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Identification of neutral tumor evolution across cancer types


Despite extraordinary efforts to profile cancer genomes, interpreting the vast amount of genomic data in the light of cancer evolution remains challenging. Here we demonstrate that neutral tumor evolution results in a power-law distribution of the mutant allele frequencies reported by next-generation sequencing of tumor bulk samples. We find that the neutral power law fits with high precision 323 of 904 cancers from 14 types and from different cohorts. In malignancies identified as evolving neutrally, all clonal selection seemingly occurred before the onset of cancer growth and not in later-arising subclones, resulting in numerous passenger mutations that are responsible for intratumoral heterogeneity. Reanalyzing cancer sequencing data within the neutral framework allowed the measurement, in each patient, of both the in vivo mutation rate and the order and timing of mutations. This result provides a new way to interpret existing cancer genomic data and to discriminate between functional and non-functional intratumoral heterogeneity.

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Figure 1: Neutral evolution is common in colon cancer and allows measurement of the mutation rate in each tumor.
Figure 2: Neutral evolution across the whole genome of gastric cancers.
Figure 3: Neutral evolution and mutation rates across cancer types.
Figure 4: Reconstruction of the mutational timeline in two patients.
Figure 5: Neutral evolution and tumor phylogeny.

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We thank D. Shibata, C. Curtis, S. Tavaré and R. Durrett for fruitful discussions. We would like to thank N. Andor (Stanford University) for supplying mutation calls for the TCGA data. We also thank V. Mustonen for useful suggestions.

A.S. is supported by The Chris Rokos Fellowship in Evolution and Cancer. B.W. is supported by the Geoffrey W. Lewis Post-Doctoral Training fellowship. This work was supported by the Wellcome Trust (105104/Z/14/Z). C.P.B. acknowledges funding from the Wellcome Trust through a Research Career Development Fellowship (097319/Z/11/Z). This work was supported by a Cancer Research UK Career Development Award to T.A.G. M.J.W. is supported by a UK Medical Research Council student fellowship.

This study makes use of data generated by the Department of Pathology of the University of Hong Kong and Pfizer, Inc.; a full list of the investigators who contributed to the generation of the data is available from ref. 28.

Author information

Authors and Affiliations



M.J.W. and B.W. contributed to the development of the model. M.J.W. designed and performed computational simulations with support from C.P.B. M.J.W., A.S. and T.A.G. analyzed the data. C.P.B. contributed to the analysis. T.A.G. and A.S. jointly conceived, designed and developed the model, interpreted the results and wrote the manuscript.

Corresponding authors

Correspondence to Trevor A Graham or Andrea Sottoriva.

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Competing interests

The authors declare no competing financial interests.

Integrated supplementary information

Supplementary Figure 1 Rates of different mutation types in CRC.

(a) Stratification by mutation type indicates that C>T mutations occur at a significantly greater rate than other types. (b) As for the overall mutation rate (Fig. 1d), the rates of all mutation types were significantly higher in the MSI group.

Supplementary Figure 2 Analysis of neutral evolution in colon cancers is robust to copy number changes.

We removed mutations that fell within regions of the genome with altered copy number, that were identified by using SNP arrays paired to the exome-sequenced samples to detect regions of copy number change. (a) The consistently high values of goodness of fit demonstrate that the neutral model is robust to confounding copy number changes. Red line indicates the R2=0.98 threshold for calling a tumor neutral. (b) Estimating the mutation rates using only the mutations in copy number–devoid regions yields similar results as when all SNVs are included, confirming the robustness of our approach.

Supplementary Figure 3 Validation of the mutational signature across the frequency spectrum.

The mutational signature that characterizes the underlying biology is maintained across the frequency spectrum, providing further evidence that the identified somatic variants are reliable and are not due to sequencing errors.

Supplementary Figure 4 Synonymous/nonsynonymous ratio in colon cancers.

(a) A random base change within a codon is more likely to result in a nonsynonymous or stop-gain mutation than a synonymous mutation; hence, we expect the mutation rate per division of nonsynonymous mutations to be higher than for synonymous mutations. This is observed in the data. (b) The synonymous and nonsynonymous mutation rates become equivalent after normalizing by the total number of possible synonymous and nonsynonymous mutation sites in the exome, respectively. Therefore, synonymous and nonsynonymous mutations accrue at the same effective rate, consistent with our neutral model of cancer growth.

Supplementary Figure 5 Neutrality analysis in WGS gastric cancers data is robust to copy number changes.

(a) The goodness of fit of the neutral model was robust to copy number changes, as results were equivalent when only diploid regions or all genomic regions were considered. We note that the total number of cases considered after CNV filtering is considerably smaller because some samples did not have enough variants in the remaining diploid regions to fit the model. Red line indicates the R2=0.98 threshold for calling a tumor neutral. (b) Mutation rates were also consistent when copy number–altered regions were discarded in the analysis. We found only a single neutral MSI tumor, so a distribution could not be plotted.

