Stochastic Modelling Approach to the Incubation Time of Prionic Diseases

TL;DR

This paper presents a stochastic mean-field and cellular automata model to accurately describe the incubation time distribution of prion diseases like BSE, fitting observed data with a log-normal distribution.

Contribution

It introduces a novel analytical and simulation-based approach to model prion incubation times using stochastic variables and cellular automata.

Findings

Incubation time distribution is log-normal and matches BSE data.

The model accurately predicts incubation times at low protein densities.

Analytical and simulation results are consistent with observed disease progression.

Abstract

Transmissible spongiform encephalopathies like the bovine spongiform encephalopathy (BSE) and the Creutzfeldt-Jakob disease (CJD) in humans are neurodegenerative diseases for which prions are the attributed pathogenic agents. A widely accepted theory assumes that prion replication is due to a direct interaction between the pathologic (PrPsc) form and the host encoded (PrPc) conformation, in a kind of an autocatalytic process. Here we show that the overall features of the incubation time of prion diseases are readily obtained if the prion reaction is described by a simple mean-field model. An analytical expression for the incubation time distribution then follows by associating the rate constant to a stochastic variable log normally distributed. The incubation time distribution is then also shown to be log normal and fits the observed BSE data very well. The basic ideas of the theoretical model are then incorporated in a cellular automata model. The computer simulation results yield the correct BSE incubation time distribution at low densities of the host encoded protein.