CoV2D Browser

CoV2D Browser^TM

Parikh vectors

1OVP_1	6SXC_1	9LEE_1	Letter	Amino acid
12	18	0	T	Threonine
5	8	0	D	Aspartic acid
3	23	0	I	Isoleucine
5	16	0	F	Phenylalanine
11	17	0	S	Serine
1	9	0	K	Lycine
0	11	0	M	Methionine
1	4	0	W	Tryptophan
14	10	0	N	Asparagine
7	15	0	Q	Glutamine
11	16	97	G	Glycine
0	5	0	H	Histidine
2	16	0	R	Arginine
1	5	0	Y	Tyrosine
3	9	0	P	Proline
17	26	0	V	Valine
10	19	122	A	Alanine
0	1	64	C	Cysteine
3	12	0	E	Glutamic acid
8	37	0	L	Leucine

1OVP_1|Chain A|hypothetical protein LecB|Pseudomonas aeruginosa (287)
>6SXC_1|Chain A|Ion transport protein|Magnetococcus marinus MC-1 (156889)
>9LEE_1|Chains A, B, C, D, E, F, G, H, I, J|Sag-18RS21 Golld RNA|Streptococcus agalactiae 18RS21 (342613)

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 \(w=f(c)\)
1OVP , Knot	53	114	0.73	34	79	109	ATQGVFTLPANTRFGVTAFANSSGTQTVNVLVNNETAATFSGQSTNNAVIGTQVLNSGSSGKVQVQVSVNGRPSDLVSAQVILTNELNFALVGSEDGTDNDYNDAVVVINWPLG
6SXC , Knot	127	277	0.86	40	178	269	GSHMSRKIRDLIESKRFQNVITAIIVLNGAVLGLLTDTTLSASSQNLLERVDQLCLTIFIVEISLKIYAYGVRGFFRSGWNLFDFVIVAIALMPAQGSLSVLRTFRIFRVMRLVSVIPTMRRVVQGMLLALPGVGSVAALLTVVFYIAAVMATNLYGATFPEWFGDLSKSLYTLFQVMTLESWSMGIVRPVMNVHPNAWVFFIPFIMLTTLTVLNLFIGIIVDAMAITKEQEEEAKTGHHQEPISQTLLHLGDRLDRIEKQLAQNNELLQRQQPQKK
9LEE , Knot	86	378	0.45	8	16	62	GGAGUAGGCGUUGCGCAUUUUGUUGCUCAAAAGGCGACGAAACGCAAGGCAAUGCACGUCUGCGAUACACGAAAACAAUGCUAUUUGUUGAAAAUAUUGGAAUAAAGCAAAAGUCAUUGCCCGUCGCAAACGAAAGUGUGCUUCGGUAGCUAGGCUACCUGCUAGAGUCUCGCAAGGAUAAUAGCAAAGUCAAAGAGUAAAGCAGCUUAGACCUUUAGCGGGGUUUUCGUUAAUUGAAAAAUGGCUUAGUAGUUUGCGGCGUAACGAGUGGUUAGCGAUACUAACCGCGCAUGGUUGUUACUUGAAGGGAUUUGAGUGGAUAAAAAACUAAAACAUAAGGUUUUGAAAGACAACUGACUAAACGUGUAAUCUCAGCGU

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 \(w=f(c)\)

1OVP , Knot

114

0.73

109

ATQGVFTLPANTRFGVTAFANSSGTQTVNVLVNNETAATFSGQSTNNAVIGTQVLNSGSSGKVQVQVSVNGRPSDLVSAQVILTNELNFALVGSEDGTDNDYNDAVVVINWPLG

6SXC , Knot

127

277

0.86

178

269

GSHMSRKIRDLIESKRFQNVITAIIVLNGAVLGLLTDTTLSASSQNLLERVDQLCLTIFIVEISLKIYAYGVRGFFRSGWNLFDFVIVAIALMPAQGSLSVLRTFRIFRVMRLVSVIPTMRRVVQGMLLALPGVGSVAALLTVVFYIAAVMATNLYGATFPEWFGDLSKSLYTLFQVMTLESWSMGIVRPVMNVHPNAWVFFIPFIMLTTLTVLNLFIGIIVDAMAITKEQEEEAKTGHHQEPISQTLLHLGDRLDRIEKQLAQNNELLQRQQPQKK

9LEE , Knot

378

0.45

GGAGUAGGCGUUGCGCAUUUUGUUGCUCAAAAGGCGACGAAACGCAAGGCAAUGCACGUCUGCGAUACACGAAAACAAUGCUAUUUGUUGAAAAUAUUGGAAUAAAGCAAAAGUCAUUGCCCGUCGCAAACGAAAGUGUGCUUCGGUAGCUAGGCUACCUGCUAGAGUCUCGCAAGGAUAAUAGCAAAGUCAAAGAGUAAAGCAGCUUAGACCUUUAGCGGGGUUUUCGUUAAUUGAAAAAUGGCUUAGUAGUUUGCGGCGUAACGAGUGGUUAGCGAUACUAACCGCGCAUGGUUGUUACUUGAAGGGAUUUGAGUGGAUAAAAAACUAAAACAUAAGGUUUUGAAAGACAACUGACUAAACGUGUAAUCUCAGCGU

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 \(c\).

