Dynamical model of antibiotic responses linking expression of resistance genes to metabolism explains emergence of heterogeneity during drug exposures.

Antibiotic responses in bacteria are highly dynamic and heterogeneous, with sudden exposure of bacterial colonies to high drug doses resulting in the coexistence of recovered and arrested cells. The dynamics of the response is determined by regulatory circuits controlling the expression of resistance genes, which are in turn modulated by the drug's action on cell growth and metabolism. Despite advances in understanding gene regulation at the molecular level, we still lack a framework to describe how feedback mechanisms resulting from the interdependence between expression of resistance and cell metabolism can amplify naturally occurring noise and create heterogeneity at the population level. To understand how this interplay affects cell survival upon exposure, we constructed a mathematical model of the dynamics of antibiotic responses that links metabolism and regulation of gene expression, based on the tetracycline resistancetetoperon inE. coli. We use this model to interpret measurements of growth and expression of resistance in microfluidic experiments, both in single cells and in biofilms. We also implemented a stochastic model of the drug response, to show that exposure to high drug levels results in large variations of recovery times and heterogeneity at the population level. We show that stochasticity is important to determine how nutrient quality affects cell survival during exposure to high drug concentrations. A quantitative description of how microbes respond to antibiotics in dynamical environments is crucial to understand population-level behaviors such as biofilms and pathogenesis.

Dynamical model of antibiotic responses linking expression of resistance to metabolism explains emergence of heterogeneity during drug exposures.

Antibiotic responses in bacteria are highly dynamic and heterogeneous, with sudden exposure of bacterial colonies to high drug doses resulting in the coexistence of recovered and arrested cells. The dynamics of the response is determined by regulatory circuits controlling the expression of resistance genes, which are in turn modulated by the drug's action on cell growth and metabolism. Despite advances in understanding gene regulation at the molecular level, we still lack a framework to describe how feedback mechanisms resulting from the interdependence between expression of resistance and cell metabolism can amplify naturally occurring noise and create heterogeneity at the population level. To understand how this interplay affects cell survival upon exposure, we constructed a mathematical model of the dynamics of antibiotic responses that links metabolism and regulation of gene expression, based on the tetracycline resistance tet operon in E. coli. We use this model to interpret measurements of growth and expression of resistance in microfluidic experiments, both in single cells and in biofilms. We also implemented a stochastic model of the drug response, to show that exposure to high drug levels results in large variations of recovery times and heterogeneity at the population level. We show that stochasticity is important to determine how nutrient quality affects cell survival during exposure to high drug concentrations. A quantitative description of how microbes respond to antibiotics in dynamical environments is crucial to understand population-level behaviors such as biofilms and pathogenesis.

Stress anisotropy in confined populations of growing rods.

A central feature of living matter is its ability to grow and multiply. The mechanical activity associated with growth produces both macroscopic flows shaped by confinement, and striking self-organization phenomena, such as orientational order and alignment, which are particularly prominent in populations of rod-shaped bacteria due to their nematic properties. However, how active stresses, passive mechanical interactions and flow-induced effects interact to give rise to the observed global alignment patterns remains elusive. Here, we study in silico colonies of growing rod-shaped particles of different aspect ratios confined in channel-like geometries. A spatially resolved analysis of the stress tensor reveals a strong relationship between near-perfect alignment and an inversion of stress anisotropy for particles with large length-to-width ratios. We show that, in quantitative agreement with an asymptotic theory, strong alignment can lead to a decoupling of active and passive stresses parallel and perpendicular to the direction of growth, respectively. We demonstrate the robustness of these effects in a geometry that provides less restrictive confinement and introduces natural perturbations in alignment. Our results illustrate the complexity arising from the inherent coupling between nematic order and active stresses in growing active matter, which is modulated by geometric and configurational constraints due to confinement.

Nutrient Gradients Mediate Complex Colony-Level Antibiotic Responses in Structured Microbial Populations.

