Universal Statistical Laws for the Velocities of Collective Migrating Cells.

Migratory dynamics of collective cells is central to the morphogenesis of biological tissues. The statistical distribution of cell velocities in 2D confluent monolayers is measured through large-scale and long-term experiments of various cell types lying on different substrates. A linear relation is discovered between the variability and the mean of cell speeds during the jamming process of confluent cell monolayers, suggesting time-invariant distribution profile of cell velocities. It is further found that the probability density function of cell velocities obeys the non-canonical q-Gaussian statistics, regardless of cell types and substrate stiffness. It is the Tsallis entropy, instead of the classical Boltzmann-Gibbs entropy, that dictates the universal statistical laws of collective cell migration. The universal statistical law stems from cell-cell interactions, as demonstrated by the wound healing experiments. This previously unappreciated finding provides a linkage between cell-level heterogeneity and tissue-level ensembles in embryonic development and tumor growth.

Wrinkling patterns in soft shells.

Curvature plays an important role in the morphological evolution of soft shells under stretch. Here, through a combination of experiment, theory and simulation, we investigate the behavior of a hemispherical soft shell subject to an increasing outward point force at its pole. In contrast to an inward point force inducing a polygonal pattern of buckling in the shell, we observe a four-stage morphological transition and symmetry breaking under an increasing outward point force. The shell undergoes axisymmetric deformation around its pole and then buckles into a non-axisymmetric shape with a number of shallow wrinkles emanating from the pole, followed by the emergence of crater-like deep crumples and ultimately a transformation into a wrinkled pseudocone. Our theoretical analysis and numerical simulations yield the critical conditions for the morphological transitions at each stage of deformation and reveal the underlying interplays between elastic bending and stretching energies and the curvature of the shell.