Cancers accumulate mutations that lead to neoantigens, novel peptides that elicit an immune response, and consequently undergo evolutionary selection. Here we establish how the clonal structure of neoantigens in a growing cancer is shaped by negative selection, by constructing a mathematical model of neoantigen evolution. The model predicts that, without immune escape, tumour neoantigens are either clonal or absent from large subclones, and hyper-mutated tumours can only establish following the evolution of immune evasion. Strong negative selection on neoantigens leads to an increased number of neutrally-evolving tumours, as a consequence of selective pressure for immune escape. The clone size distribution under negative selection is effectivelyneutral, and becomes more neutral-like under stronger negative selection. These results are consistent with the analysis of neoantigen clone sizes and immune escape in exome and RNA sequencing data from colon, stomach and endometrial cancers. 4 RESULTS Mathematical model of tumour growth predicts distinct antigen-hot and -cold tumoursWe created a mathematical model of neoantigen evolution during tumour growth, based on a stochastic branching process (Figure 1a and Methods). At each step, tumour cells of lineage i produced two surviving offspring at birth rate b=1 per unit time or died with death rate determined by the strength of negative selection against the cumulative antigenicity of neoantigens in the lineage. Neoantigens accumulated at rate µ per cell per division, and had antigenicity s drawn from a pre-specified distribution. s can be interpreted as the effectiveness of immune predation against an antigen: s=0 indicates no selection pressure (neutral evolution), and s<0 strong negative selection (following ref 34 ). Tumour growth was simulated until the tumour reached a predefined population size (approximating a clinically detectable size) or until a sufficiently long time elapsed without tumour establishment (corresponding to no cancer formation within a person's lifetime).We first examined the temporal neoantigen burden in simulated tumours. We defined the 'antigen score' of a tumour as the proportion of tumour cells carrying cumulative antigenicity ≥ ! . Tumours simulated with identical parameters separated into two distinct groups: 'antigen-hot' and 'antigen-cold'. Antigen-hot tumours had an antigen score close to 1, corresponding to every tumour cell in the population being highly antigenic, whereas in antigen-cold tumours the majority of cells lacked immunogenic mutations (Figure 1b&c). The proportion of antigen-hot tumours depended on the selection strength (Figure S1a): increased negative selection for neoantigens decreased the probability of observing antigen-hot tumours. In antigen-cold tumours, the proportion of neoantigen-carrying cells also decreased inversely with negative selection.

Genetic and epigenetic variation, together with transcriptional plasticity, contribute to intratumour heterogeneity1. The interplay of these biological processes and their respective contributions to tumour evolution remain unknown. Here we show that intratumour genetic ancestry only infrequently affects gene expression traits and subclonal evolution in colorectal cancer (CRC). Using spatially resolved paired whole-genome and transcriptome sequencing, we find that the majority of intratumour variation in gene expression is not strongly heritable but rather ‘plastic’. Somatic expression quantitative trait loci analysis identified a number of putative genetic controls of expression by cis-acting coding and non-coding mutations, the majority of which were clonal within a tumour, alongside frequent structural alterations. Consistently, computational inference on the spatial patterning of tumour phylogenies finds that a considerable proportion of CRCs did not show evidence of subclonal selection, with only a subset of putative genetic drivers associated with subclone expansions. Spatial intermixing of clones is common, with some tumours growing exponentially and others only at the periphery. Together, our data suggest that most genetic intratumour variation in CRC has no major phenotypic consequence and that transcriptional plasticity is, instead, widespread within a tumour.

Colorectal malignancies are a leading cause of cancer-related death1 and have undergone extensive genomic study2,3. However, DNA mutations alone do not fully explain malignant transformation4–7. Here we investigate the co-evolution of the genome and epigenome of colorectal tumours at single-clone resolution using spatial multi-omic profiling of individual glands. We collected 1,370 samples from 30 primary cancers and 8 concomitant adenomas and generated 1,207 chromatin accessibility profiles, 527 whole genomes and 297 whole transcriptomes. We found positive selection for DNA mutations in chromatin modifier genes and recurrent somatic chromatin accessibility alterations, including in regulatory regions of cancer driver genes that were otherwise devoid of genetic mutations. Genome-wide alterations in accessibility for transcription factor binding involved CTCF, downregulation of interferon and increased accessibility for SOX and HOX transcription factor families, suggesting the involvement of developmental genes during tumourigenesis. Somatic chromatin accessibility alterations were heritable and distinguished adenomas from cancers. Mutational signature analysis showed that the epigenome in turn influences the accumulation of DNA mutations. This study provides a map of genetic and epigenetic tumour heterogeneity, with fundamental implications for understanding colorectal cancer biology.