Supplementary Figure 6 Validation of the mutational signature across the frequency spectrum in WGS gastric cancer data.

The mutational signature is conserved through the allelic frequency spectrum also in this cohort of whole genome–sequenced gastric cancers, thus supporting the authenticity of the called variants.

Supplementary Figure 7 Synonymous/nonsynonymous ratio in whole genome–sequenced gastric cancers.

Adjusted synonymous versus nonsynonymous mutation rates were consistent with neutral evolution in the gastric cancer cohort.

Supplementary Figure 8 Mutation rates by channel across cancer types.

When measured separately between different mutational channels, the mutation rate estimated by the model was consistent with the underlying biology: rates of C>A mutations were higher in lung cancer (tobacco smoking) and C>T mutation rates were higher than other channels in all cancer types.

Supplementary Figure 9 Stochastic simulations of neutral evolution recapitulate the observed NGS data.

(a) We produced realistic synthetic NGS data using a stochastic simulation of tumor growth that accounts for the neutral accumulation of mutations in the tumor as well as the different sources of sequencing noise (sampling, sequencing depth and normal contamination). (b) The prediction of the analytical model on the cumulative distribution of subclonal allelic frequencies agrees with the stochastic simulation. We generated synthetic data to test the accuracy with which tumor parameters could be reliably recovered when faced with confounding factors. Illustrative synthetic data are shown for (c) low mutation rate, (d) a high number of clonal mutations, (e) significant normal contamination and (f) a low detection limit. (g) Over 10,000 simulations, the interquartile range of the percentage error in the estimates of the mutation rate is <5%, demonstrating the ability of the analytical model to accurately estimate tumor growth parameters from NGS data. (h) The R2 values of the fits are consistently high over 10,000 simulations. Unless otherwise stated, the input parameters for the simulation and subsequent sampling were μ=100 mutations/cell division, λ=ln(2), detection limit=10%, normal contamination=0%, mean Ni=100 and number of clonal mutations=200.

Supplementary Figure 10 Robustness of the parameter estimation analysis.

By varying the parameters of the simulation, we show that the analytical model can accurately identify neutrality of tumor growth and recover the mutation rate in the face of (a) different numbers of clonal mutations and (b) different detection limits, and that we can correct for normal contamination accurately (to within 5%) for contamination below 30% (c,d). (e,f) The effect of varying read depth. Less accurate mutation rate estimates were achieved at low read depth (<25) and poorer fits of the analytical model. (g,h) The effect of mutation rate: lower mutation rates lead to poorer model fits and a higher variance in the mutation estimate because fewer variants are available to fit the model. (i,j) The effect of growth rate λ: the variance in the mutation rate estimate increases as tumor growth slows (l decreases) and the fit of the model becomes worse. The offspring probability distributions for the different values of λ were Pλ= ln(2) = (p0 = 0, p1 = 0, p2 = 1), Pλ = ln(1.8) = (p0 = 0.05, p1 = 0.1, p2 = 0.85), Pλ= ln(1.6) = (p0 = 0.1, p1 = 0.2, p2 = 0.7), Pλ= ln(1.4) = (p0 = 0.2, p1 = 0.2, p2 = 0.6) and Pλ = ln(2) = (p0 = 0.2, p1 = 0.4, p2 = 0.4).

Supplementary Figure 11 Clonal expansions and microenvironmental niches produce a deviation from the power-law.

By introducing a second population with a 65% fitness advantage (P = (p0 = 0, p1 = 0.8, p2 = 0.2), Q = (p0 = 0, p1 = 0.02, p2 = 0.98)) when the tumor comprises 80 cells, we see a second peak at VAF ~0.2 (a) and a bend in the cumulative distribution plot (b). A subclonal tumor architecture where mutations from the same subclone cluster around allelic frequencies would not show patterns consistent with neutrality, both when we consider two (c,d) and three (e,f) different subclones within a sample. A new phenotypically distinct clone introduced with a tenfold higher mutation rate (20 per division to 200 per division) also produces a deviation from the neutral power-law (g,h).

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–11. (PDF 1799 kb)

Supplementary Data Set 1: Pan-cancer whole-exome data set.

Table of analyzed pan-cancer samples from TCGA. (XLS 399 kb)

Supplementary Data Set 2: Gastric cancer whole-genome data set.

Table of analyzed gastric cancer samples from Wang et al. (XLS 87 kb)

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Williams, M., Werner, B., Barnes, C. et al. Identification of neutral tumor evolution across cancer types. Nat Genet 48, 238–244 (2016).

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