Tumor growth is an evolutionary process governed by somatic mutation, clonal selection and random genetic drift, constrained by the co-evolution of the microenvironment1,2. Tumor subclones are subpopulations of tumor cells with a common set of mutations resulting from the expansion of a single cell during tumor development, and have been observed in a significant fraction of cancers and across multiple cancer types3. Peter Nowell proposed that tumors evolve through sequential genetic events4, whereby one cell acquires a selective advantage so that its lineage becomes predominant. According to this traditional model, the selective advantage is conferred by a small set of driver mutations, but, as the subclones that bear them expand successively, they accumulate passenger mutations as well, which can be detected in sequencing experiments1. Genomes of individual tumors contain hundreds to many thousands of these genetic variants, at a wide range of frequencies5,6. Given that genetic drift alone can drive novel variants to high frequencies, it is of great interest to discern the relative importance of selection and drift in shaping the frequency distribution of variants in any given tumor.
Williams et al.7 recently proposed a way to do so. They found that a simple model of tumor growth in which all novel variants are selectively neutral, that is, whose dynamics are governed entirely by drift, predicts a linear relationship between the number of mutations M(f) present in a fraction f of cells and the reciprocal of that fraction: 
. They argued that deviation from this null model, i.e. the R-squared of the linear fit is below the minimum observed in neutral simulations (R2 < 0.98), indicates the presence of selection and that this can be tested by means of variant allele frequencies (VAFs) from which f can be derived. Applying this rationale to real cancer data from The Cancer Genome Atlas (TCGA), the test proposed by Williams et al. did not reject the null model, that is neutrality, in about one third of the cases and the authors concluded that these tumors are neutrally evolving. More recently, multiple myelomas with evidence for the proposed linear relationship were associated with poorer prognosis8.
While providing an interesting approach to infer selection in human cancers, unfortunately four major simplifying assumptions underlie the analysis by Williams et al. that might render the conclusions questionable.
First, inferring f of variants from their VAF requires accurate estimates of local copy number, overall tumor purity and ploidy. Williams et al. attempted to account for some of these factors by restricting their analyses to variants with VAF between 0.12 and 0.24 and located in copy-neutral regions of the genome. However, even in that limited VAF window, the VAF of a mutation does not reflect its true f in many cases. For example, in tumors with whole genome duplications, i.e. 37% of tumors in the analyzed dataset9, the peak of clonal mutations acquired after the whole genome doubling event is at or below VAF = 0.25 (one out of four copies in a 100% pure tumor sample), which would lead to artificial deviation from the linear fit within that VAF window.
Second, the interpretation of the analyses is inconsistent with the use of neutrality as a null model. Failure to reject the null hypothesis is not the same as proving it true, i.e. that all neutral simulations have R2 > 0.98 does not prove that non-neutral simulations would never yield R2 > 0.98. One would need to demonstrate that this condition is sufficient to infer neutrality but also, no equally suited models of non-neutral tumor growth should yield R2 > 0.98.
To assess this, we simulated simple tumor growth in which we explicitly model one subclonal expansion with a selective advantage, i.e. increasing its division rate λ and/or the mutation rate μ of the subclone (Supplementary Methods). Using the original method described by Williams et al., neutrality is rejected only within a narrow range of λ and μ values tested that would lead to detectable subclones (true rejection of neutrality in ~11% of simulations; Fig. 1a). We conclude that a linear fit with R2 > 0.98 is not sufficient to call neutrality and that improper use of this model could result in substantial over-calling of neutrality.
(a) Neutrality calls in simulations of tumor growth with subclonal expansion underlying selective sweeps. The tree topology being modelled is represented on the right together with the parameters of the neutral evolution equations for the two subpopulations of cells (Supplementary Methods). The subclone’s fraction (subclone %) increases with its selective advantage advsubclone. We vary the λ = 1 + advsubclone and μ parameters of the subclone along a grid. Simulations are defined as true non-neutral (light blue) or false neutral (dark blue) when the growing subclone has expanded sufficiently to be detectable and the sweep is not complete, i.e. 10% ≤ subclone % ≤ 90%, otherwise the subclone is considered beyond detection (light green). Non-neutral call: R2 < 0.98; neutral call: R2 ≥ 0.98. (b) As (a), using the Gillespie algorithm to simulate branching processes10. Simulations leading to subclones beyond detection are either called neutral (light green) or non-neutral (dark green). Because of the stochastic nature of branching processes, different subclone % values are obtained across simulations from the same advsubclone values. For five increasing advsubclone values, we report median ± mad of the subclone % across the simulations. (c) Summary ROC curve for the neutral vs. non-neutral classification based on the R2 values in 1,919 non-neutral simulations from (b), and 1,919 simulations of neutral tumors. The false positive rate and the true positive rate are highlighted for R2 = 0.98 used by Williams et al. (d) dN/dS analysis. Maximum likelihood estimates of the dN/dS ratios and associated 95% confidence intervals for (sub)clonal mutations in TCGA tumors categorized into neutral and non-neutral groups. Ratios for missense and truncating mutations are given. dN/dS > 1 indicates positive selection.
