CoV2D BrowserTM

CoV2D project home | Random page
Parikh vectors
2IMG_1 4BPY_1 4URN_1 Letter Amino acid
19 15 17 L Leucine
7 5 8 F Phenylalanine
8 7 16 E Glutamic acid
5 2 9 H Histidine
13 13 5 P Proline
4 6 8 Y Tyrosine
10 13 17 V Valine
14 14 7 A Alanine
4 1 0 C Cysteine
6 9 13 I Isoleucine
3 17 20 K Lycine
1 1 4 M Methionine
6 6 19 S Serine
14 4 8 R Arginine
7 9 6 Q Glutamine
14 14 27 G Glycine
6 17 13 T Threonine
1 1 1 W Tryptophan
2 3 14 N Asparagine
7 18 13 D Aspartic acid 

2IMG_1|Chain A|Dual specificity protein phosphatase 23|Homo sapiens (9606)
>4BPY_1|Chain A|SCO PROTEIN|STREPTOMYCES LIVIDANS (1916)
>4URN_1|Chains A, B, C|DNA TOPOISOMERASE IV, B SUBUNIT|STAPHYLOCOCCUS AUREUS (1280)
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 \(w=f(c)\)
2IMG , Knot 73 151 0.80 40 112 145 
SLGVQPPNFSWVLPGRLAGLALPRLPAHYQFLLDLGVRHLVSLTERGPPHSDSCPGLTLHRLRIPDFCPPAPDQIDRFVQIVDEANARGEAVGVHCALGFGRTGTMLACYLVKERGLAAGDAIAEIRRLRPGSIETYEQEKAVFQFYQRTK
4BPY , Knot 80 175 0.78 40 120 169 
QAATVLDKPFEKPDLVLTDTQGKKYDLREQTAGKPTLIYFGYTHCPDVAPLTMNNIAVAKKQLSQAEQDKLRVVFVSTDPERDTPAALGKWLKGIDPQIVGLTGEFDTIQAGARTLGISIDPPTKDKDGKIVSTHGTQVVAFSPKSDAGYVLYGEDATVDDYTKDLPKLIKGENP
4URN , Knot 105 225 0.84 38 153 220 
MAMNKQNNYSDDSIQVLEGLEAVRKRPGMYIGSTDKRGLHHLVYEIVDNSVDEVLNGYGNEIDVTINKDGSISIEDNGRGMPTGIHKSGKPTVEVIFTVLHAGGKFGQGGYKTSGGLHGVGASVVNALSEWLEVEIHRDGNIYHQSFKNGGSPSSGLVKKGKTKKTGTKVTFKPDDTIFKASTSFNFDVLSERLQESAFLLKNLKITLNDLRSGKERQEHYHYEE

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 \(c\).

\(|P_{f(2IMG_1)}(2) \setminus P_{f(4BPY_1)}(2)|=67\), \(|P_{f(4BPY_1)}(2) \setminus P_{f(2IMG_1)}(2)|=75\). 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 1:0111011010111110111111101110001110111001101000111000001110100101101011110010011011001010101111001111100101110011000111110111010010110100000001110100000
Pair \(Z_2\) Length of longest common subsequence
2IMG_1,4BPY_1 142 3
2IMG_1,4URN_1 171 3
4BPY_1,4URN_1 151 4

Newick tree

 
[
	4URN_1:83.62,
	[
		2IMG_1:71,4BPY_1:71
	]:12.62
]

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 \((0.85)(0.8)(\frac{326 }{\log_{20} 326}-\frac{151}{\log_{20}151})=53.4\)
Status Protein1 Protein2 d d1/2
Query variables 2IMG_1 4BPY_1 69 63.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]