CoV2D BrowserTM

CoV2D project home | Random page
Parikh vectors
3TWY_1 4QKI_1 8XNR_1 Letter Amino acid
8 4 4 N Asparagine
10 8 2 D Aspartic acid
0 6 1 C Cysteine
6 11 3 G Glycine
4 7 9 F Phenylalanine
7 2 4 V Valine
13 7 22 L Leucine
3 8 8 A Alanine
11 7 6 E Glutamic acid
1 10 0 H Histidine
15 8 4 K Lycine
4 0 6 M Methionine
10 12 7 S Serine
8 7 1 R Arginine
3 9 3 Q Glutamine
6 7 11 I Isoleucine
10 4 6 P Proline
9 7 10 T Threonine
4 7 4 W Tryptophan
5 4 4 Y Tyrosine 

3TWY_1|Chain A|Protein kinase C alpha type|Rattus norvegicus (10116)
>4QKI_1|Chains A, B|C-type lectin domain family 2 member D|Homo sapiens (9606)
>8XNR_1|Chain A|NADH-ubiquinone oxidoreductase chain 3|Mus musculus (10090)
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 \(w=f(c)\)
3TWY , Knot 68 137 0.81 38 112 132 
TEKRGRIYLKAEVTDEKLHVTVRDAKNLIPMDPNGLSDPYVKLKLIPDPKNESKQKTKTIRSTLNPQWNESFTFKLKPSDKDRRLSVEIWDWDRTTRNDFMGSLSFGVSELMKMPASGWYKLLNQEEGEYYNVPIPE
4QKI , Knot 65 135 0.78 38 107 126 
ITGQAACPESWIGFQRKCFYFSDDTKNWTSSQRFCDSQDADLAQVESFQELNFLLRYKGPSDHWIGLSREQGQPWKWINGTEWTRQFPILGAGECAYLNDKGASSARCYTERKWICSKSDIHVGTKHHHHHHHHG
8XNR , Knot 57 115 0.78 38 85 107 
MNLYTVIFINILLSLTLILVAFWLPQMNLYSEKANPYECGFDPTSSARLPFSMKFFLVAITFLLFDLEIALLLPLPWAIQTIKTSTMMIMAFILVTILSLGLAYEWTQKGLEWTE

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 \(c\).

\(|P_{f(3TWY_1)}(2) \setminus P_{f(4QKI_1)}(2)|=85\), \(|P_{f(4QKI_1)}(2) \setminus P_{f(3TWY_1)}(2)|=80\). 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 1:00001010101010000101010010011110101100101010111010000000000100010101000101010100000010101101000000011101011100110111011001100001000011110
Pair \(Z_2\) Length of longest common subsequence
3TWY_1,4QKI_1 165 3
3TWY_1,8XNR_1 147 2
4QKI_1,8XNR_1 144 4

Newick tree

 
[
	3TWY_1:80.06,
	[
		8XNR_1:72,4QKI_1:72
	]:8.06
]

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 \((0.85)(0.8)(\frac{272 }{\log_{20} 272}-\frac{135}{\log_{20}135})=42.7\)
Status Protein1 Protein2 d d1/2
Query variables 3TWY_1 4QKI_1 58 55.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]