Quantifying the dynamics of prion infection: a bifurcation analysis of Laurent's model

Laurent(1996a, Medecine/sciences 12, 774-785; 1996b, Biochem. J. 318, 35-39 ; 1998, Bio-phys. Chem. 72, 211-222) proposed a model for the dynamics of d iseases of the central nervous system caused by prions. It is based on the protein-only hypothesis (Prusiner ct al., 1981, Proc. Natl. Acad. Sci. U.S. A. 78, 6675-6679), which assumes that infection can be spread by particular proteins (prions) that can exist in two forms that share the same sequence , but have a different structure. The normal form is harmless, while the in fectious isoform of the prion protein catalyses a transconformation from th e native isoform to itself within a specialized compartment of the brain ce lls. This paper systematically explores the model behavior with the aim of quantifying the fundamental parameters characterizing the dynamics of prion infection. To this end we use data from the literature to fix orders of ma gnitude for the rates of synthesis and degradation of the native form of pr ion protein and for the shape of the autocatalytic function. The dynamical behavior is classified with respect to two unknown parameters (bifurcation analysis): the rate of spontaneous transconformation and the rate of output of the infectious isoform from the specialized compartment. We thus find t hat the bistability properties evidenced by Laurent are confined to a certa in range of parameters and that permanent oscillations of the two isoforms concentrations are possible. The bifurcation analysis allows us to estimate approximate ranges for the values of the two unknown parameters and conseq uently to derive incubation times and compare them with actual data for ham ster. Also, our study predicts that the output rate of the infectious isofo rm is relatively insensitive to variations of model parameters. (C) 2000 Ac ademic Press.