DNA walk

A DNA walk of a genome represents how the frequency of each nucleotide of a pairing nucleotide couple changes locally. This analysis implies measurement of the local distribution of Gs in the content of GC and of Ts in the content of TA. Lobry was the first to propose this analysis (1996, 1999). Two complementary representations can be derived from the DNA walk: the cumulative TA- and the GC-skew analysis. 

Aim: By reading these description of the algorithm, a reader not trained in genomics is able to redraw our graphs, using the basic genometric data file that is posted on our web resource for each organism as a zip file (.zip).

 DNA walk

1) Drawing a DNA walk by reading a sequence file nucleotide by nucleotide.

A simple algorithm is used to draw a DNA walk by simply assigning a direction to each nucleotide. We propose the following assignment, slightly different from Lobry's: to T, C, A, and G correspond the E(ast), S(outh), W(est), and N(orth) directions, respectively (Lobry, 1999). Reading the nucleotide sequence nucleotide by nucleotide, and following the rule, a path clearly emerges on the graph: Figure 1.

Figure 1: DNA walk of the sequence  GTCTGGTGTCTGGAGTTCCTGGGTCTTGAGACCACAGGACCCACCAGGGACCCAGGACCC Starting from the bottom left (bold blue line), the curve end at the bottom left (pink line)

2) Drawing a DNA walk by slicing a sequence file nucleotide into small windows

A simple way to draw quickly this kind of graph is suggested by Lobry (1996) by cutting a genome into windows of equal length.

Figure 2: DNA walk of the same sequence as the one presented in Figure 1: GTCTGGTGTCTGGAGTTCCTGGGTCTTGAGACCACAGGACCCACCAGGGACCCAGGACCC The sequence was sliced into 5-nucleotide windows. Only the fifth nucleotide per window is plotted. We can also work with the mean values of the window…

Comment: this method is not as precise as the first one. We could use it with a spreadsheet software without affecting the final resolution of the curve at the genome level.

2.1) The genome is cut into a number n of windows W, of equal size (the last window being smaller or equal to the other ones).

W1

W2

W3

...

...

Wn-1

Wn

2.2) In each of these windows a count for each nucleotide is performed: cA, cC, cG, and cT respectively.

W1	cA1	cC1	cG1	cT1
W2	cA2	cC2	cG2	cT2
W3	cA3	cC3	cG3	cT3
...	...	...	...	...
...	...	...	...	...
Wn-1	cAn-1	cCn-1	cGn-1	cTn-1
Wn	cAn	cCn	cGn	cTn

Example: Mycoplasma genitalium genome (download the compressed text file), cut into windows of 1000 nucleotides.

(Mycoplasma genitalium G37 complete genome, L43967.1, 580074 bp, window: 1000 bp).

Center position
Position of the window center (nt)	cA	cC	cG	cT
500	453	93	86	368
1500	400	120	133	347
2500	374	122	164	340
3500	345	145	200	310
...	...	...	...	...
...	...	...	...	...
578500	313	138	141	408
579500	318	149	145	388
580037	33	8	4	29

2.3) Two calculations are performed for each window: xi and yi are determined.

W1	cA1	cC1	cG1	cT1	x1=cT1-cA1	y1=cG1-cC1
W2	cA2	cC2	cG2	cT2	x2=cT2-cA2	y2=cG2-cC2
...	...	...	...	...	...	...
Wn	cAn	cCn	cGn	cTn	xn=cTn-cAn	yn=cGn-cCn

2.4) A cumulative curve is calculated : Xi and Yi are determined.

W1 ...	x1=cT1-cA1	y1=cG1-cC1	X1=sum(x1 to x1)	Y1=sum(y1 to y1)
W2 ...	x2=cT2-cA2	y2=cG2-cC2	X2=sum(x1 to x2)	Y2=sum(y1 to y2)
...	...	...	...	...
Wn ...	xn=cTn-cAn	yn=cGn-cCn	Xn=sum(x1 to xn)	Yn=sum(y1 to yn)

2.5) A cumulative curve is drawn by respecting the order of data, from X1 to Xn and by assigning to Xi the value of Yi.

2.6) According to the previous description the DNA walk was written like this on our graphs, generated by the method "nucleotide by nucleotide":

TmAc vs GmCc meaning that in x is plotted the cumulation of numbers of Ts minus numbers of As vs in y the cumulation of numbers of Gs minus numbers of Cs.

Lobry has chosen to use this assignment: T, G, A, and C correspond to E, S, W, and N directions, respectively. Lobry's outputs are similar to ours (mirror images along the X axis). Compare the DNA walk of Borrelia burgdorferi in Lobry's drawing system and ours.

Lobry's system	our system
Figure 3: DNA walk of Borrelia burdorferi