A long DNA segment in a linear nanoscale Paul trap

Abstract

We study the dynamics of a linearly distributed line charge such as single stranded DNA (ssDNA) in a nanoscale, linear 2D Paul trap in vacuum. Using molecular dynamics simulations we show that a line charge can be trapped effectively in the trap for a well defined range of stability parameters. We investigated (i) a flexible bonded string of charged beads and (ii) a ssDNA polymer of variable length, for various trap parameters. A line charge undergoes oscillations or rotations as it moves, depending on its initial angle, the position of the center of mass and the velocity. The stability region for a strongly bonded line of charged beads is similar to that of a single ion with the same charge to mass ratio. Single stranded DNA as long as 40 nm does not fold or curl in the Paul trap, but could undergo rotations about the center of mass. However, we show that a stretching field in the axial direction can effectively prevent the rotations and increase the confinement stability.

Figure 1

(a) Schematic sketch of a Paul trap, and (b), stability diagram for an ideal 2D Paul trap, showing the ranges of q and afor which the trap is stable.

Figure 2

(a) x-coordinate, (b) y-coordinate, (c) radial distance of a particle from the center of a linear Paul Trap. The trap parameters q=0.2938 and frequency f=10 GHz. (d) The PSD S(ω): The first peak at 2.1 GHz corresponds to the secular oscillation frequency.

Figure 3

(a) The motion of the center of mass of a chain initially parallel to the z-axis for bond angle force constant of k=0.01 eV/rad². (b) The power-spectral density of the center of mass trajectories for different harmonic bond angle force constants k=0, 0.001 and k=0.01 eV/rad² for the trajectories in (a), showing overlapping trajectories. (c) The motion of the center of mass of the chains of various angular force constants with the initial orientation at an angle to the trap axis. The trajectories overlap except for k=0.01 eV/rad² which becomes unstable after 4 ns. (d) The PSD of the center of mass trajectories for different harmonic bond angle strengths k=0, 0.001, 0.01 eV/rad² for the trajectories in (c).

Figure 4

(a), (b) and (c) are different conformations of the chain as it oscillates in the trap. The z-axis is the trap axis. The bending is a result of the initial orientation, which is here 10°to the z-axis, while k=0.

Figure 5

a),b),c)The variation of the angle between a line joining the center atom of a chain and one of the ends with respect to the trap axis for different flexibilities as a function of time.

Figure 6

(a) A snapshot of a 60 G base ssDNA as it oscillates in the trap. The z-axis denotes the trap axis. The DNA remains straight though it undergoes some oscillations and is not parallel to the z-axis. (b) A schematic of a parabolic stretching potential that could be applied in the z-direction to confine the DNA (c) DNA position after stretching potential is applied.

Figure 7

(a) r trajectory of the center of mass (green) as well as the center of mass of the end groups (red and blue) as a function of time. (b),(c), and (d) are x,y and r coordinates of the trajectories of a 60 G base ssDNA as a function of time, compared with the trajectory of a single particle. (e) PSD for the center of mass of the DNA as well as the center of mass of the end groups denoted by DG5 and DG3. (f) Comparison of the center of mass PSD for the ssDNA with that of a particle with the same q-factor.

Figure 8

(a) r(t) coordinate of trajectory of the center of mass of ssDNAs with different bases with V_dc=0.02 V, and (b) r(t) of the center of mass for V_dc=0 V. (c) The r(t) of center of masses of G, A, T, C of a 60 base ssDNA with 15 contiguous bases of G, A, T and C. (d) PSD of a 60 base, ssDNA in (a). (e) The PSD for case in (b). Also shown in dashed lines is the PSD of the r(t) for a single particle with different q-factors corresponding to different DNA bases (f) The PSD for case (c).

Figure 9

(a) r trajectory of the center of mass of two end bases (DC5 and DG3) and two interior bases (DA and DC) in a mixed base ssDNAs consisting of 60 bases; V_dc=0V, V_ac=1V, r₀=50 nm, f=5Ghz and (b) The PSD of the center of mass of the bases.

Figure 10

Shown are the variations with time of the angle of the line connecting the end bases with the z-axis. (a): 15 bases of G, 15A, 15C, 15T. (b): The variation of the angle for an ssDNA with 180 bases (replicated the DNA above 3 times) but with the stretching field. Corresponding power spectral densities are shown at (c) and (d).