CoV2D BrowserTM

CoV2D project home | Random page
Parikh vectors
8BLM_1 3KYN_1 8HPU_1 Letter Amino acid
24 25 14 A Alanine
18 18 14 G Glycine
13 17 9 D Aspartic acid
13 15 5 Q Glutamine
9 26 5 E Glutamic acid
20 19 12 L Leucine
4 8 0 M Methionine
18 17 8 T Threonine
16 14 17 V Valine
16 7 15 F Phenylalanine
14 14 12 P Proline
6 14 15 Y Tyrosine
9 24 10 R Arginine
8 6 18 N Asparagine
2 5 8 C Cysteine
4 9 2 H Histidine
12 6 7 I Isoleucine
8 8 9 K Lycine
12 14 12 S Serine
4 9 2 W Tryptophan 

8BLM_1|Chains A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P|Ureidoacrylate amidohydrolase RutB|Escherichia coli (strain K12) (83333)
>3KYN_1|Chain A|MHC class I antigen|Homo sapiens (9606)
>8HPU_1|Chain A|Spike protein S2'|Severe acute respiratory syndrome coronavirus 2 (2697049)
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 \(w=f(c)\)
8BLM , Knot 108 230 0.85 40 163 226 
MTTLTARPEAITFDPQQSALIVVDMQNAYATPGGYLDLAGFDVSTTRPVIANIQTAVTAARAAGMLIIWFQNGWDEQYVEAGGPGSPNFHKSNALKTMRKQPQLQGKLLAKGSWDYQLVDELVPQPGDIVLPKPRYSGFFNTPLDSILRSRGIRHLVFTGIATNVCVESTLRDGFFLEYFGVVLEDATHQAGPKFAQKAALFNIETFFGWVSDVETFCDALSPTSFAHIA
3KYN , Knot 125 275 0.85 40 190 265 
MSHSMRYFSAAVSRPGRGEPRFIAMGYVDDTQFVRFDSDSASPRMEPRAPWVEQEGPEYWEEETRNTKAHAQTDRMNLQTLRGYYNQSEASSHTLQWMIGCDLGSDGRLIRGYERYAYDGKDYLALNEDLRSWTAADTAAQISKRKCEAANVAEQRRAYLEGTCVEWLHRYLENGKEMLQRADPPKTHVTHHPVFDYEATLRCWALGFYPAEIILTWQRDGEDQTQDVELVETRPAGDGTFQKWAAVVVPSGEEQRYTCHVQHEGLPEPLMLRWK
8HPU , Knot 91 194 0.82 38 134 187 
NLCPFDEVFNATRFASVYAWNRKRISNCVADYSVLYNFAPFFAFKCYGVSPTKLNDLCFTNVYADSFVIRGNEVSQIAPGQTGNIADYNYKLPDDFTGCVIAWNSNKLDSKVGGNYNYRYRLFRKSNLKPFERDISTEIYQAGNKPCNGVAGVNCYFPLQSYGFRPTYGVGHQPYRVVVLSFELLHAPATVCGP

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 \(c\).

\(|P_{f(8BLM_1)}(2) \setminus P_{f(3KYN_1)}(2)|=74\), \(|P_{f(3KYN_1)}(2) \setminus P_{f(8BLM_1)}(2)|=101\). 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 1:10010101011010100011111010010101110101111010000111101001101101111111110011000010111110101000011001000101010111010100011001110110111101000111001100110001100111011100101000100111100111110010001110110011110100111110010010011010011011
Pair \(Z_2\) Length of longest common subsequence
8BLM_1,3KYN_1 175 3
8BLM_1,8HPU_1 167 3
3KYN_1,8HPU_1 212 3

Newick tree

 
[
	3KYN_1:10.34,
	[
		8BLM_1:83.5,8HPU_1:83.5
	]:17.84
]

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 \((0.85)(0.8)(\frac{505 }{\log_{20} 505}-\frac{230}{\log_{20}230})=79.1\)
Status Protein1 Protein2 d d1/2
Query variables 8BLM_1 3KYN_1 103 93.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]