Stochastic activation of a DNA damage response causes cell-to-cell mutation rate variation

Parametric sensitivity analysis for models of reaction networks within interacting compartments

Models of reaction networks within interacting compartments (RNIC) are a generalization of stochastic reaction networks. It is most natural to think of the interacting compartments as "cells" that can appear, degrade, split, and even merge, with each cell containing an evolving copy of the underlying stochastic reaction network. Such models have a number of parameters, including those associated with the internal chemical model and those associated with the compartment interactions, and it is natural to want efficient computational methods for the numerical estimation of sensitivities of model statistics with respect to these parameters. Motivated by the extensive work on computational methods for parametric sensitivity analysis in the context of stochastic reaction networks over the past few decades, we provide a number of methods in the basic RNIC setting. Provided methods include the (unbiased) Girsanov transformation method (also called the likelihood ratio method) and a number of coupling methods for the implementation of finite differences, each motivated by methods from previous work related to stochastic reaction networks. We provide several numerical examples comparing the various methods in the new setting. We find that the relative performance of each method is in line with its analog in the "standard" stochastic reaction network setting. We have made all the MATLAB codes used to implement the various methods freely available for download.

Antibiotic resistance evolution driven synergistically by antibiotics and typical organic pollutants in antibiotic production wastewater

A major concern regarding the risk of antibiotic production wastewater (APW) for the transmission of antibiotic resistance (AR) stems from the residual antibiotics. However, APW also contains high concentrations of organic pollutants, many of which have severe biological toxicity and joint toxicity with antibiotics. The contribution of these organic pollutants to the development of AR in the APW treatment system is unknown. In this study, a wild-type Escherichia coli strain was exposed to six typical organic pollutants in APW individually and synergistically with the antibiotic ampicillin (AMP). Independent exposure to organic compounds had negligible effects on the evolution of AR, whereas they synergistically induced AR mutations and increased antibiotic persistence with AMP, especially the raw material d-p-hydroxyphenylglycine (DHPG), at relevant concentrations in APW. Combined exposure to 1-500 mg/L DHPG and 1 mg/L AMP synergistically increased the mutation frequencies against multiple antibiotics by up to 2928.9-fold in a dose-time pattern, and the combination index reached 445.7. Phenotypic and genotypic analyses revealed that the synergism between DHPG and AMP was associated with increased antibacterial activity, enhanced oxidative stress, and stimulation of efflux pump expression. Overall, our results highlight the elevated risk of AR induction caused by antibiotics and organic pollutants in APW.

Harnessing microbial heterogeneity for improved biosynthesis fueled by synthetic biology

Metabolic engineering-driven microbial cell factories have made great progress in the efficient bioproduction of biochemical and recombinant proteins. However, the low efficiency and robustness of microbial cell factories limit their industrial applications. Harnessing microbial heterogeneity contributes to solving this. In this review, the origins of microbial heterogeneity and its effects on biosynthesis are first summarized. Synthetic biology-driven tools and strategies that can be used to improve biosynthesis by increasing and reducing microbial heterogeneity are then systematically summarized. Next, novel single-cell technologies available for unraveling microbial heterogeneity and facilitating heterogeneity regulation are discussed. Furthermore, a combined workflow of increasing genetic heterogeneity in the strain-building step to help in screening highly productive strains - reducing heterogeneity in the production process to obtain highly robust strains (IHP-RHR) facilitated by single-cell technologies was proposed to obtain highly productive and robust strains by harnessing microbial heterogeneity. Finally, the prospects and future challenges are discussed.

Drug tolerance and persistence in bacteria, fungi and cancer cells: Role of non-genetic heterogeneity

A common feature of bacterial, fungal and cancer cell populations upon treatment is the presence of tolerant and persistent cells able to survive, and sometimes grow, even in the presence of usually inhibitory or lethal drug concentrations, driven by non-genetic differences among individual cells in a population. Here we review and compare data obtained on drug survival in bacteria, fungi and cancer cells to unravel common characteristics and cellular pathways, and to point their singularities. This comparative work also allows to cross-fertilize ideas across fields. We particularly focus on the role of gene expression variability in the emergence of cell-cell non-genetic heterogeneity because it represents a possible common basic molecular process at the origin of most persistence phenomena and could be monitored and tuned to help improve therapeutic interventions.

Robust Quantification of Live-Cell Single-Molecule Tracking Data for Fluorophores with Different Photophysical Properties

High-speed single-molecule tracking in live cells is becoming an increasingly popular method for quantifying the spatiotemporal behavior of proteins in vivo. The method provides a wealth of quantitative information, but users need to be aware of biases that can skew estimates of molecular mobilities. The range of suitable fluorophores for live-cell single-molecule imaging has grown substantially over the past few years, but it remains unclear to what extent differences in photophysical properties introduce biases. Here, we tested two fluorophores with entirely different photophysical properties, one that photoswitches frequently between bright and dark states (TMR) and one that shows exceptional photostability without photoswitching (JFX650). We used a fusion of the Escherichia coli DNA repair enzyme MutS to the HaloTag and optimized sample preparation and imaging conditions for both types of fluorophore. We then assessed the reliability of two common data analysis algorithms, mean-square displacement (MSD) analysis and Hidden Markov Modeling (HMM), to estimate the diffusion coefficients and fractions of MutS molecules in different states of motion. We introduce a simple approach that removes discrepancies in the data analyses and show that both algorithms yield consistent results, regardless of the fluorophore used. Nevertheless, each dye has its own strengths and weaknesses, with TMR being more suitable for sampling the diffusive behavior of many molecules, while JFX650 enables prolonged observation of only a few molecules per cell. These characterizations and recommendations should help to standardize measurements for increased reproducibility and comparability across studies.

Regulatory properties of transcription factors with diverse mechanistic function

Transcription factors (TFs) regulate the process of transcription through the modulation of different kinetic steps. Although models can often describe the observed transcriptional output of a measured gene, predicting a TFs role on a given promoter requires an understanding of how the TF alters each step of the transcription process. In this work, we use a simple model of transcription to assess the role of promoter identity, and the degree to which TFs alter binding of RNAP (stabilization) and initiation of transcription (acceleration) on three primary characteristics: the range of steady-state regulation, cell-to-cell variability in expression, and the dynamic response time of a regulated gene. We find that steady state regulation and the response time of a gene behave uniquely for TFs that regulate incoherently, i.e that speed up one step but slow the other. We also find that incoherent TFs have dynamic implications, with one type of incoherent mode configuring the promoter to respond more slowly at intermediate TF concentrations. We also demonstrate that the noise of gene expression for these TFs is sensitive to promoter strength, with a distinct non-monotonic profile that is apparent under stronger promoters. Taken together, our work uncovers the coupling between promoters and TF regulatory modes with implications for understanding natural promoters and engineering synthetic gene circuits with desired expression properties.

