Figure 1.
The nature of relationships between age, stem cell number, mutation rate and cancer incidence by the bad luck model. The cumulative incidence of cancer increases with age in a threshold relationship. (A) The stem cell number affects the threshold age, but in all cases the trend saturates only at 100% incidence. (B) At any given lifespan, the stem cell number holds a threshold relationship with cancer incidence. For tissues with stem cell numbers below the threshold, the cancer probability is close to zero and above the threshold it rises to almost unity. (C) The mutation rate also influences the threshold age for a given cancer type and given a fixed lifespan, the mutation rates holds a threshold relationship with incidence (D). The age threshold and the sharpness of the threshold measured by the slope at 50% cumulative incidence (I50) have an inverse relationship (E) shown at k = 5 and 8 respectively. If we take only those cancers for which the threshold lies beyond the maximum lifespan, the relationship of stem cell number with lifetime cancer incidence on a log-log plot is linear (F) with the slope = 1. Lifespan and other parameters change the position of the line, but the slope remains unaltered. Shown in the graph are analytical results. Simulations at population size 10,000 and above follow the analytical predictions very closely. Parameters: For A and B, p = 10−6, n ranges from (curves right to left) 103 to 1010. For C and D, n = 109 and p ranges from (curves left to right) 10−6 to 10−9. In all results displayed here k = 5 and d = 1000.