Quantifying the Biophysical Impact of Budding Cell Division on the Spatial Organization of Growing Yeast Colonies

Equations describing semi-confluent cell growth (I) Analytical approximations

A set of differential equations with analytical solutions are presented that can quantitatively account for variable degrees of contact inhibition on cell growth in two- and three-dimensional cultures. The developed equations can be used for comparative purposes when assessing contribution of higher-order effects, such as culture geometry and nutrient depletion, on mean cell growth rate. These equations also offer experimentalists the opportunity to characterize cell culture experiments using a single reductive parameter.

MIL-CELL: a tool for multi-scale simulation of yeast replication and prion transmission

The single-celled baker's yeast, Saccharomyces cerevisiae, can sustain a number of amyloid-based prions, the three most prominent examples being [URE3], [PSI+], and [PIN+]. In the laboratory, haploid S. cerevisiae cells of a single mating type can acquire an amyloid prion in one of two ways (i) spontaneous nucleation of the prion within the yeast cell, and (ii) receipt via mother-to-daughter transmission during the cell division cycle. Similarly, prions can be lost due to (i) dissolution of the prion amyloid by its breakage into non-amyloid monomeric units, or (ii) preferential donation/retention of prions between the mother and daughter during cell division. Here we present a computational tool (Monitoring Induction and Loss of prions in Cells; MIL-CELL) for modelling these four general processes using a multiscale approach describing both spatial and kinetic aspects of the yeast life cycle and the amyloid-prion behavior. We describe the workings of the model, assumptions upon which it is based and some interesting simulation results pertaining to the wave-like spread of the epigenetic prion elements through the yeast population. MIL-CELL is provided as a stand-alone GUI executable program for free download with the paper. MIL-CELL is equipped with a relational database allowing all simulated properties to be searched, collated and graphed. Its ability to incorporate variation in heritable properties means MIL-CELL is also capable of simulating loss of the isogenic nature of a cell population over time. The capability to monitor both chronological and reproductive age also makes MIL-CELL potentially useful in studies of cell aging.

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.

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/.