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The aim of this paper is to further develop mathematical models for bleb formation in cells, including cell-membrane interactions with linker proteins. This leads to nonlinear reaction-diffusion equations on a surface coupled to fluid dynamics in the bulk. We provide a detailed mathematical analysis and investigate some singular limits of the model, connecting it to previous literature. Moreover, we provide numerical simulations in different scenarios, confirming that the model can reproduce experimental results on bleb initation.
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential equations of trans
We study a mathematical model describing the dynamics of a pluripotent stem cell population involved in the blood production process in the bone marrow. This model is a differential equation with a time delay. The delay describes the cell cycle durat
We consider density solutions for gradient flow equations of the form $u_t = abla cdot ( gamma(u) abla mathrm N(u))$, where $mathrm N$ is the Newtonian repulsive potential in the whole space $mathbb R^d$ with the nonlinear convex mobility $gamma(u)
In the development of multiscale biological models it is crucial to establish a connection between discrete microscopic or mesoscopic stochastic models and macroscopic continuous descriptions based on cellular density. In this paper a continuous limi
Recent biological research has sought to understand how biochemical signaling pathways, such as the mitogen-activated protein kinase (MAPK) family, influence the migration of a population of cells during wound healing. Fishers Equation has been used