CoV2D Browser

CoV2D Browser^TM

Parikh vectors

3AWH_1	9NVK_1	5HRX_1	Letter	Amino acid
1	2	8	Y	Tyrosine
6	5	6	N	Asparagine
2	3	3	Q	Glutamine
4	12	10	S	Serine
2	1	0	W	Tryptophan
10	8	12	L	Leucine
6	11	12	K	Lycine
14	6	6	V	Valine
9	6	8	R	Arginine
4	5	9	D	Aspartic acid
7	17	9	E	Glutamic acid
14	10	3	G	Glycine
13	8	5	A	Alanine
3	6	10	M	Methionine
5	8	6	P	Proline
9	9	5	T	Threonine
0	0	1	C	Cysteine
2	1	2	H	Histidine
5	21	6	I	Isoleucine
6	8	3	F	Phenylalanine

3AWH_1|Chains A, B|FMN-binding protein|Desulfovibrio vulgaris (883)
>9NVK_1|Chains A, AA[auth B], BA[auth E], B[auth D], CA[auth G], C[auth F], DA[auth I], D[auth H], EA[auth K], E[auth J], FA[auth M], F[auth L], GA[auth P], G[auth N], HA[auth R], H[auth Q], IA[auth V], I[auth U], JA[auth X], J[auth W], K[auth Y], L[auth Z], M[auth b], N[auth c], O[auth d], P[auth e], Q[auth f], R[auth g], S[auth h], T[auth i], U[auth j], V[auth k], W[auth l], X[auth m], Y[auth n], Z[auth o]|Small heat shock protein HSP16.5|Methanocaldococcus jannaschii (2190)
>5HRX_1|Chains A, B|Protein polybromo-1|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 \(w=f(c)\)
3AWH , Knot	65	122	0.85	38	96	117	MLPGTFFEVLKNKGVVAIATQGEDGPHLVNTWNSYLKVLDGNRIVVPVGGMHKTEANVARDERVLMTLGSRKVAGRNGPGTGFLIRGSAAFRTDGPEFEAIARFKWARAALVITVVSAEQTL
9NVK , Knot	72	147	0.81	38	110	144	MFGRDPFDSLFERMFKEFFATPMTGTTMIQSSTGIQISGKGFMPISIIEGDQHIKVIAWLPGVNKEDIILNAVGDTLEIRAKRSPLMITESERIIYSEIPEEEEIYRTIKLPATVKEENASAKFENGVLSVILPKAESSIKKGINIE
5HRX , Knot	64	124	0.83	38	111	122	SMSGISPKKSKYMTPMQQKLNEVYEAVKNYTDKRGRRLSAIFLRLPSRSELPDYYLTIKKPMDMEKIRSHMMANKYQDIDSMVEDFVMMFNNACTYNEPESLIYKDALVLHKVLLETRRDLEGD

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 \(w=f(c)\)

3AWH , Knot

122

0.85

117

MLPGTFFEVLKNKGVVAIATQGEDGPHLVNTWNSYLKVLDGNRIVVPVGGMHKTEANVARDERVLMTLGSRKVAGRNGPGTGFLIRGSAAFRTDGPEFEAIARFKWARAALVITVVSAEQTL

9NVK , Knot

147

0.81

110

144

MFGRDPFDSLFERMFKEFFATPMTGTTMIQSSTGIQISGKGFMPISIIEGDQHIKVIAWLPGVNKEDIILNAVGDTLEIRAKRSPLMITESERIIYSEIPEEEEIYRTIKLPATVKEENASAKFENGVLSVILPKAESSIKKGINIE

5HRX , Knot

124

0.83

111

122

SMSGISPKKSKYMTPMQQKLNEVYEAVKNYTDKRGRRLSAIFLRLPSRSELPDYYLTIKKPMDMEKIRSHMMANKYQDIDSMVEDFVMMFNNACTYNEPESLIYKDALVLHKVLLETRRDLEGD

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 \(c\).

\(|P_{f(3AWH_1)}(2) \setminus P_{f(9NVK_1)}(2)|=59\), \(|P_{f(9NVK_1)}(2) \setminus P_{f(3AWH_1)}(2)|=73\). 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 1:11110110110001111110010011011001000101101001111111100001011000011101100011100111011110101110001101011101011011111011010001

Pair	\(Z_2\)	Length of longest common subsequence
3AWH_1,9NVK_1	132	3
3AWH_1,5HRX_1	157	3
9NVK_1,5HRX_1	143	3

Newick tree

 
[
	5HRX_1:77.87,
	[
		3AWH_1:66,9NVK_1:66
	]:11.87
]

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 \((0.85)(0.8)(\frac{269 }{\log_{20} 269}-\frac{122}{\log_{20}122})=46.2\)

Status	Protein1	Protein2	d	d₁/2
Query variables	3AWH_1	9NVK_1	59	54

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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

CoV2D BrowserTM

Newick tree

CoV2D Browser^TM