Estimating mutation rates under heterogeneous stress responses

Exposure to environmental stressors, including certain antibiotics, induces stress responses in bacteria. Some of these responses increase mutagenesis and thus potentially accelerate resistance evolution. Many studies report increased mutation rates under stress, often using the standard experimental approach of fluctuation assays. However, single-cell studies have revealed that many stress responses are heterogeneously expressed in bacterial populations, which existing estimation methods have not yet addressed. We develop a population dynamic model that considers heterogeneous stress responses (subpopulations of cells with the response off or on) that impact both mutation rate and cell division rate, inspired by the DNA-damage response in Escherichia coli (SOS response). We derive the mutant count distribution arising in fluctuation assays under this model and then implement maximum likelihood estimation of the mutation-rate increase specifically associated with the expression of the stress response. Using simulated mutant count data, we show that our inference method allows for accurate and precise estimation of the mutation-rate increase, provided that this increase is sufficiently large and the induction of the response also reduces the division rate. Moreover, we find that in many cases, either heterogeneity in stress responses or mutant fitness costs could explain similar patterns in fluctuation assay data, suggesting that separate experiments would be required to identify the true underlying process. In cases where stress responses and mutation rates are heterogeneous, current methods still correctly infer the effective increase in population mean mutation rate, but we provide a novel method to infer distinct stress-induced mutation rates, which could be important for parameterising evolutionary models.

Genomic and metabolic instability during long-term fermentation of an industrial Saccharomyces cerevisiae strain engineered for C5 sugar utilization

The genetic stability and metabolic robustness of production strains is one of the key criteria for the production of bio-based products by microbial fermentation on an industrial scale. These criteria were here explored in an industrial ethanol-producer strain of Saccharomyces cerevisiae able to co-ferment D-xylose and L-arabinose with glucose through the chromosomal integration of several copies of pivotal genes for the use of these pentose (C5) sugars. Using batch sequential cultures in a controlled bioreactor that mimics long-term fermentation in an industrial setting, this strain was found to exhibit significant fluctuations in D-xylose and L-arabinose consumption as early as the 50th generation and beyond. These fluctuations seem not related to the few low-consumption C5 sugar clones that appeared throughout the sequential batch cultures at a frequency lower than 1.5% and that were due to the reduction in the number of copies of transgenes coding for C5 sugar assimilation enzymes. Also, subpopulations enriched with low or high RAD52 expression, whose expression level was reported to be proportional to homologous recombination rate did not exhibit defect in C5-sugar assimilation, arguing that other mechanisms may be responsible for copy number variation of transgenes. Overall, this work highlighted the existence of genetic and metabolic instabilities in an industrial yeast which, although modest in our conditions, could be more deleterious in harsher industrial conditions, leading to reduced production performance.

Widespread prevalence of a methylation-dependent switch to activate an essential DNA damage response in bacteria

DNA methylation plays central roles in diverse cellular processes, ranging from error-correction during replication to regulation of bacterial defense mechanisms. Nevertheless, certain aberrant methylation modifications can have lethal consequences. The mechanisms by which bacteria detect and respond to such damage remain incompletely understood. Here, we discover a highly conserved but previously uncharacterized transcription factor (Cada2), which orchestrates a methylation-dependent adaptive response in Caulobacter. This response operates independently of the SOS response, governs the expression of genes crucial for direct repair, and is essential for surviving methylation-induced damage. Our molecular investigation of Cada2 reveals a cysteine methylation-dependent posttranslational modification (PTM) and mode of action distinct from its Escherichia coli counterpart, a trait conserved across all bacteria harboring a Cada2-like homolog instead. Extending across the bacterial kingdom, our findings support the notion of divergence and coevolution of adaptive response transcription factors and their corresponding sequence-specific DNA motifs. Despite this diversity, the ubiquitous prevalence of adaptive response regulators underscores the significance of a transcriptional switch, mediated by methylation PTM, in driving a specific and essential bacterial DNA damage response.

The divergence of mutation rates and spectra across the Tree of Life

Owing to advances in genome sequencing, genome stability has become one of the most scrutinized cellular traits across the Tree of Life. Despite its centrality to all things biological, the mutation rate (per nucleotide site per generation) ranges over three orders of magnitude among species and several-fold within individual phylogenetic lineages. Within all major organismal groups, mutation rates scale negatively with the effective population size of a species and with the amount of functional DNA in the genome. This relationship is most parsimoniously explained by the drift-barrier hypothesis, which postulates that natural selection typically operates to reduce mutation rates until further improvement is thwarted by the power of random genetic drift. Despite this constraint, the molecular mechanisms underlying DNA replication fidelity and repair are free to wander, provided the performance of the entire system is maintained at the prevailing level. The evolutionary flexibility of the mutation rate bears on the resolution of several prior conundrums in phylogenetic and population-genetic analysis and raises challenges for future applications in these areas.

Protein secretion zones during overexpression of amylase within the Gram-positive cell wall

BACKGROUND

Whereas the translocation of proteins across the cell membrane has been thoroughly investigated, it is still unclear how proteins cross the cell wall in Gram-positive bacteria, which are widely used for industrial applications. We have studied the secretion of α-amylase AmyE within two different Bacillus strains, B. subtilis and B. licheniformis.

RESULTS

We show that a C-terminal fusion of AmyE with the fluorescent reporter mCherry is secreted via discrete patches showing very low dynamics. These are visible at many places within the cell wall for many minutes. Expression from a high copy number plasmid was required to be able to see these structures we term "secretion zones". Zones corresponded to visualized AmyE activity on the surface of cells, showing that they release active enzymes. They overlapped with SecA signals but did not frequently co-localize with the secretion ATPase. Single particle tracking showed higher dynamics of SecA and of SecDF, involved in AmyE secretion, at the cell membrane than AmyE. These experiments suggest that SecA initially translocates AmyE molecules through the cell membrane, and then diffuses to a different translocon. Single molecule tracking of SecA suggests the existence of three distinct diffusive states of SecA, which change during AmyE overexpression, but increased AmyE secretion does not appear to overwhelm the system.

CONCLUSIONS

Because secretion zones were only found during the transition to and within the stationary phase, diffusion rather than passive transport based on cell wall growth from inside to outside may release AmyE and, thus, probably secreted proteins in general. Our findings suggest active transport through the cell membrane and slow, passive transition through the cell wall, at least for overexpressed proteins, in bacteria of the genus Bacillus.

