CoV2D BrowserTM

CoV2D project home | Random page
Parikh vectors
4AOU_1 2PUT_1 7DCF_1 Letter Amino acid
11 12 10 P Proline
22 32 18 S Serine
27 19 10 T Threonine
28 27 14 V Valine
30 24 13 A Alanine
34 24 19 E Glutamic acid
36 19 12 K Lycine
16 8 3 M Methionine
19 8 12 Y Tyrosine
25 19 23 D Aspartic acid
7 8 5 H Histidine
28 32 23 I Isoleucine
6 2 4 W Tryptophan
18 13 15 N Asparagine
9 14 11 Q Glutamine
17 13 12 F Phenylalanine
17 20 23 R Arginine
3 10 20 C Cysteine
25 24 17 G Glycine
24 39 19 L Leucine 

4AOU_1|Chain A|ISOCITRATE DEHYDROGENASE [NADP]|CLOSTRIDIUM THERMOCELLUM (1515)
>2PUT_1|Chains A, B, C, D|isomerase domain of glutamine-fructose-6-phosphate transaminase (isomerizing)|Candida albicans (237561)
>7DCF_1|Chains A, B|Histone-lysine N-methyltransferase EHMT2|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 \(w=f(c)\)
4AOU , Knot 173 402 0.86 40 235 381 
MSKIKMKVPLVEMDGDEMTRIIWRLIKENLLEPYIELNTEYYDLGLENRDKTEDQVTIDAARAIQKYGVGVKCATITPNAQRVEEYNLKKMWKSPNGTIRAILDGTVFRAPIVVNSIKPFVKGWKKPISIARHAYGDVYKNVEYYVPSAGKAELVFTSENGEVSRQTIHEFDGPGVIMGMHNTDKSIRSFARACFNYALDMNQDLWFSTKDTISKTYDHRFKDIFQEIYENEYKEKFEAKNLQYFYTLIDDAVARIIRSEGGMVWACKNYDGDVMSDMVASAFGSLAMMTSVLVSPDGKYEFEAAHGTVTRHYYKHLKGEETSTNSMATIFAWTGALKKRGELDGIKELVDFATKLEQASVQTIENGVMTKDLASLSEVPEKKIVNTEDFLKEIRKTFEGMA
2PUT , Knot 155 367 0.83 40 205 352 
MKGPYKHFMQKEIFEQPDSAFNTMRGRIDFENCVVTLGGLKSWLSTIRRCRRIIMIACGTSYHSCLATRSIFEELTEIPVSVELASDFLDRRSPVFRDDTCVFVSQSGETADSILALQYCLERGALTVGIVNSVGSSMSRQTHCGVHINAGPEIGVASTKAYTSQYIALVMFALSLSNDSISRKGRHEEIIKGLQKIPEQIKQVLKLENKIKDLCNSSLNDQKSLLLLGRGYQFATALEGALKIKEISYMHSEGVLAGELKHGILALVDEDLPIIAFATRDSLFPKVMSAIEQVTARDGRPIVICNEGDAIISNDKVHTTLEVPETVDCLQGLLNVIPLQLISYWLAVNRGIDVDFPRNLAKSVTVE
7DCF , Knot 132 283 0.87 40 195 277 
GSNRAIRTEKIICRDVARGYENVPIPCVNGVDGEPCPEDYKYISENCETSTMNIDRNITHLQHCTCVDDCSSSNCLCGQLSIRCWYDKDGRLLQEFNKIEPPLIFECNQACSCWRNCKNRVVQSGIKVRLQLYRTAKMGWGVRALQTIPQGTFICEYVGELISDAEADVREDDSYLFDLDNKDGEVYCIDARYYGNISRFINHLCDPNIIPVRVFMLHQDLRFPRIAFFSSRDIRTGEELGFDYGDRFWDIKSKYFTCQCGSEKCKHSAEAIALEQSRLARLD

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 \(c\).

\(|P_{f(4AOU_1)}(2) \setminus P_{f(2PUT_1)}(2)|=97\), \(|P_{f(2PUT_1)}(2) \setminus P_{f(4AOU_1)}(2)|=67\). 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 1:100101011110101001001110110001101010100000011100000000010101101100011110010101010010000100110010101011101011011111001011101100110110010101000100011011010111000010100001001011111111000000100110101001101000111000001000000010011001000000001010010010011001110110001111110000010110011101110111100111010100010110101000000010100000001101111011100010101100110110010010100100111000110100110001100001100100010111
Pair \(Z_2\) Length of longest common subsequence
4AOU_1,2PUT_1 164 4
4AOU_1,7DCF_1 196 4
2PUT_1,7DCF_1 172 3

Newick tree

 
[
	7DCF_1:95.35,
	[
		4AOU_1:82,2PUT_1:82
	]:13.35
]

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 \((0.85)(0.8)(\frac{769 }{\log_{20} 769}-\frac{367}{\log_{20}367})=109.\)
Status Protein1 Protein2 d d1/2
Query variables 4AOU_1 2PUT_1 142 133
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]