Channel-Facilitated Diffusion Boosted by Particle Binding at the Channel Entrance

We investigate single-file diffusion of Brownian particles in arrays of closely confining microchannels permeated by a variety of attractive optical potentials and connecting two baths with equal particle concentration. We simultaneously test free diffusion in the channel, diffusion in optical traps coupled in the center of the channel, and diffusion in traps extending into the baths. We found that both classes of attractive optical potentials enhance the translocation rate through the channel with respect to free diffusion. Surprisingly, for the latter class of potentials we measure a 40-fold enhancement in the translocation rate with respect to free diffusion and find a sublinear power law dependence of the translocation rate on the average number of particles in the channel. Our results reveal the function of particle binding at the channel entrances for diffusive transport and open the way to a better understanding of membrane transport and design of synthetic membranes with enhanced diffusion rate.

Figure 1

Array of microfluidic channels with different energy landscapes. (a) Scheme of an array of laser traps generated via holographic optical tweezers and coupled into microfluidic channels that create independent attractive energy landscapes for Brownian particles. (b) Bright field image (left) and corresponding map of the number of particle occurrences (per bin and per hour, right) of four microfluidic channels with similar dimensions connecting two 3D baths. The baths have a depth of $16\mu \mathrm{m}$. The spherical particles have a diameter $(505\pm 8)\mathrm{nm}$. Laser line traps are coupled in each channel occupying, $5/4$, 1, $1/2$, and 0 of the channel length from top to bottom, respectively. The total coupled laser power is 900 mW and we programmed the SLM to generate the 3 lines with a relative intensity of 1, 0.7, and 0.6 from top to bottom, respectively.

Figure 2

Comparison of transport through channels with shallow internal and external attractive potentials. Dependence of $J_A$ (a), and $J_T$ (b) on $P/L$ (bottom axis) and $U$ (top axis) for $\lambda \approx 5/4$ (circles), 1 (squares), $1/2$ (upward triangles), and 0 (solid line). Each data point and corresponding error bar are the mean and standard deviation of three independent measurements lasting 1 h. Lines are guides for the eye. The solid lines connect the seven data points for the channel in free diffusion; error bars are omitted. The three optical line traps are coupled in a different channel in every video. The total applied power is randomized to cover 7 discrete steps from 0 to 900 mW. Insets: illustration of an attempt (a) and a translocation (b) in two different channels, the top with a coupled laser line, the bottom in free diffusion.

Figure 3

Transport enhancement through channels with deeper external attractive potentials. (a) $J_A$ and (b) $J_T$ as a function of $P/L$ (bottom axis) and $U$ (top axis) for $\lambda \approx 5/4$ (circles). The transport through the channel with the attractive potential is compared with the one through a channel in free diffusion ($\lambda =0$, squares). Each data point and corresponding error bar are the mean and standard deviation of three independent measurements.

Figure 4

Correlation between translocation rate and particle number. (a) Dependence of $N$ on $P/L$ (bottom axis) and $U$ (top axis) for $\lambda \approx 5/4$ (circles) and comparison with a control channel in free diffusion ($\lambda =0$, squares). Each data point and corresponding error bar are the mean and standard deviation of three independent measurements. (b) Correlation between $J_T$ and $N$. Error bars are reported in (a) and Fig. 3. The dotted line is a linear fit of the first 4 points in the graph with the intercept forced to zero. The dashed line is a sublinear power law fit of the whole data set with the intercept forced to zero.