Phenotype switching of the mutation rate facilitates adaptive evolution

The mutation rate plays an important role in adaptive evolution. It can be modified by mutator and anti-mutator alleles. Recent empirical evidence hints that the mutation rate may vary among genetically identical individuals: evidence from bacteria suggests that the mutation rate can be affected by expression noise of a DNA repair protein and potentially also by translation errors in various proteins. Importantly, this non-genetic variation may be heritable via a transgenerational epigenetic mode of inheritance, giving rise to a mutator phenotype that is independent from mutator alleles. Here, we investigate mathematically how the rate of adaptive evolution is affected by the rate of mutation rate phenotype switching. We model an asexual population with two mutation rate phenotypes, non-mutator and mutator. An offspring may switch from its parental phenotype to the other phenotype. We find that switching rates that correspond to so-far empirically described non-genetic systems of inheritance of the mutation rate lead to higher rates of adaptation on both artificial and natural fitness landscapes. These switching rates can maintain within the same individuals both a mutator phenotype and intermediary mutations, a combination that facilitates adaptation. Moreover, non-genetic inheritance increases the proportion of mutators in the population, which in turn increases the probability of hitchhiking of the mutator phenotype with adaptive mutations. This in turns facilitates the acquisition of additional adaptive mutations. Our results rationalize recently observed noise in the expression of proteins that affect the mutation rate and suggest that non-genetic inheritance of this phenotype may facilitate evolutionary adaptive processes.

Dimerization of iLID optogenetic proteins observed using 3D single-molecule tracking in live E. coli

3D single-molecule tracking microscopy has enabled measurements of protein diffusion in living cells, offering information about protein dynamics and cellular environments. For example, different diffusive states can be resolved and assigned to protein complexes of different size and composition. However, substantial statistical power and biological validation, often through genetic deletion of binding partners, are required to support diffusive state assignments. When investigating cellular processes, real-time perturbations to protein spatial distributions is preferable to permanent genetic deletion of an essential protein. For example, optogenetic dimerization systems can be used to manipulate protein spatial distributions that could offer a means to deplete specific diffusive states observed in single-molecule tracking experiments. Here, we evaluate the performance of the iLID optogenetic system in living E. coli cells using diffraction-limited microscopy and 3D single-molecule tracking. We observed a robust optogenetic response in protein spatial distributions after 488 nm laser activation. Surprisingly, 3D single-molecule tracking results indicate activation of the optogenetic response when illuminating with high-intensity light with wavelengths at which there is minimal photon absorbance by the LOV2 domain. The preactivation can be minimized through the use of iLID system mutants, and titration of protein expression levels.

Single-molecule tracking to determine the abundances and stoichiometries of freely-diffusing protein complexes in living cells: Past applications and future prospects

Most biological processes in living cells rely on interactions between proteins. Live-cell compatible approaches that can quantify to what extent a given protein participates in homo- and hetero-oligomeric complexes of different size and subunit composition are therefore critical to advance our understanding of how cellular physiology is governed by these molecular interactions. Biomolecular complex formation changes the diffusion coefficient of constituent proteins, and these changes can be measured using fluorescence microscopy-based approaches, such as single-molecule tracking, fluorescence correlation spectroscopy, and fluorescence recovery after photobleaching. In this review, we focus on the use of single-molecule tracking to identify, resolve, and quantify the presence of freely-diffusing proteins and protein complexes in living cells. We compare and contrast different data analysis methods that are currently employed in the field and discuss experimental designs that can aid the interpretation of the obtained results. Comparisons of diffusion rates for different proteins and protein complexes in intracellular aqueous environments reported in the recent literature reveal a clear and systematic deviation from the Stokes-Einstein diffusion theory. While a complete and quantitative theoretical explanation of why such deviations manifest is missing, the available data suggest the possibility of weighing freely-diffusing proteins and protein complexes in living cells by measuring their diffusion coefficients. Mapping individual diffusive states to protein complexes of defined molecular weight, subunit stoichiometry, and structure promises to provide key new insights into how protein-protein interactions regulate protein conformational, translational, and rotational dynamics, and ultimately protein function.

New insights into the disulfide stress response by the Bacillus subtilis Spx system at a single-cell level

Spx is a global transcriptional regulator that orchestrates the Bacillus subtilis response to disulfide stress. The YjbH (SpxH) protein adapts Spx for ClpXP-mediated degradation, playing a critical role in the regulation of the cellular Spx levels. Upon stress, YjbH forms aggregates by a yet unknown mechanism, resulting in increased Spx levels due to reduced proteolysis. Here, we studied how individual cells use the Spx-YjbH system to respond to disulfide stress. We show, using fluorescent reporters, a correlation between the Spx levels and the amount of YjbH, as well as a transient growth inhibition upon disulfide stress. The in vivo dynamics and inheritance of YjbH aggregates are characterized by a bipolar distribution over time and appear to be entropy-driven by nucleoid exclusion. Moreover, we reveal that the population following disulfide stress is highly heterogenous in terms of aggregate load and that the aggregate load has strong implications for cellular fitness. We propose that the observed heterogeneity could be a mechanism to ensure population survival during stress. Finally, we find that the two YjbH domains (DsbA-like domain and winged-helix domain) contribute to its aggregation function, and show that the aggregation of the DsbA-like domain is conserved among other studied orthologs, whereas important differences are observed for the winged-helix domain.

Nonsteroidal anti-inflammatory drug diclofenac accelerates the emergence of antibiotic resistance via mutagenesis

Overuse of antimicrobial agents are generally considered to be a key factor in the occurrence of antibiotic resistance bacteria (ARB). Nevertheless, it is unclear whether ARB can be induced by non-antibiotic chemicals such as nonsteroidal anti-inflammatory drug (NSAID). Thus, the objective of this study is to investigate whether NSAID diclofenac (DCF) promote the emergence of antibiotic resistance in Escherichia coli K12 MG1655. Our results suggested that DCF induced the occurrence of ARB which showed hereditary stability of resistance. Meanwhile, gene variation was identified on chromosome of the ARB, and DCF can cause bacterial oxidative stress and SOS response. Subsequently, transcriptional levels of antioxidant (soxS, sodA, sodC, gor, katG, ahpF) and SOS (recA, lexA, uvrA, uvrB, ruvA, ruvB, dinB, umuC, polB) system-related genes were enhanced. However, the expression of related genes cannot be increased in high-dosage treatment compared with low-dosage samples because of cytotoxicity and cellular damage. Simultaneously, high-dosage DCF decreased the mutation frequency but enhanced the resistance of mutants. Our findings expand our knowledge of the promoting effect on the emergence of ARB caused by DCF. More attention and regulations should be given to these potential ecological and health risks for widespread DCF.

