Diffusion through Nanopores in Connected Lipid Bilayer Networks

A biomimetic model of cell-cell communication was developed to probe the passive molecular transport across ion channels inserted in synthetic lipid bilayers formed between contacting droplets arranged in a linear array. Diffusion of a fluorescent probe across the array was measured for different pore concentrations. The diffusion characteristic timescale is found to vary nonlinearly with the pore concentration. Our measurements are successfully modeled by a continuous time random walk description whose waiting time is the first exit time from a droplet through a cluster of pores. The size of the cluster of pores is found to increase with their concentration. Our results provide a direct link between the mesoscopic permeation properties and the microscopic characteristics of the pores, such as their number, size, and spatial arrangement.

Figure 1

(a) Sketch of the experimental setup. The aqueous solution is injected through a glass capillary pulled out periodically across the oil-air interface. The detached droplets sediment in a Plexiglas pool decorated with parallel grooves and form a DIB network. Lateral positioning of the droplets is achieved by moving the pool with a motorized translation stage. Eventually, a source droplet seeded with fluorophores is deposited. Diffusion of fluorophores is imaged in epifluorescence microscopy. (Inset) Image of three typical DIB networks. The white bar is $200\mu \mathrm{m}$ long. (b) Sketch of the diffusion process of fluorophores across DIBs decorated with $\alpha \mathrm{HL}$ protein pores.

Figure 2

(a) Composite image from bright field (gray) and fluorescence (green) microscopy of a typical diffusion process of carboxyfluorescein across a DIB network ($c=200\mu \mathrm{g}/\mathrm{ml}$) at $t=15\mathrm{h}$. The white bar is $100\mu \mathrm{m}$ long. (b) Occupancy probability $P$ of carboxyfluorescein as a function of time for the network of (a). From top to bottom, the different curves correspond, respectively, to the source droplet $S$ (green circles), the first $N_1$ (red diamonds), and the second $N_2$ (blue squares) neighboring droplets. The black disks show $P_s(t)$ for the source droplet in a typical control experiment, i.e., without any pores. The dashed line corresponds to $t=15$ h.

Figure 3

(a) Occupancy probability $P_1$ as a function of time $t$ for four different $\alpha \mathrm{HL}$ monomer concentrations, $c=150$, 200, 250, $300\mu \mathrm{g}/\mathrm{ml}$, with $N=18$, 25, 8, 10, respectively. Error bars indicate the standard deviation of the data. The dashed lines are linear fits used to extract the characteristic rate $\lambda$ (see the main text). They are shifted vertically to ease visualization. (b) Characteristic rate $\lambda$ as a function of $c$. The solid line is a power-law fit of exponent $3\pm 1$. The dashed line is a fit using an exponent of $7/2$. The dashed-dotted line is a fit using an exponent of 7. (Inset) Occupancy probability as a function of the rescaled time $⟨\lambda ⟩t$.