AbstractUnderstanding and characterising biochemical processes inside single cells requires experimental platforms that allow one to perturb and observe the dynamics of such processes as well as computational methods to build and parameterise models from the collected data. Recent progress with experimental platforms and optogenetics has made it possible to expose each cell in an experiment to an individualised input and automatically record cellular responses over days with fine time resolution. However, methods to infer parameters of stochastic kinetic models from single-cell longitudinal data have generally been developed under the assumption that experimental data is sparse and that responses of cells to at most a few different input perturbations can be observed. Here, we investigate and compare different approaches for calculating parameter likelihoods of single-cell longitudinal data based on approximations of the chemical master equation (CME) with a particular focus on coupling the linear noise approximation (LNA) or moment closure methods to a Kalman filter. We show that, as long as cells are measured sufficiently frequently, coupling the LNA to a Kalman filter allows one to accurately approximate likelihoods and to infer model parameters from data even in cases where the LNA provides poor approximations of the CME. Furthermore, the computational cost of filtering-based iterative likelihood evaluation scales advantageously in the number of measurement times and different input perturbations and is thus ideally suited for data obtained from modern experimental platforms. To demonstrate the practical usefulness of these results, we perform an experiment in which single cells, equipped with an optogenetic gene expression system, are exposed to various different light-input sequences and measured at several hundred time points and use parameter inference based on iterative likelihood evaluation to parameterise a stochastic model of the system.Author summaryA common result for the modelling of cellular processes is that available data is not sufficiently rich to uniquely determine the biological mechanism or even just to ensure identifiability of parameters of a given model. Perturbing cellular processes with informative input stimuli and measuring dynamical responses may alleviate this problem. With the development of novel experimental platforms, we are now in a position to parallelise such perturbation experiments at the single cell level. This raises a plethora of new questions. Is it more informative to diversify input perturbations but to observe only few cells for each input or should we rather ensure that many cells are observed for only few inputs? How can we calculate likelihoods and infer parameters of stochastic kinetic models from data sets in which each cell receives a different input perturbation? How does the computational efficiency of parameter inference methods scale with the number of inputs and the number of measurement times? Are there approaches that are particularly well-suited for such data sets? in this paper, we investigate these questions using the CcaS/CcaR optogenetic system driving the expression of a fluorescent reporter protein as primary case study.

Understanding and characterising biochemical processes inside single cells requires experimental platforms that allow one to perturb and observe the dynamics of such processes as well as computational methods to build and parameterise models from the collected data. Recent progress with experimental platforms and optogenetics has made it possible to expose each cell in an experiment to an individualised input and automatically record cellular responses over days with fine time resolution. However, methods to infer parameters of stochastic kinetic models from single-cell longitudinal data have generally been developed under the assumption that experimental data is sparse and that responses of cells to at most a few different input perturbations can be observed. Here, we investigate and compare different approaches for calculating parameter likelihoods of single-cell longitudinal data based on approximations of the chemical master equation (CME) with a particular focus on coupling the linear noise approximation (LNA) or moment closure methods to a Kalman filter. We show that, as long as cells are measured sufficiently frequently, coupling the LNA to a Kalman filter allows one to accurately approximate likelihoods and to infer model parameters from data even in cases where the LNA provides poor approximations of the CME. Furthermore, the computational cost of filtering-based iterative likelihood evaluation scales advantageously in the number of measurement times and different input perturbations and is thus ideally suited for data obtained from modern experimental platforms. To demonstrate the practical usefulness of these results, we perform an experiment in which single cells, equipped with an optogenetic gene expression system, are exposed to various different light-input sequences and measured at several hundred time points and use parameter inference based on iterative likelihood evaluation to parameterise a stochastic model of the system.

