Rutger Hermsen

The Innate Growth Bistability and Fitness Landscapes of Antibiotic-Resistant Bacteria

Introduction Understanding how bacteria harboring antibiotic resistance grow in the presence of antibiotics is critical for predicting the spread and evolution of drug resistance. Because drugs inhibit cell growth and a cell’s growth state globally influences its gene expression, the expression of drug resistance is subject to an innate, growth-mediated feedback, leading to complex behaviors that affect both the characterization and the prevention of antibiotic resistance. We characterized the consequences of this feedback for the growth of antibiotic-resistant bacteria. Fitness landscape and growth bistability. (A) This fitness landscape describes the fitness, or growth rates, of bacterial strains exposed to antibiotics (colored lines indicate the fitness of four example strains). Fitness drops abruptly at high drug concentrations. The shaded area shows a broad region of growth bistability, throughout which we observe that genetically identical cells possessing drug resistance are split into subpopulations of growing and nongrowing cells in response to antibiotics (B, top). Methods We studied the growth of Escherichia coli strains expressing resistance to translation-inhibiting antibiotics, by using both bulk and single-cell techniques. The growth of each strain was quantified in a broad range of drug concentrations by using time-lapse microscopy (to track the responses of individual cells to antibiotics inside a microfluidic chemostat) and by the enrichment of batch cultures for nongrowing cells. We formulated a quantitative phenomenological model to predict the growth rates of drug-resistant strains in the presence of drugs, based on the well-characterized biochemistry of drug and drug-resistance interactions and on bacterial growth laws that dictate relations between cell growth and gene expression. We tested the model predictions for various drugs and resistance mechanisms by constructing strains that constitutively express varying degrees of drug resistance. Results In strains expressing a moderate degree of drug resistance, growth rates dropped abruptly above a critical drug concentration, the minimum inhibitory concentration (MIC), whose value increased linearly with the basal level of resistance expression (see figure below, panel A). Cells exhibited growth bistability over a broad range of drug concentrations below the MIC: Isogenic cells expressing drug resistance coexisted in growing and nongrowing states in a homogeneous environment (panel B). Our model accurately predicted the range of drug concentrations in which growth bistability occurred, as well as the growth rates of the growing subpopulation, without any ad hoc fitting parameters. These findings reveal a plateau-like fitness landscape (panel A), which can be used to study the evolution of drug resistance in environments with varying drug concentrations. Discussion The broad occurrence of growth bistability in drug-resistant bacteria challenges the common notions and measures of drug efficacy and resistance. And because growth bistability can arise without complex regulation when gene expression is coupled to the state of cell growth, similar physiological links may underlie the growth bistability implicated in causing bacterial persistence. The availability of quantitative, predictive models will facilitate the formulation of strategies to limit the efficacy and evolvability of drug resistance. Keeping Quiet Many bacteria overcome antibiotic treatment by expressing proteins that confer antibiotic resistance, for instance, efflux pumps. But when a strain that expresses these antibiotic resistance proteins encounters an environment containing the corresponding drug, the resistance against the drug may paradoxically become silenced in many cells. In this case, a fraction of a population of genetically identical cells will grow in the presence of antibiotics while other subpopulations fail to grow at all. Deris et al. (10.1126/science.1237435) show that this bistable response arises from a built-in global feedback originating in antibiotic-mediated inhibition of growth, which reduces the expression of proteins that protect against growth inhibition. The resulting populations of dormant cells can exceed 50%, among otherwise identical resistance-expressing cells. This is important for antimicrobial treatment strategies because many bacterial cells may remain vulnerable to an antibiotic even when they apparently display strong resistance to it. Identical bacteria can have low-level resistance to low concentrations of drugs that can flip subpopulations into dormancy. To predict the emergence of antibiotic resistance, quantitative relations must be established between the fitness of drug-resistant organisms and the molecular mechanisms conferring resistance. These relations are often unknown and may depend on the state of bacterial growth. To bridge this gap, we have investigated Escherichia coli strains expressing resistance to translation-inhibiting antibiotics. We show that resistance expression and drug inhibition are linked in a positive feedback loop arising from an innate, global effect of drug-inhibited growth on gene expression. A quantitative model of bacterial growth based on this innate feedback accurately predicts the rich phenomena observed: a plateau-shaped fitness landscape, with an abrupt drop in the growth rates of cultures at a threshold drug concentration, and the coexistence of growing and nongrowing populations, that is, growth bistability, below the threshold.

