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.

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.

Motility mediates satellite formation in confined biofilms.

Bacteria have spectacular survival capabilities and can spread in many, vastly different environments. For instance, when pathogenic bacteria infect a host, they expand by proliferation and squeezing through narrow pores and elastic matrices. However, the exact role of surface structures-important for biofilm formation and motility-and matrix density in colony expansion and morphogenesis is still largely unknown. Using confocal laser-scanning microscopy, we show how satellite colonies emerge around Escherichia coli colonies embedded in semi-dense hydrogel in controlled in vitro assays. Using knock-out mutants, we tested how extra-cellular structures, (e.g., exo-polysaccharides, flagella, and fimbria) control this morphology. Moreover, we identify the extra-cellular matrix' density, where this morphology is possible. When paralleled with mathematical modelling, our results suggest that satellite formation allows bacterial communities to spread faster. We anticipate that this strategy is important to speed up expansion in various environments, while retaining the close interactions and protection provided by the community.

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.

Distinct Survival, Growth Lag, and rRNA Degradation Kinetics during Long-Term Starvation for Carbon or Phosphate.

The stationary phase is the general term for the state a bacterial culture reaches when no further increase in cell mass occurs due to exhaustion of nutrients in the growth medium. Depending on the type of nutrient that is first depleted, the metabolic state of the stationary phase cells may vary greatly, and the subsistence strategies that best support cell survival may differ. As ribosomes play a central role in bacterial growth and energy expenditure, ribosome preservation is a key element of such strategies. To investigate the degree of ribosome preservation during long-term starvation, we compared the dynamics of rRNA levels of carbon-starved and phosphorus-starved Escherichia coli cultures for up to 28 days. The starved cultures' contents of full-length 16S and 23S rRNA decreased as the starvation proceeded in both cases, and phosphorus starvation resulted in much more rapid rRNA degradation than carbon starvation. Bacterial survival and regrowth kinetics were also quantified. Upon replenishment of the nutrient in question, carbon-starved cells resumed growth faster than cells starved for phosphate for the equivalent amount of time, and for both conditions, the lag time increased with the starvation time. While these results are in accordance with the hypothesis that cells with a larger ribosome pool recover more readily upon replenishment of nutrients, we also observed that the lag time kept increasing with increasing starvation time, also when the amount of rRNA per viable cell remained constant, highlighting that lag time is not a simple function of ribosome content under long-term starvation conditions. IMPORTANCE The exponential growth of bacterial populations is punctuated by long or short periods of starvation lasting from the point of nutrient exhaustion until nutrients are replenished. To understand the consequences of long-term starvation for Escherichia coli cells, we performed month-long carbon and phosphorus starvation experiments and measured three key phenotypes of the cultures, namely, the survival of the cells, the time needed for them to resume growth after nutrient replenishment, and the levels of intact rRNA preserved in the cultures. The starved cultures' concentration of rRNA dropped with starvation time, as did cell survival, while the lag time needed for regrowth increased. While all three phenotypes were more severely affected during starvation for phosphorus than for carbon, our results demonstrate that neither survival nor lag time is correlated with ribosome content in a straightforward manner.

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.

Existence of log-phase Escherichia coli persisters and lasting memory of a starvation pulse.

The vast majority of a bacterial population is killed when treated with a lethal concentration of antibiotics. The time scale of this killing is often comparable with the bacterial generation time before the addition of antibiotics. Yet, a small subpopulation typically survives for an extended period. However, the long-term killing dynamics of bacterial cells has not been fully quantified even in well-controlled laboratory conditions. We constructed a week-long killing assay and followed the survival fraction of Escherichia coli K12 exposed to a high concentration of ciprofloxacin. We found that long-term survivors were formed during exponential growth, with some cells surviving at least 7 d. The long-term dynamics contained at least three time scales, which greatly enhances predictions of the population survival time compared with the biphasic extrapolation from the short-term behavior. Furthermore, we observed a long memory effect of a brief starvation pulse, which was dependent on the (p)ppGpp synthase relA Specifically, 1 h of carbon starvation before antibiotics exposure increased the surviving fraction by nearly 100-fold even after 4 d of ciprofloxacin treatment.

A scaling law of multilevel evolution: how the balance between within- and among-collective evolution is determined.

