Single-particle tracking discloses binding-mediated rocking diffusion of rod-shaped biological particles on lipid membranes

Abstract

It has been demonstrated that rod-shaped particles can achieve a high translocation efficiency for gene and drug delivery in biological samples. Previous theoretical calculations also confirmed that rod-shaped particles display higher diffusivity than their spherical counterparts in biological porous media. Understanding the diffusion dynamics of biological and non-biological rod-shaped particles in biological solutions as well as close to the lipid membrane is therefore fundamentally significant for the rational design of efficient cargos. With dark-field optical microscopy, the translational and three-dimensional (3D) orientational diffusion dynamics of individual rod-shaped particles (i.e., E. coli and upconversion microrods, UCMRs) in phosphate buffered saline (PBS) and on the lipid membrane are tracked at the single-particle level. In the buffer solution, faster rotation of E. coli in the z direction was observed even though its dynamics in the x-y plane is comparable with that of UCMRs. Interestingly, on the lipid membrane, distinct from the confined motion of UCMRs, anomalous rocking diffusion was observed, which might facilitate the subsequent survey of stronger association sites on the two-dimensional (2D) surface. These results would afford deep insight into the better understanding of the translocation mechanism by using rod-shaped particles as a delivery cargo in biological samples.

Fig. 1. (a and b) SEM images of E. coli and UCMRs. (c) The scheme of the Cartesian coordinate system. (d) Representative 2D diffusion trajectories of E. coli (red) and UCMRs (green) in the PBS solution. (e) The MSD plots of E. coli (red) and UCMRs (green). (f) The 2D diffusion coefficient distributions of E. coli and UCMRs. (g and j) The time-dependent diffusion tracks along a and b axis for E. coli and UCMRs, respectively. (h and k) The displacement distributions within a period of 0.01 s along the a axis for E. coli and UCMRs, respectively. (i and l) The MSD plots along a and b directions for E. coli and UCMRs, respectively.

Fig. 2. (a) MSAD plots of E. coli (red) and UCMRs (green) from the polar angle. (b) MSAD plots of E. coli (red) and UCMRs (green) from the azimuthal angle. (c) The rotational diffusion coefficient distributions of E. coli and UCMRs from the polar angle. (d) The rotational diffusion coefficient distributions of E. coli and UCRMs from the azimuthal angle.

Fig. 3. (a) Schematic diagram of the binding-mediated rocking diffusion on the lipid membrane of E. coli. (b) The 2D diffusion trajectories of E. coli and UCMRs on the lipid membrane. (c) The MSD plots of E. coli (red) and UCMRs (green). (d) The distributions of the 2D diffusion coefficients of E. coli and UCMRs on the lipid membrane. (e) Double-logarithmic plots of the step size distribution of E. coli and UCMRs (normalized by the initial point), respectively.

Fig. 4. (a) The angular rotational trajectories of E. coli and UCMRs on the lipid membrane along the z direction. (b) The polar angle distributions of E. coli and UCMRs. (c) Representative MSAD plots of E. coli and UCMRs from the polar angle on the lipid membrane. (d) The distribution of the rotational diffusion coefficients of E. coli and UCMRs on the lipid membrane along the z direction.

Fig. 5. (a) The angular rotational trajectories of E. coli and UCMRs on the lipid membrane in the x–y plane. (b) The azimuthal angle distributions of E. coli and UCMRs. (c) Representative MSAD plots of E. coli and UCMRs from the azimuthal angle on the lipid membrane. (d) The distribution of the rotational diffusion coefficients of E. coli and UCMRs on the lipid membrane in the x–y plane.

Fig. 6. (a) Frame-by-frame images of the rotational and translational diffusion of E. coli on the lipid membrane with an observation time window of 1 s. (b) The time-dependent trajectory of E. coli on the lipid membrane. The 3D orientations from different time periods are marked with red arrows. (c)–(h) The time-dependent trajectories from the polar angle, the azimuthal angle, the walking displacement along x and y axes, and the walking displacement along a and b axes, respectively.