A Quantitative Model for Age-Dependent Expression of the p16INK4a Tumor Suppressor

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.