Approximations for expected generation number

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/.

Reproduction-time statistics and segregation patterns in growing populations

Pattern formation in microbial colonies of competing strains under purely space-limited population growth has recently attracted considerable research interest. We show that the reproduction time statistics of individuals has a significant impact on the sectoring patterns. Generalizing the standard Eden growth model, we introduce a simple one-parameter family of reproduction time distributions indexed by the variation coefficient δ∈[0,1], which includes deterministic (δ=0) and memory-less exponential distribution (δ=1) as extreme cases. We present convincing numerical evidence and heuristic arguments that the generalized model is still in the Kardar-Parisi-Zhang (KPZ) universality class, and the changes in patterns are due to changing prefactors in the scaling relations, which we are able to predict quantitatively. With the example of Saccharomyces cerevisiae, we show that our approach using the variation coefficient also works for more realistic reproduction time distributions.

Saddlepoint approximations to the moments of multitype age-dependent branching processes, with applications

This article proposes saddlepoint approximations to the expectation and variance-covariance function of multitype age-dependent branching processes. The proposed approximations are found accurate, easy to implement, and much faster to compute than by simulating the process. Multiple applications are presented, including the analyses of clonal data on the generation of oligodendrocytes from their immediate progenitor cells, and on the proliferation of Hela cells. New estimators are also constructed to analyze clonal data. The proposed methods are finally used to approximate the distribution of the generation, which has recently found several applications in cell biology.

Calorie restriction reduces rDNA recombination independently of rDNA silencing

Calorie restriction (CR) extends lifespan in yeast, worms, flies and mammals, suggesting that it acts via a conserved mechanism. In yeast, activation of the NAD-dependent histone deacetylase, Sir2, by CR is thought to increase silencing at the ribosomal DNA, thereby reducing the recombination-induced generation of extrachromosomal rDNA circles, hence increasing replicative lifespan. Although accumulation of extrachromosomal rDNA circles is specific to yeast aging, it is thought that Sirtuin activation represents a conserved longevity mechanism through which the beneficial effects of CR are mediated in various species. We show here that growing yeast on 0.05 or 0.5% glucose (severe and moderate CR, respectively) does not increase silencing at either sub-telomeric or rDNA loci compared with standard (2% glucose) media. Furthermore, rDNA silencing was unaffected in the hxk2Δ, sch9Δ and tor1Δ genetic mimics of CR, but inhibited by FOB1 deletion. All these interventions extend lifespan in multiple yeast backgrounds, revealing a poor correlation between rDNA silencing and longevity. In contrast, CR and deletion of the FOB1, HXK2, SCH9 and TOR1 genes, all significantly reduced rDNA recombination. This silencing-independent mechanism for suppressing rDNA recombination may therefore contribute to CR-mediated lifespan extension.

The number and transmission of [PSI] prion seeds (Propagons) in the yeast Saccharomyces cerevisiae

Background

Yeast (Saccharomyces cerevisiae) prions are efficiently propagated and the on-going generation and transmission of prion seeds (propagons) to daughter cells during cell division ensures a high degree of mitotic stability. The reversible inhibition of the molecular chaperone Hsp104p by guanidine hydrochloride (GdnHCl) results in cell division-dependent elimination of yeast prions due to a block in propagon generation and the subsequent dilution out of propagons by cell division.

Principal Findings

Analysing the kinetics of the GdnHCl-induced elimination of the yeast [PSI⁺] prion has allowed us to develop novel statistical models that aid our understanding of prion propagation in yeast cells. Here we describe the application of a new stochastic model that allows us to estimate more accurately the mean number of propagons in a [PSI⁺] cell. To achieve this accuracy we also experimentally determine key cell reproduction parameters and show that the presence of the [PSI⁺] prion has no impact on these key processes. Additionally, we experimentally determine the proportion of propagons transmitted to a daughter cell and show this reflects the relative cell volume of mother and daughter cells at cell division.

Conclusions

While propagon generation is an ATP-driven process, the partition of propagons to daughter cells occurs by passive transfer via the distribution of cytoplasm. Furthermore, our new estimates of n₀, the number of propagons per cell (500–1000), are some five times higher than our previous estimates and this has important implications for our understanding of the inheritance of the [PSI⁺] and the spontaneous formation of prion-free cells.