Separation of long DNA chains using a nonuniform electric field: A numerical study

In the present study, we investigate the migration of DNA molecules through a microchannel using a series of electric traps controlled by an ac electric field. We describe the motion of DNA based on Brownian dynamics simulations of a bead-spring chain. The DNA chain captured by an electric field escapes due to thermal fluctuation. The mobility of the DNA chain was determined to depend on the chain length, the mobility of which sharply increases when the length of the chain exceeds a critical value that is strongly affected by the amplitude of the applied ac field. Thus we can optimize the separation selectivity of the channel for DNA molecules that is to be separated, without changing the structure of the channel. In addition, we present a phenomenological description for the relationship between the critical chain length and the strength of binding electric field.

Figure 1

(a) Schematic diagrams of a channel with electric traps in the $xy$ and $yz$ planes. The electrodes are square in shape and are placed along the channel at intervals of $3d$. (b) The contour lines of the electric potential $\varphi$ at the plane $y=d∕2$.

Figure 2

A DNA chain of $N=80$ that escapes from an electric trap under the conditions of (a) $c=1.0$ and (b) $c=1.2$. The gray rectangular areas indicate electrodes.

Figure 3

Trajectories of DNA chains of $N=20,30,\dots ,160$ with $c=1.0$. Only the $x$ component of the center of mass is plotted.

Figure 4

Mobility $\tilde{\mu }$ of DNA chains for $c=0.8,1.0,\dots ,1.7$ as a function of $N$. Each plot is the average and the error bars are drawn due to the standard deviations of ten trials.

Figure 5

(a) Schematic diagram of a bead-spring chain escaping from a trap. (b) Electric potential energy experienced by a bead.

Figure 6

Free energy difference $\Delta F\left(n\right)$ as a function of $n$ obtained from Eq. (10) with $A=3.4$.

Figure 7

Comparison of the critical chain length $N_c$ between the simulation result and the prediction of Eq. (14), where the black circles in Fig. 8 are estimated from the present simulation and the solid curve is a plot of Eq. (14) with parameter $A=3.4$.