Quantifying Clonal and Subclonal Passenger Mutations in Cancer Evolution

The vast majority of mutations in the exome of cancer cells are passengers, which do not affect the reproductive rate of the cell. Passengers can provide important information about the evolutionary history of an individual cancer, and serve as a molecular clock. Passengers can also become targets for immunotherapy or confer resistance to treatment. We study the stochastic expansion of a population of cancer cells describing the growth of primary tumors or metastatic lesions. We first analyze the process by looking forward in time and calculate the fixation probabilities and frequencies of successive passenger mutations ordered by their time of appearance. We compute the likelihood of specific evolutionary trees, thereby informing the phylogenetic reconstruction of cancer evolution in individual patients. Next, we derive results looking backward in time: for a given subclonal mutation we estimate the number of cancer cells that were present at the time when that mutation arose. We derive exact formulas for the expected numbers of subclonal mutations of any frequency. Fitting this formula to cancer sequencing data leads to an estimate for the ratio of birth and death rates of cancer cells during the early stages of clonal expansion

Predicted and observed numbers of subclonal mutations in colorectal cancer.

<p>Exome sequencing data for two colorectal cancers from the TCGA dataset, (A) microsatellite stable (MSS) and (B) microsatellite instable (MSI), show the corrected allele fraction of each detected mutation (observed allele fraction divided by purity). Mutations with allele frequency of 25% or more may be clonal [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004731#pcbi.1004731.ref034" target="_blank">34</a>] and mutations with corrected allele frequency below 12% can be difficult to detect reliably. Thus we focus on mutations with fractions between 0.12 and 0.25, and plot the number of mutations with fraction between <i>α</i> and 0.25 as a function of <i>α</i>. The data are fit to the formula for the number of mutations with the corresponding allele frequency <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004731#pcbi.1004731.e008" target="_blank">Eq (7)</a>. The best fit for and its corresponding 95% confidence interval is shown for each sample.</p

Frequency of passenger mutations.

<p>(A-B) Cumulative distribution function for the first three successful mutations. The y-axis shows the probability that the mutation has a frequency of less than <i>α</i>. Comparison between <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004731#pcbi.1004731.e002" target="_blank">formula (2)</a> and exact computer simulations of the stochastic process with death-birth ratios <i>δ</i> = 0.72 (A) and <i>δ</i> = 0.99 (B). For <i>δ</i> = 0.72, the median frequencies of the first three successful mutations are below 5%. For <i>δ</i> = 0.99, they are all above 40%. (C-D) Mutation frequency versus time of appearance. (C) Mean frequency attained by a mutation which arose when there were <i>z</i> other cells in the population, for different values of the death-birth ratio, <i>δ</i>. (D) Maximum likelihood and maximum a posteriori estimate (which are approximately equal) for the number of cells in the population when the mutation with frequency <i>α</i> arose. Passenger mutation rate <i>u</i> = 0.015 (product of the number of basepairs in the exome, <i>L</i> ∼ 3 ⋅ 10⁷, and the normal point mutation rate during cell division, <i>μ</i> ∼ 5 ⋅ 10⁻¹⁰).</p

Likelihood of phylogenetic trees.

<p>Likelihood of phylogenetic trees.</p

Evolutionary dynamics of passenger mutations during clonal expansion.

<p>(A) New passenger mutations can be lost due to stochastic drift (diamonds). Successful mutations form surviving lineages. We order successful mutations by their time of appearance. Individual cells can harbor many passenger mutations and various different phylogenies can arise (B). In the example shown, mutation 2 appears in a cell that already harbors mutation 1. Thus all cells that have mutation 2 also have mutation 1. Similarly, all cells cells that have mutations 4 or 5 also harbor mutations 1 and 2. Mutation 3 forms an independent clone. We calculate the likelihood of different phylogenies and the expected number of subclonal mutations of any frequency.</p

Expected number of subclonal and clonal mutations for different values of <i>δ</i> = <i>d</i>/<i>b</i>.

<p>Expected number of subclonal and clonal mutations for different values of <i>δ</i> = <i>d</i>/<i>b</i>.</p

Likelihood of phylogenetic trees.

<p>(A) All six phylogenetic trees containing the first three surviving passenger mutations are shown. (B) Probabilities of each tree for different values of the death-birth ratio, <i>δ</i> (formulas shown in Methods). For <i>δ</i> = 0.72, the first tree is the most likely. For <i>δ</i> = 0.99, the sixth tree is the most likely. For intermediate <i>δ</i> = 0.97, the most likely tree shape is that of trees 2-4. Passenger mutation rate <i>u</i> = 0.015.</p

An analysis of genetic heterogeneity in untreated cancers

Genetic intratumoural heterogeneity is a natural consequence of imperfect DNA replication. Any two randomly selected cells, whether normal or cancerous, are therefore genetically different. Here, we review the different forms of genetic heterogeneity in cancer and re-analyse the extent of genetic heterogeneity within seven types of untreated epithelial cancers, with particular regard to its clinical relevance. We find that the homogeneity of predicted functional mutations in&nbsp;driver genes is the rule rather than the exception. In primary tumours with multiple samples, 97% of driver-gene mutations in 38 patients were homogeneous. Moreover, among metastases from the same primary tumour, 100% of the driver mutations in 17 patients were homogeneous. With a single biopsy of a primary tumour in 14 patients, the likelihood of missing a functional driver-gene mutation that was present in all metastases was 2.6%. Furthermore, all functional driver-gene mutations detected in these 14 primary tumours were present among all their metastases. Finally, we found that individual metastatic lesions responded concordantly to targeted therapies in 91% of 44&nbsp;patients. These analyses indicate that the cells within the primary tumours that gave rise to metastases are genetically homogeneous with respect to functional driver-gene mutations, and we suggest that future efforts to develop combination therapies have the potential to be curative

Precancerous neoplastic cells can move through the pancreatic ductal system

Most adult carcinomas develop from noninvasive precursor lesions, a progression that is supported by genetic analysis. However, the evolutionary and genetic relationships among co-existing lesions are unclear. Here we analysed the somatic variants of pancreatic cancers and precursor lesions sampled from distinct regions of the same pancreas. After inferring evolutionary relationships, we found that the ancestral cell had initiated and clonally expanded to form one or more lesions, and that subsequent driver gene mutations eventually led to invasive pancreatic cancer. We estimate that this multi-step progression generally spans many years. These new data reframe the step-wise progression model of pancreatic cancer by illustrating that independent, high-grade pancreatic precursor lesions observed in a single pancreas often represent a single neoplasm that has colonized the ductal system, accumulating spatial and genetic divergence over time