Driver model

First, we constructed the “driver” model, which contains only driver genes, aiming to study the two Darwinian evolution modes: linear and branching evolution. We employed an agent-based model, where each agent corresponds to each cell in a tumor. The simulation started from one cell without mutations. In a unit time, a cell divides into two daughter cells with a probability g. This model assumes that an immortalized cell, which just divides without dying. In each cell division, each of the two daughter cells acquires kd driver mutations. Here, kd is sampled from a Poisson distribution with the parameter md/2, i.e., kd ∼ Pois(md/2), which means that one cell division generates md mutations on average. We assumed that driver mutations acquired by different division events occur at different genomic positions and each cell can accumulate Nd mutations at maximum. In this study, we assumed that all mutations are driver mutations, which increase the cell division rate. When the cell acquires mutations, the cell division rate increases f fold per mutation; that is, when a cell has nd (=∑kd) mutations in total, the cell division probability g is defined as g = g0fnd, where g0 is a base division probability. In each time step, every cell is subject to a cell division trial, which is repeated until population size p reaches P or the number of time steps t reaches T.

Information of variables and parameters are listed in Tables 1 and 2. In MASSIVE, we converted md, f and P to log scale, i.e., md' = log10 md', f' = log10 f and P' = log10 P, and then tested every combination of md' ∈ {-4, -3.5, -3,...,-1}, md ∈ {1, 2, 3, 4}, f' ∈ {0.1, 0.15, 0.2,...,1.0} and P' ∈ {3, 4, 5, 6}. All results are explorable in the focused and comparative view modes of the MASSIVE viewer.

Table 1. a list of the variabes

symbol description
kd number of driver mutations obtained in a cell division
nd number of driver mutations accumulated in a cell
p population size
t number of time steps
g cell division probability

Table 1. a list of the parameters

symbol description value
md expected number of driver mutations generated per cell division {10-4, 10-3.5, 10-3,...,10-1}
Nd maximum number of driver mutations accumulated in a cell {1, 2, 3, 4}
f increase of the cell division probability per driver mutation {100.1, 100.15, 100.2,...,101.0}
g0 base cell division probability 10-4
P maximum population size {103, 104, 105, 106}
T maximum number of time steps 106