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Global morphogenetic flow is accurately predicted by the spatial distribution of myosin motors.
During embryogenesis tissue layers undergo morphogenetic flow rearranging and folding into specific shapes. While developmental biology has identified key genes and local cellular processes, global coordination of tissue remodeling at the organ scale remains unclear. Here, we combine in toto light-sheet microscopy of the Drosophila embryo with quantitative analysis and physical modeling to relate cellular flow with the patterns of force generation during the gastrulation process. We find that the complex spatio-temporal flow pattern can be predicted from the measured meso-scale myosin density and anisotropy using a simple, effective viscous model of the tissue, achieving close to 90% accuracy with one time dependent and two constant parameters. Our analysis uncovers the importance of a) spatial modulation of myosin distribution on the scale of the embryo and b) the non-locality of its effect due to mechanical interaction of cells, demonstrating the need for the global perspective in the study of morphogenetic flow
A mathematical formulation for the cell-cycle model in somitogenesis: analysis, parameter constraints and numerical solutions
In this work we present an analysis, supported by numerical simulations, of the formulation of the cell-cycle model for somitogenesis proposed in Collier et al.(J. Theor. Biol. 207 (2000), 305–316). The analysis indicates that by introducing appropriate parameter constraints on model parameters the cell-cycle mechanism can indeed give rise to the periodic pattern of somites observed in normal embryos. The analysis also provides a greater understanding of the signalling process controlling somite formation and allows us to understand which parameters influence somite length
Partial differential equations for self-organization in cellular and developmental biology
Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field
Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces
The aim of this manuscript is to present for the first time the application of the finite element method for solving reaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces. Furthermore we present pattern formation generated by the reaction-diffusion systemwith cross-diffusion on evolving domains and surfaces. A two-component reaction-diffusion system with linear cross-diffusion in both u and v is presented. The finite element method is based on the approximation of the domain or surface by a triangulated domain or surface consisting of a union of triangles. For surfaces, the vertices of the triangulation lie on the continuous surface. A finite element space of functions is then defined by taking the continuous functions which are linear affine on each simplex of the triangulated domain or surface. To demonstrate the role of cross-diffusion to the theory of pattern formation, we compute patterns with model kinetic parameter values that belong only to the cross-diffusion parameter space; these do not belong to the standard parameter space for classical reaction-diffusion systems. Numerical results exhibited show the robustness, flexibility, versatility, and generality of our methodology; the methodology can deal with complicated evolution laws of the domain and surface, and these include uniform isotropic and anisotropic growth profiles as well as those profiles driven by chemical concentrations residing in the domain or on the surface
Mechanical Stress Inference for Two Dimensional Cell Arrays
Many morphogenetic processes involve mechanical rearrangement of epithelial
tissues that is driven by precisely regulated cytoskeletal forces and cell
adhesion. The mechanical state of the cell and intercellular adhesion are not
only the targets of regulation, but are themselves likely signals that
coordinate developmental process. Yet, because it is difficult to directly
measure mechanical stress {\it in vivo} on sub-cellular scale, little is
understood about the role of mechanics of development. Here we present an
alternative approach which takes advantage of the recent progress in live
imaging of morphogenetic processes and uses computational analysis of high
resolution images of epithelial tissues to infer relative magnitude of forces
acting within and between cells. We model intracellular stress in terms of bulk
pressure and interfacial tension, allowing these parameters to vary from cell
to cell and from interface to interface. Assuming that epithelial cell layers
are close to mechanical equilibrium, we use the observed geometry of the two
dimensional cell array to infer interfacial tensions and intracellular
pressures. Here we present the mathematical formulation of the proposed
Mechanical Inverse method and apply it to the analysis of epithelial cell
layers observed at the onset of ventral furrow formation in the {\it
Drosophila} embryo and in the process of hair-cell determination in the avian
cochlea. The analysis reveals mechanical anisotropy in the former process and
mechanical heterogeneity, correlated with cell differentiation, in the latter
process. The method opens a way for quantitative and detailed experimental
tests of models of cell and tissue mechanics
In silico transitions to multicellularity
The emergence of multicellularity and developmental programs are among the
major problems of evolutionary biology. Traditionally, research in this area
has been based on the combination of data analysis and experimental work on one
hand and theoretical approximations on the other. A third possibility is
provided by computer simulation models, which allow to both simulate reality
and explore alternative possibilities. These in silico models offer a powerful
window to the possible and the actual by means of modeling how virtual cells
and groups of cells can evolve complex interactions beyond a set of isolated
entities. Here we present several examples of such models, each one
illustrating the potential for artificial modeling of the transition to
multicellularity.Comment: 21 pages, 10 figures. Book chapter of Evolutionary transitions to
multicellular life (Springer
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