Shape and Orientation Matter for the Cellular Uptake of Nonspherical Particles

Recent advances in nanotechnology have made a whole zoo of particles of different shapes available for applications, but their interaction with biological cells and their toxicity is often not well understood. Experiments have shown that particle uptake by cells is determined by an intricate interplay between physicochemical particle properties like shape, size, and surface functionalization, but also by membrane properties and particle orientation. Our work provides systematic understanding, based on a mechanical description, for membrane wrapping of nanoparticles, viruses, and bacterial forms. For rod-like particles, we find stable endocytotic states with small and high wrapping fraction; an increased aspect ratio is unfavorable for complete wrapping. For high aspect ratios and round tips, the particles enter via a submarine mode, side-first with their long edge parallel to the membrane. For small aspect ratios and flat tips, the particles enter tip-first via a rocket mode

Phase diagram of bundle integrity.

<p>Phase diagram indicating stable bundles (shaded), intermittent slippage (squares), and drift states (bullets) for various flagella distances and torques on helix 2. The torques on helices 1 and 3 are .</p

Snapshots of helices for various torque differences.

<p>Snapshots of side (top) and top (bottom) views for the torque , 400, 600, and 800 (from left to right) at . See also videos S1 8 and S2 8 for and 800, respectively.</p

Average forces on bacteria body.

<p>Average forces per monomer on the anchoring plane of three helices as a function of the torque for at . The bullets indicated the forces by helix two and the solid squares those by helix one and three. The circles and open squares are the contributions by the corresponding hydrodynamics forces for unbundled helices.</p

Bacterial reorientation.

<p>Illustration of the forces and torques on a bacterium and the estimated change in orientation . and are the excess forces after the mean driving force has been subtracted. The induced torque rotates the whole structure, which gives rise to the drag forces on the cell body and on the tail.</p

Bead distance distributions and mean distances.

<p>(a) Normalized bead-distance distribution functions between helices at , is the helical pitch (cf. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0070868#pone-0070868-g001" target="_blank">Fig. 1</a>), for the torque (black), 500 (red), 600 (green), 700 (blue), and 800 (magenta) with . The distance between anchored helix ends is fixed at . The inset shows the distribution functions for (black), 300 (red), and 200 (blue). (b) Average bead distances between the helices at (black), (red), and (blue) () as a function of the torque .</p

Phase slip, lag, and drift.

<p>(a) Phase angle difference as a function of time for various applied torques on helix and the distance . The torque is changed from 200 (top) to 920 (bottom) with an increment of 40; the constant torque is . (b) Average phase lag as a function of the torque . The red line indicates the fit , where . The blue line is the tangent at . The inset provides an approximate measure of the number of occurring slips during the time interval as a function of the applied moment .</p

Capillary Assembly of Microscale Ellipsoidal, Cuboidal, and Spherical Particles at Interfaces

Micron-sized anisotropic particles with homogeneous surface properties at a fluid interface can deform the interface due to their shape. The particles thereby create excess interfacial area and interact in order to minimize this area, which lowers the total interfacial energy. We present a systematic investigation of the interface deformations around single ellipsoidal particles and cuboidal particles with rounded edges in the near field for various contact angles and particle aspect ratios. The correlation of these deformations with capillary bond energiesthe interaction energies of two particles at contactquantifies the relation between the interactions and the near-field deformations. We characterize the interactions using effective power laws and investigate how anisotropic particles self-assemble by capillary forces. Interface deformations and particle interactions for cuboidal particles are weaker compared with those for ellipsoidal particles with the same aspect ratios. For both particle shapes, the bound state in side-by-side orientation is most stable, while the interaction in tip-to-side orientation is repulsive. Furthermore, we find capillary attraction between spherical and ellipsoidal particles. Our calculations therefore suggest cluster formation of spherical and ellipsoidal particles, which elucidates the role of spherical particles as stoppers for the growth of worm-like chains of ellipsoidal particles. The interaction between spherical and ellipsoidal particles might also explain the suppression of the “coffee-ring effect” that has been observed for evaporating droplets with mixtures of spherical and ellipsoidal particles. In general, our calculations of the near-field interactions complement previous calculations in the far field and help to predict colloidal assembly and rheological properties of particle-laden interfaces