Evolutionary dynamics of neoantigens in growing tumors

Abstract

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.

DeCiFering the Elusive Cancer Cell Fraction in Tumor Heterogeneity and Evolution

“…These methods can be categorized into two different strategies. The first strategy is to severely restrict the possible mutation multiplicities of SNVs; specifically, many methods 13,16,21,35,[38][39][40][41][42][43][44][45] assume that all cells harboring an SNV have the same mutation multiplicity. We refer to this assumption as the Constant Mutation Multiplicity (CMM) assumption (Figures 1c and S1b).…”

“…The CCF is not directly observed from bulk data; rather, one observes the total number t of reads that align to the SNV locus and the corresponding number a of reads with the variant allele ( Figure 1b). If the SNV locus is diploid (i.e., no CNAs), the standard approach 13,16,19,21,35,[38][39][40][41][42][43][44][45]47 estimates the CCF c from the fractionv = a/t of variant reads as c ⇡ 1 ⇢ 2v, where ⇢ is the tumor purity -i.e., fraction of cancer cells in the sample -which also may be inferred from bulk data [26][27][28][29][30][31][32] . Note thatv is the maximum likelihood estimate (MLE) estimate of the variant allele frequency (VAF) v -i.e., the proportion of copies of the locus in the sample that contain the SNV.…”

“…Note thatv is the maximum likelihood estimate (MLE) estimate of the variant allele frequency (VAF) v -i.e., the proportion of copies of the locus in the sample that contain the SNV. More generally, if the SNV locus is aneuploid due to CNAs, nearly all existing methods 13,16,21,35,[38][39][40][41][42][43][44][45] estimate the CCF by using the following generalization of the equation for diploid case:…”

“…Second, we classify SNVs as truncal if they are inferred to occur before the most recent common ancestor of all cancer cells in the sample, and subtrunal otherwise. Most previous studies 16,19,21,35,[38][39][40][41][42][43][44]47 assume that clonal SNVs and truncal SNVs are identical. However, this assumption does not necessarily hold when SNVs are lost due to deletions in cancer cells.…”

“…While recent single-cell DNA sequencing technologies enable high-resolution measurements of tumor heterogeneity [5][6][7][8][9][10][11] , the vast majority of cancer studies in research and clinical settings [12][13][14] heterogeneity from SNVs is the Cancer Cell Fraction (CCF) -also known as the cellular prevalence or the mutation cellularity -which is the proportion of cancer cells that contain the SNV. CCFs form the basis for many cancer analyses including: studying tumor heterogeneity 13,15,16 , reconstructing clonal evolution and metastatic progression 13,[17][18][19] , identifying selection [20][21][22] , and analyzing changes in mutational processes over time [23][24][25] . In these and other studies, the underlying assumption is that groups of SNVs with the same CCF are likely to be present in the same cancer cells and thus occurred on the same branch of the phylogenetic tree that describes the evolution of the tumor (Figure 1a).…”