Toxins, Targets, and Triggers: An Overview of Toxin-Antitoxin Biology.

Bacterial toxin-antitoxin (TA) modules are abundant genetic elements that encode a toxin protein capable of inhibiting cell growth and an antitoxin that counteracts the toxin. The majority of toxins are enzymes that interfere with translation or DNA replication, but a wide variety of molecular activities and cellular targets have been described. Antitoxins are proteins or RNAs that often control their cognate toxins through direct interactions and, in conjunction with other signaling elements, through transcriptional and translational regulation of TA module expression. Three major biological functions of TA modules have been discovered, post-segregational killing ("plasmid addiction"), abortive infection (bacteriophage immunity through altruistic suicide), and persister formation (antibiotic tolerance through dormancy). In this review, we summarize the current state of the field and highlight how multiple levels of regulation shape the conditions of toxin activation to achieve the different biological functions of TA modules.

Protection of bacteriophage-sensitive Escherichia coli by lysogens.

SignificanceSome viruses that infect bacteria, temperate bacteriophages, can confer immunity to infection by the same virus. Here we report λ-immune bacteria could protect λ-sensitive bacteria from killing by phage λ in mixed culture. The protection depended on the extent to which the immune bacteria were able to adsorb the phage. Reconciling modeling with experiment led to identifying a decline in protection as bacteria stopped growing. Adsorption of λ was compromised by inhibition of bacterial energy metabolism, explaining the loss of protection as bacterial growth ceased.

The dynamics of phage predation on a microcolony.

Phage predation is an important factor for controlling the bacterial biomass. At face value, dense microbial habitats are expected to be vulnerable to phage epidemics due to the abundance of fresh hosts immediately next to any infected bacteria. Despite this, the bacterial microcolony is a common habitat for bacteria in nature. Here, we experimentally quantify the fate of microcolonies of Escherichia coli exposed to virulent phage T4. It has been proposed that the outer bacterial layers of the colony will shield the inner layers from the phage invasion and thereby constrain the phage to the colony's surface. We develop a dynamical model that incorporates this shielding mechanism and fit the results with experimental measurements to extract important phage-bacteria interaction parameters. The analysis suggests that, while the shielding mechanism delays phage attack, T4 phage are able to diffuse so deep into the dense bacterial environment that colony-level survival of the bacterial community is challenged.

From kill the winner to eliminate the winner in open phage-bacteria systems.

Phages and bacteria manage to coexist and sustain ecosystems with a high diversity of strains, despite limited resources and heavy predation. This diversity can be explained by the "kill the winner" model where virulent phages predominantly prey on fast-growing bacteria and thereby suppress the competitive exclusion of slower-growing bacteria. Here we computationally investigate the robustness of these systems against invasions, where new phages or bacteria may interact with more than one of the resident strains. The resulting interaction networks were found to self-organize into a network with strongly interacting specialized predator-prey pairs, resembling that of the "kill the winner" model. Furthermore, the "kill the winner" dynamics is enforced with the occasional elimination of even the fastest-growing bacteria strains due to a phage infecting the fast and slow growers. The frequency of slower-growing strains was increased with the introduction of even a few non-diagonal interactions. Hence, phages capable of infecting multiple hosts play significant roles both in the evolution of the ecosystem by eliminating the winner and in supporting diversity by allowing slow growers to coexist with faster growers.

When to wake up? The optimal waking-up strategies for starvation-induced persistence.

Prolonged lag time can be induced by starvation contributing to the antibiotic tolerance of bacteria. We analyze the optimal lag time to survive and grow the iterative and stochastic application of antibiotics. A simple model shows that the optimal lag time can exhibit a discontinuous transition when the severeness of the antibiotic application, such as the probability to be exposed the antibiotic, the death rate under the exposure, and the duration of the exposure, is increased. This suggests the possibility of reducing tolerant bacteria by controlled usage of antibiotics application. When the bacterial populations are able to have two phenotypes with different lag times, the fraction of the second phenotype that has different lag time shows a continuous transition. We then present a generic framework to investigate the optimal lag time distribution for total population fitness for a given distribution of the antibiotic application duration. The obtained optimal distributions have multiple peaks for a wide range of the antibiotic application duration distributions, including the case where the latter is monotonically decreasing. The analysis supports the advantage in evolving multiple, possibly discrete phenotypes in lag time for bacterial long-term fitness.

