A quantitative model for age-dependent expression of the p16INK4a tumor suppressor

Abstract

Recent work has shown that expression of the p16(INK4a) tumor suppressor increases with chronological age. Expression is accelerated by gerontogenic behaviors such as tobacco use and physical inactivity, and is also influenced by allelic genotype of a polymorphic single nucleotide polymorphism (SNP) rs10757278 that is physically linked with the p16(INK4a) ORF. To understand the relationship between p16(INK4a) expression, chronologic age, subject characteristics and host genetics, we sought to develop a mathematical model that links p16(INK4a) expression with aging. Using an annotated dataset of 170 healthy adults for whom p16(INK4a) expression and subject genotypes were known, we developed two alternative stochastic models that relate p16(INK4a) expression to age, smoking, exercise and rs10757278 genotype. Levels of p16(INK4a) increased exponentially and then saturated at later chronologic ages. The model, which best fit the data, suggests saturation occurs because of p16(INK4a)-dependent attrition of subjects at older chronologic ages, presumably due to death or chronic illness. An important feature of our model is that factors that contribute to death in a non p16(INK4a)-dependent manner do not affect our analysis. Interestingly, tobacco-related increases in p16(INK4a) expression are predicted to arise from a decrease in the rate of p16(INK4a)-dependent death. This analysis is most consistent with the model that p16(INK4a) expression monotonically increases with age, and higher expression is associated with increased subject attrition.

Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.

Schematic diagram for the models of stochastic p16INK4a expression. The gray dots represent p16INK4a expression levels. In both models, the p16INK4a level increases at a rate uk. Model I includes transitions that decrease the p16INK4a level. These backward transitions occur at a rate wk. In contrast, model II includes transitions that terminate the stochastic process. These transitions occur at a rate dk.

Fig. 2.

Comparison of the models with population data for p16INK4a expression levels. The blue lines represent a moving average of the data (3-year increments averaged of a 20-year interval). The green lines are the results for model I and the red lines are the results for model II. The thick lines represent the mean values and the thin dashed lines are the standard deviations. (Left) The results plotted on a linear scale. (Right) The same results plotted on a log2 scale.

Fig. 3.

The data split into groups according to gender (A), tobacco use (B), genotype (C), and physical activity (D). Solid lines represent moving averages computed in the same way as Fig. 2.

Fig. 4.

Model II results for smokers (red) vs. non-smokers (blue). The initial expression level is fixed at μ0 = 4 and the two free parameters u (growth rate) and d (death rate) are fit to the mean expression level. (Left) The data plotted on a linear scale. (Right) The same data on a log2 scale. The standard deviation is plotted according to Eq. 3 with σ0 = √μ0 = 2.

Fig. 5.

Model II results for different genotypes (A/A, blue; A/G, red; G/G, green). In this figure, the initial mean expression level is fixed at μ0 = 4 and the free parameters u (growth rate) and d (death rate) are fit to the mean expression level. The parameters are u = 0.10/year and d = 0.0026/year for A/A, u = 0.08/year and d = 0.0017/year for A/G, and u = 0.08/year and d = 0.0037/year for G/G (see also parameters for Fig. S1). (Left) The data plotted on a linear scale. (Right) The same data plotted on log2 scale. The standard deviations are plotted according to Eq. 3 with σ0 = √μ0 = 2.

Fig. 6.

Model II results for people who reported exercising >240 min per month (blue dots and curves) and 0 is taken to be a free parameter for each group. The estimate values of the parameters are u = 0.021, d = 0.012, μ0 = 8 and u = 0.010, d = 0.010, μ0 = 23, respectively. (Left) The data plotted on a linear scale. (Right) The same data plotted on log2 scale.