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Aspirin and the chemoprevention of cancers: A mathematical and evolutionary dynamics perspective

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Abstract Epidemiological data indicate that long‐term low dose aspirin administration has a protective effect against the occurrence of colorectal cancer, both in sporadic and in hereditary forms of the disease. The mechanisms underlying this protective effect, however, are incompletely understood. The molecular events that lead to protection have been partly defined, but remain to be fully characterized. So far, however, approaches based on evolutionary dynamics have not been discussed much, but can potentially offer important insights. The aim of this review is to highlight this line of investigation and the results that have been obtained. A core observation in this respect is that aspirin has a direct negative impact on the growth dynamics of the cells, by influencing the kinetics of tumor cell division and death. We discuss the application of mathematical models to experimental data to quantify these parameter changes. We then describe further mathematical models that have been used to explore how these aspirin‐mediated changes in kinetic parameters influence the probability of successful colony growth versus extinction, and how they affect the evolution of the tumor during aspirin administration. Finally, we discuss mathematical models that have been used to investigate the selective forces that can lead to the rise of mismatch‐repair deficient cells in an inflammatory environment, and how this selection can be potentially altered through aspirin‐mediated interventions. This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Analytical and Computational Methods > Analytical Methods Analytical and Computational Methods > Computational Methods
Dependence of kinetic parameters on aspirin dose, as estimated from mathematical models (Zumwalt et al., ). (a) Overall growth rate versus dose shows a significant negative correlation (p < 10−4). (b) Rate of cell division versus dose shows a significant negative correlation (p < 10−4). (c) Death rate of cells versus dose shows a significant positive correlation (p = .0013)
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Simulations of the agent‐based model, assuming repeated disturbance of tissue homeostasis (Wodarz, Goel, & Komarova, ). Every 1,000 time steps, the overall population was reduced by 10%, leading to subsequent tissue regeneration (seen in the rugged shape of the lines). (a) The competition dynamics of non‐arresting and arresting cell populations are shown. The blue and red lines are the average numbers of arresting and non‐arresting cells, respectively. The light curves around the average lines represent average ± SD. (b) Fixation probability of one non‐arresting mutant placed into a population of arresting cells at equilibrium (red line), running >106 iterations of the simulation (Wodarz, Goel, & Komarova, ). The fixation probability is plotted against the magnitude of tissue homeostasis disturbance, expressed as the fraction of cells that is removed every 300 time steps. The blue line indicates the neutral control, where the fixation probability of one arresting cell was determined when placed into an established arresting population with identical parameters
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Fixation probability of a single non‐arresting cell placed into an established arresting cell population at equilibrium (Wodarz, Goel, & Komarova, ). Simulations for each case were run repeatedly (>106 times), recording the fraction of fixation events. The “neutral” bar is the control simulation where the fixation probability was determined for a mutant that is equivalent to the established cell population (i.e., arresting, with same parameters). The horizontal line indicates the expected fixation probability for a neutral mutant, given by 1/M, where M is the average number of arresting cells in isolation around equilibrium. The remaining bars show the fixation probability of a single non‐arresting cell placed into an established arresting cell population, characterized by different probabilities to exit the arresting state, Pexit. The lower the value of Pexit, the lower the fixation probability for the arresting cells
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Competition of arresting and non‐arresting cells. (a) “Don't stop for repair in a war zone” (from (Breivik, )). (b) A schematic showing the life‐stage strategies of arresting and non‐arresting cells (Wodarz, Goel, & Komarova, ). (c) Computer simulations showing the growth of an arresting and non‐arresting cell population in isolation, that is, in the absence of competition (Wodarz, Goel, & Komarova, ). An agent‐based model was simulated and the average trajectories are shown (solid lines). The dashed lines are the average ± SD
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(a) Effect of aspirin treatment on the division and death rates of cells in the mouse xenografts, as determined by model fitting to experimental data (Shimura et al., ). (b) Effect of aspirin on the probability to establish successful colony growth in a set of virtual cell lines that are characterized by different turnover rates, defined by the ratio of death rate (D)/division rate (L), in the absence of aspirin. Both parameters were changed by an amount that was given by the average change across all cell lines at maximal aspirin dosage. The black line shows the probability of successful colony formation in the absence of aspirin, while the red line shows the same in the presence of maximal aspirin dosage (starting from a single cell). The blue line shows the probability that a cell clone goes extinct. The probabilities were determined by simulating a 3D agent‐based model of cell growth (Shimura et al., )
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Effect of aspirin on the probability for a cell to exist that is characterized by (a) one, (b) two, and (c) three independent neutral mutations by the time a cell colony has grown from 1 to 1010 cells (Wodarz, Goel, Boland, & Komarova, ). Again, the relative change in the probabilities is shown, dividing the probability for a mutant to exist in the presence of aspirin by the probability in the absence of the drug. The dots represent the different cell lines. (d) This graph plots the average over all cell lines for each dose, along with error bars that represent the SE
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Effect of aspirin on basic evolutionary dynamics (Wodarz, Goel, Boland, & Komarova, ). (a) Relative change in the number of cell divisions required to expand from 1 to 1010 cells, brought about by aspirin. The number of cell divisions in the presence of aspirin was divided by the number in the absence of the drug. This measure shows the increase in the evolutionary potential of the cell population. The relative aspirin‐induced change in the average number of neutral one‐hit mutants when the cell colony has reached 1010 cells is identical and thus not plotted separately. (b) Relative change in the average number of disadvantageous mutants that are predicted to be present when the cell colony has grown from 1 to 1010 cells. (c) Relative change in the average number of advantageous mutants that are predicted to be present when the cell colony has grown from 1 to 1010 cells. The dots in the plots correspond to predictions for the different cell lines for each aspirin dose, and the line represents the average over all cell lines for each dose
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Effect of aspirin on the basic parameters and the dynamics of tumor cell growth, estimated by the application of mathematical models to experimental data (Wodarz, Goel, Boland, & Komarova, ). (a) Effect on the ratio of the rate of cell division to cell death, R/D. The value of R/D for each aspirin dose is divided by the value in the absence of the drug, yielding the relative fold‐change in this measure brought about by aspirin treatment. (b) Effect on the probability for one cell to successfully establish clonal expansion rather than going extinct through stochastic effects. The graph shows the relative change in the probability to establish growth, brought about by aspirin. That is, the probability to establish growth in the presence of aspirin is divided by the probability in the absence of the drug. (c) Effect on the time it takes for one cell to expand to a population of 1010 cells. Again, the relative change is shown, dividing the time in the presence of aspirin (conditioned on non‐extinction) by the time in the absence of aspirin (conditioned on non‐extinction). For all graphs, the dots represent all the different cell lines that were used. The line shows the average over all cell lines for each aspirin dose
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The effect of aspirin on the number if viable cells, as a function of the growth rate in the absence of aspirin (Zumwalt et al., ). The different curves correspond to different time points. For all of these time‐points, the negative correlation is statistically significant with p value < .05 (starting with t = 72 hr, p < .01). The cell lines are marked next to their growth rates. The three PIK3CA w.t. lines correspond to the highest growth rates
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Analytical and Computational Methods > Analytical Methods
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