CoV2D BrowserTM

CoV2D project home | Random page
Parikh vectors
2KHI_1 6QRK_1 6ZQB_1 Letter Amino acid
3 0 14 W Tryptophan
3 2 34 Q Glutamine
3 0 13 M Methionine
2 0 60 F Phenylalanine
6 0 52 T Threonine
10 2 61 E Glutamic acid
5 1 55 I Isoleucine
8 2 86 S Serine
7 2 75 L Leucine
4 0 25 P Proline
4 1 58 A Alanine
2 4 8 C Cysteine
10 1 53 G Glycine
10 0 18 H Histidine
2 2 22 Y Tyrosine
14 2 64 V Valine
6 0 44 R Arginine
5 2 54 N Asparagine
5 0 75 D Aspartic acid
6 0 52 K Lycine 

2KHI_1|Chain A|30S ribosomal protein S1|Escherichia coli (83333)
>6QRK_1|Chain A|Insulin|Bos taurus (9913)
>6ZQB_1|Chain A[auth UA]|Periodic tryptophan protein 2|Saccharomyces cerevisiae (strain ATCC 204508 / S288c) (559292)
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 \(w=f(c)\)
2KHI , Knot 58 115 0.79 40 95 109 
MGSSHHHHHHSSGLVPRGSHWVAIAKRYPEGTKLTGRVTNLTDYGCFVEIEEGVEGLVHVSEMDWTNKNIHPSKVVNVGDVVEVMVLDIDEERRRISLGLKQCKANPWQQFAETH
6QRK , Knot 15 21 0.72 22 20 19 
GIVEQCCASVCSLYQLENYCN
6ZQB , Knot 340 923 0.83 40 294 821 
MKSDFKFSNLLGTVYRQGNITFSDDGKQLLSPVGNRVSVFDLINNKSFTFEYEHRKNIAAIDLNKQGTLLISIDEDGRAILVNFKARNVLHHFNFKEKCSAVKFSPDGRLFALASGRFLQIWKTPDVNKDRQFAPFVRHRVHAGHFQDITSLTWSQDSRFILTTSKDLSAKIWSVDSEEKNLAATTFNGHRDYVMGAFFSHDQEKIYTVSKDGAVFVWEFTKRPSDDDDNESEDDDKQEEVDISKYSWRITKKHFFYANQAKVKCVTFHPATRLLAVGFTSGEFRLYDLPDFTLIQQLSMGQNPVNTVSVNQTGEWLAFGSSKLGQLLVYEWQSESYILKQQGHFDSTNSLAYSPDGSRVVTASEDGKIKVWDITSGFCLATFEEHTSSVTAVQFAKRGQVMFSSSLDGTVRAWDLIRYRNFRTFTGTERIQFNCLAVDPSGEVVCAGSLDNFDIHVWSVQTGQLLDALSGHEGPVSCLSFSQENSVLASASWDKTIRIWSIFGRSQQVEPIEVYSDVLALSMRPDGKEVAVSTLKGQISIFNIEDAKQVGNIDCRKDIISGRFNQDRFTAKNSERSKFFTTIHYSFDGMAIVAGGNNNSICLYDVPNEVLLKRFIVSRNMALNGTLEFLNSKKMTEAGSLDLIDDAGENSDLEDRIDNSLPGSQRGGDLSTRKMRPEVRVTSVQFSPTANAFAAASTEGLLIYSTNDTILFDPFDLDVDVTPHSTVEALREKQFLNALVMAFRLNEEYLINKVYEAIPIKEIPLVASNIPAIYLPRILKFIGDFAIESQHIEFNLIWIKALLSASGGYINEHKYLFSTAMRSIQRFIVRVAKEVVNTTTDNKYTYRFLVSTDGSMEDGAADDDEVLLKDDADEDNEENEENDVVMESDDEEGWIGFNGKDNKLPLSNENDSSDEEENEKELP

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 \(c\).

\(|P_{f(2KHI_1)}(2) \setminus P_{f(6QRK_1)}(2)|=92\), \(|P_{f(6QRK_1)}(2) \setminus P_{f(2KHI_1)}(2)|=17\). 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 1:1100000000001111010011111000101001010100100010110100110111010010100001010011011011011110100000010111000010110011000
Pair \(Z_2\) Length of longest common subsequence
2KHI_1,6QRK_1 109 2
2KHI_1,6ZQB_1 237 3
6QRK_1,6ZQB_1 290 2

Newick tree

 
[
	6ZQB_1:14.62,
	[
		2KHI_1:54.5,6QRK_1:54.5
	]:95.12
]

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 \((0.85)(0.8)(\frac{136 }{\log_{20} 136}-\frac{21}{\log_{20}21})=42.3\)
Status Protein1 Protein2 d d1/2
Query variables 2KHI_1 6QRK_1 53 31.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]