Third, the deterministic model of tumor growth described by Williams et al. relies on strong biological assumptions, among which are synchronous cell divisions, constant cell death and constant mutation and division rates. Stochastic models of tumor growth are biologically more realistic, as they allow for asynchronous divisions and probabilistic mutation acquisition, cell death and division rates. Using simple branching processes to simulate neutral and non-neutral growth10 (Supplementary Methods), we show that R2 > 0.98 for 
is neither a necessary nor a sufficient property of neutrally evolving tumors (Fig. 1b). Although it can be shown that the expected cumulative number of mutations - i.e. the average over many independent samples 
due to the biological noise modeled in branching processes, a typical realization of the neutral process in a single sample deviates substantially from the expected linear fit, rendering an R-squared threshold inaccurate to infer neutrality. As a result, discrimination of neutral and non-neutral simulated tumors using a linear fit is almost arbitrary, with 53.5% false positive neutral calls in non-neutral tumors (Fig. 1b) and an area under the ROC curve of 0.42 for the classification of 1,919 neutral and 1,919 non-neutral tumors (Fig. 1c).
Fourth, we reason that in tumors called neutral, no subclonal selection should be detected. To evaluate this, we use an orthogonal method to identify selection, based on the observed variants themselves rather than on their allele frequencies. dN/dS analysis derives the fraction of mutated non-synonymous positions to the fraction of mutated synonymous positions in the coding regions. It has been widely used to detect the presence of negative or positive selection of non-synonymous variants in coding regions11,12. We applied a dN/dS model optimized for the detection of selection in somatic cancer variants13 to TCGA exome data using a published list of 192 cancer genes14 (Supplementary Methods). The analysis was performed separately using variants called as clonal or subclonal (Supplementary Methods), in tumors called neutral and non-neutral based on the rationale outlined by Williams and colleagues7. dN/dS ratio analysis revealed significant positive selection in subclonal mutations of tumors classified as neutral (Fig. 1d), further suggesting that the approach described by Williams et al. is under-equipped to detect the presence or absence of selection.
In summary, Williams et al. proposed that about one third of tumors are neutrally evolving. However, we highlight four simplifying assumptions - to our knowledge not previously highlighted - and find that the proposed approach will often identify individual tumors as neutral when they are non-neutral and non-neutral when they are neutral. A new paper by the same group15 introduces a Bayesian test for detecting selection from VAFs. The test estimates selection coefficients and, as such, is an important advance over Williams et al.’s frequentist test, which does not. The authors acknowledge that the test can only detect large fitness differences, but nevertheless call tumors that fail it “neutral’’ when they are merely those in which a weak test has failed to detect selection. We note that neutral theory has been developed in population genetics, ecology and cultural evolution and that similar tests have been proposed in all of these fields and, in all, eventually been found wanting for the same reason: variant abundance distributions do not contain enough information to exclude selection16-18. It is of clinical importance to identify and better understand the drivers of the potentially more aggressive (sub)clones expanding under selective biological or therapeutic pressure, as these are good candidates for predicting resistance and exploring combination therapy. Williams et al. are to be commended for having introduced explicit neutral tumor growth models into tumor genomics. However, quantifying the relative importance of drift and selection in shaping the allele frequencies of single tumors clearly remains an open challenge. Studies relying on their proposed test (e.g. 8) might, then, need reevaluation.
Competing interest
The authors declare no competing interests.
Author contribution
MT, IM, MG, AML, FM, PTS, QDM, OCL, DCW, PVL participated in argumentation. MT, OCL, DCW and PVL derived the deterministic equations. MT wrote the code and generated the figures, with input from IM, MG, OCL, DCW and PVL. MT, OCL, DCW, PVL drafted the manuscript, revised by IM, MG, AML, FM, PTS, and QDM. All authors read and approved the manuscript.
