Extended Data Fig. 6: Schematic illustration of a 3-D spatial-agent based model of tumor growth and metastasis.
Tumor growth is simulated via the expansion of deme subpopulations (mimicking the glandular structures often found in epithelial tumors and metastases) within a defined 3-D cubic lattice according to explicit rules dictated by spatial constraints, where cells within each deme are well-mixed and grow via a stochastic branching (birth-death) process (Methods). To model monoclonal seeding, a single cell at the tumor periphery was randomly sampled as the metastasis founder cell. To model polyclonal seeding, a cluster of cells (n = 10) was randomly sampled from the whole tumor in order to maximize the clonal diversity within the metastasis founder cells. Metastatic growth follows the same spatial-constraints as the primary and starts from the metastasis founder cell or cell cluster. The final sizes of both the primary tumor and metastasis is ~109 cells (~2×105 demes). Clonal selection is modeled by assuming a constant beneficial mutation rate that alters the cell birth/death probability according to the selection coefficient (denoted s). By simulating the acquisition of random mutations (neutral or beneficial), tracing the mutational genealogy of each cell as the tumor expands and subsequently spatially sampling (~106 cells in each sample) and sequencing the ‘final’ virtual tumor as is done experimentally after resection or biopsy, we obtain the variant allele frequencies (VAF) and cancer cell fraction (CCF) in both primary tumor and metastasis.