Bacteria regulate genes to survive antibiotic stress, but regulation can be far from perfect. When regulation is not optimal, mutations that change gene expression can contribute to antibiotic resistance. It is not systematically understood to what extent natural gene regulation is or is not optimal for distinct antibiotics, and how changes in expression of specific genes quantitatively affect antibiotic resistance. Here we discover a simple quantitative relation between fitness, gene expression, and antibiotic potency, which rationalizes our observation that a multitude of genes and even innate antibiotic defense mechanisms have expression that is critically nonoptimal under antibiotic treatment. First, we developed a pooled-strain drug-diffusion assay and screened Escherichia coli overexpression and knockout libraries, finding that resistance to a range of 31 antibiotics could result from changing expression of a large and functionally diverse set of genes, in a primarily but not exclusively drug-specific manner. Second, by synthetically controlling the expression of single-drug and multidrug resistance genes, we observed that their fitness-expression functions changed dramatically under antibiotic treatment in accordance with a log-sensitivity relation. Thus, because many genes are nonoptimally expressed under antibiotic treatment, many regulatory mutations can contribute to resistance by altering expression and by activating latent defenses.

Bacteria in groups vary individually, and interact with other bacteria and the environment to produce population-level patterns of gene expression. Investigating such behavior in detail requires measuring and controlling populations at the single-cell level alongside precisely specified interactions and environmental characteristics. Here we present an automated, programmable platform that combines image-based gene expression and growth measurements with on-line optogenetic expression control for hundreds of individual Escherichia coli cells over days, in a dynamically adjustable environment. This integrated platform broadly enables experiments that bridge individual and population behaviors. We demonstrate: (i) population structuring by independent closed-loop control of gene expression in many individual cells, (ii) cell-cell variation control during antibiotic perturbation, (iii) hybrid bio-digital circuits in single cells, and freely specifiable digital communication between individual bacteria. These examples showcase the potential for real-time integration of theoretical models with measurement and control of many individual cells to investigate and engineer microbial population behavior.

We developed a competition-based screening strategy to identify compounds that invert the selective advantage of antibiotic resistance. Using our assay, we screened over 19,000 compounds for the ability to select against the TetA tetracycline-resistance efflux pump in Escherichia coli and identified two hits, β-thujaplicin and disulfiram. Treating a tetracycline-resistant population with β-thujaplicin selects for loss of the resistance gene, enabling an effective second-phase treatment with doxycycline.

Antibiotic-sensitive and -resistant bacteria coexist in natural environments with low, if detectable, antibiotic concentrations. Except possibly around localized antibiotic sources, where resistance can provide a strong advantage, bacterial fitness is dominated by stresses unaffected by resistance to the antibiotic. How do such mixed and heterogeneous conditions influence the selective advantage or disadvantage of antibiotic resistance? Here we find that sub-inhibitory levels of tetracyclines potentiate selection for or against tetracycline resistance around localized sources of almost any toxin or stress. Furthermore, certain stresses generate alternating rings of selection for and against resistance around a localized source of the antibiotic. In these conditions, localized antibiotic sources, even at high strengths, can actually produce a net selection against resistance to the antibiotic. Our results show that interactions between the effects of an antibiotic and other stresses in inhomogeneous environments can generate pervasive, complex patterns of selection both for and against antibiotic resistance.

A key aspect of bacterial survival is the ability to evolve while migrating across spatially varying environmental challenges. Laboratory experiments, however, often study evolution in well-mixed systems. Here, we introduce an experimental device, the microbial evolution and growth arena (MEGA)-plate, in which bacteria spread and evolved on a large antibiotic landscape (120 × 60 centimeters) that allowed visual observation of mutation and selection in a migrating bacterial front.While resistance increased consistently, multiple coexisting lineages diversified both phenotypically and genotypically. Analyzing mutants at and behind the propagating front,we found that evolution is not always led by the most resistant mutants; highly resistant mutants may be trapped behindmore sensitive lineages.TheMEGA-plate provides a versatile platformfor studying microbial adaption and directly visualizing evolutionary dynamics.

We present a protocol for building and operating an automated fluidic system for continuous culture that we call the 'morbidostat'. The morbidostat is used to follow the evolution of microbial drug resistance in real time. Instead of exposing bacteria to predetermined drug environments, the morbidostat constantly measures the growth rates of evolving microbial populations and dynamically adjusts drug concentrations inside culture vials in order to maintain a constant drug-induced inhibition. The growth rate measurements are done using an optical detection system that is based on measuring the intensity of back-scattered light from bacterial cells suspended in the liquid culture. The morbidostat can additionally be used as a chemostat or a turbidostat. The whole system can be built from readily available components within 2-3 weeks by biologists with some electronics experience or engineers familiar with basic microbiology. © 2013 Nature America, Inc. All rights reserved.