SOS-independent bacterial DNA damage responses: diverse mechanisms, unifying function

Cells across domains of life have dedicated pathways to sense and respond to DNA damage. These responses are broadly termed as DNA damage responses (DDRs). In bacteria, the best studied DDR is the Save our Soul (SOS) response. More recently, several SOS-independent DDRs have also been discovered. Studies further report diversity in the types of repair proteins present across bacterial species as well as differences in their mechanisms of action. Although the primary function of DDRs is preservation of genome integrity, the diverse organization, conservation, and function of bacterial DDRs raises important questions about how genome error correction mechanisms could influence or be influenced by the genomes that encode them. In this review, we discuss recent insights on three SOS-independent bacterial DDRs. We consider open questions in our understanding of how diversity in response and repair mechanisms is generated, and how action of these pathways is regulated in cells to ensure maintenance of genome integrity.

Phenotypic heterogeneity in the bacterial oxidative stress response is driven by cell-cell interactions

Genetically identical bacterial cells commonly display different phenotypes. This phenotypic heterogeneity is well known for stress responses, where it is often explained as bet hedging against unpredictable environmental threats. Here, we explore phenotypic heterogeneity in a major stress response of Escherichia coli and find it has a fundamentally different basis. We characterize the response of cells exposed to hydrogen peroxide (H2O2) stress in a microfluidic device under constant growth conditions. A machine-learning model reveals that phenotypic heterogeneity arises from a precise and rapid feedback between each cell and its immediate environment. Moreover, we find that the heterogeneity rests upon cell-cell interaction, whereby cells shield each other from H2O2 via their individual stress responses. Our work shows how phenotypic heterogeneity in bacterial stress responses can emerge from short-range cell-cell interactions and result in a collective phenotype that protects a large proportion of the population.

Microfluidics for long-term single-cell time-lapse microscopy: Advances and applications

Cells are inherently dynamic, whether they are responding to environmental conditions or simply at equilibrium, with biomolecules constantly being made and destroyed. Due to their small volumes, the chemical reactions inside cells are stochastic, such that genetically identical cells display heterogeneous behaviors and gene expression profiles. Studying these dynamic processes is challenging, but the development of microfluidic methods enabling the tracking of individual prokaryotic cells with microscopy over long time periods under controlled growth conditions has led to many discoveries. This review focuses on the recent developments of one such microfluidic device nicknamed the mother machine. We overview the original device design, experimental setup, and challenges associated with this platform. We then describe recent methods for analyzing experiments using automated image segmentation and tracking. We further discuss modifications to the experimental setup that allow for time-varying environmental control, replicating batch culture conditions, cell screening based on their dynamic behaviors, and to accommodate a variety of microbial species. Finally, this review highlights the discoveries enabled by this technology in diverse fields, such as cell-size control, genetic mutations, cellular aging, and synthetic biology.

POLQ suppresses genome instability and alterations in DNA repeat tract lengths

DNA polymerase theta (POLQ) is a principal component of the alternative non-homologous end-joining (ANHEJ) DNA repair pathway that ligates DNA double-strand breaks. Utilizing independent models of POLQ insufficiency during telomere-driven crisis, we found that POLQ - /- cells are resistant to crisis-induced growth deceleration despite sustaining inter-chromosomal telomere fusion frequencies equivalent to wild-type (WT) cells. We recorded longer telomeres in POLQ - / - than WT cells pre- and post-crisis, notwithstanding elevated total telomere erosion and fusion rates. POLQ - /- cells emerging from crisis exhibited reduced incidence of clonal gross chromosomal abnormalities in accordance with increased genetic heterogeneity. High-throughput sequencing of telomere fusion amplicons from POLQ-deficient cells revealed significantly raised frequencies of inter-chromosomal fusions with correspondingly depreciated intra-chromosomal recombinations. Long-range interactions culminating in telomere fusions with centromere alpha-satellite repeats, as well as expansions in HSAT2 and HSAT3 satellite and contractions in ribosomal DNA repeats, were detected in POLQ - / - cells. In conjunction with the expanded telomere lengths of POLQ - /- cells, these results indicate a hitherto unrealized capacity of POLQ for regulation of repeat arrays within the genome. Our findings uncover novel considerations for the efficacy of POLQ inhibitors in clinical cancer interventions, where potential genome destabilizing consequences could drive clonal evolution and resistant disease.

Non-genetic resistance facilitates survival while hindering the evolution of drug resistance due to intraspecific competition

Rising rates of resistance to antimicrobial drugs threaten the effective treatment of infections across the globe. Drug resistance has been established to emerge from non-genetic mechanisms as well as from genetic mechanisms. However, it is still unclear how non-genetic resistance affects the evolution of genetic drug resistance. We develop deterministic and stochastic population models that incorporate resource competition to quantitatively investigate the transition from non-genetic to genetic resistance during the exposure to static and cidal drugs. We find that non-genetic resistance facilitates the survival of cell populations during drug treatment while hindering the development of genetic resistance due to competition between the non-genetically and genetically resistant subpopulations. Non-genetic resistance in the presence of subpopulation competition increases the fixation times of drug resistance mutations, while increasing the probability of mutation before population extinction during cidal drug treatment. Intense intraspecific competition during drug treatment leads to extinction of susceptible and non-genetically resistant subpopulations. Alternating between drug and no drug conditions results in oscillatory population dynamics, increased resistance mutation fixation timescales, and reduced population survival. These findings advance our fundamental understanding of the evolution of resistance and may guide novel treatment strategies for patients with drug-resistant infections.

Quantifying biochemical reaction rates from static population variability within incompletely observed complex networks

Quantifying biochemical reaction rates within complex cellular processes remains a key challenge of systems biology even as high-throughput single-cell data have become available to characterize snapshots of population variability. That is because complex systems with stochastic and non-linear interactions are difficult to analyze when not all components can be observed simultaneously and systems cannot be followed over time. Instead of using descriptive statistical models, we show that incompletely specified mechanistic models can be used to translate qualitative knowledge of interactions into reaction rate functions from covariability data between pairs of components. This promises to turn a globally intractable problem into a sequence of solvable inference problems to quantify complex interaction networks from incomplete snapshots of their stochastic fluctuations.

Dynamic gene expression and growth underlie cell-to-cell heterogeneity in Escherichia coli stress response

Individual bacteria that share identical genomes and growth environments can display substantial cell-to-cell differences in expression of stress-response genes and single-cell growth rates. This phenotypic heterogeneity can impact the survival of single cells facing sudden stress. However, the windows of time that cells spend in vulnerable or tolerant states are often unknown. We quantify the temporal expression of a suite of stress-response reporters, while simultaneously monitoring growth. We observe pulsatile expression across genes with a range of stress-response functions, finding that single-cell growth rates are often anticorrelated with reporter levels. These dynamic phenotypic differences have a concrete link to function, in which individual cells undergoing a pulse of elevated expression and slow growth are predisposed to survive antibiotic exposure.

