Autoregulation of mazEF expression underlies growth heterogeneity in bacterial populations.

The MazF toxin sequence-specifically cleaves single-stranded RNA upon various stressful conditions, and it is activated as a part of the mazEF toxin-antitoxin module in Escherichia coli. Although autoregulation of mazEF expression through the MazE antitoxin-dependent transcriptional repression has been biochemically characterized, less is known about post-transcriptional autoregulation, as well as how both of these autoregulatory features affect growth of single cells during conditions that promote MazF production. Here, we demonstrate post-transcriptional autoregulation of mazF expression dynamics by MazF cleaving its own transcript. Single-cell analyses of bacterial populations during ectopic MazF production indicated that two-level autoregulation of mazEF expression influences cell-to-cell growth rate heterogeneity. The increase in growth rate heterogeneity is governed by the MazE antitoxin, and tuned by the MazF-dependent mazF mRNA cleavage. Also, both autoregulatory features grant rapid exit from the stress caused by mazF overexpression. Time-lapse microscopy revealed that MazF-mediated cleavage of mazF mRNA leads to increased temporal variability in length of individual cells during ectopic mazF overexpression, as explained by a stochastic model indicating that mazEF mRNA cleavage underlies temporal fluctuations in MazF levels during stress.

Thermodynamic Stability of the Transcription Regulator PaaR2 from Escherichia coli O157:H7.

PaaR2 is a putative transcription regulator encoded by a three-component parDE-like toxin-antitoxin module from Escherichia coli O157:H7. Although this module's toxin, antitoxin, and toxin-antitoxin complex have been more thoroughly investigated, little remains known about its transcription regulator PaaR2. Using a wide range of biophysical techniques (circular dichroism spectroscopy, size-exclusion chromatography-multiangle laser light scattering, dynamic light scattering, small-angle x-ray scattering, and native mass spectrometry), we demonstrate that PaaR2 mainly consists of α-helices and displays a concentration-dependent octameric build-up in solution and that this octamer contains a global shape that is significantly nonspherical. Thermal unfolding of PaaR2 is reversible and displays several transitions, suggesting a complex unfolding mechanism. The unfolding data obtained from spectroscopic and calorimetric methods were combined into a unifying thermodynamic model, which suggests a five-state unfolding trajectory. Furthermore, the model allows the calculation of a stability phase diagram, which shows that, under physiological conditions, PaaR2 mainly exists as a dimer that can swiftly oligomerize into an octamer depending on local protein concentrations. These findings, based on a thorough biophysical and thermodynamic analysis of PaaR2, may provide important insights into biological function such as DNA binding and transcriptional regulation.

Molecular mechanism governing ratio-dependent transcription regulation in the ccdAB operon.

Bacteria can become transiently tolerant to several classes of antibiotics. This phenomenon known as persistence is regulated by small genetic elements called toxin-antitoxin modules with intricate yet often poorly understood self-regulatory features. Here, we describe the structures of molecular complexes and interactions that drive the transcription regulation of the ccdAB toxin-antitoxin module. Low specificity and affinity of the antitoxin CcdA2 for individual binding sites on the operator are enhanced by the toxin CcdB2, which bridges the CcdA2 dimers. This results in a unique extended repressing complex that spirals around the operator and presents equally spaced DNA binding sites. The multivalency of binding sites induces a digital on-off switch for transcription, regulated by the toxin:antitoxin ratio. The ratio at which this switch occurs is modulated by non-specific interactions with the excess chromosomal DNA. Altogether, we present the molecular mechanisms underlying the ratio-dependent transcriptional regulation of the ccdAB operon.

Hidden States within Disordered Regions of the CcdA Antitoxin Protein.

The bacterial toxin-antitoxin system CcdB-CcdA provides a mechanism for the control of cell death and quiescence. The antitoxin protein CcdA is a homodimer composed of two monomers that each contain a folded N-terminal region and an intrinsically disordered C-terminal arm. Binding of the intrinsically disordered C-terminal arm of CcdA to the toxin CcdB prevents CcdB from inhibiting DNA gyrase and thereby averts cell death. Accurate models of the unfolded state of the partially disordered CcdA antitoxin can therefore provide insight into general mechanisms whereby protein disorder regulates events that are crucial to cell survival. Previous structural studies were able to model only two of three distinct structural states, a closed state and an open state, that are adopted by the C-terminal arm of CcdA. Using a combination of free energy simulations, single-pair Förster resonance energy transfer experiments, and existing NMR data, we developed structural models for all three states of the protein. Contrary to prior studies, we find that CcdA samples a previously unknown state where only one of the disordered C-terminal arms makes extensive contacts with the folded N-terminal domain. Moreover, our data suggest that previously unobserved conformational states play a role in regulating antitoxin concentrations and the activity of CcdA's cognate toxin. These data demonstrate that intrinsic disorder in CcdA provides a mechanism for regulating cell fate.

