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Posts from the ‘Lab News!’ Category

Invasion Probabilities paper accepted

Congratulations to Becky Borchering! The research paper stemming from the second chapter of her dissertation was accepted today.

This paper has a fun working title that we always joke about in the Stochastics Lab. Originally, we expected this to be an easy project — almost too trivial to write up as a research article. I remember telling Becky, “Sometimes you just have to take a simple project, write out the results, and share them with people. Even if it’s just a ten-page paper, it can start a conversation that is much more substantial.” That was in November of 2014. Here we are and finally “10 Page Paper” is accepted … a mere three yearsa and thirty-one pages later.

Never underestimate an simple idea!!

Continuum Approximation of Invasion Probabilities ( pdf )

In the last decade there has been growing criticism of the use of stochastic differential equations to approximate discrete-state-space, continuous-time Markov chain population models. In particular, several authors have demonstrated the failure of Diffusion Approximation, as it is often called, to approximate expected extinction times for populations that start in a quasi-stationary state. In this work we investigate a related, but distinct, population dynamics property for which Diffusion Approximation is unreliable: invasion probabilities. We consider the situation in which a few individuals are introduced into a population and ask whether their collective lineage can successfully invade. Because the population count is so small during the critical period of success or failure, the process is intrinsically stochastic and discrete. In addition to demonstrating how and why the Diffusion Approximation fails in the large population limit, we contrast this analysis with that of a sometimes more successful alternative WKB-like approach. Through numerical investigations, we also study how these approximations perform in an important intermediate regime. Surprisingly, we find that there are times when the Diffusion Approximation performs well, particularly when parameters are near-critical and the population size is small to intermediate.

Update! the paper is now published online here:

Stem Cell Paper Accepted

Congratulations are in order for Vin Cannataro today.  The research paper stemming from the second chapter of his dissertation was accepted today by Evolutionary Applications.

The Evolutionary Trade-off between Stem Cell Niche Size, Aging, and Tumorigenesis

Vincent L. Cannataro, Scott A. McKinley, Colette M. St. Mary

Many epithelial tissues within large multicellular organisms are continually replenished by small independent populations of stem cells. These stem cells divide within their niches and differentiate into the constituent cell types of the tissue, and are largely responsible for maintaining tissue homeostasis. Mutations can accumulate in stem cell niches and change the rate of stem cell division and differentiation, contributing to both aging and tumorigenesis. Here, we create a mathematical model of the intestinal stem cell niche, crypt system, and epithelium. We calculate the expected effect of fixed mutations in stem cell niches and their expected effect on tissue homeostasis throughout the intestinal epithelium over the lifetime of an organism. We find that, due to the small population size of stem cell niches, fixed mutations are expected to accumulate via genetic drift and decrease stem cell fitness, leading to niche and tissue attrition, and contributing to organismal aging. We also explore mutation accumulation at various stem cell niche sizes, and demonstrate that an evolutionary trade-off exists between niche size, tissue aging, and the risk of tumorigenesis; where niches exist at a size that minimizes the probability of tumorigenesis, at the expense of accumulating deleterious mutations due to genetic drift. Finally, we show that the probability of tumorigenesis and the extent of aging trade-off differently depending on whether mutational effects confer a selective advantage, or not, in the stem cell niche.