Numerous living systems are hierarchically organized, whereby replicating components are grouped into reproducing collectives-e.g., organelles are grouped into cells, and cells are grouped into multicellular organisms. In such systems, evolution can operate at two levels: evolution among collectives, which tends to promote selfless cooperation among components within collectives (called altruism), and evolution within collectives, which tends to promote cheating among components within collectives. The balance between within- and among-collective evolution thus exerts profound impacts on the fitness of these systems. Here, we investigate how this balance depends on the size of a collective (denoted by N) and the mutation rate of components (m) through mathematical analyses and computer simulations of multiple population genetics models. We first confirm a previous result that increasing N or m accelerates within-collective evolution relative to among-collective evolution, thus promoting the evolution of cheating. Moreover, we show that when within- and among-collective evolution exactly balance each other out, the following scaling relation generally holds: Nmα is a constant, where scaling exponent α depends on multiple parameters, such as the strength of selection and whether altruism is a binary or quantitative trait. This relation indicates that although N and m have quantitatively distinct impacts on the balance between within- and among-collective evolution, their impacts become identical if m is scaled with a proper exponent. Our results thus provide a novel insight into conditions under which cheating or altruism evolves in hierarchically organized replicating systems.

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.

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.

Valine-Induced Isoleucine Starvation in Escherichia coli K-12 Studied by Spike-In Normalized RNA Sequencing.

Escherichia coli cells respond to a period of famine by globally reorganizing their gene expression. The changes are known as the stringent response, which is orchestrated by the alarmone ppGpp that binds directly to RNA polymerase. The resulting changes in gene expression are particularly well studied in the case of amino acid starvation. We used deep RNA sequencing in combination with spike-in cells to measure global changes in the transcriptome after valine-induced isoleucine starvation of a standard E. coli K12 strain. Owing to the whole-cell spike-in method that eliminates variations in RNA extraction efficiency between samples, we show that ribosomal RNA levels are reduced during isoleucine starvation and we quantify how the change in cellular RNA content affects estimates of gene regulation. Specifically, we show that standard data normalization relying on sample sequencing depth underestimates the number of down-regulated genes in the stringent response and overestimates the number of up-regulated genes by approximately 40%. The whole-cell spike-in method also made it possible to quantify how rapidly the pool of total messenger RNA (mRNA) decreases upon amino acid starvation. A principal component analysis showed that the first two components together described 69% of the variability of the data, underlining that large and highly coordinated regulons are at play in the stringent response. The induction of starvation by sudden addition of high valine concentrations provoked prominent regulatory responses outside of the expected ppGpp, RpoS, and Lrp regulons. This underlines the notion that with the high resolution possible in deep RNA sequencing analysis, any different starvation method (e.g., nitrogen-deprivation, removal of an amino acid from an auxotroph strain, or valine addition to E. coli K12 strains) will produce measurable variations in the stress response produced by the cells to cope with the specific treatment.

Sustainability of spatially distributed bacteria-phage systems.

Virulent phages can expose their bacterial hosts to devastating epidemics, in principle leading to complete elimination of their hosts. Although experiments indeed confirm a large reduction of susceptible bacteria, there are no reports of complete extinctions. We here address this phenomenon from the perspective of spatial organization of bacteria and how this can influence the final survival of them. By modelling the transient dynamics of bacteria and phages when they are introduced into an environment with finite resources, we quantify how time delayed lysis, the spatial separation of initial bacterial positions, and the self-protection of bacteria growing in spherical colonies favour bacterial survival. Our results suggest that spatial structures on the millimetre and submillimetre scale play an important role in maintaining microbial diversity.

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.

Birth and Resuscitation of (p)ppGpp Induced Antibiotic Tolerant Persister Cells.

Transient antibiotic treatment typically eradicates most sensitive bacteria except a few survivors called persisters. The second messenger (p)ppGpp plays a key role in persister formation in Escherichia coli populations but the underlying mechanisms have remained elusive. In this study we induced (p)ppGpp synthesis by modulating tRNA charging and then directly observed the stochastic appearance, antibiotic tolerance, and resuscitation of persister cells using live microscopy. Different physiological parameters of persister cells as well as their regularly growing ancestors and sisters were continuously monitored using fluorescent reporters. Our results confirmed previous findings that high (p)ppGpp levels are critical for persister formation, but the phenomenon remained strikingly stochastic without any correlation between (p)ppGpp levels and antibiotic tolerance on the single-cell level. We could not confirm previous notions that persisters exhibit markedly low concentrations of intracellular ATP or were linked to post-transcriptional effects of (p)ppGpp through the activation of small genetic elements known as toxin-antitoxin (TA) modules. Instead, we suggest that persister cell formation under regular conditions is driven by the transcriptional response to increased (p)ppGpp levels.

Gene Expression Changes with Minor Effects on the Population Average Have Major Effects on the Occurrence of Cells with Extreme Protein Concentrations.

