Positive feedback from growth burden in stochastic protein expression

Abstract

We study a protein that is stochastically expressed and imposes a fitness cost when overproduced by slowing down cell growth. This growth burden creates an inherent positive feedback loop: higher protein levels reduce cellular growth, which slows dilution, thereby sustaining higher protein levels. We develop a discrete-state model to capture this feedback mechanism, integrating stochastic simulations with differential equation approaches. Our analysis explores both single-cell dynamics and population-level behavior, revealing how noise and feedback together shape protein expression distributions.