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Skeletal patterning in the vertebrate limb,
i.e., the spatiotemporal regulation of cartilage differentiation
(chondrogenesis) during embryogenesis and regeneration, is one
of the best studied examples of a multicellular developmental process.
Recently [Alber et al., The morphostatic limit for a model of
skeletal pattern formation in the vertebrate limb, Bulletin of
Mathematical Biology, 2008, v70, pp. 460-483], a simplified two-equation
reaction-diffusion system was developed to describe the interaction...
Vasculogenesis and angiogenesis are two different mechanisms for blood vessel formation. Angiogenesis occurs when new vessels sprout from pre-existing vasculature in response to external chemical stimuli. Vasculogenesis occurs via the reorganization of randomly distributed cells into a blood vessel network. Experimental models of vasculogenesis have suggested that the cells exert traction forces onto the extracellular matrix and that these forces may play an important role in the network forming...
Vasculogenesis and angiogenesis are two different mechanisms for blood
vessel formation. Angiogenesis occurs when new vessels sprout from
pre-existing vasculature in response to external chemical stimuli.
Vasculogenesis occurs via the reorganization of randomly distributed
cells into a blood vessel network. Experimental models
of vasculogenesis have suggested that the cells exert traction forces
onto the extracellular matrix and that these forces may play
an important role in the network forming...
A conceptual minimal model demonstrating spatially heterogeneous wave regimes
interpreted as pursuit-evasion in predator-prey system is constructed and investigated. The
model is based on the earlier proposed hypothesis that taxis accelerations of prey and
predators are proportional to the density gradient of another population playing a role
of taxis stimulus. Considering acceleration rather than immediate velocity allows
obtaining realistic solutions even while ignoring variations of total...
Proteus mirabilis are bacteria that make strikingly regular spatial-temporal patterns on agar surfaces.
In this paper we investigate a mathematical model that has been
shown to display these structures when solved numerically. The model consists of an ordinary
differential equation coupled with a partial differential equation involving a first-order
hyperbolic aging term together with nonlinear degenerate diffusion. The system is shown to
admit global weak solutions.
Recently, adult stem cells have become a focus of intensive biomedical research, but the
complex regulation that allows a small population of stem cells to replenish depleted tissues is still
unknown. It has been suggested that specific tissue structures delimit the spaces where stem cells
undergo unlimited proliferation (stem cell niche). In contrast, mathematical analysis suggests that
a feedback control of stem cells on their own proliferation and differentiation (denoted Quorum
Sensing) suffices...
The paper deals with the issue of self-organization in applied sciences. It is particularly related to the emergence of Turing patterns. The goal is to analyze the domain size driven instability: We introduce the parameter , which scales the size of the domain. We investigate a particular reaction-diffusion model in 1-D for two species. We consider and analyze the steady-state solution. We want to compute the solution branches by numerical continuation. The model in question has certain symmetries....
Plants and animals have highly ordered structure both in time and in space, and one of the main questions of modern developmental biology is the transformation of genetic information into the regular structure of organism. Any multicellular plant begins its development from the universal unicellular state and acquire own species-specific structure in the course of cell divisions, cell growth and death, according to own developmental program. However the cellular mechanisms of plant development are...
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