Robustness of DNA looping across multiple cell divisions in individual bacteria.

DNA looping has emerged as a central paradigm of transcriptional regulation, as it is shared across many living systems. One core property of DNA looping-based regulation is its ability to greatly enhance repression or activation of genes with only a few copies of transcriptional regulators. However, this property based on a small number of proteins raises the question of the robustness of such a mechanism with respect to the large intracellular perturbations taking place during growth and division of the cell. Here we address the issue of sensitivity to variations of intracellular parameters of gene regulation by DNA looping. We use the lac system as a prototype to experimentally identify the key features of the robustness of DNA looping in growing Escherichia coli cells. Surprisingly, we observe time intervals of tight repression spanning across division events, which can sometimes exceed 10 generations. Remarkably, the distribution of such long time intervals exhibits memoryless statistics that is mostly insensitive to repressor concentration, cell division events, and the number of distinct loops accessible to the system. By contrast, gene regulation becomes highly sensitive to these perturbations when DNA looping is absent. Using stochastic simulations, we propose that the observed robustness to division emerges from the competition between fast, multiple rebinding events of repressors and slow initiation rate of the RNA polymerase. We argue that fast rebinding events are a direct consequence of DNA looping that ensures robust gene repression across a range of intracellular perturbations.

Protein concentration fluctuations in the high expression regime: Taylor's law and its mechanistic origin.

Protein concentration in a living cell fluctuates over time due to noise in growth and division processes. In the high expression regime, variance of the protein concentration in a cell was found to scale with the square of the mean, which belongs to a general phenomenon called Taylor's law (TL). To understand the origin for these fluctuations, we measured protein concentration dynamics in single E. coli cells from a set of strains with a variable expression of fluorescent proteins. The protein expression is controlled by a set of constitutive promoters with different strength, which allows to change the expression level over 2 orders of magnitude without introducing noise from fluctuations in transcription regulators. Our data confirms the square TL, but the prefactor A has a cell-to-cell variation independent of the promoter strength. Distributions of the normalized protein concentration for different promoters are found to collapse onto the same curve. To explain these observations, we used a minimal mechanistic model to describe the stochastic growth and division processes in a single cell with a feedback mechanism for regulating cell division. In the high expression regime where extrinsic noise dominates, the model reproduces our experimental results quantitatively. By using a mean-field approximation in the minimal model, we showed that the stochastic dynamics of protein concentration is described by a Langevin equation with multiplicative noise. The Langevin equation has a scale invariance which is responsible for the square TL. By solving the Langevin equation, we obtained an analytical solution for the protein concentration distribution function that agrees with experiments. The solution shows explicitly how the prefactor A depends on strength of different noise sources, which explains its cell-to-cell variability. By using this approach to analyze our single-cell data, we found that the noise in production rate dominates the noise from cell division. The deviation from the square TL in the low expression regime can also be captured in our model by including intrinsic noise in the production rate.

Filtering input fluctuations in intensity and in time underlies stochastic transcriptional pulses without feedback.

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.

Stochastic transcriptional pulses orchestrate flagellar biosynthesis in Escherichia coli.

The classic picture of flagellum biosynthesis in Escherichia coli, inferred from population measurements, depicts a deterministic program where promoters are sequentially up-regulated and are maintained steadily active throughout exponential growth. However, complex regulatory dynamics at the single-cell level can be masked by bulk measurements. Here, we discover that in individual E. coli cells, flagellar promoters are stochastically activated in pulses. These pulses are coordinated within specific classes of promoters and comprise "on" and "off" states, each of which can span multiple generations. We demonstrate that in this pulsing program, the regulatory logic of flagellar assembly dictates which promoters skip pulses. Surprisingly, pulses do not require specific transcriptional or translational regulation of the flagellar master regulator, FlhDC, but instead appears to be essentially governed by an autonomous posttranslational circuit. Our results suggest that even topologically simple transcriptional networks can generate unexpectedly rich temporal dynamics and phenotypic heterogeneities.