One-dimensional model of yeast prion aggregation

Abstract

Mammalian prion proteins (PrP) are of significant public health interest. Yeasts have proteins, which can undergo similar reconformation and aggregation processes to PrP, without posing a threat to the organism. These yeast "prions," such as SUP35, are simpler to experimentally study and model. Recent in vitro studies of the SUP35 protein found long aggregates, pure exponential growth of the misfolded form, and a lag time which depended weakly on the monomer concentration. To explain this data, we have extended a previous model of aggregation kinetics along with a stochastic approach. We assume reconformation only upon aggregation and include aggregate fissioning and an initial nucleation barrier. We find that for sufficiently small nucleation rates or seeding by a small number of preformed nuclei, the models achieve the requisite exponential growth, long aggregates, and a lag time which depends weakly on monomer concentration. The spread in aggregate sizes is well described by the Weibull distribution. All these properties point to the preeminent role of fissioning in the growth of misfolded proteins.

From Macroscopic Measurements to Microscopic Mechanisms of Protein Aggregation

“…1,2,[7][8][9]25,35,[53][54][55] For many simple primary nucleation reaction schemes, 6,25,56-64 the early-time rise in the reaction time course is quadratic in time, ∼ t 2 . For more complicated primary nucleation processes involving intermediate species, sometimes known as cascade nucleation, 25 the early-time rise in the sigmoidal reaction time course remains polynomial, but with a cubic 39 or higher dependence on time, ∼t m for a constant m.…”

Nucleated polymerization with secondary pathways. III. Equilibrium behavior and oligomer populations

“…Letting f(t, j) denote the number of filaments of size j the master equation reads [32][33][34][35][36]:…”

“…(36) and in the case of mass conservation Eq. (19) allow an understanding to be developed of the full time evolution of the length distribution of filaments growing in a closed system conserving total mass.…”

Nucleation of amyloid fibrils

“…34,35 So far, a considerable effort has been devoted to understanding how the amino acid sequence of proteins and the experimental conditions affect the kinetics of amyloid fibril formation. 30,32,33,[36][37][38][39][40][41][42][43][44] Experiments that investigate the physiochemical properties of the natural amino acids (such as -propensity, hydrophobicity, aromatic content and charge) have been used to substantiate phenomenological models able to predict changes in the aggregation rate upon mutation as well as to predict amino acid sequences of proteins, so-called hot spots, that are likely to belong to the fibril core. [45][46][47][48][49][50] Although both the experimental studies and the theoretical models show that the kinetic parameters of aggregation depend strongly on the specificity of the amino acid sequence of the protein, it may be expected that this specificity is a particular expression of a common fibril nucleation/growth mechanism which could be treated in the framework of existing general theories of nucleation and growth of new phases.…”