Allele Frequency Spectrum in a Cancer Cell Population

Hisashi Ohtsuki, Hideki Innan

 

Abstract

A cancer grows from a single cell, thereby constituting a large cell population. In this work, we are interested in how mutations accumulate in a cancer cell population. We provide a theoretical framework of the stochastic process in a cancer cell population and obtain near exact expressions of allele frequency spectrum or AFS (only continuous approximation is involved) from both forward and backward treatments under a simple setting; all cells undergo cell division and die at constant rates, b and d, respectively, such that the entire population grows exponentially. This setting means that once a parental cancer cell is established, in the following growth phase, all mutations are assumed to have no effect on b or d (i.e., neutral or passengers). Our theoretical results show that the difference from organismal population genetics is mainly in the coalescent time scale, and the mutation rate is defined per cell division, not per time unit (e.g., generation). Except for these two factors, the basic logic are very similar between organismal and cancer population genetics, indicating that a number of well established theories of organismal population genetics could be translated to cancer population genetics with simple modifications.

doi: http://biorxiv.org/content/early/2017/01/30/104158 

 

 

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

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

Abstract

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.

http://dx.doi.org/10.1101/059279

Cooperation between Noncanonical Ras Network Mutations in Cancer

Edward C Stites, Paul C Trampont, Lisa B Haney, Scott F Walk, Kodi S Ravichandran

doi: http://dx.doi.org/10.1101/004846

Cancer develops after the acquisition of a collection of mutations that together create the ‘cancer phenotype’. How collections of mutations work together within a cell, and whether there is selection for certain combinations of mutations, are not well understood. Using a Ras signaling network mathematical model we tested potential synergistic combinations within the Ras network. Intriguingly, our modeling, including a “computational random mutagenesis” approach, and subsequent experiments revealed that mutations of the tumor suppressor gene NF1 can amplify the effects of mutations in multiple other components of the Ras pathway, including weakly activating, noncanonical, Ras mutants. Since conventional wisdom holds that mutations within the same pathway do not co-occur, it was surprising that modeling and experiments both suggested a functional benefit for co-occurring Ras pathway mutations. Furthermore, we analyzed >3900 sequenced cancer specimens from the Cancer Cell Line Encyclopedia (CCLE) and The Cancer Genome Atlas (TCGA) and we uncovered an increased rate of co-occurrence between mutations the model predicted could display synergy. Overall, these data suggest that selective combinations of Ras pathway mutations could serve the role of cancer “driver”. More generally, this work presents a mechanism by which the context created by one mutation influences the evolutionary trajectories of cancer development, and this work suggests that mutations that result in “network instability” may promote cancer in a manner analogous to genomic instability.

Link: http://www.biorxiv.org/content/early/2014/05/06/004846

A tug-of-war between driver and passenger mutations in cancer and other adaptive processes

Christopher Dennis McFarland, Leonid A Mirny, Kirill S Korolev

doi: 10.1101/003053

Abstract

Cancer progression is an example of a rapid adaptive process where evolving new traits is essential for survival and requires a high mutation rate. Precancerous cells acquire a few key mutations that drive rapid population growth and carcinogenesis. Cancer genomics demonstrates that these few ‘driver’ mutations occur alongside thousands of random ‘passenger’ mutations––a natural consequence of cancer's elevated mutation rate. Some passengers can be deleterious to cancer cells, yet have been largely ignored in cancer research. In population genetics, however, the accumulation of mildly deleterious mutations has been shown to cause population meltdown. Here we develop a stochastic population model where beneficial drivers engage in a tug-of-war with frequent mildly deleterious passengers. These passengers present a barrier to cancer progression that is described by a critical population size, below which most lesions fail to progress, and a critical mutation rate, above which cancers meltdown. We find support for the model in cancer age-incidence and cancer genomics data that also allow us to estimate the fitness advantage of drivers and fitness costs of passengers. We identify two regimes of adaptive evolutionary dynamics and use these regimes to rationalize successes and failures of different treatment strategies. We find that a tumor’s load of deleterious passengers can explain previously paradoxical treatment outcomes and suggest that it could potentially serve as a biomarker of response to mutagenic therapies. The collective deleterious effect of passengers is currently an unexploited therapeutic target. We discuss how their effects might be exacerbated by both current and future therapies.

From the bioRxiv :  http://biorxiv.org/content/early/2014/02/26/003053

Cancer initiation with epistatic interactions between driver and passenger mutations

Benedikt Bauer, Arne Traulsen

(Submitted on 4 Oct 2013)

We investigate the dynamics of cancer initiation in a model with one driver mutation and several passenger mutations. In contrast to previous models, the change in fitness induced by the driver mutation depends on the genetic background of the cell, in our case on the number of passenger mutations. The passenger mutations themselves have no or only a very small impact on the cell's fitness. This approach is motivated by the Burkitt Lymphoma, where the hallmark mutation, a translocation between the MYC gene and an immunoglobulin gene, alters the rate of apoptosis, but also the proliferation rate of cells. This way we obtain an epistatic fitness landscape, where the fitness of cells with the driver mutation is advantageous only if enough passenger genes have mutated. Otherwise the fitness might even be deleterious. Our analysis is based on an individual cell model in which the cells can divide or undergo apoptosis. In case of division the two daughter cells can mutate. This model shows a very interesting dynamical behavior. Since the driver mutation is deleterious on a background with only a few passenger mutations, there is a long period of stasis in the number of cells until a clone of cells has evolved with enough passenger mutations. Only when the driver mutation occurs in one of those cells, the cell population starts to grow exponentially.

Link: http://arxiv.org/abs/1310.1853

Spatial evolution of tumors with successive driver mutations

Tibor Antal, P. L. Krapivsky, M. A. Nowak

(Submitted on 7 Aug 2013)

We study the spatial evolutionary dynamics of solid tumors as they obtain additional driver mutations. We start with a cancer clone that expands uniformly in three dimensions giving rise to a spherical shape. We assume that cell division occurs on the surface of the growing tumor. Each cell division has a chance to give rise to a mutation that activates an additional driver gene. The resulting clone has an enhanced growth rate, which generates a local ensemble of faster growing cells, thereby distorting the spherical shape of the tumor. We derive analytic formulas for the geometric boundary that separates the original cancer clone from the new mutant as well as the expanding frontier of the new mutant. The total number of original cancer cells converges to a constant as time goes to infinity, because this clone becomes enveloped by mutants. We derive formulas for the abundance and diversity of additional driver mutations as function of time. Our model is semi-deterministic: the spatial growth of the various cancer clones follows deterministic equations, but the arrival of a new mutant is a stochastic event.

http://arxiv.org/abs/1308.1564