Methods
Outline
First, we describe the two tumor growth models that were used. The first is based on the deterministic continuous model presented by Williams et al.1. The second is based on a branching process, a commonly used discrete and fully stochastic growth model. We next explain how, using these two models, we can simulate variant allele fractions encountered in tumor sequencing studies. We describe our implementation of the approach by Williams et al.1 to infer the most likely evolutionary path after the emergence of the most recent common ancestor (MRCA), i.e. neutral vs. non-neutral evolution. Finally, using real data from The Cancer Genome Atlas, we compare neutrality calls to results of dN/dS analysis, an independent and well-established approach to detect selection. We further describe the availability of the code as a tarball containing R and Java scripts and a Java runnable jar file called via one of the R scripts.
Simulations - continuous deterministic models
The deterministic equations described in Williams et al.1 relate the number of cells in a tissue growing exponentially, N,
and the cumulative number of mutations, M:
at any given time t ≥ 0, where λ > 0 is the division rate per unit of time, β ≥ 0 is the unitless “effective” division fraction, i.e. the fraction of divisions in which both daughter cells survive (β = 1 for no cell death, β < 1 to model cell death), and μ > 0 is the mutation rate per cell division.
We have used these continuous deterministic models to simulate tumor growth in silico and followed each mutation and its corresponding variant cell fraction. To derive the cell fractions, we follow the progeny of the mother cell within which each mutation occurred.
Assume that the MRCA appears at time t1, with division coefficient β1, division rate λ1, and mutation rate μ1. To model a selective sweep within the cell population spawned from the MRCA, we assume that at time t2 > t1, a subclone is initiated with division coefficient β2 division rate λ2, and mutation rate μ2.
There is positive selection when λ2β2 > λ1β1. At time t the number of cells spawned from the MRCA but not part of the subclone (i.e. the cells with parameters β1, λ1, μ1; further referred to as the MRCA lineage) is
where the second term is omitted when t < t2. Similarly, the number of cells at time t from the subclonal lineage (i.e. with parameters β2, λ2, μ2) is
when t > t2 and N2(t) = 0 otherwise. The total cell count at time t is
The tumor growth simulation is terminated at time T > t2 and we derive the distribution at time T of the cell fractions for all mutations in the tumor.
Following the number of mutations and their cell fraction
Because the equations are continuous, they can lead to non-integer numbers of mutations and cell divisions. Hence, rather than deriving the number of mutations and their allele frequencies f at discrete time points, we model divisions in continuous time. We assess the number of additional mutations that have been added in fixed (small) time intervals of length dt. From Eq. (1), we find that the number of additional mutations occurring in the time interval [t, t + dt] within a population of cells from the same lineage (i.e. parameters β, division rate λ, and mutation rate μ) is:
For a mutation occurring at time t, we may compute the variant cell fraction at time T. If the mutation occurred in a cell from the MRCA lineage that was not inherited by the subclone-initiating cell, then the variant cell fraction is
If the mutation occurred in the subclone, then the variant cell fraction is
Finally, if the mutation occurred in an ancestor cell of the subclone-initiating cell, then the variant cell fraction is
Alternatively, we may calculate variant cell fractions in two steps, first determining the variant cell fraction of a mutation within the subpopulation of cells from the same lineage, and then scaling the variant cell fraction by the size of that subpopulation relative to the total cell population.
Setting the parameters for the grid of simulations
In each of our simulations the subclone growing under selective advantage appears at the 11th generation and the tumor is sampled at the 40th generation with a virtual purity of 100%. The number of initial clonal mutations μ0 is not part of these models, and we arbitrarily set μ0 = μ2. We fix the following parameters: clonal mutation rate μ1 = 16, clonal division rate λ1 = 1, clonal division efficiency β1 = 0.4, subclonal β2 = 0.4. The depth of sequencing of the variants cov ~ Pois(10,000) to approach the theoretical distribution and the alternate read counts ~ Bin(cov, f/2), where f is the variant allele frequency derived from the model (see section on simulating tumor variant allele frequencies from sequencing data). We explore the results of the neutrality calls for a grid of parameter values wide enough to encompass many realistic combinations:
and
where
Simulations – fully stochastic models
To model stochastic discrete tumor growth, we use branching processes with the Gillespie algorithm2. These simulated tumors grow under asynchronous division, with zero or one subclone.
