CoV2D BrowserTM

CoV2D project home | Random page
Parikh vectors
5VIZ_1 1VIF_1 8SJI_1 Letter Amino acid
4 1 0 C Cysteine
2 7 2 G Glycine
2 2 14 L Leucine
0 1 3 M Methionine
2 4 3 S Serine
1 6 4 V Valine
1 3 5 N Asparagine
0 1 2 H Histidine
2 3 4 I Isoleucine
0 2 8 K Lycine
0 2 2 F Phenylalanine
2 3 4 Y Tyrosine
0 1 6 D Aspartic acid
2 3 7 Q Glutamine
0 4 3 P Proline
1 3 8 T Threonine
0 2 2 W Tryptophan
0 7 25 A Alanine
0 3 2 R Arginine
2 4 10 E Glutamic acid 

5VIZ_1|Chain A|Insulin, chain beta|Homo sapiens (9606)
>1VIF_1|Chain A|DIHYDROFOLATE REDUCTASE|Escherichia coli (562)
>8SJI_1|Chains A, B, C|Topoisomerase 1|synthetic construct (32630)
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 \(w=f(c)\)
5VIZ , Knot 15 21 0.72 22 20 19 
GIVEQCCTSICSLYQLENYCG
1VIF , Knot 38 62 0.84 40 59 60 
VFPSNATFGMGDRVRKKSGAAWQGQIVGWYCTNLTPEGYAVESEAHPGSVQIYPVAALERIN
8SJI , Knot 56 114 0.77 38 85 105 
QDWEDAMETLNDNLKVIEKADNADQVIAALLYMLAAAIAAATATPPKLEDKSPTSEEALAFRLGMHELAALITKATALAYQGLVKEAQAAAEQLKTTVNAHWQKYRSAENLYFQ

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 \(c\).

\(|P_{f(5VIZ_1)}(2) \setminus P_{f(1VIF_1)}(2)|=15\), \(|P_{f(1VIF_1)}(2) \setminus P_{f(5VIZ_1)}(2)|=54\). 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 1:111000000100100100001
Pair \(Z_2\) Length of longest common subsequence
5VIZ_1,1VIF_1 69 2
5VIZ_1,8SJI_1 91 2
1VIF_1,8SJI_1 116 3

Newick tree

 
[
	8SJI_1:56.79,
	[
		5VIZ_1:34.5,1VIF_1:34.5
	]:22.29
]

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 \((0.85)(0.8)(\frac{83 }{\log_{20} 83}-\frac{21}{\log_{20}21})=24.2\)
Status Protein1 Protein2 d d1/2
Query variables 5VIZ_1 1VIF_1 32 20.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

Graphviz Engine:
Graphviz Engine: