Trapping probability analysis of a DNA trap using electric and hydrodrag force fields in tapered microchannels

This paper describes a quantitative analysis of the trapping probability for the DNA trap, which is a method of trapping and concentrating DNA in a tapered microchannel by electric and hydrodrag force fields. In order to calculate the trapping probability, a series of connections of triangle-shaped taper stages was used. The fluorescent intensity of trapped DNA molecules at each stage was measured. The trapping probability per stage was calculated from the distribution of the fluorescent increase rate along with the stage number. The trapping probabilities were measured as a function of DNA size, electric field, and average hydraulic velocity. The electric field that gives a trap probability of 0.5 was found to be proportional to the average hydraulic velocity for all DNA sizes. For all measured conditions and accuracy, the trapping probability was found to be determined only by the ratio of the electric field to the average hydraulic velocity. These results reveal that the DNA trap is not simply caused by balance between the dielectrophoresis and hydrodrag forces.

Figure 1

Schematic of DNA trapping.

Figure 2

Schematic of the analysis model. $Q_{in}\left(n\right)$ indicates the quantity of DNA flow into the $n\text{th}$ taper. $Q_{Trap}\left(n\right)$ expresses the quantity of trapped DNA in the $n\text{th}$ taper. $Q_{out}\left(n\right)$ represents the quantity of DNA flow out from the $n\text{th}$ taper.

Figure 3

Assumed time evolution of a trapped DNA quantity at the single taper stage. The dashed curve indicates a quantity of trapped DNA molecules. The solid line is a tangent to the curve when time $t$ is close to 0.

Figure 4

Structure of the tapered microchannel. The depth is $1\mu \text{m}$ and the distance between the two reservoir holes is about 1 cm (left figure). Each line for the series of tapered structures consists of ten connected triangular tapers (middle figure). The narrowest part of the single tapered microchannel is $1\mu \text{m}$ (right figure).

Figure 5

Schematic of experimental setup. Fluorescent-labeled DNA was trapped in a tapered microchannel by applying direct-current voltage and differential pressure simultaneously to both ends of the microchannel.

Figure 6

Typical snapshots for fluorescence images of trapped DNA in the series of taper shape channels for lambda DNA (48 kbp) at $t=10.4\text{s}$, $\Delta P=70\text{hPa}$, and $V=11\text{V}$. The white lines indicate the position of one series of the tapers. The white bright spots are trapped DNA molecules.

Figure 7

Integration areas to measure the fluorescence intensity of each taper stage. The white lines separate the fluorescent spots of trapped DNA in Fig. 6 into each taper stage. The numbers of the taper stages are indicated at the left side of the figure.

Figure 8

Typical time dependence of measured fluorescence intensity for lambda DNA at 62 hPa and 11 V. The eight curves from the top are for the first to eighth taper stages, respectively. The zero frame corresponds to $t=0$ when voltage was applied.

Figure 9

Increase in the rate of fluorescence intensity versus the taper-stage number. The solid line indicates linear fitting for data of the second to seventh taper stages.

Figure 10

Calculated trapping probabilities for T4 DNA at various differential pressures plotted as a function of applied direct-current voltage.

Figure 11

Calculated trapping probabilities for lambda DNA at various differential pressures plotted as a function of applied direct-current voltage.

Figure 12

Calculated trapping probabilities for M13mp9 DNA at various differential pressures plotted as a function of applied direct-current voltage.

Figure 13

$E_{s,0.5}$ and hydraulic velocity at a trapping probability of 0.5. This figure indicates a plot of the $E_{s,0.5}$ as a function of $⟨u_h⟩$ for each DNA size. The hydraulic velocity $⟨u_h⟩$ is measured at each condition of $\Delta P$ and DNA size by averaging the velocity of DNA molecules released by removing $V_a$ after they are trapped once by $V_a$ and $\Delta P$. For the representative electric field, we chose the strength of the electric field $\left(E_s\right)$ at the straight part of the channel in Fig. 4. For each $⟨u_h⟩$ and DNA size, we obtained the $E_{s,0.5}$ where the trapping probability was 0.5.

Figure 14

DNA trap probability as a function of $E_s/⟨u_h⟩$.

Figure 15

Trapping probability of T4 DNA versus normalized voltage. The voltage was normalized at the value of 0.5 for the trapping probability at each pressure difference shown in Fig. 10. The solid curve and dotted line are the (A) Gauss and (B) linear functions for all plot marks, respectively.

Figure 16

Trapping probability of lambda DNA versus normalized voltage. The voltage was normalized at the value of 0.5 for the trapping probability at each pressure difference shown in Fig. 11. The solid curve and dotted line are the (C) Gauss and (D) linear functions for all plot marks, respectively.

Figure 17

Trapping probability of M13mp9 DNA versus normalized voltage. The voltage was normalized at the value of 0.5 for the trapping probability at each pressure difference shown in Fig. 12. The solid curve and dotted line are the (E) Gauss and (F) linear functions for all plot marks, respectively.