Diffusion and aggregation process in biological physics: prionic diseases and random walks with memory

Abstract

In this project we will study two problems: prionic diseases and non-Markovian random walks. Specifically, with prions we will study the incubation time distributions starting from existent experimental data for cattle and hamsters. Recently, we obtained an important result, showing that a simple mean field model of purely autocatalytic kinetics can reproduce experimental data; in that same work we introduced an automaton cellular model that gave qualitatively good results. However, those models do not possess the minimum ingredients for generalization of the results, because they do not reproduce "microscopically" the topology of the aggregation phenomenon. In this work we propose models, similar to epidemic models, which can be solved with Dynamic Monte Carlo, whose kinetics can generate aggregates. In these more general models we will analyse the importance of the autocatalytic term in the prionic reactions. For random walks with memory, we showed recently that loss of old memory above certain limit leads to Markovian behaviour. Differently, in recent memory loss it appears anomalous diffusion in a region of negative feedback, which can explain repetitive behaviours just as in the Alzheimer disease. We got experimentally (computational simulation), a complete phase diagram for that system. In this work we intend to find analytical results in order to define rigorously the observed transitions. Another objective is to analyse big systems (~10**8) with Monte Carlo simulation for several memory profiles. (AU)