A growing microcolony can survive and support persistent propagation of virulent phages.

Bacteria form colonies and secrete extracellular polymeric substances that surround the individual cells. These spatial structures are often associated with collaboration and quorum sensing between the bacteria. Here we investigate the mutual protection provided by spherical growth of a monoclonal colony during exposure to phages that proliferate on its surface. As a proof of concept we exposed growing colonies of Escherichia coli to a virulent mutant of phage P1. When the colony consists of less than [Formula: see text]50,000 members it is eliminated, while larger initial colonies allow long-term survival of both phage-resistant mutants and, importantly, colonies of mostly phage-sensitive members. A mathematical model predicts that colonies formed solely by phage-sensitive bacteria can survive because the growth of bacteria throughout the colony exceeds the killing of bacteria on the surface and pinpoints how the critical colony size depends on key parameters in the phage infection cycle.

On Phage Adsorption to Bacterial Chains.

Bacteria often arrange themselves in various spatial configurations, which changes how they interact with their surroundings. In this work, we investigate how the structure of the bacterial arrangements influences the adsorption of bacteriophages. We quantify how the adsorption rate scales with the number of bacteria in the arrangement and show that the adsorption rates for microcolonies (increasing with exponent ∼1/3) and bacterial chains (increasing with exponent ∼0.5-0.8) are substantially lower than for well-mixed bacteria (increasing with exponent 1). We further show that, after infection, the spatially clustered arrangements reduce the effective burst size by more than 50% and cause substantial superinfections in a very short time interval after phage lysis.

How pirate phage interferes with helper phage: Comparison of the two distinct strategies.

Pirate phages use the structural proteins encoded by unrelated helper phages to propagate. The best-studied example is the pirate P4 and helper P2 of coliphages, and it has been known that the Staphylococcus aureus pathogenicity islands (SaPIs) that can encode virulence factors act as pirate phages, too. When alone in the host, the pirate phages act as a prophage, but when the helper phage gene is also in the same host cell, the pirate phage has ability to exploit the helper phages structural proteins to produce pirate phage particles and spread, interfering with the helper phage production. The known helper phages in these systems are temperate phages. Interestingly, the interference of the pirate phage to the helper phage occurs in a different manner between the SaPI-helper system and the P4-P2 system. SaPIs cannot lyse a helper lysogen upon infection, while when a helper phage lyse a SaPI lysogen, most of the phage particles produced are the SaPI particles. On the contrary, in the P4-P2 system, a pirate phage P4 can lyse a helper P2 lysogen to produce mostly the P4 particles, while when P2 phage lyses a P4 lysogen, most of the produced phages are the P2 particles. Here, the consequences of these different strategies in the pirate and helper phage spreading among uninfected host is analyzed by using mathematical models. It is found that SaPI's strategy interferes with the helper phage spreading significantly more than the P4's strategy, because SaPI interferes with the helper phage's main reproduction step, while P4 interferes only by forcing the helper lysogens to lyse. However, the interference is found to be weaker in the spatially structured environment than in the well-mixed environment. This is because, in the spatial setting, the system tends to self-organize so that the helper phages take over the front of propagation due to the need of helper phage for the pirate phage spreading.

Modeling slow-processing of toxin messenger RNAs in type-I toxin-antitoxin systems: post-segregational killing and noise filtering.

In type-I toxin-antitoxin (TA) systems, the action of growth-inhibiting toxin proteins is counteracted by the antitoxin small RNAs (sRNAs) that prevent the translation of toxin messenger RNAs (mRNAs). When a TA module is encoded on a plasmid, the short lifetime of antitoxin sRNA compared to toxin mRNAs mediates post-segregational killing (PSK) that contribute the plasmid maintenance, while some of the chromosomal encoded TA loci have been reported to contribute to persister formation in response to a specific upstream signal. Some of the well studied type-I TA systems such as hok/sok are known to have a rather complex regulatory mechanism. Transcribed full-length toxin mRNAs fold such that the ribosome binding site is not accessible and hence cannot be translated. The mRNAs are slowly processed by RNases, and the truncated mRNAs can be either translated or bound by antitoxin sRNA to be quickly degraded. We analyze the role of this extra processing by a mathematical model. We first consider the PSK scenario, and demonstrate that the extra processing compatibly ensures the high toxin expression upon complete plasmid loss, without inducing toxin expression upon acquisition of a plasmid or decrease of plasmid number to a non-zero number. We further show that the extra processing help filtering the transcription noise, avoiding random activation of toxins in transcriptionally regulated TA systems as seen in chromosomal ones. The present model highlights impacts of the slow processing reaction, offering insights on why the slow processing reactions are commonly identified in multiple type-I TA systems.

