Title:
Mathematical Modeling of the Evolution and Development of Myelin
Abstract:
Nerve impulses exhibit an increased conduction velocity in axons that are wrapped with myelin. Although unmyelinated and myelinated axons are well studied, the process of myelination that allow the formation of myelin on previously unmyelinated axons is not well understood. In this paper we develop a mathematical model of myelination. By varying a parameter that represents the tightness of myelin, this model was made to describe the unmyelinated axon, the fully myelinated axon, and the transitional states in between. As myelin tightens, a slowdown in conduction velocity occurs in the transitional states before a speedup. Varying other geometric parameters such as the thickness and length of myelin shows that some sequences of geometric changes are more optimal than others.
Title: A HYBRID CONTROL MODEL OF FRACTONE-DEPENDENT MORPHOGENESIS
Abstract: It has been hypothesized that the generation of new neural cells (neurogenesis) resulting from cell proliferation and differentiation in the developing and adult brain is guided by the extracellular matrix. The extracellular matrix of the neurogenic niches comprises specialized structures termed fractones, which are scattered in between stem/progenitor cells. Fractones have been found to bind and activate growth factors at the surface of stem/progenitor cells to influence their proliferation. We present a mathematical control model that considers the role of fractones as captors and activators of growth factors, controlling the rate of proliferation and directing the location of the newly generated neuroepithelial cells in the forming brain. The model is a hybrid control system that incorporates both continuous and discrete mechanics. The continuous portion of the model features the diffusion of multiple growth factor concentrations through the mass of cells, with fractones acting as sinks that absorb and hold growth factor. When a sufficient amount has been captured, growth is assumed to occur instantaneously in the discrete portion of the model, causing an immediate rearrangement of cells, and potentially altering the dynamics of the diffusion. The fractones in the model are represented by controls that allow for their dynamic placement in and removal from the evolving cell mass. These controls allows us to govern its developing shape. A version of the model has been implemented for computer simulation and initialized with real biological data. We hope to show the potential usefulness of such a model to verify the plausibility of the fractone hypothesis.
Speaker: Yitzhak Weit (University of Haifa)
Title: On the characterization of harmonic functions on weighted spaces and the Heat equation
Abstract: See attached.