Significance: The bacterial flagellar motor (BFM) is the rotary motor powering swimming of many motile bacteria. Many of the components of this molecular machine are dynamic, a property which allows the cell to optimize its behavior in accordance with the surrounding environment. A prime example is the stator unit, a membrane-bound ion channel that is responsible for applying torque to the rotor. The stator units are mechanosensitive, with the number of engaged units dependent on the viscous load on the motor. We measure the kinetics of the stators as a function of the viscous load and find that the mechanosensitivity of the BFM is governed by a catch bond: a counterintuitive type of bond that becomes stronger under force.

Although the structure of a genetically encoded regulatory circuit is an important determinant of its function, the relationship between circuit topology and the dynamical behaviors it can exhibit is not well understood. Here, we explore the range of behaviors available to the AC-DC circuit. This circuit consists of three genes connected as a combination of a toggle switch and a repressilator. Using dynamical systems theory, we show that the AC-DC circuit exhibits both oscillations and bistability within the same region of parameter space; this generates emergent behaviors not available to either the toggle switch or the repressilator alone. The AC-DC circuit can switch on oscillations via two distinct mechanisms, one of which induces coherence into ensembles of oscillators. In addition, we show that in the presence of noise, the AC-DC circuit can behave as an excitable system capable of spatial signal propagation or coherence resonance. Together, these results demonstrate how combinations of simple motifs can exhibit multiple complex behaviors.

During tissue development, patterns of gene expression determine the spatial arrangement of cell types. In many cases, gradients of secreted signalling molecules—morphogens—guide this process by controlling downstream transcriptional networks. A mechanism commonly used in these networks to convert the continuous information provided by the gradient into discrete transitions between adjacent cell types is the genetic toggle switch, composed of cross-repressing transcriptional determinants. Previous analyses have emphasised the steady state output of these mechanisms. Here, we explore the dynamics of the toggle switch and use exact numerical simulations of the kinetic reactions, the corresponding Chemical Langevin Equation, and Minimum Action Path theory to establish a framework for studying the effect of gene expression noise on patterning time and boundary position. This provides insight into the time scale, gene expression trajectories and directionality of stochastic switching events between cell states. Taking gene expression noise into account predicts that the final boundary position of a morphogen-induced toggle switch, although robust to changes in the details of the noise, is distinct from that of the deterministic system. Moreover, the dramatic increase in patterning time close to the boundary predicted from the deterministic case is substantially reduced. The resulting stochastic switching introduces differences in patterning time along the morphogen gradient that result in a patterning wave propagating away from the morphogen source with a velocity determined by the intrinsic noise. The wave sharpens and slows as it advances and may never reach steady state in a biologically relevant time. This could explain experimentally observed dynamics of pattern formation. Together the analysis reveals the importance of dynamical transients for understanding morphogen-driven transcriptional networks and indicates that gene expression noise can qualitatively alter developmental patterning. The bistable switch, a common regulatory sub-network, is found in many biological processes. It consists of cross-repressing components that generate a switch-like transition between two possible states. In developing tissues, bistable switches, created by cross-repressing transcriptional determinants, are often controlled by gradients of secreted signalling molecules—morphogens. These provide a mechanism to convert a morphogen gradient into stripes of gene expression that determine the arrangement of distinct cell types. Here we use mathematical models to analyse the temporal response of such a system. We find that the behaviour is highly dependent on the intrinsic fluctuations that result from the stochastic nature of gene expression. This noise has a marked effect on both patterning time and the location of the stripe boundary. One of the techniques we use, Minimum Action Path theory, identifies key features of the switch without computationally expensive calculations. The results reveal a noise driven switching wave that propels the stripe boundary away from the morphogen source to eventually settle, at steady state, further from the morphogen source than in the deterministic description. Together the analysis highlights the importance dynamics in patterning and demonstrates a set of mathematical tools for studying this problem.

The engineering of transcriptional networks presents many challenges due to the inherent uncertainty in the system structure, changing cellular context, and stochasticity in the governing dynamics. One approach to address these problems is to design and build systems that can function across a range of conditions; that is they are robust to uncertainty in their constituent components. Here we examine the parametric robustness landscape of transcriptional oscillators, which underlie many important processes such as circadian rhythms and the cell cycle, plus also serve as a model for the engineering of complex and emergent phenomena. The central questions that we address are: Can we build genetic oscillators that are more robust than those already constructed? Can we make genetic oscillators arbitrarily robust? These questions are technically challenging due to the large model and parameter spaces that must be efficiently explored. Here we use a measure of robustness that coincides with the Bayesian model evidence, combined with an efficient Monte Carlo method to traverse model space and concentrate on regions of high robustness, which enables the accurate evaluation of the relative robustness of gene network models governed by stochastic dynamics. We report the most robust two and three gene oscillator systems, plus examine how the number of interactions, the presence of autoregulation, and degradation of mRNA and protein affects the frequency, amplitude, and robustness of transcriptional oscillators. We also find that there is a limit to parametric robustness, beyond which there is nothing to be gained by adding additional feedback. Importantly, we provide predictions on new oscillator systems that can be constructed to verify the theory and advance design and modeling approaches to systems and synthetic biology.

How morphogen gradients govern the pattern of gene expression in developing tissues is not well understood. Here, we describe a statistical thermodynamic model of gene regulation that combines the activity of a morphogen with the transcriptional network it controls. Using Sonic hedgehog (Shh) patterning of the ventral neural tube as an example, we show that the framework can be used together with the principled parameter selection technique of approximate Bayesian computation to obtain a dynamical model that accurately predicts tissue patterning. The analysis indicates that, for each target gene regulated by Gli, which is the transcriptional effector of Shh signalling, there is a neutral point in the gradient, either side of which altering the Gli binding affinity has opposite effects on gene expression. This explains recent counterintuitive experimental observations. The approach is broadly applicable and provides a unifying framework to explain the temporospatial pattern of morphogen-regulated gene expression.

Many models of gene expression do not explicitly incorporate a cell cycle description. Here, we derive a theory describing how messenger RNA (mRNA) fluctuations for constitutive and bursty gene expression are influenced by stochasticity in the duration of the cell cycle and the timing of DNA replication. Analytical expressions for the moments show that omitting cell cycle duration introduces an error in the predicted mean number of mRNAs that is a monotonically decreasing function of η , which is proportional to the ratio of the mean cell cycle duration and the mRNA lifetime. By contrast, the error in the variance of the mRNA distribution is highest for intermediate values of η consistent with genome-wide measurements in many organisms. Using eukaryotic cell data, we estimate the errors in the mean and variance to be at most 3% and 25%, respectively. Furthermore, we derive an accurate negative binomial mixture approximation to the mRNA distribution. This indicates that stochasticity in the cell cycle can introduce fluctuations in mRNA numbers that are similar to the effect of bursty transcription. Finally, we show that for real experimental data, disregarding cell cycle stochasticity can introduce errors in the inference of transcription rates larger than 10%.