKGSLKCAQYWPQKEEKEMIFEDTNLKLTLISEDIKSYYTVRQLELENLTTQETREILHFHYTTWPDFGVPESPASFLNFLFKVRESGSLSPEHGPVVVHCSAGIGRSGTFCLADTCLLLMDKRKDPSSVDIKKVLLEMRKFRMGLIQTADQLRFSYLAVIEGAKFIMGDSSVQDQWKELSHED
8VCH , Knot 214 536 0.83 40 260 497 
MSAWSHPQFEKGGGSGGGSGGSAWSHPQFEKLVPRGSMTVATGDPVDEAAAHPGHPQDTYDPEADHECCERVVINISGLRFETQLKTLAQFPETLLGDPKKRMRYFDPLRNEYFFDRNRPSFDAILYYYQSGGRLRRPVNVPLDIFSEEIRFYELGEEAMEMFREDEGYIKEEERPLPENEFQRQVWLLFEYPESSGPARIIAIVSVMVILISIVSFCLETLPIFRDENEDMHGSGVTFHTYSQSTIGYQQSTSFTDPFFIVETLCIIWFSFEFLVRFFACPSKAGFFTNIMNIIDIVAIIPYFITLGTELAEKPEDAQQGQQAMSLAILRVIRLVRVFRIFKLSRHSKGLQILGQTLKASMRELGLLIFFLFIGVILFSSAVYFAEADERDSQFPSIPDAFFWAVVSMTTVGYGDMVPTTIGGKIVGSLCAIAGVLTIALPVPVIVSNFNYFYHRETEGEEQAQYLQVTSCPKIPSSPDLKKSRSASTISKSDYMEIQEGVNNSNEDFREENLKTANCTLANTNYVNITKMLTDV

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 \(c\).

\(|P_{f(8QTC_1)}(2) \setminus P_{f(1BZJ_1)}(2)|=66\), \(|P_{f(1BZJ_1)}(2) \setminus P_{f(8QTC_1)}(2)|=106\). 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 1:110100011011011001000001101100101110100101000011011000111100101011001000000010000101100000010001011001110110001111110100011010101000001101001000001100011100010011010111001101111101011000110010010011001100111010011000000001110110001011000100
Pair \(Z_2\) Length of longest common subsequence
8QTC_1,1BZJ_1 172 4
8QTC_1,8VCH_1 178 4
1BZJ_1,8VCH_1 160 3

Newick tree

 
[
	8QTC_1:89.87,
	[
		1BZJ_1:80,8VCH_1:80
	]:9.87
]

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 \((0.85)(0.8)(\frac{537 }{\log_{20} 537}-\frac{240}{\log_{20}240})=84.8\)
Status Protein1 Protein2 d d1/2
Query variables 8QTC_1 1BZJ_1 106 95.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]