(A) The output of NGS data, such as whole-exome sequencing, can be summarized as a histogram of mutant allele frequencies, here for sample TB. Considering purity and ploidy, mutations with relatively high frequency (>0.25) are likely to be clonal (public), whereas low frequency mutations capture the tumor subclonal architecture. (B) The same data can be represented as the cumulative distribution M(f) of subclonal mutations. This was found to be linear with 1/f, precisely as predicted by the neutral model. (C) R² goodness of fit of our CRC cohort (n=7) and the TCGA colon cancer cohort (n=101) grouped by CIN versus MSI confirmed that neutral evolution is common (38/108, 35.1% with R²≥0.98). (D) Measurements of the mutation rate showed that the CIN groups had median mutation rate of µ_e=2.31×10^-7, whereas MSI tumors reported a 15-fold higher rate (median: µ_e=3.65×10^-6, F-test: p=2.24×10^-8), as predicted due to their DNA mismatch repair deficiency.

(A) Large number of coding and non-coding mutations can be identified using WGS. (B) All detected mutations precisely accumulate as 1/f following the neutral model in this example. (C) Neutral evolution is very common in gastric cancer, with 60/78 (76.9%) samples showing goodness of fit of the neutral model R²≥0.98. This was consistent using all, exonic or non-coding subclonal mutations. The same tumors were identified as neutral by all three methods, although limitations in detecting neutrality were present when considering exonic mutations due to the limited number of variants. (D) Mutation rates were more than 4 times higher in MSI (µ_e=3.30×10^-6) versus MSS (µ_e=7.82×10^-7; F-test: p=1.35×10^-4) cancers, consistently with the underlying biology.

(A) R² values from 819 cancers of 14 different types supported neutral evolution in a large proportion of cases (259/819, 31.6% of R²≥0.98) and across different cancer types, particularly in stomach (validating the WGS analysis), lung, bladder, cervical and colon. On the contrary, renal, melanoma, pancreatic, thyroid, and glioblastoma were characterized by non-neutral evolution. The other types displayed a mixed dynamics. (B) The highest mutation rates were found in lung cancer. Lower rates were found in thyroid, low grade glioma and prostate.

The allelic frequency of a mutation within the tumor predicts the size of the tumor when the mutation occurred. (A,B) The deconvolution of the mutational timeline is illustrated for samples TB and TCGA-AA-3712 respectively. Whereas established CRC drivers (APC, KRAS, TP53) were found to be present from the first malignant cell, several recurrent putative drivers not yet validated were mutated after malignant seeding, despite the underlying neutral dynamics. This suggests that some of these candidate alterations may not be fundamental drivers of growth in all cases. Confidence intervals are calculated using a binomial test on the number of variant reads versus the depth of coverage for each mutation.

After the accumulation of key genomic alterations, in neutral malignancies the cancer expansion is likely triggered by a single critical genomic event (the accumulation of a “full house” of genomic changes) followed by neutral evolution that generates a large number of new mutations in ever-smaller subclones. While the tumor heterogeneity rapidly increases, the allele frequency of heterogeneous mutations decreases. In this context, the accumulation of mutations M(f) follows a characteristic 1/f distribution. Moreover, the tumor phylogeny displays a characteristic fractal topology that is self-similar. Sampling in different regions of the phylogenetic tree exposes distinct mutations that however show the same 1/f distribution. Clonal mutations in a sample (not considered in the model) arose in to the most recent common ancestor of the sampled cells. Due to the large population of cells sampled using bulk sequencing, the majority of detected clonal mutations belongs to the trunk of the tree and therefore is found in the first cancer cell. Deviations from the 1/f law indicate different dynamics from neutral growth.