Event timing precision in stochastic gene expression withbursty production

Optimal feedback control of bursty stochastic gene expression reshapes first-passage-time variability, with degradation and burstiness producing qualitatively different optimal production-rate structures across low- and high-threshold regimes.

• Why it matters: Cellular event timing depends on reaching a regulatory threshold, and stochastic gene expression creates first-passage-time variability that feedback regulation aims to reduce.
• What they did: The study derives optimality conditions using backward equations and a Lagrange multiplier formulation with a fixed mean FPT constraint, then extends the framework to bursty production and numerically characterizes optimal feedback in low- and high-threshold regimes.
• The result: For low thresholds it gives exact results, while high thresholds with small degradation show production rates increasing approximately linearly with molecule number before decreasing near the threshold; larger degradation yields multiple solution branches, fold behavior, and potentially nonmonotonic optimal rates.