On the patterns of genetic intra-tumour heterogeneity before and after treatment

Genetic intra-tumour heterogeneity (gITH) is a universal property of all cancers. It emerges from the interplay of cell division, mutation accumulation and selection with important implications for the evolution of treatment resistance. Theoretical and data-driven approaches extensively studied gITH in ageing somatic tissues or cancers at detection. Yet, the expected patterns of gITH during and after treatment are less well understood. Here, we use stochastic birth-death processes to investigate the expected patterns of gITH across different treatment scenarios. We consider homogeneous treatment response with shrinking, growing and stable disease, and follow up investigating heterogeneous treatment response with sensitive and resistant cell types. We derive analytic expressions for the site frequency spectrum, the total mutational burden and the single-cell mutational burden distribution that we validate with computer simulations. We find that the SFS after homogeneous treatment response retains its characteristic power-law tail, while emergent resistant clones cause peaks corresponding to their sizes. The frequency of the largest resistant clone is subdominant and independent of the population size at detection, whereas the relative total number of resistant cells increases with detection size. Furthermore, the growth dynamics under treatment determine whether the total mutational burden is dominated by preexisting or newly acquired mutations, suggesting different possible treatment strategies.