A filter-and-integrate mechanism generates stochastictranscriptional pulses in E.coli flagellar synthesis

Stochastic pulsatile dynamics have been observed in an increasing number of biological circuits with typical mechanism involving feedback control. Surprisingly, recent single-cell experiments showed that E. coli flagellar class-2&3 promoters are activated in stochastic pulses without the means of feedback, however, the underlying design principles of pulse generation have remained unclear. Here, by developing a system-level stochastic model constrained by a large set of E. coli flagellar synthesis data from different strains and mutants, we identify the underlying design principles for generating stochastic transcriptional pulses without feedback. Our model shows that YdiV, an inhibitor of the class-1 master regulator (FlhDC), creates an ultrasensitve switch that serves as a digital filter to eliminate small amplitude FlhDC fluctuations. Additionally, we demonstrate that fast temporal fluctuations of FlhDC are smoothed out and integrated over time before affecting class-2 downstream genes. Together, our results reveal the existence of a filter-and-integrate design that is necessary for generating stochastic pulses without feedback. This strategy suggests that E. coli may avoid premature activation of the expensive flagellar gene expression by filtering input fluctuations in intensity and in time.