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

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.Author summary: In this work we investigate the transmissible [PSI+] phenotype in yeast. The agents responsible for this phenotype are propagons, misfolded protein aggregates of a naturally occurring protein. These propagons increase in number within a cell and are distributed between cells during division. We use mathematical modeling to infer the replication rate of propagons within cells and if propagons are transmitted equally or unequally during cell division. Prior models in this area assumed only symmetric transmission when fitting replication rates. We couple this model with a novel likelihood framework allowing us to exclude influential outliers from our datasets when inferring parameters. We find that for all six protein variants we study, propagons are transmitted asymmetrically with different biases. Our results can be reproduced with the code and data available at https://github.com/FS-CodeBase/propagon_replication_and_transmission/.