Stochastic pulsatile dynamics have been observed in an increasing number of biological circuits with known mechanism involving feedback control and bistability. Surprisingly, recent single-cell experiments in Escherichia coli flagellar synthesis showed that flagellar genes are activated in stochastic pulses without the means of feedback. However, the mechanism for pulse generation in these feedbackless circuits has remained unclear. Here, by developing a system-level stochastic model constrained by a large set of single-cell E. coli flagellar synthesis data from different strains and mutants, we identify the general underlying design principles for generating stochastic transcriptional pulses without feedback. Our study shows that an inhibitor (YdiV) of the transcription factor (FlhDC) creates a monotonic ultrasensitive switch that serves as a digital filter to eliminate small-amplitude FlhDC fluctuations. Furthermore, we find that the high-frequency (fast) fluctuations of FlhDC are filtered out by integration over a timescale longer than the timescale of the input fluctuations. Together, our results reveal a filter-and-integrate design for generating stochastic pulses without feedback. This filter-and-integrate mechanism enables a general strategy for cells to avoid premature activation of the expensive downstream gene expression by filtering input fluctuations in both intensity and time so that the system only responds to input signals that are both strong and persistent.

在越来越多的具有反馈控制和双稳态的已知机制的生物回路中，已经观察到随机搏动动力学。令人惊讶地，最近在大肠杆菌鞭毛合成中的单细胞实验表明，鞭毛基因在随机脉冲中被激活而没有反馈手段。然而，在这些无反馈电路中产生脉冲的机制仍然不清楚。在这里，通过开发受大量单细胞大肠杆菌约束的系统级随机模型来自不同菌株和突变体的鞭毛合成数据，我们确定了在没有反馈的情况下产生随机转录脉冲的一般基本设计原则。我们的研究表明，转录因子（FlhDC）的抑制剂（YdiV）产生了单调的超灵敏开关，该开关用作数字滤波器以消除小幅度的FlhDC波动。此外，我们发现FlhDC的高频（快速）波动在比输入波动的时间范围更长的时间范围内通过积分被滤出。在一起，我们的结果揭示了一种滤波器和积分设计，可以产生没有反馈的随机脉冲。