Synchronized switching of multiple toxin-antitoxin modules by (p)ppGpp fluctuation.

Toxin-antitoxin (TA) loci are widespread in bacteria including important pathogenic species. Recent studies suggest that TA systems play a key role in persister formation. However, the persistence phenotype shows only weak dependence on the number of TA systems, i.e. they are functionally redundant. We use a mathematical model to investigate the interaction of multiple TA systems in the switching between growth and persistence. We explore two scenarios: (i) TA systems are bistable and each TA system experiences its own noise and (ii) the noise in the level of common stress signal (e.g. (p)ppGpp) coordinates all TA systems simultaneously. We find that in the first scenario the exit from the persister state strongly depends on the number of TA systems. However in the second case, we could reproduce the weak dependence. The duration of the high (p)ppGpp state was found to be the key parameter for persistence. The (p)ppGpp-driven synchronized transition of all TA systems results in the redundancy.

Food Web Assembly Rules for Generalized Lotka-Volterra Equations.

In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this requirement is equivalent to demanding that each species be part of a non-overlapping pairing, which substantially constrains the food web structure. We demonstrate that a stable food web can always be obtained if a non-overlapping pairing exists. If it does not, the matrix rank can be used to quantify the lack of niches, corresponding to unpaired species. For the species richness at each trophic level, we derive the food web assembly rules, which specify sustainable combinations. In neighboring levels, these rules allow the higher level to avert competitive exclusion at the lower, thereby incorporating apparent competition. In agreement with data, the assembly rules predict high species numbers at intermediate levels and thinning at the top and bottom. Using comprehensive food web data, we demonstrate how omnivores or parasites with hosts at multiple trophic levels can loosen the constraints and help obtain coexistence in food webs. Hence, omnivory may be the glue that keeps communities intact even under extinction or ecological release of species.

Population Dynamics of Phage and Bacteria in Spatially Structured Habitats Using Phage λ and Escherichia coli.

UNLABELLED: Bacteria living in physically structured habitats are exposed heterogeneously to both resources and different types of phages. While there have been numerous experimental approaches to examine spatially distributed bacteria exposed to phages, there is little theory to guide the design of these experiments, interpret their results, or expand the inferences drawn to a broader ecological and evolutionary context. Plaque formation provides a window into understanding phage-bacterium interactions in physically structured populations, including surfaces, semisolids, and biofilms. We develop models to address the plaque dynamics for a temperate phage and its virulent mutants. The models are compared with phage λ-Escherichia coli system to quantify their applicability. We found that temperate phages gave an increasing number of gradually smaller colonies as the distance increased from the plaque center. For low-lysogen frequency this resulted in plaques with most of the visible colonies at an intermediate distance between the center and periphery. Using spot inoculation, where phages in excess of bacteria were inoculated in a circular area, we measured the frequency and spatial distribution of lysogens. The spot morphology of cII-negative (cII(-)) and cIII(-) mutants of phage λ displays concentric rings of high-density lysogenic colonies. The simplest of these ring morphologies was reproduced by including multiplicity of infection (MOI) sensitivity in lysis-lysogeny decisions, but its failure to explain the occasional observation of multiple rings in cIII(-) mutant phages highlights unknown features of this phage. Our findings demonstrated advantages of temperate phages over virulent phages in exploiting limited resources in spatially distributed microbial populations. IMPORTANCE: Phages are the most abundant organisms on earth, and yet little is known about how phages and bacterial hosts are influencing each other in density and evolution. Phages can be either virulent or temperate, a difference that is highlighted when a spatially structured bacterial population is infected. Phage λ is a temperate phage, with a capacity for dormancy that can be modified by single gene knockouts. The stochastic bias in the lysis-lysogeny decision's probability is reflected in plaque morphologies on bacterial lawns. We present a model for plaque morphology of both virulent and temperate phages, taking into account the underlying survival of bacterial microcolonies. It reproduces known plaque morphologies and speaks to advantages of temperate phages in a spatially structured environment.

Rapid Curtailing of the Stringent Response by Toxin-Antitoxin Module-Encoded mRNases.

