Stochastic Modelling Approach to the Incubation Time of Prionic Diseases

摘要

Transmissible spongiform encephalopathies like the bovine spongiformencephalopathy (BSE) and the Creutzfeldt-Jakob disease (CJD) in humans areneurodegenerative diseases for which prions are the attributed pathogenicagents. A widely accepted theory assumes that prion replication is due to adirect interaction between the pathologic (PrPsc) form and the host encoded(PrPc) conformation, in a kind of an autocatalytic process. Here we show thatthe overall features of the incubation time of prion diseases are readilyobtained if the prion reaction is described by a simple mean-field model. Ananalytical expression for the incubation time distribution then follows byassociating the rate constant to a stochastic variable log normallydistributed. The incubation time distribution is then also shown to be lognormal and fits the observed BSE data very well. The basic ideas of thetheoretical model are then incorporated in a cellular automata model. Thecomputer simulation results yield the correct BSE incubation time distributionat low densities of the host encoded protein.