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Durrett, R.

Publications and source records attributed to Durrett, R..

7 recordsLinked to original sources

Signatures of neutral evolution in exponentially growing tumors: a theoretical perspective

We investigate the site frequency spectrum in the two-type model of clonal evolution. If the fitnesses of the two types are {lambda}0 < {lambda}1 then the site frequency spectrum is c/f where = {lambda}0/{lambda}1. This is due to the advantageous mutations that produce the founders of the type 1 population. Mutations within the growing type 0 and type 1 populations follow the 1/f law. Our results show that neutral evolution can be distinguished from the two-type model using the site frequency spectrum.

cancer biology↗

Expressed barcodes enable clonal characterization of chemotherapeutic responses in chronic lymphocytic leukemia

The remarkable evolutionary capacity of cancer is a major challenge to current therapeutic efforts. Fueling this evolution is its vast clonal heterogeneity and ability to adapt to diverse selective pressures. Although the genetic and transcriptional mechanisms underlying these responses have been independently evaluated, the ability to couple genetic alterations present within individual clones to their respective transcriptional or functional outputs has been lacking in the field. To this end, we developed a high-complexity expressed barcode library that integrates DNA barcoding with single-cell RNA sequencing through use of the CROP-seq sgRNA expression/capture system, and which is compatible with the COLBERT clonal isolation workflow for subsequent genomic and epigenomic characterization of specific clones of interest. We applied this approach to study chronic lymphocytic leukemia (CLL), a mature B cell malignancy notable for its genetic and transcriptomic heterogeneity and variable disease course. Here, we demonstrate the clonal composition and gene expression states of HG3, a CLL cell line harboring the common alteration del(13q), in response to front-line cytotoxic therapy of fludarabine and mafosfamide (an analog of the clinically used cyclophosphamide). Analysis of clonal abundance and clonally-resolved single-cell RNA sequencing revealed that only a small fraction of clones consistently survived therapy. These rare highly drug tolerant clones comprise 94% of the post-treatment population and share a stable, pre-existing gene expression state characterized by upregulation of CXCR4 and WNT signaling and a number of DNA damage and cell survival genes. Taken together, these data demonstrate at unprecedented resolution the diverse clonal characteristics and therapeutic responses of a heterogeneous cancer cell population. Further, this approach provides a template for the high-resolution study of thousands of clones and the respective gene expression states underlying their response to therapy.

cancer biology↗

A heterogeneous spatial model in which savanna and forest coexist in a stable equilibrium

In work with a variety of co-authors, Staver and Levin have argued that savanna and forest coexist as alternative stable states with discontinuous changes in density of trees at the boundary. Here we formulate a nonhomogeneous spatial model of the competition between forest and savanna. We prove that coexistence occurs for a time that is exponential in the size of the system, and that after an initial transient, boundaries between the alternative equilibria remain stable.

ecology↗

Genotype patterns in growing solid tumors

Over the past decade, the theory of tumor evolution has largely focused on the selective sweeps model. According to this theory, tumors evolve by a succession of clonal expansions that are initiated by driver mutations. In a 2015 analysis of colon cancer data, Sottoriva et al [34] proposed an alternative theory of tumor evolution, the so-called Big Bang model, in which one or more driver mutations are acquired by the founder gland, and the evolutionary dynamics within the expanding population are predominantly neutral. In this paper we will describe a simple mathematical model that reproduces qualitative features of the observed paatterns of genetic variability and makes quantitative predictions.

cancer biology↗

Extrapolating Weak Selection in Evolutionary Games

This work is inspired by a 2013 paper from Arne Traulsens lab at the Max Plank Institute for Evolutionary Biology [10]. They studied the small mutation limit of evolutionary games. It has been shown that for 2 x 2 games the ranking of the strategies does not change as strength of selection is increased [11]. The point of the 2013 paper is that when there are three or more strategies the ordering can change as selection is increased. Wu et al [10] did numerical computations for fixed N. Here, we will instead let the strength of selection {beta} = c/N and let N [->] {infty} to obtain formulas for the invadability probabilities{phi} ij that determine the rankings. These formulas, which are integrals on [0, 1], are intractable calculus problems but can be easily evaluated numerically. Here, we concentrate on simple formulas for the ranking order when c is small or c is large. The results we have obtained for five concrete examples lead us to doubt the accuracy of insights that are derived in the small mutation limit for games with three strategies.

evolutionary biology↗

Genealogies in Growing Solid Tumors

Over the past two decades, the theory of tumor evolution has largely focused on the selective sweeps model. According to this theory, tumors evolve by a succession of clonal expansions that are initiated by driver mutations that have a fitness advantage over the resident types. A 2015 study of colon cancer [44] has suggested an alternative theory of tumor evolution, the so-called Big Bang model, in which all of the necessary driver mutations are acquired before expansion began, and the evolutionary dynamics within the expanding population are predominantly neutral. In this paper, we will describe a simple mathematical model inspired by work of Hallatschek and Nelson [25] that makes quantitative predictions about spatial patterns of genetic variability. While this model has some success in matching observed patterns in two dimensions, it fails miserably in three dimensions. Despite this failure, we think the model analyzed here will be a useful first step in building an accurate model.

cancer biology↗

A new look at multi-stage models of cancer incidence

Multi-stage models have long been used in combination with SEER data to make inferences about the mechanisms underlying cancer initiation. The main method for studying these models mathematically has been the computation of generating functions by solving hyperbolic partial differential equations. Here, we analyze these models using a probabilistic approach similar to the one Durrett and Moseley [7] used to study branching process models of cancer. This more intuitive approach leads to simpler formulas and new insights into the behavior of these models. Unfortunately, the examples we consider suggest that fitting multi-stage models has very little power to make inferences about the number of stages unless parameters are constrained to take on realistic values.

cancer biology↗