Estimating network changes from lifespan measurements using a parsimonious gene network model of cellular aging

Cellular aging is best studied in the budding yeast Saccharomyces cerevisiae. As an example of a pleiotropic trait, yeast lifespan is influenced by hundreds of interconnected genes. However, no quantitative methods are currently available to infer system-level changes in gene networks during cellular aging.

We propose a parsimonious mathematical model of cellular aging based on stochastic gene interaction networks. This network model is made of only non-aging components: the strength of gene interactions declines with a constant mortality rate. Death of a cell occurs in the model when an essential node loses all of its interactions with other nodes, and is equivalent to the deletion of an essential gene. Stochasticity of gene interactions is modeled using a binomial distribution. We show that the exponential increase of mortality rate over time can emerge from this gene network model during the early stages of aging.We developed a maximal likelihood approach to estimate three lifespan-influencing network parameters from experimental lifespans: t₀, the initial virtual age of the network system; n, the average lifespan-influencing interactions per essential node; and R, the initial mortality rate. We applied this model to yeast mutants with known effects on replicative lifespans. We found that deletion of SIR2, FOB1, and HXK2 considerably altered the initial virtual age but not the average lifespan-influencing interactions per essential node, suggesting that these mutations mainly influence the reliability of gene interactions but not the overall configurations of gene networks.We applied this model to investigate replicative lifespans of yeast natural isolates. We estimated that the average number of lifespan-influencing interactions per essential node is 7.0 (6.1-8) and the average estimated initial virtual age is 45.4 (30.6-74) cell divisions in these isolates. We also found that t₀ could potentially mediate the observed Strehler-Mildvan correlation in yeast natural isolates.

Our theoretical model provides a parsimonious interpretation of experimental lifespan data from the perspective of gene networks. We hope that our work will stimulate more interest in developing network models to study aging as a pleiotropic trait.