Collective migration dominates many phenomena, from cell movement in living systems to abiotic selfpropelling particles. Focusing on the early stages of tumor evolution, we enunciate the principles involved in cell dynamics and highlight their implications in understanding similar behavior in seemingly unrelated soft glassy materials and possibly chemokine-induced migration of CD8 þ T cells. We performed simulations of tumor invasion using a minimal three-dimensional model, accounting for cell elasticity and adhesive cell-cell interactions, as well as cell birth and death, to establish that cell-growth-ratedependent tumor expansion results in the emergence of distinct topological niches. Cells at the periphery move with higher velocity perpendicular to the tumor boundary, while the motion of interior cells is slower and isotropic. The mean-square displacement ΔðtÞ of cells exhibits glassy behavior at times comparable to the cell cycle time, while exhibiting superdiffusive behavior, ΔðtÞ ≈ t α (α > 1), at longer times. We derive the value of α ≈ 1.33 using a field theoretic approach based on stochastic quantization. In the process, we establish the universality of superdiffusion in a class of seemingly unrelated nonequilibrium systems. Superdiffusion at long times arises only if there is an imbalance between cell birth and death rates. Our findings for the collective migration, which also suggest that tumor evolution occurs in a polarized manner, are in quantitative agreement with in vitro experiments. Although set in the context of tumor invasion, the findings should also hold in describing the collective motion in growing cells and in active systems, where creation and annihilation of particles play a role.

We report measurements of the superconducting transition temperature, T c , in CoO/Co/Cu/Co/Nb multilayers as a function of the angle α between the magnetic moments of the Co layers. Our measurements reveal that T c (α) is a nonmonotonic function, with a minimum near α = π/2. Numerical self-consistent solutions of the Bogoliubov-de Gennes equations quantitatively and accurately describe the behavior of T c as a function of α and layer thicknesses in these superconductor / spin-valve heterostructures. We show that experimental data and theoretical evidence agree in relating T c (α) to enhanced penetration of the triplet component of the condensate into the Co/Cu/Co spin valve in the maximally noncollinear magnetic configuration.

Morphogenesis is governed by the interplay of molecular signals and mechanical forces across multiple length scales. The last decade has seen tremendous advances in our understanding of the dynamics of protein localization and turnover at sub-cellular length scales, and at the other end of the spectrum, of mechanics at tissue-level length scales. Integrating the two remains a challenge, however, because we lack a detailed understanding of the subcellular patterns of mechanical properties of cells within tissues. Here, in the context of the elongating body axis of Xenopus embryos, we combine tools from cell biology and physics to demonstrate that individual cell-cell junctions display finely-patterned local mechanical heterogeneity along their length. We show that such local mechanical patterning is essential for the cell movements of convergent extension and is imparted by locally patterned clustering of a classical cadherin. Finally, the patterning of cadherins and thus local mechanics along cell-cell junctions are controlled by Planar Cell Polarity signaling, a key genetic module for CE that is mutated in diverse human birth defects.

Spatially heterogenous dynamics inside a growing tumor spheroid.