CoV2D BrowserTM

CoV2D project home | Random page
Parikh vectors
1QXE_1 6ECR_1 3WQL_1 Letter Amino acid
10 6 9 H Histidine
0 23 16 I Isoleucine
2 7 6 M Methionine
8 16 21 D Aspartic acid
3 12 21 R Arginine
1 5 4 C Cysteine
4 22 19 E Glutamic acid
18 24 26 L Leucine
3 4 16 Y Tyrosine
21 24 18 A Alanine
9 20 14 T Threonine
1 2 3 W Tryptophan
13 28 20 V Valine
4 16 8 N Asparagine
7 23 19 G Glycine
11 21 11 K Lycine
7 5 21 F Phenylalanine
7 17 13 P Proline
11 13 22 S Serine
1 8 9 Q Glutamine 

1QXE_1|Chains A, C|Hemoglobin alpha chain|Homo sapiens (9606)
>6ECR_1|Chains A, B|methylenetetrahydrofolate dehydrogenase cyclohydrolase|Homo sapiens (9606)
>3WQL_1|Chains A, B, C, D|Diterpene synthase|Mycobacterium tuberculosis (1773)
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 \(w=f(c)\)
1QXE , Knot 69 141 0.80 38 99 137 
VLSPADKTNVKAAWGKVGAHAGEYGAEALERMFLSFPTTKTYFPHFDLSHGSAQVKGHGKKVADALTNAVAHVDDMPNALSALSDLHAHKLRVDPVNFKLLSHCLLVTLAAHLPAEFTPAVHASLDKFLASVSTVLTSKYR
6ECR , Knot 128 296 0.82 40 185 286 
MAPAEILNGKEISAQIRARLKNQVTQLKEQVPGFTPRLAILQVGNRDDSNLYINVKLKAAEEIGIKATHIKLPRTTTESEVMKYITSLNEDSTVHGFLVQLPLDSENSINTEEVINAIAPEKDVDGLTSINAGRLARGDLNDCFIPCTPKGCLELIKETGVPIAGRHAVVVGRSKIVGAPMHDLLLWNNATVTTCHSKTAHLDEEVNKGDILVVATGQPEMVKGEWIKPGAIVIDCGINYVPDDKKPNGRKVVGDVAYDEAKERASFITPVPGGVGPMTVAMLMQSTVESAKRFLE
3WQL , Knot 130 296 0.83 40 198 286 
MNLVSEKEFLDLPLVSVAEIVRCRGPKVSVFPFDGTRRWFHLECNPQYDDYQQAALRQSIRILKMLFEHGIETVISPIFSDDLLDRGDRYIVQALEGMALLANDEEILSFYKEHEVHVLFYGDYKKRLPSTAQGAAVVKSFDDLTISTSSNTEHRLCFGVFGNDAAESVAQFSISWNETHGKPPTRREIIEGYYGEYVDKADMFIGFGRFSTFDFPLLSSGKTSLYFTVAPSYYMTETTLRRILYDHIYLRHFRPKPDYSAMSADQLNVLRNRYRAQPDRVFGVGCVHDGIWFAEG

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 \(c\).

\(|P_{f(1QXE_1)}(2) \setminus P_{f(6ECR_1)}(2)|=42\), \(|P_{f(6ECR_1)}(2) \setminus P_{f(1QXE_1)}(2)|=128\). 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 1:110110000101111011101100110110011101100000110101001010101010011011001110100110110110010100101011010110001110111011101011101010011101001100000
Pair \(Z_2\) Length of longest common subsequence
1QXE_1,6ECR_1 170 3
1QXE_1,3WQL_1 173 3
6ECR_1,3WQL_1 175 3

Newick tree

 
[
	3WQL_1:87.65,
	[
		1QXE_1:85,6ECR_1:85
	]:2.65
]

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 \((0.85)(0.8)(\frac{437 }{\log_{20} 437}-\frac{141}{\log_{20}141})=88.3\)
Status Protein1 Protein2 d d1/2
Query variables 1QXE_1 6ECR_1 110 81
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]