\(|P_{f(1OVP_1)}(2) \setminus P_{f(6SXC_1)}(2)|=34\), \(|P_{f(6SXC_1)}(2) \setminus P_{f(1OVP_1)}(2)|=133\). 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 1:100111011100011101110001000101110000110101000001111001100100101010101010100110101110001011111000100000001111101111

Pair	\(Z_2\)	Length of longest common subsequence
1OVP_1,6SXC_1	167	3
1OVP_1,9LEE_1	93	2
6SXC_1,9LEE_1	190	2

Newick tree

 
[
	6SXC_1:99.72,
	[
		1OVP_1:46.5,9LEE_1:46.5
	]:53.22
]

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 \((0.85)(0.8)(\frac{391 }{\log_{20} 391}-\frac{114}{\log_{20}114})=84.4\)

Status	Protein1	Protein2	d	d₁/2
Query variables	1OVP_1	6SXC_1	111	76.5

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

digraph G {
							AT->TQ;
							TQ->QG;
							QG->GV;
							GV->VF;
							VF->FT;
							FT->TL;
							TL->LP;
							LP->PA;
							PA->AN;
							AN->NT;
							NT->TR;
							TR->RF;
							RF->FG;
							FG->GV;
							GV->VT;
							VT->TA;
							TA->AF;
							AF->FA;
							FA->AN;
							AN->NS;
							NS->SS;
							SS->SG;
							SG->GT;
							GT->TQ;
							TQ->QT;
							QT->TV;
							TV->VN;
							VN->NV;
							NV->VL;
							VL->LV;
							LV->VN;
							VN->NN;
							NN->NE;
							NE->ET;
							ET->TA;
							TA->AA;
							AA->AT;
							AT->TF;
							TF->FS;
							FS->SG;
							SG->GQ;
							GQ->QS;
							QS->ST;
							ST->TN;
							TN->NN;
							NN->NA;
							NA->AV;
							AV->VI;
							VI->IG;
							IG->GT;
							GT->TQ;
							TQ->QV;
							QV->VL;
							VL->LN;
							LN->NS;
							NS->SG;
							SG->GS;
							GS->SS;
							SS->SG;
							SG->GK;
							GK->KV;
							KV->VQ;
							VQ->QV;
							QV->VQ;
							VQ->QV;
							QV->VS;
							VS->SV;
							SV->VN;
							VN->NG;
							NG->GR;
							GR->RP;
							RP->PS;
							PS->SD;
							SD->DL;
							DL->LV;
							LV->VS;
							VS->SA;
							SA->AQ;
							AQ->QV;
							QV->VI;
							VI->IL;
							IL->LT;
							LT->TN;
							TN->NE;
							NE->EL;
							EL->LN;
							LN->NF;
							NF->FA;
							FA->AL;
							AL->LV;
							LV->VG;
							VG->GS;
							GS->SE;
							SE->ED;
							ED->DG;
							DG->GT;
							GT->TD;
							TD->DN;
							DN->ND;
							ND->DY;
							DY->YN;
							YN->ND;
							ND->DA;
							DA->AV;
							AV->VV;
							VV->VV;
							VV->VI;
							VI->IN;
							IN->NW;
							NW->WP;
							WP->PL;
							PL->LG;

}

Graphviz Engine:

digraph G {
							subgraph cluster_theyellow {
								G [style=filled; fillcolor=yellow];
								A [style=filled; fillcolor=yellow];
								V [style=filled; fillcolor=yellow];
								C [style=filled; fillcolor=yellow];
								P [style=filled; fillcolor=yellow];
								L [style=filled; fillcolor=yellow];
								I [style=filled; fillcolor=yellow];
								M [style=filled; fillcolor=yellow];
								W [style=filled; fillcolor=yellow];
								F [style=filled; fillcolor=yellow];
							}
							subgraph cluster_thegreen {
								K [style=filled; fillcolor=green];
								R [style=filled; fillcolor=green];
								H [style=filled; fillcolor=green];
							}
							subgraph cluster_theblue {
								S [style=filled; fillcolor=blue];
								T [style=filled; fillcolor=blue];
								Y [style=filled; fillcolor=blue];
								N [style=filled; fillcolor=blue];
								Q [style=filled; fillcolor=blue];
							}
							subgraph cluster_thepurple {
								D [style=filled; fillcolor=purple];
								E [style=filled; fillcolor=purple];
							}
		
							A->T
							T->Q
							Q->G
							G->V
							V->F
							F->T
							T->L
							L->P
							P->A
							A->N
							N->T
							T->R
							R->F
							F->G
							V->T
							T->A
							A->F
							F->A
							N->S
							S->S
							S->G
							G->T
							Q->T
							T->V
							V->N
							N->V
							V->L
							L->V
							N->N
							N->E
							E->T
							A->A
							T->F
							F->S
							G->Q
							Q->S
							S->T
							T->N
							N->A
							A->V
							V->I
							I->G
							Q->V
							L->N
							G->S
							G->K
							K->V
							V->Q
							V->S
							S->V
							N->G
							G->R
							R->P
							P->S
							S->D
							D->L
							S->A
							A->Q
							I->L
							L->T
							E->L
							N->F
							A->L
							V->G
							S->E
							E->D
							D->G
							T->D
							D->N
							N->D
							D->Y
							Y->N
							D->A
							V->V
							I->N
							N->W
							W->P
							P->L
							L->G
						}

Graphviz Engine:

CoV2D BrowserTM

Newick tree

CoV2D Browser^TM