Simulation of single-molecule trapping in a nanochannel

Abstract

The detection and trapping of single fluorescent molecules in solution within a nanochannel is studied using numerical simulations. As optical forces are insufficient for trapping molecules much smaller than the optical wavelength, a means for sensing a molecule's position along the nanochannel and adjusting electrokinetic motion to compensate diffusion is assessed. Fluorescence excitation is provided by two adjacently focused laser beams containing temporally interleaved laser pulses. Photon detection is time-gated, and the displacement of the molecule from the middle of the two foci alters the count rates collected in the two detection channels. An algorithm for feedback control of the electrokinetic motion in response to the timing of photons, to reposition the molecule back toward the middle for trapping and to rapidly reload the trap after a molecule photobleaches or escapes, is evaluated. While accommodating the limited electrokinetic speed and the finite latency of feedback imposed by experimental hardware, the algorithm is shown to be effective for trapping fast-diffusing single-chromophore molecules within a micron-sized confocal region. Studies show that there is an optimum laser power for which loss of molecules from the trap due to either photobleaching or shot-noise fluctuations is minimized.

Figure 1

Irradiance profiles of each of the two laser beams, I₁(x) and I₂(x), and the total irradiance (dotted-dashed line) experienced by a molecule at a position x within the nanochannel.

Figure 2

Histograms of the timing delays (1024 channels at 12.89 ps/channel) between the pulsed laser excitation (beam 1, left) and the detection of photons due to fluorescence from each beam (blue and red curves), background (green curve), detector afterpulses (purple curve), and all combined (orange curve), as collected during a simulation of sequential single-molecule trapping for a total simulated duration of 1000 s. (Color online only.)

Figure 3

Jablonski diagram for the decay possibilities of the molecule. S₀ is the singlet ground state, S₁ is the singlet excited state, and T₁ is the triplet state.

Figure 4

Flowchart of the trapping algorithm.

Figure 5

Example of the total photon count rate R(t) (first plot, red), and molecule trajectories x(t) (second plot); (position given in units of grid spaces, Δx=0.01 μm) during a simulation of trapping using parameters in Table 4. A small section of the trajectory data is expanded in the inset. The red dashed lines indicate the centers of the laser foci (x=±0.25 μm). The lower plot in the inset shows the changes to the flow direction imposed by the trapping algorithm during the same time. (Color online only.)

Figure 6

Autocorrelation functions for a laser power of $\overline{P}=30\mu \mathrm{W}$ for free diffusion (D, blue) and for constant electrokinetic flow (F, green) and for trapping for a range of values for the feedback latency from 1×10⁻² s to 6×10⁻⁶ s. (Color online only.)

Figure 7

Autocorrelation functions for free diffusion (D, blue) and for constant electrokinetic flow (F, green), each at a laser power of $\overline{P}=30\mu \mathrm{W}$, and for trapping for a range of laser powers from 5 μW to 100 μW, all with feedback latency of 6×10⁻⁶ s. The inset shows the mean number of molecules per grid point (Δx=0.01 μm) under the same conditions. (Color online only.)

Figure 8

Effect of laser power and latency of feedback on the trapping performance. The red curves show the mean number of photons detected (photons) before the molecule photobleaches or escapes versus latency (solid line, bottom scale) and versus power $\overline{P}$ (dashed line, top scale). The blue curves show the mean time that a molecule remains in the trap (trap occupancy time) versus latency (solid line) and power (dashed line). (Color online only.)

Figure 9

Time-averaged concentration profile of trapped molecules or the mean number of molecules per grid point (Δx=0.01 μm) for different values of laser powers (μW) of the two beams. The inset shows the irradiance profile for a +20% power imbalance, i.e., 12 μW and 18 μW.

Figure 10

Effect of fluorescence lifetime on the trapping performance. The red curve shows the mean number of photons detected (photons) before the molecule photobleaches or escapes, the blue curve shows the mean time that a molecule remains in the trap (trap occupancy time), and the green curve shows the percentage of fluorescence photons that have incorrect timing (incorrect timing percentage). The inset shows the effect of an incorrect timing delay on the trapping performance for a fluorescence lifetime of 3 ns. (Color online only.)