In the age of stem cell engineering it is critical to understand how stem cell activity is regulated during regeneration. Hairs are miniorgans that undergo cyclic regeneration throughout adult life 1 , and are an important model for organ regeneration. Hair stem cells located in the follicle bulge 2 are regulated by the surrounding microenvironment, or niche 3 . The activation of such stem cells is cyclic, involving periodic b-catenin activity [4][5][6][7] . In the adult mouse, regeneration occurs in waves in a follicle population, implying coordination among adjacent follicles and the extrafollicular environment. Here we show that unexpected periodic expression of bone morphogenetic protein 2 (Bmp2) and Bmp4 in the dermis regulates this process. This BMP cycle is out of phase with the WNT/b-catenin cycle, thus dividing the conventional telogen into new functional phases: one refractory and the other competent for hair regeneration, characterized by high and low BMP signalling, respectively. Overexpression of noggin, a BMP antagonist, in mouse skin resulted in a markedly shortened refractory phase and faster propagation of the regenerative wave. Transplantation of skin from this mutant onto a wild-type host showed that follicles in donor and host can affect their cycling behaviours mutually, with the outcome depending on the equilibrium of BMP activity in the dermis. Administration of BMP4 protein caused the competent region to become refractory. These results show that BMPs may be the long-sought 'chalone' inhibitors of hair growth postulated by classical experiments. Taken together, results presented in this study provide an example of hierarchical regulation of local organ stem cell homeostasis by the inter-organ macroenvironment. The expression of Bmp2 in subcutaneous adipocytes indicates physiological integration between these two thermoregulatory organs. Our findings have practical importance for studies using mouse skin as a model for carcinogenesis, intracutaneous drug delivery and stem cell engineering studies, because they highlight the acute need to differentiate supportive versus inhibitory regions in the host skin.Mammalian skin contains thousands of hair follicles, each undergoing continuous regenerative cycling. A hair follicle cycles through anagen (growth), catagen (involution) and telogen (resting) phases, and then re-enters the anagen phase. At the base of this cycle is the ability of hair follicle stem cells to briefly exit their quiescent status to generate transient amplifying progeny, but maintain a cluster of stem cells. It is generally believed that a niche microenvironment is important in the control of stem cell homeostasis in various systems 8 . Within a single hair follicle, periodic activation of b-catenin in bulge stem cells is responsible for their cyclic activity 3 . However, how these stem cell activation events are coordinated among neighbouring hairs remains unclear. It is possible that a population of hair follicles could cycle simultaneously, randomly or in coordinated waves...

The dynamic behavior of epithelial cell sheets plays a central role during numerous developmental processes. Genetic and imaging studies of epithelial morphogenesis in a wide range of organisms have led to increasingly detailed mechanisms of cell sheet dynamics. Computational models offer a useful means by which to investigate and test these mechanisms, and have played a key role in the study of cell-cell interactions. A variety of modeling approaches can be used to simulate the balance of forces within an epithelial sheet. Vertex models are a class of such models that consider cells as individual objects, approximated by two-dimensional polygons representing cellular interfaces, in which each vertex moves in response to forces due to growth, interfacial tension, and pressure within each cell. Vertex models are used to study cellular processes within epithelia, including cell motility, adhesion, mitosis, and delamination. This review summarizes how vertex models have been used to provide insight into developmental processes and highlights current challenges in this area, including progressing these models from two to three dimensions and developing new tools for model validation.

Vertebrate embryos are characterized by an elongated antero-posterior (AP) body axis, which forms by progressive cell deposition from a posterior growth zone in the embryo. Here, we used tissue ablation in the chicken embryo to demonstrate that the caudal presomitic mesoderm (PSM) plays a key role in axis elongation. Using time-lapse microscopy, we analysed the movements of fluorescently labelled cells in the PSM during embryo elongation which revealed a clear posterior-to-anterior gradient of cell motility and directionality in the PSM. We tracked the movement of the PSM extracellular matrix in parallel with the labelled cells and subtracted the extracellular matrix movement from the global motion of cells. After subtraction, cell motility remained graded but lacked directionality, indicating that the posterior cell movements associated with axis elongation in the PSM are not intrinsic but reflect tissue deformation. The gradient of cell motion along the PSM parallels the fibroblast growth factor (FGF)/mitogen-activated protein kinase (MAPK) gradient 1, which has been implicated in the control of cell motility in this tissue2. Both FGF signalling gain- and loss-of-function experiments lead to disruption of the motility gradient and a slowing down of axis elongation. Furthermore, embryos treated with cell movement inhibitors (Blebbistatin or RhoK inhibitor), but not cell cycle inhibitors, show a slower axis elongation rate. We propose that the gradient of random cell motility downstream of FGF signalling in the PSM controls posterior elongation in the amniote embryo. Our data suggest that tissue elongation is an emergent property that arises from the collective regulation of graded, random cell motion rather than by the regulation of directionality of individual cellular movements.

On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description.

Stem cells cycle through active and quiescent states. Large populations of stem cells in an organ may cycle randomly or in a coordinated manner. Although stem cell cycling within single hair follicles has been studied, less is known about regenerative behavior in a hair follicle population. By combining predictive mathematical modeling with in vivo studies in mice and rabbits, we show that a follicle progresses through cycling stages by continuous integration of inputs from intrinsic follicular and extrinsic environmental signals based on universal patterning principles. Signaling from the WNT/bone morphogenetic protein activator/inhibitor pair is coopted to mediate interactions among follicles in the population. This regenerative strategy is robust and versatile because relative activator/inhibitor strengths can be modulated easily, adapting the organism to different physiological and evolutionary needs.