Transcriptional Regulation by Competing Transcription Factor Modules

Gene regulatory networks lie at the heart of cellular computation. In these networks, intracellular and extracellular signals are integrated by transcription factors, which control the expression of transcription units by binding to cis-regulatory regions on the DNA. The designs of both eukaryotic and prokaryotic cis-regulatory regions are usually highly complex. They frequently consist of both repetitive and overlapping transcription factor binding sites. To unravel the design principles of these promoter architectures, we have designed in silico prokaryotic transcriptional logic gates with predefined input–output relations using an evolutionary algorithm. The resulting cis-regulatory designs are often composed of modules that consist of tandem arrays of binding sites to which the transcription factors bind cooperatively. Moreover, these modules often overlap with each other, leading to competition between them. Our analysis thus identifies a new signal integration motif that is based upon the interplay between intramodular cooperativity and intermodular competition. We show that this signal integration mechanism drastically enhances the capacity of cis-regulatory domains to integrate signals. Our results provide a possible explanation for the complexity of promoter architectures and could be used for the rational design of synthetic gene circuits.

On the rapidity of antibiotic resistance evolution facilitated by a concentration gradient

The rapid emergence of bacterial strains resistant to multiple antibiotics is posing a growing public health risk. The mechanisms underlying the rapid evolution of drug resistance are, however, poorly understood. The heterogeneity of the environments in which bacteria encounter antibiotic drugs could play an important role. E.g., in the highly compartmentalized human body, drug levels can vary substantially between different organs and tissues. It has been proposed that this could facilitate the selection of resistant mutants, and recent experiments support this. To study the role of spatial heterogeneity in the evolution of drug resistance, we present a quantitative model describing an environment subdivided into relatively isolated compartments with various antibiotic concentrations, in which bacteria evolve under the stochastic processes of proliferation, migration, mutation and death. Analytical and numerical results demonstrate that concentration gradients can foster a mode of adaptation that is impossible in uniform environments. It allows resistant mutants to evade competition and circumvent the slow process of fixation by invading compartments with higher drug concentrations, where less resistant strains cannot subsist. The speed of this process increases sharply with the sensitivity of the growth rate to the antibiotic concentration, which we argue to be generic. Comparable adaptation rates in uniform environments would require a high selection coefficient (s > 0.1) for each forward mutation. Similar processes can occur if the heterogeneity is more complex than just a linear gradient. The model may also be applicable to other adaptive processes involving environmental heterogeneity and range expansion.

A growth-rate composition formula for the growth of E.coli on co-utilized carbon substrates

When bacteria are cultured in medium with multiple carbon substrates, they frequently consume these substrates simultaneously. Building on recent advances in the understanding of metabolic coordination exhibited by Escherichia coli cells through cAMP‐Crp signaling, we show that this signaling system responds to the total carbon‐uptake flux when substrates are co‐utilized and derive a mathematical formula that accurately predicts the resulting growth rate, based only on the growth rates on individual substrates.

