Fig 1.
Schematic representation of the stochastic model of tumor evolution.
a, Transformed cells (blue) divide with rate b, obtain an additional driver mutation with rate u, and die with rate d. Cells with the additional driver (red) divide with rate b1 and die with rate d1. The ratio of net growth rates of cells with and without the driver, c = (b1-d1)/(b-d) is greater than 1. b, Growth begins with a single parental cell. We are interested in the fraction of cells with the driver as a function of the total number of tumor cells M.
Fig 2.
Cancer cell frequency of a subclonal driver is biased towards 0 and 1.
a, b, c, Probability that a subclonal driver is in the detectable range (0.2 ≤ fsub ≤ 0.8), and thus able to skew the distribution of mutational cancer cell frequencies expected from neutral evolution, for three parameter regimes. For each parameter regime, we depict three levels of selection: moderate selection (driver increases net growth rate by g = 30%), strong selection (g = 70%), and very strong selection (g = 100%). Parameter values for a, moderately growing tumor [20]: b = 0.14, r = 0.01; b, fast growing tumor [36]: b = 0.25, r = 0.07; c, slow-growing tumor [21]: b = 0.33, r = 0.0013. Driver mutation rate [21] u = 10−5. All rates are per day and b = b1. d, e, f, Probability density for the frequency of a subclonal driver that increases the net growth rate by 70%, in a moderately growing tumor (a). d, Driver frequency is biased towards 0 when tumor size is small. e, When tumor size is large, driver frequency is biased towards 1. f, When detection is most likely (at intermediate size), driver frequency distribution is almost flat.
Fig 3.
Probability of detection of a subclonal driver for a wide range of driver mutation rates and growth rate advantages is always below 60%.
Contour plots depict the probability that a subclonal driver is in the detectable range (0.2 ≤ fsub ≤ 0.8) and thus able to skew the distribution of mutation frequencies expected from neutral evolution, for a, small; b, intermediate; and c, large tumor size. Parameter values for moderately growing tumor b = b1 = 0.14, r = 0.01. All rates are per day.
Fig 4.
Comparison of formula (1) for the cumulative distribution of driver frequency and exact computer simulations.
On the y-axis we plot the probability that driver frequency is below a particular value. Error bars are standard errors of the mean (s.e.m.) obtained via bootstrapping. Parameters: a, b = b1 = 0.14, d = 0.13, c = 1.7, u = 10−5, M = 108; b, b = b1 = 0.14, d = 0.13, c = 1.5, u = 10−4, M = 108; c, b = b1 = 0.14, d = 0.13, c = 1.5, u = 10−5, M = 108; d, b = b1 = 0.14, d = 0.17, c = 1.9, u = 10−5, M = 108.