This was coded in Java. Each cell is a Java object and has four attributes: a Boolean value reporting whether the cell is alive or dead; an integer for the average number of mutations per division; an integer with mother cell ID; and an ArrayList of all MutationSets inherited from the mother cell. MutationSet is another class, for which each object contains one integer for the mother cell ID and one integer for the number of mutations within them. The constructor of MutationSet takes the mutation rate of the mother cell as average number of events per interval of a Poisson distribution to draw the number of mutations.
Starting with an ArrayList of one tumor initiating cell, for each of 220 cell division events, one cell is picked randomly from the living cells and either dies with probability P(cell death) or divides into two daughter cells with probability P(division) = 1 - P(cell death), akin to the Gillespie algorithm.
In our simulations, the subclone appears at the 28 th division (~8th generation) by changing the division rate value of one of the cells, and the tumor is sampled at the 220 th division (~20th generation). In these simulations, the number of mutations acquired at each cell division for each daughter cell is drawn from a Poisson distribution for the MRCA lineage μ ~ Pois(μMRCA) and the subclone lineage μ ~ Pois(μsubclone).
The subclone is selected for division with probability
where Nsubclone and NMRCA are the number of cells from the subclonal lineage and the MRCA lineage, respectively, and advsubclone > 0 for positive selection and advsubclone = 0 for neutral growth. The MRCA population will be selected for division with probability 1 - P(subclone divides).
Within the selected clone, one cell is selected randomly for division with probability
where N = NMRCA if the cells belong to the MRCA lineage or N = Nsubclone if the cell belongs to the subclonal lineage.
With higher P(cell death), the first divisions are more likely to lead to the death of all cells and the tumor quickly stops growing. To limit this effect when cell death is high, we force the D first divisions to happen, i.e. P(cell death) = 0 transiently until at least 2D cells are alive.
Setting the parameters for the grid simulations
In our simulations, starting from one tumor initiating cell, for each of the 220 cell division events, one cell is picked randomly and either dies with probability P(cell death) = 0.2 or divides into two daughter cells with probability P(division) = 1 - P(cell death) = 0.8. The subclone appears at the 28 th division (~8th generation) and the tumor is sampled at the 220-th division (~20th generation). The ancestor clone’s mutation rate μ ~ Pois(16). The average depth of coverage is 100X (see section on simulating tumor variant allele frequencies from sequencing data). In our simulations, D = 6.
We explore a grid of values for
and
This leads to 19*101=1,919 simulated tumor simulations covering the grid.
Simulating tumor variant allele frequencies from sequencing data
Using the tumor growth models presented here, we can derive the exact number of mutations and their prevalence within a virtual tumor. These are taken as input to simulate the frequencies that would be observed in the sequencing reads from real tumor tissue.
In order to test the initial hypothesis, i.e. 
, we start with the simplest models and assume: (i) the absence of non-tumor contaminant, (ii) 100% of the tumor cells are resected, and (iii) a fully diploid cancer genome.
Given exact cell fractions, f of each mutation and an average sequencing coverage, cov, we draw for each individual mutation the total number of reads covering its genomic position N from a Poisson distribution N ~ Pois(cov), and the alternate read counts alt ~ Bin(N,f/2), where f/2 is the allelic fraction for diploid regions. Finally, we generate variant calls by taking mutations with alt > 2 and derive the variant allelic fraction (VAF) of each variant 
. We then use the VAF distribution to call neutral and non-neutral tumors, as described by Williams et al.1
Calling neutral tumors
We followed the description by Williams et al.1 to call neutral and non-neutral tumors based on the variant allele frequencies of their somatic single nucleotide variants. Tumors with less than 12 mutations with 0.12 ≤ VAF ≤ 0.24 were removed. From the TCGA dataset, only tumors with a purity of at least 70%, as inferred by ASCAT3, were analyzed.
We calculated the explained variance (R2) for linear regression models both with fixed intercept (intercept = 0) and without fixing the intercept, using the R commands:
and
respectively, where y is the cumulative number of mutations and x is the inverse allelic frequency minus the upper limit 
. Results presented in the manuscript were obtained using a variable intercept. In Supplementary Fig. 1, we show the heat map of Figure 1a using a fixed intercept. Both methods show 97.5% agreement (Supplementary Fig. 2).
The tree topology being modelled is represented on the right together with the parameters of the neutral evolution equations for the two subpopulations of cells. The subclone’s fraction (subclone %) increases with its selective advantage advsubclone. We vary the λ = 1 + advsubclone and μ parameters of the subclone along a grid. Simulations are defined as true non-neutral (light blue) or false neutral (dark blue) when the growing subclone is sizable enough to be detected and the sweep is not complete, i.e. 10% ≤subclone % ≤ 90%, otherwise the subclone is considered beyond detection (light green). Non-neutral call: R2 < 0.98; neutral call: R2 ≥ 0.98.
