Vasculogenesis, the de novo growth of the primary vascular network from initially dispersed endothelial cells, is the first step in the development of the circulatory system in vertebrates. In the first stages of vasculogenesis, endothelial cells elongate and form a network-like structure, called the primary capillary plexus, which subsequently remodels, with the size of the vacancies between ribbons of endothelial cells coarsening over time. To isolate such intrinsic morphogenetic ability of endothelial cells from its regulation by long-range guidance cues and additional cell types, we use an in vitro model of human umbilical vein endothelial cells (HUVEC) in Matrigel. This quasi-two-dimensional endothelial cell culture model would most closely correspond to vasculogenesis in flat areas of the embryo like the yolk sac. Several studies have used continuum mathematical models to explore in vitro vasculogenesis: such models describe cell ensembles but ignore the endothelial cells' shapes and active surface fluctuations. While these models initially reproduce vascular-like morphologies, they eventually stabilize into a disconnected pattern of vascular "islands." Also, they fail to reproduce temporally correct network coarsening. Using a cell-centered computational model, we show that the endothelial cells' elongated shape is key to correct spatiotemporal in silico replication of stable vascular network growth. We validate our simulation results against HUVEC cultures using time-resolved image analysis and find that our simulations quantitatively reproduce in vitro vasculogenesis and subsequent in vitro remodeling.

During development cells and tissues undergo changes in pattern and form that employ a wider range of physical mechanisms than at any other time in an organism's life. This book shows how physics can be used to analyze these biological phenomena. Written to be accessible to both biologists and physicists, major stages and components of the biological development process are introduced and then analyzed from the viewpoint of physics. The presentation of physical models requires no mathematics beyond basic calculus. Physical concepts introduced include diffusion, viscosity and elasticity, adhesion, dynamical systems, electrical potential, percolation, fractals, reaction-diffusion systems, and cellular automata. With full-color figures throughout, this comprehensive textbook teaches biophysics by application to developmental biology and is suitable for graduate and upper-undergraduate courses in physics and biology.

We present a classification of developmental mechanisms that have been shown experimentally to generate pattern and form in metazoan organisms. We propose that all such mechanisms can be organized into three basic categories and that two of these may act as composite mechanisms in two different ways. The simple categories are cell autonomous mechanisms in which cells enter into specific arrangements ('patterns') without interacting, inductive mechanisms in which cell communication leads to changes in pattern by reciprocal or hierarchical alteration of cell phenotypes ('states') and morphogenetic mechanisms in which pattern changes by means of cell interactions that do not change cell states. The latter two types of mechanism can be combined either morphostatically, in which case inductive mechanisms act first, followed by the morphogenetic mechanism, or morphodynamically, in which case both types of mechanisms interact continuously to modify each other's dynamics. We propose that this previously unexplored distinction in the operation of composite developmental mechanisms provides insight into the dynamics of many developmental processes. In particular, morphostatic and morphodynamic mechanisms respond to small changes in their genetic and microenvironmental components in dramatically different ways. We suggest that these differences in 'variational properties' lead to morphostatic and morphodynamic mechanisms being represented to different extents in early and late stages of development and to their contributing in distinct ways to morphological transitions in evolution.

We describe a 'reactor-diffusion' mechanism for precartilage condensation based on recent experiments on chondrogenesis in the early vertebrate limb and additional hypotheses. Cellular differentiation of mesenchymal cells into subtypes with different fibroblast growth factor (FGF) receptors occurs in the presence of spatio-temporal variations of FGFs and transforming growth factor-betas (TGF-βs). One class of differentiated cells produces elevated quantities of the extracellular matrix protein fibronectin, which initiates adhesion-mediated preskeletal mesenchymal condensation. The same class of cells also produces an FGFdependent laterally acting inhibitor that keeps condensations from expanding beyond a critical size. We show that this 'reactor-diffusion' mechanism leads naturally to patterning consistent with skeletal form, and describe simulations of spatio-temporal distribution of these differentiated cell types and the TGF-β and inhibitor concentrations in the developing limb bud.

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