CoV2D BrowserTM

CoV2D project home | Random page
Parikh vectors
1KLC_1 2RHY_1 2ZOW_1 Letter Amino acid
8 24 8 S Serine
7 22 15 V Valine
4 11 4 R Arginine
10 22 8 L Leucine
4 17 8 E Glutamic acid
8 17 10 K Lycine
1 5 1 M Methionine
3 16 4 F Phenylalanine
9 7 3 C Cysteine
5 13 3 Q Glutamine
5 20 25 G Glycine
3 17 8 H Histidine
5 10 9 I Isoleucine
7 19 9 A Alanine
6 9 6 N Asparagine
3 11 12 T Threonine
3 13 0 W Tryptophan
8 12 1 Y Tyrosine
4 24 11 D Aspartic acid
9 30 6 P Proline 

1KLC_1|Chains A, B|TRANSFORMING GROWTH FACTOR-BETA 1|Homo sapiens (9606)
>2RHY_1|Chain A|Lethal(3)malignant brain tumor-like protein|Homo sapiens (9606)
>2ZOW_1|Chains A, B|Superoxide dismutase [Cu-Zn]|Bos taurus (9913)
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 \(w=f(c)\)
1KLC , Knot 60 112 0.84 40 94 108 
ALDTNYCFSSTEKNCCVRQLYIDFRKDLGWKWIHEPKGYHANFCLGPCPYIWSLDTQYSKVLALYNQHNPGASAAPCCVPQALEPLPIVYYVGRKPKVEQLSNMIVRSCKCS
2RHY , Knot 135 319 0.81 40 193 282 
GPLGSWSWESYLEEQKAITAPVSLFQDSQAVTHNKNGFKLGMKLEGIDPQHPSMYFILTVAEVCGYRLRLHFDGYSECHDFWVNANSPDIHPAGWFEKTGHKLQPPKGYKEEEFSWSQYLRSTRAQAAPKHLFVSQSHSPPPLGFQVGMKLEAVDRMNPSLVCVASVTDVVDSRFLVHFDNWDDTYDYWCDPSSPYIHPVGWCQKQGKPLTPPQDYPDPDNFCWEKYLEETGASAVPTWAFKVRPPHSFLVNMKLEAVDRRNPALIRVASVEDVEDHRIKIHFDGWSHGYDFWIDADHPDIHPAGWCSKTGHPLQPPLG
2ZOW , Knot 73 151 0.80 38 115 146 
ATKAVCVLKGDGPVQGTIHFEAKGDTVVVTGSITGLTEGDHGFHVHQFGDNTQGCTSAGPHFNPLSKKHGGPKDEERHVGDLGNVTADKNGVAIVDIVDPLISLSGEYSIIGRTMVVHEKPDDLGRGGNEESTKTGNAGSRLACGVIGIAK

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 \(c\).

\(|P_{f(1KLC_1)}(2) \setminus P_{f(2RHY_1)}(2)|=44\), \(|P_{f(2RHY_1)}(2) \setminus P_{f(1KLC_1)}(2)|=143\). 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 1:1100000100000000100101010001110110010100101011101011010000001111000001110111001101101111100110010100100111000000
Pair \(Z_2\) Length of longest common subsequence
1KLC_1,2RHY_1 187 4
1KLC_1,2ZOW_1 153 3
2RHY_1,2ZOW_1 184 3

Newick tree

 
[
	2RHY_1:97.57,
	[
		1KLC_1:76.5,2ZOW_1:76.5
	]:21.07
]

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 \((0.85)(0.8)(\frac{431 }{\log_{20} 431}-\frac{112}{\log_{20}112})=96.3\)
Status Protein1 Protein2 d d1/2
Query variables 1KLC_1 2RHY_1 119 79.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]