The x-axis represents R2 values (squared Pearson’s correlation coefficients) for the linear regression between M(f) and f for the simulations in Supp. Fig. 1. The y-axis represents R2 values with fixed intercept = 0. Neutral calls, made if R2 ≥ 0.98, agree for 97.5% of these simulations (grey) and disagree for 2.5% of them (red).
ROC and area under the curve
Using fully stochastic branching processes, we simulated 1,919 non-neutral tumors and 1,919 neutral tumors and derived the R2 values of the linear fit between the cumulative number of mutations and their inverse variant allelic fraction (VAF) within 0.12 ≤ VAF ≤ 0.24. We then plotted the ROC using the R package ROCR version 1.0–7 and calculated the false positive rate and the true positive rate assuming the R2 = 0.98 threshold used by Williams et al.1
Detection of selection in neutral and non-neutral tumors - dN/dS
Dataset
We ran our analyses on the data from The Cancer Genome Atlas, using CaVeMan4,5 single nucleotide variant calls, and ASCAT3 copy number calls, as described by Martincorena et al.6
Grouping variants into clonal and subclonal categories
To classify variants as clonal or subclonal, we used a one-sided proportion test to assess whether the alternate and total read counts of each variant were compatible with its clonality, given its underlying number of DNA copies, and the overall tumor purity. This method is previously described in Alexandrov et al.7
dN/dS analysis and control gene sets
We performed dN/dS analysis to detect positive or negative selection of non-synonymous variants, as described by Martincorena et al.6 The R package dNdScv was used to derive the dN/dS values and is available on github: https://github.com/im3sanger/dndscv. We ran dN/dS separately on clonal and subclonal mutations and separately in the neutral and non-neutral tumors, using a published list of 192 cancer genes (COSMIC v.80 - cancer.sanger.ac.uk8)a.
As a control, we ran dN/dS on subclonal mutations using 100 random sets of 192 genes, uniformly sampled from 20,090 annotated genes from hg196. The 95% interval of dN/dS values was above 1, i.e. showed evidence for positive selection, in 3 out 100 random gene sets. We further reasoned that not all genes are equally “important” to the 192 COSMIC genes across tissues and took their gene expression across tissues as a proxy for their importance. We downloaded the human bodymap 2.0 (https://www.ebi.ac.uk/gxa/experiments/E-MTAB-513/Results) TPM matrix of expression and ranked genes by their values. We summed the ranks across relevant tissues (adrenal gland, brain, breast, colon, kidney, leukocyte, liver, lung, ovary, prostate gland, thyroid gland) and rerun dN/dS on 4×100 192-gene sets randomly sampled from the 10,000, 5,000, 2,500 and 1,000 top-ranked (highly-expressed) genes in those tissues. Among these four lists of highly expressed genes, the 95% intervals of dN/dS values were >1 in 2, 6, 4, 5 out of the 4×100 gene sets, respectively, confirming that the dN/dS signal is (cancer-)gene specific and is not biased in random gene sets. We then reasoned that gene co-expression levels might be a better proxy for “cancer-relevance” of the genes. To this end, the tool Gemma9 (https://gemma.msl.ubc.ca/home.html) was run to identify genes showing evidence for co-expression with one of the 192 cancer genes in >21 out of 442 gene expression datasets from the Master set for human. This identified 2,089 unique co-expressed genes (with a median of 2 co-expressed genes per cancer gene), from which we removed the 227 genes overlapping with the 719 cancer genes from the most recent cancer gene census (COSMIC v.84 - cancer.sanger.ac.uk8). We then sampled 192 unique genes from the 1,862 genes with probabilities of each gene g being sampled 
, where G are the genes from the 192 genes that are co-expressed with g, and Ni is the number of co-expressed genes with gene i. We ran dN/dS again on 100 of these 192-gene sets and found that 4 and 5 out of 100 gene lists yielded 95% confidence intervals of dN/dS >1 for subclonal mutations in neutral and non-neutral tumours, respectively.
Effect of copy number
We repeated the analyses after selecting only variants that fall within diploid regions, i.e. 1 copy of allele A and 1 copy of allele B according to ASCAT3, to show that the results were not induced by unreliable neutral calls, which could have resulted from the distortion of allele frequencies by copy number changes (Supplementary Fig. 3).