A general model for toxin-antitoxin module dynamics can explain persister cell formation in E. coli.

Toxin-Antitoxin modules are small operons involved in stress response and persister cell formation that encode a "toxin" and its corresponding neutralizing "antitoxin". Regulation of these modules involves a complex mechanism known as conditional cooperativity, which is supposed to prevent unwanted toxin activation. Here we develop mathematical models for their regulation, based on published molecular and structural data, and parameterized using experimental data for F-plasmid ccdAB, bacteriophage P1 phd/doc and E. coli relBE. We show that the level of free toxin in the cell is mainly controlled through toxin sequestration in toxin-antitoxin complexes of various stoichiometry rather than by gene regulation. If the toxin translation rate exceeds twice the antitoxin translation rate, toxins accumulate in all cells. Conditional cooperativity and increasing the number of binding sites on the operator serves to reduce the metabolic burden of the cell by reducing the total amounts of proteins produced. Combining conditional cooperativity and bridging of antitoxins by toxins when bound to their operator sites allows creation of persister cells through rare, extreme stochastic spikes in the free toxin level. The amplitude of these spikes determines the duration of the persister state. Finally, increases in the antitoxin degradation rate and decreases in the bacterial growth rate cause a rise in the amount of persisters during nutritional stress.

Bistable Expression of a Toxin-Antitoxin System Located in a Cryptic Prophage of Escherichia coli O157:H7.

Type II toxin-antitoxin (TA) systems are classically composed of two genes that encode a toxic protein and a cognate antitoxin protein. Both genes are organized in an operon whose expression is autoregulated at the level of transcription by the antitoxin-toxin complex, which binds operator DNA through the antitoxin's DNA-binding domain. Here, we investigated the transcriptional regulation of a particular TA system located in the immunity region of a cryptic lambdoid prophage in the Escherichia coli O157:H7 EDL933 strain. This noncanonical paaA2-parE2 TA operon contains a third gene, paaR2, that encodes a transcriptional regulator that was previously shown to control expression of the TA. We provide direct evidence that the PaaR2 is a transcriptional regulator which shares functional similarities to the lambda CI repressor. Expression of the paaA2-parE2 TA operon is regulated by two other transcriptional regulators, YdaS and YdaT, encoded within the same region. We argue that YdaS and YdaT are analogous to lambda Cro and CII and that they do not constitute a TA system, as previously debated. We show that PaaR2 primarily represses the expression of YdaS and YdaT, which in turn controls the expression of paaR2-paaA2-parE2 operon. Overall, our results show that the paaA2-parE2 TA is embedded in an intricate lambdoid prophage-like regulation network. Using single-cell analysis, we observed that the entire locus exhibits bistability, which generates diversity of expression in the population. Moreover, we confirmed that paaA2-parE2 is addictive and propose that it could limit genomic rearrangements within the immunity region of the CP-933P cryptic prophage. IMPORTANCE Transcriptional regulation of bacterial toxin-antitoxin (TA) systems allows compensation of toxin and antitoxin proteins to maintain a neutral state and avoid cell intoxication unless TA genes are lost. Such models have been primarily studied in plasmids, but TAs are equally present in other mobile genetic elements, such as transposons and prophages. Here, we demonstrate that the expression of a TA system located in a lambdoid cryptic prophage is transcriptionally coupled to the prophage immunity region and relies on phage transcription factors. Moreover, competition between transcription factors results in bistable expression, which generates cell-to-cell heterogeneity in the population, but without, however, leading to any detectable phenotype, even in cells expressing the TA system. We show that despite the lack of protein sequence similarity, this locus retains major lambda prophage regulation features.

Nanobody-aided crystallization of the transcription regulator PaaR2 from Escherichia coli O157:H7.

paaR2-paaA2-parE2 is a three-component toxin-antitoxin module found in prophage CP-993P of Escherichia coli O157:H7. Transcription regulation of this module occurs via the 123-amino-acid regulator PaaR2, which forms a large oligomeric structure. Despite appearing to be well folded, PaaR2 withstands crystallization, as does its N-terminal DNA-binding domain. Native mass spectrometry was used to screen for nanobodies that form a unique complex and stabilize the octameric structure of PaaR2. One such nanobody, Nb33, allowed crystallization of the protein. The resulting crystals belong to space group F432, with unit-cell parameter a = 317 Å, diffract to 4.0 Šresolution and are likely to contain four PaaR2 monomers and four nanobody monomers in the asymmetric unit. Crystals of two truncates containing the N-terminal helix-turn-helix domain also interact with Nb33, and the corresponding co-crystals diffracted to 1.6 and 1.75 Šresolution.

