CoV2D Browser

CoV2D Browser^TM

Parikh vectors

7ACW_1	5KVX_1	9CVW_1	Letter	Amino acid
7	11	26	K	Lycine
4	12	23	D	Aspartic acid
3	24	24	G	Glycine
3	4	18	Q	Glutamine
5	9	35	L	Leucine
1	1	11	M	Methionine
9	14	25	S	Serine
6	16	21	A	Alanine
0	16	11	C	Cysteine
5	8	24	I	Isoleucine
2	12	24	P	Proline
2	20	25	T	Threonine
0	3	13	W	Tryptophan
5	8	17	Y	Tyrosine
8	6	27	E	Glutamic acid
0	0	14	H	Histidine
2	11	19	F	Phenylalanine
9	10	25	V	Valine
2	12	22	R	Arginine
5	10	19	N	Asparagine

7ACW_1|Chains A, C|S-layer protein|Clostridioides difficile (1496)
>5KVX_1|Chain A|Thaumatin-1|Thaumatococcus daniellii (4621)
>9CVW_1|Chains A, B, C, D|Nitric oxide synthase, brain|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 \(w=f(c)\)
7ACW , Knot	45	78	0.83	34	69	76	MVRVTSAKEESIDVDSSSYISAENLAKKYVFNPKEVSEAYNAIVALQNDGIESDLVQLVNGKYQVIFYPEGKRLETKS
5KVX , Knot	99	207	0.85	38	150	203	ATFEIVNRCSYTVWAAASKGDAALDAGGRQLNSGESWTINVEPGTNGGKIWARTDCYFDDSGSGICKTGDCGGLLRCKRFGRPPTTLAEFSLNQYGKDYIDISNIKGFNVPMNFSPTTRGCRGVRCAADIVGQCPAKLKAPGGGCNDACTVFQTSEYCCTTGKCGPTEYSRFFKRLCPDAFSYVLDKPTTVTCPGSSNYRVTFCPTA
9CVW , Knot	184	423	0.87	40	261	410	CPRFLKVKNWETEVVLTDTLHLKSTLETGCTEYICMGSIMHPSQHARRPEDVATKDQLFPLAKEFIDQYYSSIKRFGSKAHMERLEEVNKEIDTTSTYQLKDTELIYGAKHAWRNASRCVGRIQWSKLQVFDARDCTTAHGMFNYICNHVKYATNKGNLRSAITIFPQRTDGKHDFRVWNSQLIRYAGYKQPDGSTLGDPANVQFTEICIQQGWKPPRGRFDVLPLLLQANGNDPELFQIPPELVLEVPIRHPKFEWFKDLGLKWYGLPAVSNMLLEIGGLEFSACPFSGWYMGTEIGVRDYCDNSRYNILEEVAKKMNLDMRKTSSLWKDQALVEINIAVLYSFQSDKVTIVDHHSATESFIKHMENEYRCRGGCPADWVWIVPPMSGSITPVFHQEMLNYRLTPSFEYQPDPWNTHVWKLV

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 \(w=f(c)\)

7ACW , Knot

0.83

MVRVTSAKEESIDVDSSSYISAENLAKKYVFNPKEVSEAYNAIVALQNDGIESDLVQLVNGKYQVIFYPEGKRLETKS

5KVX , Knot

207

0.85

150

203

ATFEIVNRCSYTVWAAASKGDAALDAGGRQLNSGESWTINVEPGTNGGKIWARTDCYFDDSGSGICKTGDCGGLLRCKRFGRPPTTLAEFSLNQYGKDYIDISNIKGFNVPMNFSPTTRGCRGVRCAADIVGQCPAKLKAPGGGCNDACTVFQTSEYCCTTGKCGPTEYSRFFKRLCPDAFSYVLDKPTTVTCPGSSNYRVTFCPTA

