MAGE: an efficient algorithm for identifying Maximal Age-indexed GEne sets

Aging alters transcriptional regulation in a tissue- and time-specific manner, reshaping gene regulatory networks and shifting regulatory influence dynamics. Traditional in silico influence maximization methods often rely on static gene expression snapshots and fail to capture gene-to-gene influence variations over time. To address this, we introduce the Age Index, a network-based metric that quantifies time-varying gene influence. We define the Maximal and Minimal Age Index Problems (MAP$^{+}$ and MAP$^{-}$) as the tasks of identifying gene sets with the highest and lowest Age Index, and prove these problems are NP-hard. To solve them, we develop MAGE (Maximal Age-Index Algorithm), a stochastic method that iteratively constructs gene sets by prioritizing genes likely to optimize the Age Index. MAGE identifies statistically significant gene sets at the genome scale, with strong literature support, highlighting its potential to uncover age-sensitive regulatory mechanisms.