Combinatorial Gene Regulation Using Auto-Regulation

As many as 59% of the transcription factors in Escherichia coli regulate the transcription rate of their own genes. This suggests that auto-regulation has one or more important functions. Here, one possible function is studied. Often the transcription rate of an auto-regulator is also controlled by additional transcription factors. In these cases, the way the expression of the auto-regulator responds to changes in the concentrations of the “input” regulators (the response function) is obviously affected by the auto-regulation. We suggest that, conversely, auto-regulation may be used to optimize this response function. To test this hypothesis, we use an evolutionary algorithm and a chemical–physical model of transcription regulation to design model cis-regulatory constructs with predefined response functions. In these simulations, auto-regulation can evolve if this provides a functional benefit. When selecting for a series of elementary response functions—Boolean logic gates and linear responses—the cis-regulatory regions resulting from the simulations indeed often exploit auto-regulation. Surprisingly, the resulting constructs use auto-activation rather than auto-repression. Several design principles show up repeatedly in the simulation results. They demonstrate how auto-activation can be used to generate sharp, switch-like activation and repression circuits and how linearly decreasing response functions can be obtained. Auto-repression, on the other hand, resulted only when a high response speed or a suppression of intrinsic noise was also selected for. The results suggest that, while auto-repression may primarily be valuable to improve the dynamical properties of regulatory circuits, auto-activation is likely to evolve even when selection acts on the shape of response function only.

Speed, sensitivity, and bistability in auto-activating signaling circuits.

Cells employ a myriad of signaling circuits to detect environmental signals and drive specific gene expression responses. A common motif in these circuits is inducible auto-activation: a transcription factor that activates its own transcription upon activation by a ligand or by post-transcriptional modification. Examples range from the two-component signaling systems in bacteria and plants to the genetic circuits of animal viruses such as HIV. We here present a theoretical study of such circuits, based on analytical calculations, numerical computations, and simulation. Our results reveal several surprising characteristics. They show that auto-activation can drastically enhance the sensitivity of the circuits response to input signals: even without molecular cooperativity, an ultra-sensitive threshold response can be obtained. However, the increased sensitivity comes at a cost: auto-activation tends to severely slow down the speed of induction, a stochastic effect that was strongly underestimated by earlier deterministic models. This slow-induction effect again requires no molecular cooperativity and is intimately related to the bimodality recently observed in non-cooperative auto-activation circuits. These phenomena pose strong constraints on the use of auto-activation in signaling networks. To achieve both a high sensitivity and a rapid induction, an inducible auto-activation circuit is predicted to acquire low cooperativity and low fold-induction. Examples from Escherichia colis two-component signaling systems support these predictions.

Chance and necessity in chromosomal gene distributions

By analyzing the spacing of genes on chromosomes, we find that transcriptional and RNA-processing regulatory sequences outside coding regions leave footprints on the distribution of intergenic distances. Using analogies between genes on chromosomes and one-dimensional gases, we constructed a statistical null model. We used this to estimate typical upstream and downstream regulatory sequence sizes in various species. Deviations from this model reveal bi-directional transcriptional regulatory regions in Saccharomyces cerevisiae and bi-directional terminators in Escherichia coli.

The adaptation rate of a quantitative trait in an environmental gradient

The spatial range of a species habitat is generally determined by the ability of the species to cope with biotic and abiotic variables that vary in space. Therefore, the species range is itself an evolvable property. Indeed, environmental gradients permit a mode of evolution in which range expansion and adaptation go hand in hand. This process can contribute to rapid evolution of drug resistant bacteria and viruses, because drug concentrations in humans and livestock treated with antibiotics are far from uniform. Here, we use a minimal stochastic model of discrete, interacting organisms evolving in continuous space to study how the rate of adaptation of a quantitative trait depends on the steepness of the gradient and various population parameters. We discuss analytical results for the mean-field limit as well as extensive stochastic simulations. These simulations were performed using an exact, event-driven simulation scheme that can deal with continuous time-, density- and coordinate-dependent reaction rates and could be used for a wide variety of stochastic systems. The results reveal two qualitative regimes. If the gradient is shallow, the rate of adaptation is limited by dispersion and increases linearly with the gradient slope. If the gradient is steep, the adaptation rate is limited by mutation. In this regime, the mean-field result is highly misleading: it predicts that the adaptation rate continues to increase with the gradient slope, whereas stochastic simulations show that it in fact decreases with the square root of the slope. This discrepancy underscores the importance of discreteness and stochasticity even at high population densities; mean-field results, including those routinely used in quantitative genetics, should be interpreted with care.