Exposure of an isogenic bacterial population to a cidal antibiotic typically fails to eliminate a small fraction of refractory cells. Historically, fractional killing has been attributed to infrequently dividing or nondividing "persisters." Using microfluidic cultures and time-lapse microscopy, we found that Mycobacterium smegmatis persists by dividing in the presence of the drug isoniazid (INH). Although persistence in these studies was characterized by stable numbers of cells, this apparent stability was actually a dynamic state of balanced division and death. Single cells expressed catalase-peroxidase (KatG), which activates INH, in stochastic pulses that were negatively correlated with cell survival. These behaviors may reflect epigenetic effects, because KatG pulsing and death were correlated between sibling cells. Selection of lineages characterized by infrequent KatG pulsing could allow nonresponsive adaptation during prolonged drug exposure.

Antibiotic resistance can evolve through the sequential accumulation of multiple mutations1. To study such gradual evolution, we developed a selection device, the 'morbidostat', that continuously monitors bacterial growth and dynamically regulates drug concentrations, such that the evolving population is constantly challenged 2-5. We analyzed the evolution of resistance in Escherichia coli under selection with single drugs, including chloramphenicol, doxycycline and trimethoprim. Over a period of ∼ 20 days, resistance levels increased dramatically, with parallel populations showing similar phenotypic trajectories. Whole-genome sequencing of the evolved strains identified mutations both specific to resistance to a particular drug and shared in resistance to multiple drugs. Chloramphenicol and doxycycline resistance evolved smoothly through diverse combinations of mutations in genes involved in translation, transcription and transport 3. In contrast, trimethoprim resistance evolved in a stepwise manner 1,6, through mutations restricted to the gene encoding the enzyme dihydrofolate reductase (DHFR) 7,8. Sequencing of DHFR over the time course of the experiment showed that parallel populations evolved similar mutations and acquired them in a similar order 9.

Antibiotics increase the frequency of resistant bacteria by providing them a competitive advantage over sensitive strains. Here, we develop a versatile assay for differential chemical inhibition of competing microbial strains, and use it to identify compounds that preferentially inhibit tetracycline-resistant relative to sensitive bacteria, thus "inverting" selection for resistance. Our assay distinguishes compounds selecting directly against specific resistance mechanisms and compounds whose selection against resistance is based on their physiological interaction with tetracycline and is more general with respect to resistance mechanism. We find that both types of selection-inverting compounds are secreted by soil microbes, indicating that nature has evolved a repertoire of chemicals that counteracts antibiotic resistance. Finally, we show that our assay can more generally permit simple, direct screening for drugs based on their differential activity against different strains or targets. © 2010 Chait et al.

The rapid proliferation of antibiotic-resistant pathogens has spurred the use of drug combinations to maintain clinical efficacy and combat the evolution of resistance. Drug pairs can interact synergistically or antagonistically, yielding inhibitory effects larger or smaller than expected from the drugs' individual potencies. Clinical strategies often favor synergistic interactions because they maximize the rate at which the infection is cleared from an individual, but it is unclear how such interactions affect the evolution of multi-drug resistance. We used a mathematical model of in vivo infection dynamics to determine the optimal treatment strategy for preventing the evolution of multi-drug resistance. We found that synergy has two conflicting effects: it clears the infection faster and thereby decreases the time during which resistant mutants can arise, but increases the selective advantage of these mutants over wild-type cells. When competition for resources is weak, the former effect is dominant and greater synergy more effectively prevents multi-drug resistance. However, under conditions of strong resource competition, a tradeoff emerges in which greater synergy increases the rate of infection clearance, but also increases the risk of multi-drug resistance. This tradeoff breaks down at a critical level of drug interaction, above which greater synergy has no effect on infection clearance, but still increases the risk of multi-drug resistance. These results suggest that the optimal strategy for suppressing multi-drug resistance is not always to maximize synergy, and that in some cases drug antagonism, despite its weaker efficacy, may better suppress the evolution of multi-drug resistance. © 2010 Torella et al.

