A structured model and likelihood approach to estimate yeast prion propagon replication rates and their asymmetric transmission

Abstract

Prion proteins cause a variety of fatal neurodegenerative diseases in mammals but are generally harmless to Baker's yeast (Saccharomyces cerevisiae). This makes yeast an ideal model organism for investigating the protein dynamics associated with these diseases. The rate of disease onset is related to both the replication and transmission kinetics of propagons, the transmissible agents of prion diseases. Determining the kinetic parameters of propagon replication in yeast is complicated because the number of propagons in an individual cell depends on the intracellular replication dynamics and the asymmetric division of yeast cells within a growing yeast cell colony. We present a structured population model describing the distribution and replication of prion propagons in an actively dividing population of yeast cells. We then develop a likelihood approach for estimating the propagon replication rate and their transmission bias during cell division. We first demonstrate our ability to correctly recover known kinetic parameters from simulated data, then we apply our likelihood approach to estimate the kinetic parameters for six yeast prion variants using propagon recovery data. We find that, under our modeling framework, all variants are best described by a model with an asymmetric transmission bias. This demonstrates the strength of our framework over previous formulations assuming equal partitioning of intracellular constituents during cell division.

Fig 1. Multiscale yeast prion aggregate (propagon) dynamics.

(A) Within each cell in the colony is a mixture of normal protein and prion (alternatively folded) protein. Prion proteins are contained in propagons of multiple alternatively folded monomers. (B) Within each cell normal protein is produced (synthesis) and incorporated into existing propagons which leads to conversion of the normal protein to the prion form and increases the size of a propagon. Aggregates may increase in number by fragmentation and must be spread from mother to daughter cells during division (transmission). (C) Under normal growth conditions, the number of propagons increases during the lifetime of a cell and is split during cell division. (D) When cells are grown under GdnHCl fragmentation is assumed to stop and the number of propagons remains unchanged during the lifetime of a cell.

Fig 2. Propagon amplification assay.

A two-step process is used to count the number of transmissible prion aggregates (propagons) in a single cell. Left: A single target cell is isolated, and propagon fragmentation is stopped through exposure to GdnHCl. Since propagons (pinwheels) cannot increase in number, they are diluted through cell division (green arrows). Right: After sufficient dilution, i.e. each yeast cell is likely to contain at most one propagon, the colony is replated onto solid media. In the absence of GdnHCl, each single cell serves as a founder of a distinct yeast colony. The number of propagons in the target cell corresponds to the number of white colonies in the plate.

Fig 3. Simulated data.

The simulated data was generated using a replication rate of λ = 0.70 hr⁻¹ and four different transmission biases (ρ). Samples were generated per experimental hour at a rate of 16 samples per hour. Data points outlined in red were determined to be outliers by the IQR method.

Fig 4. Experimental propagon counts for six prion variants.

This experimental data was obtained through propagon recovery experiments (see the biological background section for more details). Data points outlined in red were determined to be outliers by the IQR method.

Fig 5. Asymmetric transmission of propagons model schematic.

The model dynamics of intracellular propagon replication and cell division from generation i to generation i + 1. The black arrow (→) illustrates the intracellular increase in the number of propagons over time. The remaining parameters are detailed in the methods.