Article Figures & Data
Figures
- Figure 1.
A schematic of the genome of a simulated cell. The placement of the loci on different chromosomes is arbitrary. All loci are effectively linked due to the asexual reproduction of neoplastic cells, but mutations affect each locus independently. In most runs of the model, each diploid cell had three loci in which a dominant mutation gave the cell a selective advantage by increasing its rate of mitosis. The cells also had two loci, which required recessive mutations in both alleles before the cell increased its rate of mitosis. Mutation of a single allele in the mutator locus increased the mutation rate of the cell, and a drug resistance locus conferred resistance to the drug associated with that locus.
- Figure 2.
The probability of achieving a cure with a cocktail of cytotoxic drugs. The base mutation rate of the cells in the neoplasm is lowest (10-6) in the upper left-hand panel and greatest (10-5) in the lower right-hand panel. The number of drugs requiring independent mutations for resistance and the time since initiation of the neoplasm at which the therapy is applied varied within each panel. Time since initiation is measured in simulated years since the initiation of the neoplasm.
- Figure 3.
The effect of benign cell booster therapies at 11, 22, or 33 years after the initiation of the neoplasm for mutation rates of μ = 10-6, 2 × 10-6, 4 × 10-6, and 10-5 per allele per cell division. The different types of benign cell boosters are distinguished by the type of targeted locus that had to have a wild-type allele in order for the cell to receive the benefit of the booster. Upper panels, the phenotypes of the loci could be rescued by mutations to produce the wild-type phenotype either by a back mutation or by a compensating mutation. Lower panels, mutant phenotypes could not be rescued. The neutral (cytotoxic resistance) locus could be rescued in either case, but its state had no effect on the reproduction or survival of the cells in the absence of the booster therapy.
- Figure 4.
The frequency of the HGD cells are plotted (red) and can be seen to take over the neoplasm around time step 4,000. The “benign” cells with at least one wild-type allele in the targeted recessive locus are driven near to extinction. However, mutations at the loci can be rescued by further mutations, and so when the benign cell booster is applied at time step 8,000, benign cells emerge that outcompete the HGD cells and any cells resistant to the benign cell booster.
- Figure 5.
Cure and minimal residual disease (MRD) probabilities for “weak” benign cell boosters that only allow the benign cells to reproduce at the same but not a greater rate than the HGD cells. Large SE bars on therapies applied at 11 years are due to the fact that few cancers evolve in only 11 simulated years in 4,096 cells and so the estimates are based on only a few data points.
- Figure 6.
A comparison of five different simulated therapies early, intermediate, and late in progression for mutation rate μ = 10-6 per allele per cell division. Minimal residual disease has been excluded from these results and so the cure rates for the benign therapies seem lower than those shown in Fig. 3.
Tables
- Table 1.
The parameters of the model and the values that were used
Parameter Values Description Dominant loci 0-6 loci (3 for therapy experiments) A mutation in either allele of these loci reduces the average cell cycle time of the cell by one-time step. Recessive loci 1-6 loci (2 for therapy experiments) Both alleles of these loci must be mutated to reduce the average cell cycle time by one-time step. Mutator loci 1 locus No. of loci that when mutated increase the mutation rate of the cell. Mutation rate 10−5, 4 × 10−6, 2 × 10−6, 10−6 The base mutation rate of the cells per locus per cell division. Mutator factor 10 or 100 (100 in experiments) Increase in the mutation rate for cells with mutator mutations (1 or 2 orders of magnitude). Reversible mutations Yes/no Whether a mutant phenotype can be rescued by further mutations. Time of chemotherapy 8,000, 16,000, or 24,000 time steps The time step at which the cytotoxic therapy starts (∼11, 22, and 33 years after initiation). Follow-up time 3,600 time steps 5 years of follow-up after therapy to test the efficacy of the simulated treatment. No. of drugs (no. of drug resistance loci) 1-6 drugs (loci) No. of cytotoxic drugs requiring independent mutations for resistance. There is one resistance locus per drug. Chemotherapy duration One-time step Cytotoxic therapies are applied in a single time step. Chemotherapy efficacy 1 The probability a sensitive cell dies in one-time step in the presence of cytotoxins. Time of benign booster 8,000, 16,000, or 24,000 time steps Time at which the benign booster treatment begins. Benign booster duration 3,600 time steps The benign boosters are applied over the entire duration of the follow-up (5 years). Benign target locus Dominant, recessive, mutator, drug resistance The locus used by the benign cell booster to distinguish benign (wild-type at locus) from nonbenign (mutated at locus) cells. No. of cells in the neoplasm 4,096 cells The simulated neoplasm consists of 4,096 cells in a 64 × 64 cell grid on the surface of a simulated tube. NOTE: The model can simulate a variety of assumptions about the nature of progression and dysplasia.
- Table 2.
The present chance of developing high grade dysplasia
Time since intiation Mutation rate (μ) 10−6 2 × 10−6 4 × 10−6 10−5 11 years (8,000 time steps) 0.07 (0.01) 2.25 (0.74) 15.00 (1.79) 58.50 (2.46) 22 years (16,000 time steps) 2.76 (0.33) 15.50 (1.81) 36.25 (2.40) 74.50 (2.18) 33 years (24,000 time steps) 7.72 (0.53) 17.25 (1.89) 44.75 (2.49) 89.00 (1.56) NOTE: Results are based on a neoplasm of 4,096 cells with three dominant and two recessive mutations necessary for HGD, mutation rate μ per locus per cell division, reversible mutations, and mutator phenotype increasing the mutation rate by a factor f = 100. The simulations are stochastic based on the use of a random number generator, and so there is variation in the results across runs. SEs calculated from a Bernoulli process are in parentheses. There were at least 400 runs for each parameter setting.
Volume 13, Issue 8