UNLABELLED: Escherichia coli regulates its metabolism to adapt to changes in the environment, in particular to stressful downshifts in nutrient quality. Such shifts elicit the so-called stringent response, coordinated by the alarmone guanosine tetra- and pentaphosphate [(p)ppGpp]. On sudden amino acid (aa) starvation, RelA [(p)ppGpp synthetase I] activity is stimulated by binding of uncharged tRNAs to a vacant ribosomal site; the (p)ppGpp level increases dramatically and peaks within the time scale of a few minutes. The decrease of the (p)ppGpp level after the peak is mediated by the decreased production of mRNA by (p)ppGpp-associated transcriptional regulation, which reduces the vacant ribosomal A site and thus constitutes negative feedback to the RelA-dependent (p)ppGpp synthesis. Here we showed that on sudden isoleucine starvation, this peak was higher in an E. coli strain that lacks the 10 known mRNase-encoding toxin-antitoxin (TA) modules present in the wild-type (wt) strain. This observation suggested that toxins are part of the negative-feedback mechanism to control the (p)ppGpp level during the early stringent response. We built a ribosome trafficking model to evaluate the fold increase in RelA activity just after the onset of aa starvation. Combining this with a feedback model between the (p)ppGpp level and the mRNA level, we obtained reasonable fits to the experimental data for both strains. The analysis revealed that toxins are activated rapidly, within a minute after the onset of starvation, reducing the mRNA half-life by ∼30%. IMPORTANCE: The early stringent response elicited by amino acid starvation is controlled by a sharp increase of the cellular (p)ppGpp level. Toxin-antitoxin module-encoded mRNases are activated by (p)ppGpp through enhanced degradation of antitoxins. The present work shows that this activation happens over a very short time scale and that the activated mRNases negatively affect the (p)ppGpp level. The proposed mathematical model of (p)ppGpp regulation through the mRNA level highlights the importance of several feedback loops in early (p)ppGpp regulation.

Bifurcation of transition paths induced by coupled bistable systems.

We discuss the transition paths in a coupled bistable system consisting of interacting multiple identical bistable motifs. We propose a simple model of coupled bistable gene circuits as an example and show that its transition paths are bifurcating. We then derive a criterion to predict the bifurcation of transition paths in a generalized coupled bistable system. We confirm the validity of the theory for the example system by numerical simulation. We also demonstrate in the example system that, if the steady states of individual gene circuits are not changed by the coupling, the bifurcation pattern is not dependent on the number of gene circuits. We further show that the transition rate exponentially decreases with the number of gene circuits when the transition path does not bifurcate, while a bifurcation facilitates the transition by lowering the quasi-potential energy barrier.

Conditional cooperativity of toxin - antitoxin regulation can mediate bistability between growth and dormancy.

Many toxin-antitoxin operons are regulated by the toxin/antitoxin ratio by mechanisms collectively coined "conditional cooperativity". Toxin and antitoxin form heteromers with different stoichiometric ratios, and the complex with the intermediate ratio works best as a transcription repressor. This allows transcription at low toxin level, strong repression at intermediate toxin level, and then again transcription at high toxin level. Such regulation has two interesting features; firstly, it provides a non-monotonous response to the concentration of one of the proteins, and secondly, it opens for ultra-sensitivity mediated by the sequestration of the functioning heteromers. We explore possible functions of conditional regulation in simple feedback motifs, and show that it can provide bistability for a wide range of parameters. We then demonstrate that the conditional cooperativity in toxin-antitoxin systems combined with the growth-inhibition activity of free toxin can mediate bistability between a growing state and a dormant state.

Conditional cooperativity in toxin-antitoxin regulation prevents random toxin activation and promotes fast translational recovery.

Many toxin-antitoxin (TA) loci are known to strongly repress their own transcription. This auto-inhibition is often called 'conditional cooperativity' as it relies on cooperative binding of TA complexes to operator DNA that occurs only when toxins are in a proper stoichiometric relationship with antitoxins. There has recently been an explosion of interest in TA systems due to their role in bacterial persistence, however the role of conditional cooperativity is still unclear. We reveal the biological function of conditional cooperativity by constructing a mathematical model of the well studied TA system, relBE of Escherichia coli. We show that the model with the in vivo and in vitro established parameters reproduces experimentally observed response to nutritional stress. We further demonstrate that conditional cooperativity stabilizes the level of antitoxin in rapidly growing cells such that random induction of relBE is minimized. At the same time it enables quick removal of free toxin when the starvation is terminated.

