STUDIES OF THE INCUBATION TIMES OF PRIONIC DISEASES BY DYNAMICAL MONTE CARLO METHOD.

FQ10

Naira Rezende Maciel (1) naira@fcfrp.usp.br, Arlan da Silva Ferreira (2), José Carlos Cressoni (2), Marco Antonio Alves da Silva (1)

(1) Departamento de Física e Química da FCFRP, Universidade de São Paulo, Ribeirão Preto, SP, Brasil

(2) Departamento de Física da Universidade Federal de Alagoas, Maceió, AL, Brasil

Introduction: Prions are the infectious agents responsible for a group of fatal neurodegenerative disorders. An pathogenic isoform of the prion protein (PrP^Sc) generated by a posttranslational process involving the conversion of alpha-helices into beta-sheets of the normal cellular prion protein (PrP^c) is believed to be the main component of this infectious agents. This conversion of a normal PrP^c into an abnormal isoform PrP^Sc kinetically behaves as an autocatalytic process. To better understand this kind of abnormal protein propagation, many analytical models has been proposed. Thus, we studied, using the Monte Carlo method, the distribution of the incubation periods in some of these neurodegenerative disorders such as bovine spongiform encephalopathy well-known as mad-cow disease (BSE), Variant Creutzfeldt-Jakob disease (vCJD) and murine scrapie, an experimental murine prionic disease. The probabilities of the incubation time distribution of these diseases were considered lognormal. Objectives: The aim of this study was to investigate some aspects of the toxicity and replication of the prionic diseases by comparing the results of computational simulations with the incubation time periods of BSE, vCJD and murine scrapie, previously established. Methods: Computational simulations using a Dynamical Monte Carlo method (DMC) and the diffusion-limited aggregation model (DLA) were worked out. At first, we evaluate the Eigen model through computational simulations using the DMC. Following the results, we studied the toxicity of the prionic diseases using the DMC and the DLA model, considering that PrP^C converting in PrP^Sc just when there is contact (autocatalysis) and free PrP^cs are allowed to diffuse randomly to their nearest neighbor sites in a square lattice, while isotated PrP^Scs or aggregate of PrP^Scs are fixed. Results: The more important parameter in the equation of the prionic kinetic is the Michaelis-Menten constant or the autocatalytic term. We get the fitting in different profiles of the distribution of the incubation periods (lognormal to BSE and vCJD and lognormal with a second peak to murine scrapie). Conclusion: The autocatalysis is an essential mechanism to the prionic kinetic and the spontaneous conversion of PrP^C in PrP^Sc can be neglected. Based on the DLA model, to BSE and vCJD (diseases with natural occurrence) we can conclude that and the toxicity in these diseases are caused by formation of amyloid plaques. To murine scrapie, we find the toxicity is caused by formation of amyloid plaques in addition to depletion of PrP^C. Changing the initial and terminal simulation parameters we fitting all diseases studied, in spite of the model to be very simple. Moreover, the lognormality is a result of the diffusive process. The concentrations of PrP^c must be low, less than 1% and the number of PrP^Sc must be less than 10 to lognormality take place.