Reply to 'Currently available bulk sequencing data do not necessarily support a model of neutral tumor evolution'

Characterization of Cancer Evolution Landscape Based on Accurate Detection of Somatic Mutations in Single Tumor Cells

Accurate detection of somatic mutations in single tumor cells is greatly desired as it allows us to quantify the single-cell mutation burden and construct the mutation-based phylogenetic tree. Here we developed scNanoSeq chemistry and profiled 842 single cells from 21 human breast cancer samples. The majority of the mutation-based phylogenetic trees comprise a characteristic stem evolution followed by the clonal sweep. We observed the subtype-dependent lengths in the stem evolution. To explain this phenomenon, we propose that the differences are related to different reprogramming required for different subtypes of breast cancer. Furthermore, we reason that the time that the tumor-initiating cell took to acquire the critical clonal-sweep-initiating mutation by random chance set the time limit for the reprogramming process. We refer to this model as a reprogramming and critical mutation co-timing (RCMC) subtype model. Next, in the sweeping clone, we observed that tumor cells undergo a branched evolution with rapidly decreasing selection. In the most recent clades, effectively neutral evolution has been reached, resulting in a substantially large number of mutational heterogeneities. Integrative analysis with 522-713X ultra-deep bulk whole genome sequencing (WGS) further validated this evolution mode. Mutation-based phylogenetic trees also allow us to identify the early branched cells in a few samples, whose phylogenetic trees support the gradual evolution of copy number variations (CNVs). Overall, the development of scNanoSeq allows us to unveil novel insights into breast cancer evolution.

Very large hidden genetic diversity in one single tumor: evidence for tumors-in-tumor

Despite the concern of within-tumor genetic diversity, this diversity is in fact limited by the kinship among cells in the tumor. Indeed, genomic studies have amply supported the 'Nowell dogma' whereby cells of the same tumor descend from a single progenitor cell. In parallel, genomic data also suggest that the diversity could be >10-fold larger if tumor cells are of multiple origins. We develop an evolutionary hypothesis that a single tumor may often harbor multiple cell clones of independent origins, but only one would be large enough to be detected. To test the hypothesis, we search for independent tumors within a larger one (or tumors-in-tumor). Very high density sampling was done on two cases of colon tumors. Case 1 indeed has 13 independent clones of disparate sizes, many having heavy mutation burdens and potentially highly tumorigenic. In Case 2, despite a very intensive search, only two small independent clones could be found. The two cases show very similar movements and metastasis of the dominant clone. Cells initially move actively in the expanding tumor but become nearly immobile in late stages. In conclusion, tumors-in-tumor are plausible but could be very demanding to find. Despite their small sizes, they can enhance the within-tumor diversity by orders of magnitude. Such increases may contribute to the missing genetic diversity associated with the resistance to cancer therapy.

Gattaca: Base-Pair Resolution Mutation Tracking for Somatic Evolution Studies using Agent-based Models

Research over the past two decades has made substantial inroads into our understanding of somatic mutations. Recently, these studies have focused on understanding their presence in homeostatic tissue. In parallel, agent-based mechanistic models have emerged as an important tool for understanding somatic mutation in tissue; yet no common methodology currently exists to provide base-pair resolution data for these models. Here, we present Gattaca as the first method for introducing and tracking somatic mutations at the base-pair resolution within agent-based models that typically lack nuclei. With nuclei that incorporate human reference genomes, mutational context, and sequence coverage/error information, Gattaca is able to realistically evolve sequence data, facilitating comparisons between in silico cell tissue modeling with experimental human somatic mutation data. This user-friendly method, incorporated into each in silico cell, allows us to fully capture somatic mutation spectra and evolution.

Exact site frequency spectra of neutrally evolving tumors: A transition between power laws reveals a signature of cell viability

The site frequency spectrum (SFS) is a popular summary statistic of genomic data. While the SFS of a constant-sized population undergoing neutral mutations has been extensively studied in population genetics, the rapidly growing amount of cancer genomic data has attracted interest in the spectrum of an exponentially growing population. Recent theoretical results have generally dealt with special or limiting cases, such as considering only cells with an infinite line of descent, assuming deterministic tumor growth, or taking large-time or large-population limits. In this work, we derive exact expressions for the expected SFS of a cell population that evolves according to a stochastic branching process, first for cells with an infinite line of descent and then for the total population, evaluated either at a fixed time (fixed-time spectrum) or at the stochastic time at which the population reaches a certain size (fixed-size spectrum). We find that while the rate of mutation scales the SFS of the total population linearly, the rates of cell birth and cell death change the shape of the spectrum at the small-frequency end, inducing a transition between a 1/j² power-law spectrum and a 1/j spectrum as cell viability decreases. We show that this insight can in principle be used to estimate the ratio between the rate of cell death and cell birth, as well as the mutation rate, using the site frequency spectrum alone. Although the discussion is framed in terms of tumor dynamics, our results apply to any exponentially growing population of individuals undergoing neutral mutations.

