CoV2D BrowserTM

CoV2D project home | Random page
Parikh vectors
4UVG_1 7LJI_1 6GJU_1 Letter Amino acid
20 25 17 I Isoleucine
10 15 8 M Methionine
13 23 7 P Proline
28 48 22 G Glycine
13 22 9 R Arginine
8 8 12 N Asparagine
5 12 3 H Histidine
27 24 28 L Leucine
16 29 24 S Serine
36 51 12 A Alanine
11 23 22 E Glutamic acid
13 25 15 T Threonine
6 12 8 Y Tyrosine
15 25 12 D Aspartic acid
10 8 7 Q Glutamine
9 30 21 K Lycine
7 10 16 F Phenylalanine
4 1 2 W Tryptophan
17 34 12 V Valine
1 0 4 C Cysteine 

4UVG_1|Chain A|ENOYL-[ACYL-CARRIER-PROTEIN] REDUCTASE [NADH]|MYCOBACTERIUM TUBERCULOSIS (83332)
>7LJI_1|Chains A, B|Poly(Aspartic acid) hydrolase|Sphingomonas sp. KT-1 (88363)
>6GJU_1|Chain A|Cystic fibrosis transmembrane conductance regulator|Homo sapiens (9606)
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 \(w=f(c)\)
4UVG , Knot 115 269 0.79 40 167 253 
MTGLLDGKRILVSGIITDSSIAFHIARVAQEQGAQLVLTGFDRLRLIQRITDRLPAKAPLLELDVQNEEHLASLAGRVTEAIGAGNKLDGVVHSIGFMPQTGMGINPFFDAPYADVSKGIHISAYSYASMAKALLPIMNPGGSIVGMDFDPSRAMPAYNWMTVAKSALESVNRFVAREAGKYGVRSNLVAAGPIRTLAMSAIVGGALGEEAGAQIQLLEEGWDQRAPIGWNMKDATPVAKTVCALLSDWLPATTGDIIYADGGAHTQLL
7LJI , Knot 175 425 0.83 38 205 393 
MGSSHHHHHHSSGLVPRGSHMAPKAKPEAVLKTKGYEAAVKILDRDHDRMVDEIIKLTEIPAPPFKEAARAAAYAEMLKDAGLQDVEIDAEGNAMGVYRGTGPAGGPAVMIAAHLDTVFPEGTPIKVRRDGTKLHAPGIGDDTRSLAVLLAYARAMKESGIKVKQDIIFVGNVGEEGSGDLRGVRYLLTKGKYKDRVKSFFSMDGTDASRIVTGGVGSKRYRITYKGPGGHSYGAFGLVNPMVAMSQTVVDFYKIPAPAKPKTTYAASVTGGGTSVNSIPNEVYMEFDMRSESPAELAKVEQAFLAIVQKSVEGENAARSVKEGPITADVKMIGDRPAGETAATQQIVRNADAVIRAKGLDPRPSFSSTDSNMAMSLGIPAVTIGSGGIGARAHSLDEWIDVKKTKSLEGATVGLGILLATAGTQ
6GJU , Knot 117 261 0.83 40 169 253 
SLTTTEVVMENVTAFWEEGFGELFEKAKQNNNNRKTSNGDDSLFFSNFSLLGTPVLKDINFKIERGQLLAVAGSTGAGKTSLLMMIMGELEPSEGKIKHSGRISFCPQFSWIMPGTIKENIIFGVSYDEYRYRSVIKACQLEEDISKFPEKDNTVLGEGGITLSGGQRARISLARAVYKDADLYLLDSPFGYLDVLTEKEIFESCVCKLMANKTRILVTSKMEHLKKADKILILHEGSSYFYGTFSELQNLQPDFSSKLMG

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 \(c\).

\(|P_{f(4UVG_1)}(2) \setminus P_{f(7LJI_1)}(2)|=55\), \(|P_{f(7LJI_1)}(2) \setminus P_{f(4UVG_1)}(2)|=93\). 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 1:10111010011101110000111011011000110111011001011001000111011110101000001101110100111110010111001111100111101110110101001101010001011011111101110111101010011110011011001100100111001100110001111111001110111111110011101011001100011111010010111001011100111100101101011100011
Pair \(Z_2\) Length of longest common subsequence
4UVG_1,7LJI_1 148 3
4UVG_1,6GJU_1 168 4
7LJI_1,6GJU_1 156 3

Newick tree

 
[
	6GJU_1:83.27,
	[
		4UVG_1:74,7LJI_1:74
	]:9.27
]

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 \((0.85)(0.8)(\frac{694 }{\log_{20} 694}-\frac{269}{\log_{20}269})=118.\)
Status Protein1 Protein2 d d1/2
Query variables 4UVG_1 7LJI_1 150 121.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]