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Collective cell migration underlies many biological processes, including embryonic development, wound healing, and cancer progression. In the embryo, cells have been observed to move collectively in vortices using a mode of collective migration known as coherent angular motion (CAM). To determine how CAM arises within a population and changes over time, here, we study the motion of mammary epithelial cells within engineered monolayers, in which the cells move collectively about a central axis in the tissue. Using quantitative image analysis, we find that CAM is significantly reduced when mitosis is suppressed. Particle-based simulations recreate the observed trends, suggesting that cell divisions drive the robust emergence of CAM and facilitate switches in the direction of collective rotation. Our simulations predict that the location of a dividing cell, rather than the orientation of the division axis, facilitates the onset of this motion. These predictions agree with experimental observations, thereby providing, to our knowledge, new insight into how cell divisions influence CAM within a tissue. Overall, these findings highlight the dynamic nature of CAM and suggest that regulating cell division is crucial for tuning emergent collective migratory behaviors, such as vortical motions observed in vivo., (Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Regulated deformations of epithelial sheets are frequently foreshadowed by patterning of their mechanical properties. The connection between patterns of cell properties and the emerging tissue deformations is studied in multiple experimental systems, but the general principles remain poorly understood. For instance, it is in general unclear what determines the direction in which the patterned sheet is going to bend and whether the resulting shape transformation will be discontinuous or smooth. Here these questions are explored computationally, using vertex models of epithelial shells assembled from prismlike cells. In response to rings and patches of apical cell contractility, model epithelia smoothly deform into invaginated or evaginated shapes similar to those observed in embryos and tissue organoids. Most of the observed effects can be captured by a simpler model with polygonal cells, modified to include the effects of the apicobasal polarity and natural curvature of epithelia. Our models can be readily extended to include the effects of multiple constraints and used to describe a wide range of morphogenetic processes., (Copyright © 2016 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Epithelial tissue, in which cells adhere tightly to each other and to the underlying substrate, is one of the four major tissue types in adult organisms. In embryos, epithelial sheets serve as versatile substrates during the formation of developing organs. Some aspects of epithelial morphogenesis can be adequately described using vertex models, in which the two-dimensional arrangement of epithelial cells is approximated by a polygonal lattice with an energy that has contributions reflecting the properties of individual cells and their interactions. Previous studies with such models have largely focused on dynamics confined to two spatial dimensions and analyzed them numerically. We show how these models can be extended to account for three-dimensional deformations and studied analytically. Starting from the extended model, we derive a continuum plate description of cell sheets, in which the effective tissue properties, such as bending rigidity, are related explicitly to the parameters of the vertex model. To derive the continuum plate model, we duly take into account a microscopic shift between the two sublattices of the hexagonal network, which has been ignored in previous work. As an application of the continuum model, we analyze tissue buckling by a line tension applied along a circular contour, a simplified set-up relevant to several situations in the developmental contexts. The buckling thresholds predicted by the continuum description are in good agreement with the results of stability calculations based on the vertex model. Our results establish a direct connection between discrete and continuum descriptions of cell sheets and can be used to probe a wide range of morphogenetic processes in epithelial tissues., (Copyright © 2015 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

The extracellular signal-regulated kinase (ERK) controls cellular processes by phosphorylating multiple substrates. The ERK protein can use the same domains to interact with phosphatases, which dephosphorylate and deactivate ERK, and with substrates, which connect ERK to its downstream effects. As a consequence, substrates can compete with phosphatases and control the level of ERK phosphorylation. We propose that this effect can qualitatively change the dynamics of a network that controls ERK activation. On its own, this network can be bistable, but in a larger system, where ERK accelerates the degradation of a substrate competing with a phosphatase, this network can oscillate. Previous studies proposed that oscillatory ERK signaling requires a negative feedback in which active ERK reduces the rate at which it is phosphorylated by upstream kinase. We argue that oscillations can also emerge even when this rate is constant, due to substrate-dependent control of ERK phosphorylation., (Copyright © 2011 Biophysical Society. Published by Elsevier Inc. All rights reserved.)