1,559 research outputs found
A modified Oster-Murray-Harris mechanical model of morphogenesis
There are two main modeling paradigms for biological pattern formation in developmental biology: chemical prepattern models and cell aggregation models. This paper focuses on an example of a cell aggregation model, the mechanical model developed by Oster, Murray, and Harris [Development, 78 (1983), pp. 83--125]. We revisit the Oster--Murray--Harris model and find that, due to the infinitesimal displacement assumption made in the original version of this model, there is a restriction on the types of boundary conditions that can be prescribed. We derive a modified form of the model which relaxes the infinitesimal displacement assumption. We analyze the dynamics of this model using linear and multiscale nonlinear analysis and show that it has the same linear behavior as the original Oster--Murray--Harris model. Nonlinear analysis, however, predicts that the modified model will allow for a wider range of parameters where the solution evolves to a bounded steady state. The results from both analyses are verified through numerical simulations of the full nonlinear model in one and two dimensions. The increased range of boundary conditions that are well-posed, as well as a wider range of parameters that yield bounded steady states, renders the modified model more applicable to, and more robust for, comparisons with experiments
A mechanical model for biological pattern formation: A nonlinear bifurcation analysis
We present a mechanical model for cell aggregation in embryonic development. The model is based on the large traction forces exerted by fibroblast cells which deform the extracellular matrix (ECM) on which they move. It is shown that the subsequent changes in the cell environment can combine to produce pattern. A linear analysis is carried out for this model. This reveals a wide spectrum of different types of dispersion relations. A non-linear bifurcation analysis is presented for a simple version of the field equations: a non-standard element is required. Biological applications are briefly discussed
An analysis of one- and two-dimensional patterns in a mechanical model for morphogenesis
In early embryonic development, fibroblast cells move through an extracellular matrix (ECM) exerting large traction forces which deform the ECM. We model these mechanical interactions mathematically and show that the various effects involved can combine to produce pattern in cell density. A linear analysis exhibits a wide selection of dispersion relations, suggesting a richness in pattern forming capability of the model. A nonlinear bifurcation analysis is presented for a simple version of the governing field equations. The one-dimensional analysis requires a non-standard element. The two-dimensional analysis shows the possibility of roll and hexagon pattern formation. A realistic biological application to the formation of feather germ primordia is briefly discussed
Spatial and spatio-temporal patterns in a cell-haptotaxis model
We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost through a Hopf bifurcation. We carry out a nonlinear multi-time scale perturbation procedure to study the evolution of the resulting spatio-temporal patterns. We also analyse the model in a parameter domain wherein it exhibits a singular dispersion relation
Recommended from our members
Water reuse for irrigated agriculture in Jordan: challenges of soil sustainability and the role of management strategies
Reclaimed water provides an important contribution to the water balance in water-scarce Jordan, but the quality of this water presents both benefits and challenges. Careful management of reclaimed water is required to maximize the nutrient benefits while minimizing the salinity risks. This work uses a multi-disciplinary research approach to show that soil response to irrigation with reclaimed water is a function of the management strategies adopted on the farm by the water user. The adoption of management methods to maintain soil productivity can be seen to be a result of farmers’ awareness to potentially plant-toxic ions in the irrigation water (70% of Jordan Valley farmers identified salinization as a hazard from irrigation with reclaimed water). However, the work also suggests that farmers’ management capacity is affected by the institutional management of water. About a third (35%) of farmers in the Jordan Valley claimed that their ability to manage salinization was limited by water shortages. Organizational interviews revealed that institutional awareness of soil management challenges was quite high (34% of interviewees described salinization as a risk from water reuse), but strategies to address this challenge at the institutional level require greater development
Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis
We present an in-depth study of spatio-temporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the model and show how to choose realistic boundary conditions to make the system well-posed. We firstly consider one-dimensional patterns and carry out a nonlinear perturbation analysis for the case where the uniform steady state is linearly unstable to a single mode. In two-dimensions, we show that if the displacement field in the model is represented as a sum of orthogonal parts, then the model can be decomposed into two sub-models, only one of which is capable of generating pattern. We thus focus on this particular sub-model. We present a nonlinear analysis of spatio-temporal patterns exhibited by the sub-model on a square domain and discuss mode interaction. Our analysis shows that when a two-dimensional mode number admits two or more degenerate mode pairs, the solution of the full nonlinear system of partial differential equations is a mixed mode solution in which all the degenerate mode pairs are represented in a frequency locked oscillation
Forces and pattern in limb morphogenesis
Prior to cartilage and bone formation in the limb bud chondroblasts condense into foci which provide the pattern for subsequent bone development. Formation of these condensations is, finally, a mechanical event, and so it is natural to ask what are the forces responsible for creating them.
We have constructed a model for the process of cell aggregation during chondrogenesis which involves the following forces: (1) the passive elasticity of the extracellular matrix (ECM), (2) the osmotic swelling pressure of the ECM, which is generated principally by the hyaluronate (HA) component, (3) the active cell tractions developed by the chondroblasts. By examining the balance of forces between the cells and matrix we find that patterns of cell aggregation can spontaneously arise by an instability mechanism analogous to that which occurs in chemical pattern formation models
- …