CoV2D BrowserTM

CoV2D project home | Random page
Parikh vectors
1HHP_1 8QKJ_1 2KMM_1 Letter Amino acid
3 43 4 A Alanine
13 37 5 G Glycine
2 10 2 M Methionine
1 18 2 Y Tyrosine
4 29 1 R Arginine
4 49 4 D Aspartic acid
2 8 1 C Cysteine
4 34 4 E Glutamic acid
1 24 9 H Histidine
6 23 3 P Proline
2 5 0 W Tryptophan
3 43 2 N Asparagine
6 16 2 Q Glutamine
13 40 2 I Isoleucine
12 61 9 L Leucine
6 43 5 K Lycine
2 16 2 F Phenylalanine
1 71 7 S Serine
8 17 2 T Threonine
6 44 7 V Valine 

1HHP_1|Chain A|UNLIGANDED HIV-1 PROTEASE|Human immunodeficiency virus type 1 (BRU ISOLATE) (11686)
>8QKJ_1|Chains A, B|subtilisin|Plasmodium vivax (5855)
>2KMM_1|Chain A|Guanosine-3',5'-bis(Diphosphate) 3'-pyrophosphohydrolase|Porphyromonas gingivalis (837)
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 \(w=f(c)\)
1HHP , Knot 52 99 0.80 40 81 94 
PQITLWQRPLVTIKIGGQLKEALLDTGADDTVLEEMSLPGRWKPKMIGGIGGFIKVRQYDQILIEICGHKAIGTVLVGPTPVNIIGRNLLTQIGCTLNF
8QKJ , Knot 244 631 0.83 40 259 576 
MKLCILLAVVAFVGLSLGRSGDILPNEGKKEKDDVHKIISELRFLQKVETILESSNMSVSDVEADANAYNPDRDAPKEELQKLQDQQETPSKQPNNLRNSPQKRAEKKESPGKNKKSLRLIVSENHATSPSFFEESLLQEDVVSFIQSKGKLSNLKNLKSMIIDLNSDMTDEELAEYISLLERKGALIESDKLVGADDVSLASVKDAVRRGESSVNWGKLRSTMLEVPSGESPPSHAASSGSPFDDDDDLLSEAALHREEAHLAGSKTTKGYKFNDEYRNLQWGLDLARLDETQDLINANRVSVTKICVIDSGIDYNHPDLRNNIDVNVKELHGRKGVDDDSNGVVDDVYGANFVSNSGDPMDDNYHGTHVSGIISAVGNNGIGIVGVDGHSKLVICKALDQHKLGRLGDMFKCIDYCISRQAHMISGSFSFDEYSNIFSASVEHLRSLGILFFVSASNCAHDKLSKPDIAKCDLAVNHRYPPILSKTHNNVIAVANLKRDLDESYSLSVNSFYSNIYCQLAAPGTNIYSTTPMNNYRKLNGTSMASPHVAAIASIVRSINPNLTYLQIVEILRNAIVKLPSLTERVSWGGYVDILRAVNLAIDSKAAPYIKSHSWFRWKQGSRRHHHHHH
2KMM , Knot 40 73 0.78 38 62 68 
MEVMVFTPKGEIKRLPQGATALDFAYSLHSDLGDHCIGAKVNHKLVPLSYVLNSGDQVEVLSSKSLEHHHHHH

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 \(c\).

\(|P_{f(1HHP_1)}(2) \setminus P_{f(8QKJ_1)}(2)|=23\), \(|P_{f(8QKJ_1)}(2) \setminus P_{f(1HHP_1)}(2)|=201\). 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 1:101011001110101110100111001100011001011101010111111111010000011101010011101111101101110011001100101
Pair \(Z_2\) Length of longest common subsequence
1HHP_1,8QKJ_1 224 4
1HHP_1,2KMM_1 103 2
8QKJ_1,2KMM_1 223 6

Newick tree

 
[
	8QKJ_1:12.56,
	[
		1HHP_1:51.5,2KMM_1:51.5
	]:74.06
]

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 \((0.85)(0.8)(\frac{730 }{\log_{20} 730}-\frac{99}{\log_{20}99})=181.\)
Status Protein1 Protein2 d d1/2
Query variables 1HHP_1 8QKJ_1 230 132.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]