[Paper Review] Bimodality, prion aggregates infectivity and prediction of strain phenomenon

Vincent Calvez, Natacha Lenuzza+5 more|ArXiv.org|Feb 14, 2008

Prion Diseases and Protein Misfolding43 references3 citations

TL;DR

This study extends the nucleated polymerization model of prion replication by introducing size-dependent parameters for polymerization and fragmentation, enabling the emergence of bimodal aggregate size distributions—consistent with recent experimental data. The key finding is that bimodality arises under specific non-uniform infectivity and fragmentation rates, and the model predicts that PrPsc aggregate size distribution may serve as a strain-specific signature, influencing strain adaptation and species barrier crossing.

ABSTRACT

We consider a model for the polymerization (fragmentation) process involved in infectious prion self-replication and study both its dynamics and non-zero steady state. We address several issues. Firstly, we give conditions leading to size repartitions of PrPsc aggregates that exhibit bimodal distributions, as indicated by recent experimental studies of prion aggregates distribution. Secondly, we show stability results for this steady state for general coefficients where reduction to a system of differential equations is not possible. We use a duality method based on recent ideas developed for population models. These results underline the potential influence of the amyloid precursor production rate in promoting amyloidogenic diseases. Finally, we numerically investigate the influence of different parameters of the model on PrPsc accumulation kinetics, in the aim to study specific features of prion strains.

Motivation & Objective

• To explain the experimentally observed bimodal size distribution of PrPsc aggregates, which contradicts standard models predicting unimodal distributions.
• To investigate how size-dependent parameters (e.g., infectivity, fragmentation rate) influence prion strain dynamics and stability.
• To explore the role of aggregate size distribution in prion strain adaptation and species barrier crossing.
• To establish mathematical stability results for non-zero steady states in a general, non-reducible framework.
• To propose that PrPsc size distribution could serve as a novel experimental signature for prion strain identification and transmission potential.

Proposed method

• Extends the classical nucleated polymerization model by introducing size-dependent polymerization and fragmentation rates, moving beyond constant coefficients.
• Uses a continuous fragmentation–polymerization equation with general coefficients to model PrPsc aggregate dynamics.
• Applies a duality method based on recent population dynamics theory to prove asymptotic stability of non-zero steady states.
• Employs numerical simulations to explore the influence of key parameters (e.g., transconformation rate, fragmentation) on PrPsc accumulation kinetics.
• Analyzes the dominant eigenvector of the system to model the long-term distribution of aggregates, linking it to strain-specific behavior.
• Proposes an inverse problem approach to infer size-dependent transconformation rates from observed aggregate distributions.

Experimental results

Research questions

• RQ1 Under what conditions does the model generate bimodal distributions of PrPsc aggregates, consistent with recent experimental data?
• RQ2 How do size-dependent infectivity and fragmentation rates affect the stability and dynamics of prion aggregates?
• RQ3 Can the distribution of PrPsc aggregate sizes serve as a signature of prion strain diversity and transmission potential?
• RQ4 What is the role of the dominant eigenvector in shaping the long-term distribution of aggregates during strain adaptation?
• RQ5 How does the model explain the prolonged incubation periods observed during initial prion passage across species barriers?

Key findings

• Bimodal distributions of PrPsc aggregates emerge when the transconformation rate and fragmentation rate are size-dependent, particularly when infectivity is highest in intermediate-sized aggregates.
• The model predicts that the long-term aggregate size distribution aligns with the eigenvector associated with the dominant eigenvalue, suggesting a strain-specific equilibrium distribution.
• The healthy state (no aggregates) is asymptotically stable when PrPc production is low, but becomes unstable when PrPc levels are sufficiently high, indicating a threshold for prion disease onset.
• The non-zero steady state is stable under general coefficient assumptions, even when reduction to ODEs is not possible, extending prior results to more biologically realistic settings.
• Numerical simulations show that PrPsc accumulation kinetics are highly sensitive to fragmentation and transconformation rates, with implications for strain-specific PMCA optimization.
• The model suggests that the size distribution of PrPsc aggregates could be used experimentally to predict strain-specific transmissibility across species barriers, particularly for atypical strains like BASE and CWD.