Cell-to-cell heterogeneity in gene expression and growth can have critical functional consequences, such as determining whether individual bacteria survive or die following stress. Although phenotypic variability is well documented, the dynamics that underlie it are often unknown. This information is important because dramatically different outcomes can arise from gradual versus rapid changes in expression and growth. Using single-cell time-lapse microscopy, we measured the temporal expression of a suite of stress-response reporters in Escherichia coli, while simultaneously monitoring growth rate. In conditions without stress, we found several examples of pulsatile expression. Single-cell growth rates were often anticorrelated with reporter levels, with changes in growth preceding changes in expression. These dynamics have functional consequences, which we demonstrate by measuring survival after challenging cells with the antibiotic ciprofloxacin. Our results suggest that fluctuations in both gene expression and growth dynamics in stress-response networks have direct consequences on survival.

Single cell variability of CRISPR-Cas interference and adaptation

While CRISPR-Cas defence mechanisms have been studied on a population level, their temporal dynamics and variability in individual cells have remained unknown. Using a microfluidic device, time-lapse microscopy and mathematical modelling, we studied invader clearance in Escherichia coli across multiple generations. We observed that CRISPR interference is fast with a narrow distribution of clearance times. In contrast, for invaders with escaping PAM mutations we found large cell-to-cell variability, which originates from primed CRISPR adaptation. Faster growth and cell division and higher levels of Cascade increase the chance of clearance by interference, while slower growth is associated with increased chances of clearance by priming. Our findings suggest that Cascade binding to the mutated invader DNA, rather than spacer integration, is the main source of priming heterogeneity. The highly stochastic nature of primed CRISPR adaptation implies that only subpopulations of bacteria are able to respond quickly to invading threats. We conjecture that CRISPR-Cas dynamics and heterogeneity at the cellular level are crucial to understanding the strategy of bacteria in their competition with other species and phages.

The effect of weak clonal interference on average fitness trajectories in the presence of macroscopic epistasis

Adaptation dynamics on fitness landscapes is often studied theoretically in the strong-selection, weak-mutation regime. However, in a large population, multiple beneficial mutants can emerge before any of them fixes in the population. Competition between mutants is known as clonal interference, and while it is known to slow down the rate of adaptation (when compared to the strong-selection, weak-mutation model with the same parameters), how it affects the shape of long-term fitness trajectories in the presence of epistasis is an open question. Here, by considering how changes in fixation probabilities arising from weak clonal interference affect the dynamics of adaptation on fitness-parameterized landscapes, we find that the change in the shape of fitness trajectory arises only through changes in the supply of beneficial mutations (or equivalently, the beneficial mutation rate). Furthermore, a depletion of beneficial mutations as a population climbs up the fitness landscape can speed up the rescaled fitness trajectory (where adaptation speed is measured relative to its value at the start of the experiment), while an enhancement of the beneficial mutation rate does the opposite of slowing it down. Our findings suggest that by carrying out evolution experiments in both regimes (with and without clonal interference), one could potentially distinguish the different sources of macroscopic epistasis (fitness effect of mutations vs change in fraction of beneficial mutations).

Dynamics of Proteins and Macromolecular Machines in Escherichia coli

Proteins are major contributors to the composition and the functions in the cell. They often assemble into larger structures, macromolecular machines, to carry out intricate essential functions. Although huge progress in understanding how macromolecular machines function has been made by reconstituting them in vitro, the role of the intracellular environment is still emerging. The development of fluorescence microscopy techniques in the last 2 decades has allowed us to obtain an increased understanding of proteins and macromolecular machines in cells. Here, we describe how proteins move by diffusion, how they search for their targets, and how they are affected by the intracellular environment. We also describe how proteins assemble into macromolecular machines and provide examples of how frequent subunit turnover is used for them to function and to respond to changes in the intracellular conditions. This review emphasizes the constant movement of molecules in cells, the stochastic nature of reactions, and the dynamic nature of macromolecular machines.

Cellular heterogeneity in DNA alkylation repair increases population genetic plasticity

DNA repair mechanisms fulfil a dual role, as they are essential for cell survival and genome maintenance. Here, we studied how cells regulate the interplay between DNA repair and mutation. We focused on the adaptive response that increases the resistance of Escherichia coli cells to DNA alkylation damage. Combination of single-molecule imaging and microfluidic-based single-cell microscopy showed that noise in the gene activation timing of the master regulator Ada is accurately propagated to generate a distinct subpopulation of cells in which all proteins of the adaptive response are essentially absent. Whereas genetic deletion of these proteins causes extreme sensitivity to alkylation stress, a temporary lack of expression is tolerated and increases genetic plasticity of the whole population. We demonstrated this by monitoring the dynamics of nascent DNA mismatches during alkylation stress as well as the frequency of fixed mutations that are generated by the distinct subpopulations of the adaptive response. We propose that stochastic modulation of DNA repair capacity by the adaptive response creates a viable hypermutable subpopulation of cells that acts as a source of genetic diversity in a clonal population.

Single molecule/particle tracking analysis program SMTracker 2.0 reveals different dynamics of proteins within the RNA degradosome complex in Bacillus subtilis

Single-molecule (particle) tracking is a powerful method to study dynamic processes in cells at highest possible spatial and temporal resolution. We have developed SMTracker, a graphical user interface for automatic quantifying, visualizing and managing of data. Version 2.0 determines distributions of positional displacements in x- and y-direction using multi-state diffusion models, discriminates between Brownian, sub- or superdiffusive behaviour, and locates slow or fast diffusing populations in a standardized cell. Using SMTracker, we show that the Bacillus subtilis RNA degradosome consists of a highly dynamic complex of RNase Y and binding partners. We found similar changes in molecule dynamics for RNase Y, CshA, PNPase and enolase, but not for phosphofructokinase, RNase J1 and J2, to inhibition of transcription. However, the absence of PfkA or of RNase J2 affected molecule dynamics of RNase Y-mVenus, indicating that these two proteins are indeed part of the degradosome. Molecule counting suggests that RNase Y is present as a dimer in cells, at an average copy number of about 500, of which 46% are present in a slow-diffusive state and thus likely engaged within degradosomes. Thus, RNase Y, CshA, PNPase and enolase likely play central roles, and RNase J1, J2 and PfkA more peripheral roles, in degradosome architecture.