Nuclei determine the spatial origin of mitotic waves.

Traveling waves play an essential role in coordinating mitosis over large distances, but what determines the spatial origin of mitotic waves remains unclear. Here, we show that such waves initiate at pacemakers, regions that oscillate faster than their surroundings. In cell-free extracts of Xenopus laevis eggs, we find that nuclei define such pacemakers by concentrating cell cycle regulators. In computational models of diffusively coupled oscillators that account for nuclear import, nuclear positioning determines the pacemaker location. Furthermore, we find that the spatial dimensions of the oscillatory medium change the nuclear positioning and strongly influence whether a pacemaker is more likely to be at a boundary or an internal region. Finally, we confirm experimentally that increasing the system width increases the proportion of pacemakers at the boundary. Our work provides insight into how nuclei and spatial system dimensions can control local concentrations of regulators and influence the emergent behavior of mitotic waves.

Excitable dynamics through toxin-induced mRNA cleavage in bacteria.

Toxin-antitoxin (TA) systems in bacteria and archaea are small genetic elements consisting of the genes coding for an intracellular toxin and an antitoxin that can neutralize this toxin. In various cases, the toxins cleave the mRNA. In this theoretical work we use deterministic and stochastic modeling to explain how toxin-induced cleavage of mRNA in TA systems can lead to excitability, allowing large transient spikes in toxin levels to be triggered. By using a simplified network where secondary complex formation and transcriptional regulation are not included, we show that a two-dimensional, deterministic model captures the origin of such toxin excitations. Moreover, it allows to increase our understanding by examining the dynamics in the phase plane. By systematically comparing the deterministic results with Gillespie simulations we demonstrate that even though the real TA system is intrinsically stochastic, toxin excitations can be accurately described deterministically. A bifurcation analysis of the system shows that the excitable behavior is due to a nearby Hopf bifurcation in the parameter space, where the system becomes oscillatory. The influence of stress is modeled by varying the degradation rate of the antitoxin and the translation rate of the toxin. We find that stress increases the frequency of toxin excitations. The inclusion of secondary complex formation and transcriptional regulation does not fundamentally change the mechanism of toxin excitations. Finally, we show that including growth rate suppression and translational inhibition can lead to longer excitations, and even cause excitations in cases when the system would otherwise be non-excitable. To conclude, the deterministic model used in this work provides a simple and intuitive explanation of toxin excitations in TA systems.

Delay models for the early embryonic cell cycle oscillator.

Time delays are known to play a crucial role in generating biological oscillations. The early embryonic cell cycle in the frog Xenopus laevis is one such example. Although various mathematical models of this oscillating system exist, it is not clear how to best model the required time delay. Here, we study a simple cell cycle model that produces oscillations due to the presence of an ultrasensitive, time-delayed negative feedback loop. We implement the time delay in three qualitatively different ways, using a fixed time delay, a distribution of time delays, and a delay that is state-dependent. We analyze the dynamics in all cases, and we use experimental observations to interpret our results and put constraints on unknown parameters. In doing so, we find that different implementations of the time delay can have a large impact on the resulting oscillations.

Computational Methods to Model Persistence.

Bacterial persister cells are dormant cells, tolerant to multiple antibiotics, that are involved in several chronic infections. Toxin-antitoxin modules play a significant role in the generation of such persister cells. Toxin-antitoxin modules are small genetic elements, omnipresent in the genomes of bacteria, which code for an intracellular toxin and its neutralizing antitoxin. In the past decade, mathematical modeling has become an important tool to study the regulation of toxin-antitoxin modules and their relation to the emergence of persister cells. Here, we provide an overview of several numerical methods to simulate toxin-antitoxin modules. We cover both deterministic modeling using ordinary differential equations and stochastic modeling using stochastic differential equations and the Gillespie method. Several characteristics of toxin-antitoxin modules such as protein production and degradation, negative autoregulation through DNA binding, toxin-antitoxin complex formation and conditional cooperativity are gradually integrated in these models. Finally, by including growth rate modulation, we link toxin-antitoxin module expression to the generation of persister cells.