9CVW , Knot

184

423

0.87

261

410

CPRFLKVKNWETEVVLTDTLHLKSTLETGCTEYICMGSIMHPSQHARRPEDVATKDQLFPLAKEFIDQYYSSIKRFGSKAHMERLEEVNKEIDTTSTYQLKDTELIYGAKHAWRNASRCVGRIQWSKLQVFDARDCTTAHGMFNYICNHVKYATNKGNLRSAITIFPQRTDGKHDFRVWNSQLIRYAGYKQPDGSTLGDPANVQFTEICIQQGWKPPRGRFDVLPLLLQANGNDPELFQIPPELVLEVPIRHPKFEWFKDLGLKWYGLPAVSNMLLEIGGLEFSACPFSGWYMGTEIGVRDYCDNSRYNILEEVAKKMNLDMRKTSSLWKDQALVEINIAVLYSFQSDKVTIVDHHSATESFIKHMENEYRCRGGCPADWVWIVPPMSGSITPVFHQEMLNYRLTPSFEYQPDPWNTHVWKLV

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 \(c\).

\(|P_{f(7ACW_1)}(2) \setminus P_{f(5KVX_1)}(2)|=41\), \(|P_{f(5KVX_1)}(2) \setminus P_{f(7ACW_1)}(2)|=122\). 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 1:110100100001010000010100110001101001001001111100011000110110100011101010010000

Pair	\(Z_2\)	Length of longest common subsequence
7ACW_1,5KVX_1	163	3
7ACW_1,9CVW_1	226	3
5KVX_1,9CVW_1	205	4

Newick tree

 
[
	9CVW_1:11.33,
	[
		7ACW_1:81.5,5KVX_1:81.5
	]:33.83
]

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 \((0.85)(0.8)(\frac{285 }{\log_{20} 285}-\frac{78}{\log_{20}78})=66.2\)

Status	Protein1	Protein2	d	d₁/2
Query variables	7ACW_1	5KVX_1	84	58

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 {
							MV->VR;
							VR->RV;
							RV->VT;
							VT->TS;
							TS->SA;
							SA->AK;
							AK->KE;
							KE->EE;
							EE->ES;
							ES->SI;
							SI->ID;
							ID->DV;
							DV->VD;
							VD->DS;
							DS->SS;
							SS->SS;
							SS->SY;
							SY->YI;
							YI->IS;
							IS->SA;
							SA->AE;
							AE->EN;
							EN->NL;
							NL->LA;
							LA->AK;
							AK->KK;
							KK->KY;
							KY->YV;
							YV->VF;
							VF->FN;
							FN->NP;
							NP->PK;
							PK->KE;
							KE->EV;
							EV->VS;
							VS->SE;
							SE->EA;
							EA->AY;
							AY->YN;
							YN->NA;
							NA->AI;
							AI->IV;
							IV->VA;
							VA->AL;
							AL->LQ;
							LQ->QN;
							QN->ND;
							ND->DG;
							DG->GI;
							GI->IE;
							IE->ES;
							ES->SD;
							SD->DL;
							DL->LV;
							LV->VQ;
							VQ->QL;
							QL->LV;
							LV->VN;
							VN->NG;
							NG->GK;
							GK->KY;
							KY->YQ;
							YQ->QV;
							QV->VI;
							VI->IF;
							IF->FY;
							FY->YP;
							YP->PE;
							PE->EG;
							EG->GK;
							GK->KR;
							KR->RL;
							RL->LE;
							LE->ET;
							ET->TK;
							TK->KS;

}

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];
							}
		
							M->V
							V->R
							R->V
							V->T
							T->S
							S->A
							A->K
							K->E
							E->E
							E->S
							S->I
							I->D
							D->V
							V->D
							D->S
							S->S
							S->Y
							Y->I
							I->S
							A->E
							E->N
							N->L
							L->A
							K->K
							K->Y
							Y->V
							V->F
							F->N
							N->P
							P->K
							E->V
							V->S
							S->E
							E->A
							A->Y
							Y->N
							N->A
							A->I
							I->V
							V->A
							A->L
							L->Q
							Q->N
							N->D
							D->G
							G->I
							I->E
							S->D
							D->L
							L->V
							V->Q
							Q->L
							V->N
							N->G
							G->K
							Y->Q
							Q->V
							V->I
							I->F
							F->Y
							Y->P
							P->E
							E->G
							K->R
							R->L
							L->E
							E->T
							T->K
							K->S
						}

Graphviz Engine:

CoV2D BrowserTM

Newick tree

CoV2D Browser^TM