Transgenesis of mammalian PABP reveals mRNA polyadenylation as a general stress response mechanism in bacteria

In eukaryotes, mRNA 3′-polyadenylation triggers poly(A) binding protein (PABP) recruitment and stabilization. In a stark contrast, polyadenylation marks mRNAs for degradation in bacteria. To study this difference, we trans-express the mammalian nuclear PABPN1 chromosomally and extra-chromosomally in Escherichia coli. Expression of PABPN1 but not the mutant PABPN1 stabilizes polyadenylated mRNAs and improves their half-lives. In the presence of PABPN1, 3′-exonuclease PNPase is not detected on PA-tailed mRNAs compromising the degradation. We show that PABPN1 trans-expression phenocopies pcnB (that encodes poly(A) polymerase, PAPI) mutation and regulates plasmid copy number. Genome-wide RNA-seq analysis shows a general up-regulation of polyadenylated mRNAs on PABPN1 expression, the largest subset of which are those involved in general stress response. However, major global stress regulators are unaffected on PABPN1 expression. Concomitantly, PABPN1 expression or pcnB mutation imparts cellular tolerance to multiple stresses. This study establishes mRNA 3′-polyadenylation as a general stress response mechanism in E. coli.

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Trans expression of mammalian PABPN1 stabilizes polyadenyated mRNAs in E. coli

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PABPN1 expression phenocopies pcnB mutation and regulates plasmid copy number

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3′-polyadenylation acts as a general stress response mechanism in bacteria

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This study indicates an evolutionary significance of PABP in mRNA metabolism

Mutational sources of trans-regulatory variation affecting gene expression in Saccharomyces cerevisiae

Heritable variation in a gene’s expression arises from mutations impacting cis- and trans-acting components of its regulatory network. Here, we investigate how trans-regulatory mutations are distributed within the genome and within a gene regulatory network by identifying and characterizing 69 mutations with trans-regulatory effects on expression of the same focal gene in Saccharomyces cerevisiae. Relative to 1766 mutations without effects on expression of this focal gene, we found that these trans-regulatory mutations were enriched in coding sequences of transcription factors previously predicted to regulate expression of the focal gene. However, over 90% of the trans-regulatory mutations identified mapped to other types of genes involved in diverse biological processes including chromatin state, metabolism, and signal transduction. These data show how genetic changes in diverse types of genes can impact a gene’s expression in trans, revealing properties of trans-regulatory mutations that provide the raw material for trans-regulatory variation segregating within natural populations.

Waddington's Landscapes in the Bacterial World

Conrad Waddington’s epigenetic landscape, a visual metaphor for the development of multicellular organisms, is appropriate to depict the formation of phenotypic variants of bacterial cells. Examples of bacterial differentiation that result in morphological change have been known for decades. In addition, bacterial populations contain phenotypic cell variants that lack morphological change, and the advent of fluorescent protein technology and single-cell analysis has unveiled scores of examples. Cell-specific gene expression patterns can have a random origin or arise as a programmed event. When phenotypic cell-to-cell differences are heritable, bacterial lineages are formed. The mechanisms that transmit epigenetic states to daughter cells can have strikingly different levels of complexity, from the propagation of simple feedback loops to the formation of complex DNA methylation patterns. Game theory predicts that phenotypic heterogeneity can facilitate bacterial adaptation to hostile or unpredictable environments, serving either as a division of labor or as a bet hedging that anticipates future challenges. Experimental observation confirms the existence of both types of strategies in the bacterial world.

Genome-Wide Identification and Expression Analysis of SOS Response Genes in Salmonella enterica Serovar Typhimurium

A bioinformatic search for LexA boxes, combined with transcriptomic detection of loci responsive to DNA damage, identified 48 members of the SOS regulon in the genome of Salmonella enterica serovar Typhimurium. Single cell analysis using fluorescent fusions revealed that heterogeneous expression is a common trait of SOS response genes, with formation of SOS^OFF and SOS^ON subpopulations. Phenotypic cell variants formed in the absence of external DNA damage show gene expression patterns that are mainly determined by the position and the heterology index of the LexA box. SOS induction upon DNA damage produces SOS^OFF and SOS^ON subpopulations that contain live and dead cells. The nature and concentration of the DNA damaging agent and the time of exposure are major factors that influence the population structure upon SOS induction. An analogy can thus be drawn between the SOS response and other bacterial stress responses that produce phenotypic cell variants.

Challenges of analysing stochastic gene expression in bacteria using single-cell time-lapse experiments

Stochastic gene expression causes phenotypic heterogeneity in a population of genetically identical bacterial cells. Such non-genetic heterogeneity can have important consequences for the population fitness, and therefore cells implement regulation strategies to either suppress or exploit such heterogeneity to adapt to their circumstances. By employing time-lapse microscopy of single cells, the fluctuation dynamics of gene expression may be analysed, and their regulatory mechanisms thus deciphered. However, a careful consideration of the experimental design and data-analysis is needed to produce useful data for deriving meaningful insights from them. In the present paper, the individual steps and challenges involved in a time-lapse experiment are discussed, and a rigorous framework for designing, performing, and extracting single-cell gene expression dynamics data from such experiments is outlined.

Interplay between genetic, epigenetic, and gene expression variability: Considering complexity in evolvability

Genetic variability, epigenetic variability, and gene expression variability (noise) are generally considered independently in their relationship with phenotypic variation. However, they appear to be intrinsically interconnected and influence it in combination. The study of the interplay between genetic and epigenetic variability has the longest history. This article rather considers the introduction of gene expression variability in its relationships with the two others and reviews for the first time experimental evidences over the four relationships connected to gene expression noise. They show how introducing this third source of variability complicates the way of thinking evolvability and the emergence of biological novelty. Finally, cancer cells are proposed to be an ideal model to decipher the dynamic interplay between genetic, epigenetic, and gene expression variability when one of them is either experimentally increased or therapeutically targeted. This interplay is also discussed in an evolutionary perspective in the context of cancer cell drug resistance.

Pulses and delays, anticipation and memory: seeing bacterial stress responses from a single-cell perspective

Stress responses are crucial for bacteria to survive harmful conditions that they encounter in the environment. Although gene regulatory mechanisms underlying stress responses in bacteria have been thoroughly characterised for decades, recent advances in imaging technologies helped to uncover previously hidden dynamics and heterogeneity that become visible at the single-cell level. Despite the diversity of stress response mechanisms, certain dynamic regulatory features are frequently seen in single cells, such as pulses, delays, stress anticipation and memory effects. Often, these dynamics are highly variable across cells. While any individual cell may not achieve an optimal stress response, phenotypic diversity can provide a benefit at the population level. In this review, we highlight microscopy studies that offer novel insights into how bacteria sense stress, regulate protective mechanisms, cope with response delays and prepare for future environmental challenges. These studies showcase developments in the single-cell imaging toolbox including gene expression reporters, FRET, super-resolution microscopy and single-molecule tracking, as well as microfluidic techniques to manipulate cells and create defined stress conditions.