Normal tissue architecture determines the evolutionary course of cancer

Cancer growth can be described as a caricature of the renewal process of the tissue of origin, where the tissue architecture has a strong influence on the evolutionary dynamics within the tumor. Using a classic, well-studied model of tumor evolution (a passenger-driver mutation model) we systematically alter spatial constraints and cell mixing rates to show how tissue structure influences functional (driver) mutations and genetic heterogeneity over time. This approach explores a key mechanism behind both inter-patient and intratumoral tumor heterogeneity: competition for space. Time-varying competition leads to an emergent transition from Darwinian premalignant growth to subsequent invasive neutral tumor growth. Initial spatial constraints determine the emergent mode of evolution (Darwinian to neutral) without a change in cell-specific mutation rate or fitness effects. Driver acquisition during the Darwinian precancerous stage may be modulated en route to neutral evolution by the combination of two factors: spatial constraints and limited cellular mixing. These two factors occur naturally in ductal carcinomas, where the branching topology of the ductal network dictates spatial constraints and mixing rates.

Neutral syndrome

Neutral models of evolution assume the absence of natural selection. Formerly confined to ecology and evolutionary biology, neutral models are spreading. In recent years they've been applied to explaining the diversity of baby names, scientific citations, cryptocurrencies, pot decorations, literary lexica, tumour variants and much more besides. Here, we survey important neutral models and highlight their similarities. We investigate the most widely used tests of neutrality, show that they are weak and suggest more powerful methods. We conclude by discussing the role of neutral models in the explanation of diversity. We suggest that the ability of neutral models to fit low-information distributions should not be taken as evidence for the absence of selection. Nevertheless, many studies, in increasingly diverse fields, make just such claims. We call this tendency 'neutral syndrome'.

Modeling genetic heterogeneity of drug response and resistance in cancer

Heterogeneity in tumors is recognized as a key contributor to drug resistance and spread of advanced disease, but deep characterization of genetic variation within tumors has only recently been quantifiable with the advancement of next generation sequencing and single cell technologies. These data have been essential in developing molecular models of how tumors develop, evolve, and respond to environmental changes, such as therapeutic intervention. A deeper understanding of tumor evolution has subsequently opened up new research efforts to develop mathematical models that account for evolutionary dynamics with the goal of predicting drug response and resistance in cancer. Here, we describe recent advances and limitations of how models of tumor evolution can impact treatment strategies for cancer patients.

On measuring selection in cancer from subclonal mutation frequencies

Recently available cancer sequencing data have revealed a complex view of the cancer genome containing a multitude of mutations, including drivers responsible for cancer progression and neutral passengers. Measuring selection in cancer and distinguishing drivers from passengers have important implications for development of novel treatment strategies. It has recently been argued that a third of cancers are evolving neutrally, as their mutational frequency spectrum follows a 1/f power law expected from neutral evolution in a particular intermediate frequency range. We study a stochastic model of cancer evolution and derive a formula for the probability distribution of the cancer cell frequency of a subclonal driver, demonstrating that driver frequency is biased towards 0 and 1. We show that it is difficult to capture a driver mutation at an intermediate frequency, and thus the calling of neutrality due to a lack of such driver will significantly overestimate the number of neutrally evolving tumors. Our approach provides quantification of the validity of the 1/f statistic across the entire range of relevant parameter values. We also show that our conclusions remain valid for non-exponential models: spatial 3d model and sigmoidal growth, relevant for early- and late stages of cancer growth.

Darwinian evolution in cancer is responsible for the emergence of malignant traits in initially benign tumors. As tumor cells divide, they accumulate new mutations and while most of them are “passengers” which do not confer any selective growth advantage, “driver” mutations endow cells with traits that contribute to cancer spread. Identifying driver mutations that are under selection in cancer can point to new targets for cancer therapeutics and open new avenues for personalized cancer treatment. It has recently been argued that the presence or absence of selection in cancer can be deduced from deviation of mutant allele frequencies from 1/f power law in an intermediate frequency range. Using a stochastic mathematical model of cancer evolution we derive a formula for the frequency of a subclonal driver and show that frequencies of cancer drivers are biased towards 0 and 1; thus most mutations will inevitably appear to be either neutral (frequency ≈ 0) or clonal (frequency ≈ 1) despite very different levels of selection. Consequently, the proposed 1/f statistic will significantly overestimate the number of cancers deemed to be evolving neutrally. Our work quantifies the validity of the proposed neutral evolution statistic across the entire range of relevant parameter values.