Suppressive drug interactions, in which one antibiotic can actually help bacterial cells to grow faster in the presence of another, occur between protein and DNA synthesis inhibitors. Here, we show that this suppression results from nonoptimal regulation of ribosomal genes in the presence of DNA stress. Using GFP-tagged transcription reporters in Escherichia coli, we find that ribosomal genes are not directly regulated by DNA stress, leading to an imbalance between cellular DNA and protein content. To test whether ribosomal gene expression under DNA stress is nonoptimal for growth rate, we sequentially deleted up to six of the seven ribosomal RNA operons. These synthetic manipulations of ribosomal gene expression correct the protein-DNA imbalance, lead to improved survival and growth, and completely remove the suppressive drug interaction. A simple mathematical model explains the nonoptimal regulation in different nutrient environments. These results reveal the genetic mechanism underlying an important class of suppressive drug interactions. © 2009 Elsevier Inc. All rights reserved.

Antimicrobial treatments increasingly rely on multidrug combinations, in part because of the emergence and spread of antibiotic resistance. The continued effectiveness of combination treatments depends crucially on the frequency with which multidrug resistance arises. Yet, it is unknown how this propensity for resistance depends on cross-resistance and on epistatic interactions - ranging from synergy to antagonism - between the drugs. Here, we analyzed how interactions between pairs of drugs affect the spontaneous emergence of resistance in the medically important pathogen Staphylococcus aureus. Resistance is selected for within a window of drug concentrations high enough to inhibit wild-type growth but low enough for some resistant mutants to grow. Introducing an experimental method for high-throughput colony imaging, we counted resistant colonies arising across a two-dimensional matrix of drug concentrations for each of three drug pairs. Our data show that these different drug combinations have significantly different impacts on the size of the window of drug concentrations where resistance is selected for. We framed these results in a mathematical model in which the frequencies of resistance to single drugs, cross-resistance, and epistasis combine to determine the propensity for multidrug resistance. The theory suggests that drug pairs which interact synergistically, preferred for their immediate efficacy, may in fact favor the future evolution of resistance. This framework reveals the central role of drug epistasis in the evolution of resistance and points to new strategies for combating the emergence of drug-resistant bacteria. © 2008 by the National Academy of Sciences of the USA.

Multidrug combinations are increasingly important in combating the spread of antibiotic-resistance in bacterial pathogens. On a broader scale, such combinations are also important in understanding microbial ecology and evolution. Although the effects of multidrug combinations on bacterial growth have been studied extensively, relatively little is known about their impact on the differential selection between sensitive and resistant bacterial populations. Normally, the presence of a drug confers an advantage on its resistant mutants in competition with the sensitive wild-type population. Here we show, by using a direct competition assay between doxycycline-resistant and doxycycline-sensitive Escherichia coli, that this differential selection can be inverted in a hyper-antagonistic class of drug combinations. Used in such a combination, a drug can render the combined treatment selective against the drug's own resistance allele. Further, this inversion of selection seems largely insensitive to the underlying resistance mechanism and occurs, at sublethal concentrations, while maintaining inhibition of the wild type. These seemingly paradoxical results can be rationalized in terms of a simple geometric argument. Our findings demonstrate a previously unappreciated feature of the fitness landscape for the evolution of resistance and point to a trade-off between the effect of drug interactions on absolute potency and the relative competitive selection that they impose on emerging resistant populations. ©2007 Nature Publishing Group.

A fraction of a genetically homogeneous microbial population may survive exposure to stress such as antibiotic treatment. Unlike resistant mutants, cells regrown from such persistent bacteria remain sensitive to the antibiotic. We investigated the persistence of single cells of Escherichia coli with the use of microfluidic devices. Persistence was linked to preexisting heterogeneity in bacterial populations because phenotypic switching occurred between normally growing cells and persister cells having reduced growth rates. Quantitative measurements led to a simple mathematical description of the persistence switch. Inherent heterogeneity of bacterial populations may be important in adaptation to fluctuating environments and in the persistence of bacterial infections.