CoV2D BrowserTM

CoV2D project home | Random page
Parikh vectors
2WJL_1 7MLL_1 5ARI_1 Letter Amino acid
8 5 32 E Glutamic acid
11 0 16 Y Tyrosine
21 1 41 V Valine
29 2 49 A Alanine
11 1 29 D Aspartic acid
13 2 14 F Phenylalanine
11 4 17 P Proline
18 2 26 T Threonine
8 1 0 W Tryptophan
7 1 32 R Arginine
7 2 31 K Lycine
3 1 13 N Asparagine
9 1 10 M Methionine
25 5 49 G Glycine
0 1 5 H Histidine
15 1 39 I Isoleucine
36 3 48 L Leucine
13 5 33 S Serine
0 0 2 C Cysteine
4 1 24 Q Glutamine 

2WJL_1|Chain A|Bacteriorhodopsin|Halobacterium salinarum (2242)
>7MLL_1|Chain A|Exendin-4|Heloderma suspectum (8554)
>5ARI_1|Chains A, B, C|ATP SYNTHASE SUBUNIT ALPHA, MITOCHONDRIAL|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 \(w=f(c)\)
2WJL , Knot 112 249 0.82 36 151 239 
QAQITGRPEWIWLALGTALMGLGTLYFLVKGMGVSDPDAKKFYAITTLVPAIAFTMYLSMLLGYGLTMVPFGGEQNPIYWARYADWLFTTPLLLLDLALLVDADQGTILALVGADGIMIGTGLVGALTKVYSYRFVWWAISTAAMLYILYVLFFGFTSKAESMRPEVASTFKVLRNVTVVLWSAYPVVWLIGSDGAGIVPLNIETLLFMVLDVSAKVGFGLILLRSRAIFGEAEAPEPSAGDGAAATSD
7MLL , Knot 26 40 0.80 38 36 38 
HGEGTFTSDLSKQMEEEAVRLFIEWLKNGGPSSGAPPPSX
5ARI , Knot 205 510 0.83 38 229 476 
QKTGTAEVSSILEERILGADTSVDLEETGRVLSIGDGIARVHGLRNVQAEEMVEFSSGLKGMSLNLEPDNVGVVVFGNDKLIKEGDIVKRTGAIVDVPVGEELLGRVVDALGNAIDGKGPIGSKARRRVGLKAPGIIPRISVREPMQTGIKAVDSLVPIGRGQRELIIGDRQTGKTSIAIDTIINQKRFNDGTDEKKKLYCIYVAIGQKRSTVAQLVKRLTDADAMKYTIVVSATASDAAPLQYLAPYSGCSMGEYFRDNGKHALIIYDDLSKQAVAYRQMSLLLRRPPGREAYPGDVFYLHSRLLERAAKMNDAFGGGSLTALPVIETQAGDVSAYIPTNVISITDGQIFLETELFYKGIRPAINVGLSVSRVGSAAQTRAMKQVAGTMKLELAQYREVAAFAQFGSDLDAATQQLLSRGVRLTELLKQGQYSPMAIEEQVAVIYAGVRGYLDKLEPSKITKFENAFLSHVISQHQALLGKIRTDGKISEESDAKLKEIVTNFLAGFEA

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 \(c\).

\(|P_{f(2WJL_1)}(2) \setminus P_{f(7MLL_1)}(2)|=133\), \(|P_{f(7MLL_1)}(2) \setminus P_{f(2WJL_1)}(2)|=18\). 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 1:010101010111111101111110101110111100101001011001111111010101111011011111100011011001011100111110111110100101111111011111011111100100001111110011110110111111000100101011001011001011110101111111001111111010011111101010111111110001111010110101101111000
Pair \(Z_2\) Length of longest common subsequence
2WJL_1,7MLL_1 151 3
2WJL_1,5ARI_1 154 4
7MLL_1,5ARI_1 209 5

Newick tree

 
[
	5ARI_1:96.60,
	[
		2WJL_1:75.5,7MLL_1:75.5
	]:21.10
]

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 \((0.85)(0.8)(\frac{289 }{\log_{20} 289}-\frac{40}{\log_{20}40})=81.8\)
Status Protein1 Protein2 d d1/2
Query variables 2WJL_1 7MLL_1 100 57.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]