Transient non-specific DNA binding dominates the target search of bacterial DNA-binding proteins

Despite their diverse biochemical characteristics and functions, all DNA-binding proteins share the ability to accurately locate their target sites among the vast excess of non-target DNA. Toward identifying universal mechanisms of the target search, we used single-molecule tracking of 11 diverse DNA-binding proteins in living Escherichia coli. The mobility of these proteins during the target search was dictated by DNA interactions rather than by their molecular weights. By generating cells devoid of all chromosomal DNA, we discovered that the nucleoid is not a physical barrier for protein diffusion but significantly slows the motion of DNA-binding proteins through frequent short-lived DNA interactions. The representative DNA-binding proteins (irrespective of their size, concentration, or function) spend the majority (58%–99%) of their search time bound to DNA and occupy as much as ∼30% of the chromosomal DNA at any time. Chromosome crowding likely has important implications for the function of all DNA-binding proteins.

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Protein motion was compared between unperturbed cells and DNA-free cells

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Protein mobility was dictated by DNA interactions rather than molecular weight

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The nucleoid is not a physical barrier for protein diffusion

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The proteins studied spend most (58%–99%) of their search time bound to DNA

Bacterial phenotypic heterogeneity in DNA repair and mutagenesis

Genetically identical cells frequently exhibit striking heterogeneity in various phenotypic traits such as their morphology, growth rate, or gene expression. Such non-genetic diversity can help clonal bacterial populations overcome transient environmental challenges without compromising genome stability, while genetic change is required for long-term heritable adaptation. At the heart of the balance between genome stability and plasticity are the DNA repair pathways that shield DNA from lesions and reverse errors arising from the imperfect DNA replication machinery. In principle, phenotypic heterogeneity in the expression and activity of DNA repair pathways can modulate mutation rates in single cells and thus be a source of heritable genetic diversity, effectively reversing the genotype-to-phenotype dogma. Long-standing evidence for mutation rate heterogeneity comes from genetics experiments on cell populations, which are now complemented by direct measurements on individual living cells. These measurements are increasingly performed using fluorescence microscopy with a temporal and spatial resolution that enables localising, tracking, and counting proteins with single-molecule sensitivity. In this review, we discuss which molecular processes lead to phenotypic heterogeneity in DNA repair and consider the potential consequences on genome stability and dynamics in bacteria. We further inspect these concepts in the context of DNA damage and mutation induced by antibiotics.

Subpopulations of sensorless bacteria drive fitness in fluctuating environments

Populations of bacteria often undergo a lag in growth when switching conditions. Because growth lags can be large compared to typical doubling times, variations in growth lag are an important but often overlooked component of bacterial fitness in fluctuating environments. We here explore how growth lag variation is determined for the archetypical switch from glucose to lactose as a carbon source in Escherichia coli. First, we show that single-cell lags are bimodally distributed and controlled by a single-molecule trigger. That is, gene expression noise causes the population before the switch to divide into subpopulations with zero and nonzero lac operon expression. While "sensorless" cells with zero preexisting lac expression at the switch have long lags because they are unable to sense the lactose signal, any nonzero lac operon expression suffices to ensure a short lag. Second, we show that the growth lag at the population level depends crucially on the fraction of sensorless cells and that this fraction in turn depends sensitively on the growth condition before the switch. Consequently, even small changes in basal expression can significantly affect the fraction of sensorless cells, thereby population lags and fitness under switching conditions, and may thus be subject to significant natural selection. Indeed, we show that condition-dependent population lags vary across wild E. coli isolates. Since many sensory genes are naturally low expressed in conditions where their inducer is not present, bimodal responses due to subpopulations of sensorless cells may be a general mechanism inducing phenotypic heterogeneity and controlling population lags in switching environments. This mechanism also illustrates how gene expression noise can turn even a simple sensory gene circuit into a bet hedging module and underlines the profound role of gene expression noise in regulatory responses.

Bacterial Vivisection: How Fluorescence-Based Imaging Techniques Shed a Light on the Inner Workings of Bacteria

The rise in fluorescence-based imaging techniques over the past 3 decades has improved the ability of researchers to scrutinize live cell biology at increased spatial and temporal resolution. In microbiology, these real-time vivisections structurally changed the view on the bacterial cell away from the "watery bag of enzymes" paradigm toward the perspective that these organisms are as complex as their eukaryotic counterparts. Capitalizing on the enormous potential of (time-lapse) fluorescence microscopy and the ever-extending pallet of corresponding probes, initial breakthroughs were made in unraveling the localization of proteins and monitoring real-time gene expression. However, later it became clear that the potential of this technique extends much further, paving the way for a focus-shift from observing single events within bacterial cells or populations to obtaining a more global picture at the intra- and intercellular level. In this review, we outline the current state of the art in fluorescence-based vivisection of bacteria and provide an overview of important case studies to exemplify how to use or combine different strategies to gain detailed information on the cell's physiology. The manuscript therefore consists of two separate (but interconnected) parts that can be read and consulted individually. The first part focuses on the fluorescent probe pallet and provides a perspective on modern methodologies for microscopy using these tools. The second section of the review takes the reader on a tour through the bacterial cell from cytoplasm to outer shell, describing strategies and methods to highlight architectural features and overall dynamics within cells.

Redefining fundamental concepts of transcription initiation in bacteria

Despite enormous progress in understanding the fundamentals of bacterial gene regulation, our knowledge remains limited when compared with the number of bacterial genomes and regulatory systems to be discovered. Derived from a small number of initial studies, classic definitions for concepts of gene regulation have evolved as the number of characterized promoters has increased. Together with discoveries made using new technologies, this knowledge has led to revised generalizations and principles. In this Expert Recommendation, we suggest precise, updated definitions that support a logical, consistent conceptual framework of bacterial gene regulation, focusing on transcription initiation. The resulting concepts can be formalized by ontologies for computational modelling, laying the foundation for improved bioinformatics tools, knowledge-based resources and scientific communication. Thus, this work will help researchers construct better predictive models, with different formalisms, that will be useful in engineering, synthetic biology, microbiology and genetics.

Functional roles of microbial cell-to-cell heterogeneity and emerging technologies for analysis and control

Clonal cell populations often display significant cell-to-cell phenotypic heterogeneity, even when maintained under constant external conditions. This variability can result from the inherently stochastic nature of transcription and translation processes, which leads to varying numbers of transcripts and proteins per cell. Here, we showcase studies that reveal links between stochastic cellular events and biological functions in isogenic microbial populations. Then, we highlight emerging tools from engineering, computation, and synthetic and molecular biology that enable precise measurement, control, and analysis of gene expression noise in microorganisms. The capabilities offered by this sophisticated toolbox will shape future directions in the field and generate insight into the behavior of living systems at the single-cell level.

