A Mathematical Analysis of the Dynamics of Prion Proliferation

How do the normal prion protein (PrP(C)) and infectious prion protein (PrP(Sc)) populations interact in an infected host? To answer this question, we analyse the behavior of the two populations by studying a system of differential equations. The system is constructed under the assumption that PrP(Sc) proliferates using the mechanism of nucleated polymerization. We prove that with parameter input consistent with experimentally determined values, we obtain the persistence of PrP(Sc). We also prove local stability results for the disease steady state, and a global stability result for the disease free steady state. Finally, we give numerical simulations, which are confirmed by experimental data

Aplicacion del silicato tricalcico como una alternativa biocompatible.

El seleccionar un adecuado material para la obturación apical es un acto fundamental para la resolución de un caso con una lesión periapical persistente; los principales factores que deberá tener este material es su biocompatibilidad y el crear un sellado hermético para evitar filtración; deberá poseer capacidad para inducir osteogénesis y reparación, no desarrollar toxicidad, ser radiopaco y bacteriostático. El Biodentine es un material recientemente introducido al mercado (2011), principalmente compuesto de silicato tricálcico. Es usado para tratamientos de reparación en corona y raíz, reparando perforaciones, resorciones, empleado para apexificaciones y como material de retroobturación; también puede ser utilizado como un sustituto de dentina en caries demasiado extensas.

Quantitative Analysis of Mechanisms That Govern Red Blood Cell Age Structure and Dynamics during Anaemia

Mathematical modelling has proven an important tool in elucidating and quantifying mechanisms that govern the age structure and population dynamics of red blood cells (RBCs). Here we synthesise ideas from previous experimental data and the mathematical modelling literature with new data in order to test hypotheses and generate new predictions about these mechanisms. The result is a set of competing hypotheses about three intrinsic mechanisms: the feedback from circulating RBC concentration to production rate of immature RBCs (reticulocytes) in bone marrow, the release of reticulocytes from bone marrow into the circulation, and their subsequent ageing and clearance. In addition we examine two mechanisms specific to our experimental system: the effect of phenylhydrazine (PHZ) and blood sampling on RBC dynamics. We performed a set of experiments to quantify the dynamics of reticulocyte proportion, RBC concentration, and erythropoietin concentration in PHZ-induced anaemic mice. By quantifying experimental error we are able to fit and assess each hypothesis against our data and recover parameter estimates using Markov chain Monte Carlo based Bayesian inference. We find that, under normal conditions, about 3% of reticulocytes are released early from bone marrow and upon maturation all cells are released immediately. In the circulation, RBCs undergo random clearance but have a maximum lifespan of about 50 days. Under anaemic conditions reticulocyte production rate is linearly correlated with the difference between normal and anaemic RBC concentrations, and their release rate is exponentially correlated with the same. PHZ appears to age rather than kill RBCs, and younger RBCs are affected more than older RBCs. Blood sampling caused short aperiodic spikes in the proportion of reticulocytes which appear to have a different developmental pathway than normal reticulocytes. We also provide evidence of large diurnal oscillations in serum erythropoietin levels during anaemia

Cell Modelling of Hematopoiesis

In this work, we introduce a new software created to study hematopoiesis at the cell population level with the individually based approach. It can be used as an interface between theoretical works on population dynamics and experimental observations. We show that this software can be useful to study some features of normal hematopoiesis as well as some blood diseases such as myelogenous leukemia. It is also possible to simulate cell communication and the formation of cell colonies in the bone marrow

Dynamics of the prion proliferation

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