Maximum likelihood estimates of the dN/dS ratios and associated 95% confidence intervals for (sub)clonal mutations in TCGA tumors categorized into neutral and non-neutral groups. Ratios for missense and truncating mutations are given. dN/dS > 1 indicates positive selection.
Code reproducibility and availability
Analyses and figures were generated using R version 3.1.3. The branching processes are coded in Java. The code for simulations is available as a tarball (included within this submission) with R scripts for the deterministic simulations and for deriving the figures, and a Java runnable jar file for generating variant fractions from the branching processes together with the associated Java source code.
Acknowledgments
This work was supported by the Francis Crick Institute, which receives its core funding from Cancer Research UK (FC001202), the UK Medical Research Council (FC001202), and the Wellcome Trust (FC001202). MT is a postdoctoral fellow supported by the European Union’s Horizon 2020 research and innovation program (Marie Sklodowska-Curie Grant Agreement No. 747852-SIOMICS). PVL is a Winton Group Leader in recognition of the Winton Charitable Foundation’s support towards the establishment of The Francis Crick Institute. IM is funded by a Cancer Research UK Career Development Fellowship (C57387/A21777). DCW is funded by the Li Ka Shing foundation. This work was supported by grant 1U24CA210957 to PTS. FM would like to acknowledge the support of The University of Cambridge, Cancer Research UK and Hutchison Whampoa Limited. Parts of this work was funded by CRUK core grant C14303/A17197. This project was enabled through access to the MRC eMedLab Medical Bioinformatics infrastructure, supported by the Medical Research Council (grant number MR/L016311/1). Parts of the results published here are based upon data generated by the TCGA Research Network: http://cancergenome.nih.gov/.
Footnotes
↵# These authors jointly directed the work
↵a ABL1, ACVR1, ACVR1B, AKT1, ALK, AMER1, APC, AR, ARID1A, ARID2, ASXL1, ATM, ATP1A1, ATP2B3, ATR, ATRX, AXIN1, AXIN2, BAP1, BCOR, BIRC3, BRAF, BRCA1, BRCA2, CACNA1D, CALR, CARD11, CASP8, CBL, CBLB, CD79A, CD79B, CDC73, CDH1, CDKN2A, CDKN2C, CEBPA, CIC, CNOT3, COL2A1, CREBBP, CRLF2, CSF1R, CSF3R, CTNNA1, CTNNB1, CUX1, CXCR4, CYLD, DAXX, DICER1, DNM2, DNMT3A, EGFR, EML4, EP300, ERBB2, ERG, ESR1, ETNK1, EZH2, FAT1, FAT4, FBXO11, FBXW7, FGFR1, FGFR2, FGFR3, FLT3, FOXA1, FOXL2, FUBP1, GATA1, GATA2, GATA3, GNA11, GNAQ, GNAS, GRIN2A, H3F3A, H3F3B, HIF1A, HIST1H3B, HNF1A, HRAS, IDH1, IDH2, IKBKB, IKZF1, IL6ST, IL7R, JAK1, JAK2, JAK3, KCNJ5, KDM5C, KDM6A, KDR, KIT, KLF4, KMT2C, KMT2D, KRAS, MAP2K1, MAP2K2, MAP2K4, MAX, MED12, MEN1, MET, MLH1, MPL, MSH2, MSH6, MTOR, MYD88, MYOD1, NF1, NF2, NFE2L2, NFKBIE, NOTCH1, NOTCH2, NPM1, NRAS, NT5C2, NTRK3, PAX5, PBRM1, PDGFRA, PHF6, PHOX2B, PIK3CA, PIK3R1, PLCG1, POLE, POT1, PPP2R1A, PPP6C, PRDM1, PRKACA, PRKAR1A, PTCH1, PTEN, PTPN11, PTPN13, PTPRB, RAC1, RAD21, RB1, RET, RHOA, RNF43, RPL10, RPL5, RUNX1, SETBP1, SETD2, SF3B1, SH2B3, SMAD4, SMARCA4, SMARCB1, SMO, SOCS1, SPEN, SPOP, SRC, SRSF2, STAG2, STAT3, STAT5B, STK11, SUFU, TBL1XR1, TBX3, TERT, TET2, TNFAIP3, TNFRSF14, TP53, TRAF7, TSC1, TSC2, TSHR, U2AF1, UBR5, USP8, VHL, WT1, XPO1, ZRSR2.