SIR2 Expression Noise Can Generate Heterogeneity in Viability but Does Not Affect Cell-to-Cell Epigenetic Silencing of Subtelomeric URA3 in Yeast

Chromatin structure clearly modulates gene expression noise, but the reverse influence has never been investigated, namely how the cell-to-cell expression heterogeneity of chromatin modifiers may generate variable rates of epigenetic modification. Sir2 is a well-characterized histone deacetylase of the Sirtuin family. It strongly influences chromatin silencing, especially at telomeres, subtelomeres and rDNA. This ability to influence epigenetic landscapes makes it a good model to study the largely unexplored interplay between gene expression noise and other epigenetic processes leading to phenotypic diversification. Here, we addressed this question by investigating whether noise in the expression of SIR2 was associated with cell-to-cell heterogeneity in the frequency of epigenetic silencing at subtelomeres in Saccharomyces cerevisiae Using cell sorting to isolate subpopulations with various expression levels, we found that heterogeneity in the cellular concentration of Sir2 does not lead to heterogeneity in the epigenetic silencing of subtelomeric URA3 between these subpopulations. We also noticed that SIR2 expression noise can generate cell-to-cell variability in viability, with lower levels being associated with better viability. This work shows that SIR2 expression fluctuations are not sufficient to generate cell-to-cell heterogeneity in the epigenetic silencing of URA3 at subtelomeres in Saccharomyces cerevisiae but can strongly affect cellular viability.

Visualizing mutagenic repair: novel insights into bacterial translesion synthesis

DNA repair is essential for cell survival. In all domains of life, error-prone and error-free repair pathways ensure maintenance of genome integrity under stress. Mutagenic, low-fidelity repair mechanisms help avoid potential lethality associated with unrepaired damage, thus making them important for genome maintenance and, in some cases, the preferred mode of repair. However, cells carefully regulate pathway choice to restrict activity of these pathways to only certain conditions. One such repair mechanism is translesion synthesis (TLS), where a low-fidelity DNA polymerase is employed to synthesize across a lesion. In bacteria, TLS is a potent source of stress-induced mutagenesis, with potential implications in cellular adaptation as well as antibiotic resistance. Extensive genetic and biochemical studies, predominantly in Escherichia coli, have established a central role for TLS in bypassing bulky DNA lesions associated with ongoing replication, either at or behind the replication fork. More recently, imaging-based approaches have been applied to understand the molecular mechanisms of TLS and how its function is regulated. Together, these studies have highlighted replication-independent roles for TLS as well. In this review, we discuss the current status of research on bacterial TLS, with emphasis on recent insights gained mostly through microscopy at the single-cell and single-molecule level.

For the Greater (Bacterial) Good: Heterogeneous Expression of Energetically Costly Virulence Factors

Bacterial populations are phenotypically heterogeneous, which allows subsets of cells to survive and thrive following changes in environmental conditions. For bacterial pathogens, changes within the host environment occur over the course of the immune response to infection and can result in exposure to host-derived, secreted antimicrobials or force direct interactions with immune cells. Many recent studies have shown host cell interactions promote virulence factor expression, forcing subsets of bacterial cells to battle the host response, while other bacteria reap the benefits of this pacification. It still remains unclear whether virulence factor expression is truly energetically costly within host tissues and whether expression is sufficient to impact the growth kinetics of virulence factor-expressing cells. However, it is clear that slow-growing subsets of bacteria emerge during infection and that these subsets are particularly difficult to eliminate with antibiotics. This minireview will focus on our current understanding of heterogenous virulence factor expression and discuss the evidence that supports or refutes the hypothesis that virulence factor expression is linked to slowed growth and antibiotic tolerance.

Absolutely robust controllers for chemical reaction networks

In this work, we design a type of controller that consists of adding a specific set of reactions to an existing mass-action chemical reaction network in order to control a target species. This set of reactions is effective for both deterministic and stochastic networks, in the latter case controlling the mean as well as the variance of the target species. We employ a type of network property called absolute concentration robustness (ACR). We provide applications to the control of a multisite phosphorylation model as well as a receptor-ligand signalling system. For this framework, we use the so-called deficiency zero theorem from chemical reaction network theory as well as multiscaling model reduction methods. We show that the target species has approximately Poisson distribution with the desired mean. We further show that ACR controllers can bring robust perfect adaptation to a target species and are complementary to a recently introduced antithetic feedback controller used for stochastic chemical reactions.

The Beacon Calculus: A formal method for the flexible and concise modelling of biological systems

Biological systems are made up of components that change their actions (and interactions) over time and coordinate with other components nearby. Together with a large state space, the complexity of this behaviour can make it difficult to create concise mathematical models that can be easily extended or modified. This paper introduces the Beacon Calculus, a process algebra designed to simplify the task of modelling interacting biological components. Its breadth is demonstrated by creating models of DNA replication dynamics, the gene expression dynamics in response to DNA methylation damage, and a multisite phosphorylation switch. The flexibility of these models is shown by adapting the DNA replication model to further include two topics of interest from the literature: cooperative origin firing and replication fork barriers. The Beacon Calculus is supported with the open-source simulator bcs (https://github.com/MBoemo/bcs.git) to allow users to develop and simulate their own models.

Simulating a model of a biological system can suggest ideas for future experiments and help ensure that conclusions about a mechanism are consistent with data. The Beacon Calculus is a new language that makes modelling simple by allowing users to simulate a biological system in only a few lines of code. This simplicity is critical as it allows users the freedom to come up with new ideas and rapidly test them. Models written in the Beacon Calculus are also easy to modify and extend, allowing users to add new features to the model or incorporate it into a larger biological system. We demonstrate the breadth of applications in this paper by applying the Beacon Calculus to DNA replication and DNA damage repair, both of which have implications for genome stability and cancer. We also apply it to multisite phosphorylation, which is important for cellular signalling. To enable users to create their own models, we created the open-source Beacon Calculus simulator bcs (https://github.com/MBoemo/bcs.git) which is easy to install and is well-supported by documentation and examples.

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.

Mutation Rate Heterogeneity Increases Odds of Survival in Unpredictable Environments

Mutation rates affect both a population's present fitness and its capacity to adapt to future environmental changes. When the available genetic variability limits adaptation to environmental change, natural selection favors high mutations rates. However, constitutively high mutation rates compromise the fitness of a population in stable environments. This problem may be resolved if an increase in mutation rates is limited to times of stress, restricted to some genomic regions, and occurs only in a subpopulation of cells. Such within-population heterogeneity of mutation rates can result from genetic, environmental, and stochastic effects. The presence of subpopulations of transient mutator cells does not jeopardize the overall fitness of a population under stable environmental conditions. However, they can increase the odds of survival in changing environments because they represent reservoirs of increased genetic variability. This article presents evidence that such heterogeneity of mutation rates is more the norm than the exception.