CoV2D BrowserTM

CoV2D project home | Random page
Parikh vectors
1WJW_1 1NKR_1 6RAT_1 Letter Amino acid
0 2 0 W Tryptophan
11 13 9 V Valine
12 10 12 A Alanine
6 5 7 Q Glutamine
5 6 3 I Isoleucine
12 24 15 S Serine
5 11 10 T Threonine
9 10 4 R Arginine
0 12 4 H Histidine
7 15 4 P Proline
0 4 8 C Cysteine
4 6 10 K Lycine
0 5 4 M Methionine
2 8 3 F Phenylalanine
3 4 10 N Asparagine
6 10 5 D Aspartic acid
7 12 5 E Glutamic acid
10 17 3 G Glycine
9 19 2 L Leucine
4 8 6 Y Tyrosine 

1WJW_1|Chain A|Phosphoacetylglucosamine mutase|Mus musculus (10090)
>1NKR_1|Chain A|P58-CL42 KIR|Homo sapiens (9606)
>6RAT_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 \(w=f(c)\)
1WJW , Knot 55 112 0.77 32 84 105 
GSSGSSGAIYVDLPNRQLKVKVADRRVISTTDAERQAVTPPGLQEAINDLVKKYTLARAFVRPSGTEDIVRVYAEANSQESADRLAYEVSLLVFQLAGGIGERPQPSGPSSG
1NKR , Knot 93 201 0.81 40 136 187 
MHEGVHRKPSLLAHPGPLVKSEETVILQCWSDVMFEHFLLHREGMFNDTLRLIGEHHDGVSKANFSISRMTQDLAGTYRCYGSVTHSPYQVSAPSDPLDIVIIGLYEKPSLSAQPGPTVLAGENVTLSCSSRSSYDMYHLSREGEAHERRLPAGPKVNGTFQADFPLGPATHGGTYRCFGSFHDSPYEWSKSSDPLLVSVT
6RAT , Knot 64 124 0.83 38 107 121 
KETAAAKFERQHMDSSTSAASSSNYCNQMMKSRNLTKDRCKPVNTFVHESLADVQAVCSQKNVACKNGQTNCYQSYSTMSITDCRETGSSKYPNCAYKTTQANKHIIVACEGNPYVPVHFDASV

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 \(c\).

\(|P_{f(1WJW_1)}(2) \setminus P_{f(1NKR_1)}(2)|=45\), \(|P_{f(1NKR_1)}(2) \setminus P_{f(1WJW_1)}(2)|=97\). 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 1:1001001110101100010101100011000010001101111001100110000110111010100011010101000001001100101111011111100101011001
Pair \(Z_2\) Length of longest common subsequence
1WJW_1,1NKR_1 142 3
1WJW_1,6RAT_1 141 3
1NKR_1,6RAT_1 169 2

Newick tree

 
[
	1NKR_1:80.39,
	[
		1WJW_1:70.5,6RAT_1:70.5
	]:9.89
]

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 \((0.85)(0.8)(\frac{313 }{\log_{20} 313}-\frac{112}{\log_{20}112})=62.6\)
Status Protein1 Protein2 d d1/2
Query variables 1WJW_1 1NKR_1 79 60
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]