The role of incoherent feedforward circuits in regulating precision of event timing

Triggering of cellular events often relies on the level of a key gene product crossing a critical threshold. Achieving precision in event timing in spite of noisy gene expression facilitates high-fidelity functioning of diverse processes from biomolecular clocks, apoptosis and cellular differentiation. Here we investigate the role of an incoherent feedforward circuit in regulating the time taken by a bacterial virus (bacteriophage lambda) to lyse an infected Escherichia coli cell. Lysis timing is the result of expression and accumulation of a single lambda protein (holin) in the E. coli cell membrane up to a critical threshold level, which triggers the formation of membrane lesions. This easily visualized process provides a simple model system for characterizing event-timing stochasticity in single cells. Intriguingly, lambdas lytic pathway synthesizes two functionally opposite proteins: holin and antiholin from the same mRNA in a 2:1 ratio. Antiholin sequesters holin and inhibits the formation of lethal membrane lesions, thus creating an incoherent feedforward circuit. We develop and analyze a stochastic model for this feedforward circuit that considers correlated bursty expression of holin/antiholin, and their concentrations are diluted from cellular growth. Interestingly, our analysis shows the noise in timing is minimized when both proteins are expressed at an optimal ratio, hence revealing an important regulatory role for antiholin. These results are in agreement with single cell data, where removal of antiholin results in enhanced stochasticity in lysis timing.