The cell-to-cell heterogeneity in a bacterial population provides a rich response to environmental changes and robust survival of an isogenic population. Especially, the rare, extreme phenotypes can be important for survival under transient lethal conditions. We analyze the probability of having an extremely high or low protein level in a stochastic model of gene expression. The fraction of rare state cells defined as the cells in the tails of distributions is found to be highly sensitive to small changes of the mean protein level. The result highlights the importance of relatively weak changes to the mean for the occurrence of rare phenotypes.

Fast Translation within the First 45 Codons Decreases mRNA Stability and Increases Premature Transcription Termination in E. coli.

We show here that the specific use of fast or slowly translated codons in the early coding region of a gene may influence both the mRNA stability and premature transcription termination. We first inserted a pair of nearly identical 42-base-pair (bp)-long sequences into codon 3 of the Escherichia coli lacZ gene. The only difference between the two inserts was that the first base in one was moved to become the last base in the other, providing a difference in the reading frame, one of which had the biased codons typical for ribosomal protein genes and which previously was shown to be faster translated than average. This insert reduced the mRNA stability and increased premature transcription termination and together resulted in a hundred-fold difference in lacZ expression. We next generated lacZ variants with 7, 14 or 21 fast translated, ribosomal-type codons inserted into codon 13 of lacZ. This gave progressively more unstable mRNAs and also progressively increased transcription termination up to 90%. By modeling, based on estimates of the translation rate of individual codons, we can explain these observations by an increased susceptibility of the mRNA to degradation, determined by the length and degree of the early mRNA being uncovered by ribosomes. Thus, we suggest that the translation rate differences among the synonymous codons early in a gene enable a "velocity code" within the amino acid coding ability, where the translation rate differences encode the mRNA stability and the premature termination of the RNA polymerase.

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.

Dynamic Modeling of Indole Glucosinolate Hydrolysis and Its Impact on Auxin Signaling.

Plants release chemicals to deter attackers. Arabidopsis thaliana relies on multiple defense compounds, including indol-3-ylmethyl glucosinolate (I3G), which upon hydrolysis initiated by myrosinase enzymes releases a multitude of bioactive compounds, among others, indole-3-acetonitrile and indole-3-acetoisothiocyanate. The highly unstable isothiocyanate rapidly reacts with other molecules. One of the products, indole-3-carbinol, was reported to inhibit auxin signaling through binding to the TIR1 auxin receptor. On the contrary, the nitrile product of I3G hydrolysis can be converted by nitrilase enzymes to form the primary auxin molecule, indole-3-acetic acid, which activates TIR1. This suggests that auxin signaling is subject to both antagonistic and protagonistic effects of I3G hydrolysis upon attack. We hypothesize that I3G hydrolysis and auxin signaling form an incoherent feedforward loop and we build a mathematical model to examine the regulatory network dynamics. We use molecular docking to investigate the possible antagonistic properties of different I3G hydrolysis products by competitive binding to the TIR1 receptor. Our simulations reveal an uncoupling of auxin concentration and signaling, and we determine that enzyme activity and antagonist binding affinity are key parameters for this uncoupling. The molecular docking predicts that several I3G hydrolysis products strongly antagonize auxin signaling. By comparing a tissue disrupting attack - e.g., by chewing insects or necrotrophic pathogens that causes rapid release of I3G hydrolysis products - to sustained cell-autonomous I3G hydrolysis, e.g., upon infection by biotrophic pathogens, we find that each scenario gives rise to distinct auxin signaling dynamics. This suggests that plants have different defense versus growth strategies depending on the nature of the attack.

Theory of invasion extinction dynamics in minimal food webs.

When food webs are exposed to species invasion, secondary extinction cascades may be set off. Although much work has gone into characterizing the structure of food webs, systematic predictions on their evolutionary dynamics are still scarce. Here we present a theoretical framework that predicts extinctions in terms of an alternating sequence of two basic processes: resource depletion by or competitive exclusion between consumers. We first propose a conceptual invasion extinction model (IEM) involving random fitness coefficients. We bolster this IEM by an analytical, recursive procedure for calculating idealized extinction cascades after any species addition and simulate the long-time evolution. Our procedure describes minimal food webs where each species interacts with only a single resource through the generalized Lotka-Volterra equations. For such food webs ex- tinction cascades are determined uniquely and the system always relaxes to a stable steady state. The dynamics and scale invariant species life time resemble the behavior of the IEM, and correctly predict an upper limit for trophic levels as observed in the field.