Quantifying stretching and rearrangement in epithelial sheet migration

Although understanding the collective migration of cells, such as that seen in epithelial sheets, is essential for understanding diseases such as metastatic cancer, this motion is not yet as well characterized as individual cell migration. Here we adapt quantitative metrics used to characterize the flow and deformation of soft matter to contrast different types of motion within a migrating sheet of cells. Using a Finite-Time Lyapunov Exponent (FTLE) analysis, we find that - in spite of large fluctuations - the flow field of an epithelial cell sheet is not chaotic. Stretching of a sheet of cells (i.e., positive FTLE) is localized at the leading edge of migration. By decomposing the motion of the cells into affine and non-affine components using the metric D$^{2}_{min}$, we quantify local plastic rearrangements and describe the motion of a group of cells in a novel way. We find an increase in plastic rearrangements with increasing cell densities, whereas inanimate systems tend to exhibit less non-affine rearrangements with increasing density.Comment: 21 pages, 7 figures This is an author-created, un-copyedited version of an article accepted for publication in the New Journal of Physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at doi:10.1088/1367-2630/15/2/02503

Centrifugal Compression of Soft Particle Packings: Theory and Experiment

An exact method is developed for computing the height of an elastic medium subjected to centrifugal compression, for arbitrary constitutive relation between stress and strain. Example solutions are obtained for power-law media and for cases where the stress diverges at a critical strain—for example as required by packings composed of deformable but incompressible particles. Experimental data are presented for the centrifugal compression of thermo-responsive N-isopropylacrylamide (NIPA) microgel beads in water. For small radial acceleration, the results are consistent with Hertzian elasticity, and are analyzed in terms of the Young elastic modulus of the bead material. For large radial acceleration, the sample compression asymptotes to a value corresponding to a space-filling particle volume fraction of unity. Therefore we conclude that the gel beads are incompressible, and deform without deswelling. In addition, we find that the Young elastic modulus of the particulate gel material scales with cross-link density raised to the power 3.3±0.8, somewhat larger than the Flory expectation

Jamming and flow of soft particle suspensions

This thesis focuses on the study of soft spherical particles near jamming. N-isopropylacrylamide (NIPA) microgel spheres were studied in both static and flowing states. As the particles are soft, they may be packed above the jamming volume fraction &phis; ∼ 0.64, corresponding to random close packing. To study them in static jammed configurations, we developed a novel centrifigation technique that allowed us to probe the elasticity of the packed bed of particles. Using effective medium theory, we were then able to obtain information about the elastic properties of the individual spheres, discovering they are Hertzian with a Poisson ratio ν = 0.5. Next, we studied the flowing state of the particles in a microfluidic channel. Through a careful choice of the channel geometry, we were able to relate the velocity profiles to stress and strain rate, thus obtaining rheological flow curves for the system. We found we could collapse these curves onto two master curves: one above the jamming density and one below the jamming density. Such collapse had been seen before in simulation, but not in experiment prior to this work. Interestingly, the critical exponents for this collapse seem to be dependent on the interparticle interaction, thus undermining previous notions of universality for the jamming transition. Finally, we looked for evidence of a growing time and length scale near jamming by looking at the dynamical heterogeneities in the system. We found evidence of these time and length scales, which seem to grow in the same way above and below jamming. We also found critical exponents for these parameters, and saw again that the interparticle potential governs their values. We conclude that jamming is similar to a phase transition, but with interaction-dependent critical exponents