Genetic mixing and demixing on expanding spherical frontiers.

Genetic fluctuation during range expansion is a key process driving evolution. When a bacterial population is expanding on a 2D surface, random fluctuations in the growth of the pioneers at the front line cause a strong demixing of genotypes. Even when there is no selective advantage, sectors of low genetic diversity are formed. Experimental studies of range expansions in surface-attached colonies of fluorescently labelled micro-organisms have contributed significantly to our understanding of fundamental evolutionary dynamics. However, experimental studies on genetic fluctuations in 3D range expansions have been sparse, despite their importance for tumour or biofilm development. We encapsulated populations of two fluorescent Escherichia coli strains in inoculation droplets (volumes [Formula: see text] nl). The confined ensemble of cells grew when embedded in a hydrogel-with nutrients-and developed 3D colonies with well-defined, sector-like regions. Using confocal laser scanning microscopy, we imaged the development of 3D colonies and the emergence of sectors. We characterized how cell concentration in the inoculation droplet controls sectors, growth rate, and the transition from branched colonies to quasi-spherical colonies. We further analysed how sectors on the surface change over time. We complement these experimental results with a modified 3D Eden growth model. The model in 3D spherical growth predicts a phase, where sectors are merging, followed by a steady increase (constant rate), and the experimentally analysed sectors were consistent with this prediction. Therefore, our results demonstrate qualitative differences between radial (2D) and spherical (3D) range expansions and their importance in gene fixation processes.

The Gompertz Law emerges naturally from the inter-dependencies between sub-components in complex organisms.

Understanding and facilitating healthy aging has become a major goal in medical research and it is becoming increasingly acknowledged that there is a need for understanding the aging phenotype as a whole rather than focusing on individual factors. Here, we provide a universal explanation for the emergence of Gompertzian mortality patterns using a systems approach to describe aging in complex organisms that consist of many inter-dependent subsystems. Our model relates to the Sufficient-Component Cause Model, widely used within the field of epidemiology, and we show that including inter-dependencies between subsystems and modeling the temporal evolution of subsystem failure results in Gompertizan mortality on the population level. Our model also provides temporal trajectories of mortality-risk for the individual. These results may give insight into understanding how biological age evolves stochastically within the individual, and how this in turn leads to a natural heterogeneity of biological age in a population.

Control of ribosome traffic by position-dependent choice of synonymous codons.

Messenger RNA (mRNA) encodes a sequence of amino acids by using codons. For most amino acids, there are multiple synonymous codons that can encode the amino acid. The translation speed can vary from one codon to another, thus there is room for changing the ribosome speed while keeping the amino acid sequence and hence the resulting protein. Recently, it has been noticed that the choice of the synonymous codon, via the resulting distribution of slow- and fast-translated codons, affects not only on the average speed of one ribosome translating the mRNA but also might have an effect on nearby ribosomes by affecting the appearance of 'traffic jams' where multiple ribosomes collide and form queues. To test this 'context effect' further, we here investigate the effect of the sequence of synonymous codons on the ribosome traffic by using a ribosome traffic model with codon-dependent rates, estimated from experiments. We compare the ribosome traffic on wild-type (WT) sequences and sequences where the synonymous codons were swapped randomly. By simulating translation of 87 genes, we demonstrate that the WT sequences, especially those with a high bias in codon usage, tend to have the ability to reduce ribosome collisions, hence optimizing the cellular investment in the translation apparatus. The magnitude of such reduction of the translation time might have a significant impact on the cellular growth rate and thereby have importance for the survival of the species.

Entrainment of noise-induced and limit cycle oscillators under weak noise.

Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed point is linearly stable with complex eigenvalues, and addition of noise gives oscillations around the fixed point with fluctuating amplitude. We investigate how each class of models behaves under the external periodic forcing, taking the well-studied van der Pol equation as an example. We find that when the forcing is additive, the noise-induced oscillator can show only one-to-one entrainment to the external frequency, in contrast to the limit cycle oscillator which is known to entrain to any ratio. When the external forcing is multiplicative, on the other hand, the noise-induced oscillator can show entrainment to a few ratios other than one-to-one, while the limit cycle oscillator shows entrain to any ratio. The noise blurs the entrainment in general, but clear entrainment regions for limit cycles can be identified as long as the noise is not too strong.