Antibiotic treatments often fail to eliminate bacterial populations due to heterogeneity in how individual cells respond to the drug. In structured bacterial populations such as biofilms, bacterial metabolism and environmental transport processes lead to an emergent phenotypic structure and self-generated nutrient gradients toward the interior of the colony, which can affect cell growth, gene expression and susceptibility to the drug. Even in single cells, survival depends on a dynamic interplay between the drug's action and the expression of resistance genes. How expression of resistance is coordinated across populations in the presence of such spatiotemporal environmental coupling remains elusive. Using a custom microfluidic device, we observe the response of spatially extended microcolonies of tetracycline-resistant E. coli to precisely defined dynamic drug regimens. We find an intricate interplay between drug-induced changes in cell growth and growth-dependent expression of resistance genes, resulting in the redistribution of metabolites and the reorganization of growth patterns. This dynamic environmental feedback affects the regulation of drug resistance differently across the colony, generating dynamic phenotypic structures that maintain colony growth during exposure to high drug concentrations and increase population-level resistance to subsequent exposures. A mathematical model linking metabolism and the regulation of gene expression is able to capture the main features of spatiotemporal colony dynamics. Uncovering the fundamental principles that govern collective mechanisms of antibiotic resistance in spatially extended populations will allow the design of optimal drug regimens to counteract them.

Arrhythmia Mechanism and Dynamics in a Humanized Mouse Model of Inherited Cardiomyopathy Caused by Phospholamban R14del Mutation.

BACKGROUND: Arginine (Arg) 14 deletion (R14del) in the calcium regulatory protein phospholamban (hPLNR14del) has been identified as a disease-causing mutation in patients with an inherited cardiomyopathy. Mechanisms underlying the early arrhythmogenic phenotype that predisposes carriers of this mutation to sudden death with no apparent structural remodeling remain unclear. METHODS: To address this, we performed high spatiotemporal resolution optical mapping of intact hearts from adult knock-in mice harboring the human PLNWT (wildtype [WT], n=12) or the heterozygous human PLNR14del mutation (R14del, n=12) before and after ex vivo challenge with isoproterenol and rapid pacing. RESULTS: Adverse electrophysiological remodeling was evident in the absence of significant structural or hemodynamic changes. R14del hearts exhibited increased arrhythmia susceptibility compared with wildtype. Underlying this susceptibility was preferential right ventricular action potential prolongation that was unresponsive to ß-adrenergic stimulation. A steep repolarization gradient at the left ventricular/right ventricular interface provided the substrate for interventricular activation delays and ultimately local conduction block during rapid pacing. This was followed by the initiation of macroreentrant circuits supporting the onset of ventricular tachycardia. Once sustained, these circuits evolved into high-frequency rotors, which in their majority were pinned to the right ventricle. These rotors exhibited unique spatiotemporal dynamics that promoted their increased stability in R14del compared with wildtype hearts. CONCLUSIONS: Our findings highlight the crucial role of primary electric remodeling caused by the hPLNR14del mutation. These inherently arrhythmogenic features form the substrate for adrenergic-mediated VT at early stages of PLNR14del induced cardiomyopathy.

Local measures enable COVID-19 containment with fewer restrictions due to cooperative effects.

BACKGROUND: Many countries worldwide are faced with the choice between the (re)surgence of COVID-19 and endangering the economic and mental well-being of their citizens. While infection numbers are monitored and measures adjusted, a systematic strategy for balancing contact restrictions and socioeconomic life in the absence of a vaccine is currently lacking. METHODS: In a mathematical model, we determine the efficacy of regional containment strategies, where contact restrictions are triggered locally in individual regions upon crossing critical infection number thresholds. Our stochastic meta-population model distinguishes between contacts within a region and cross-regional contacts. We use current data on the spread of COVID-19 in Germany, Italy, England, New York State and Florida, including the effects of their individual national lockdowns, and county population sizes obtained from census data to define individual regions. As a performance measure, we determine the number of days citizens will experience contact restrictions over the next 5 years ('restriction time') and compare it to an equivalent national lockdown strategy. To extract crucial parameters, we vary the proportion of cross-regional contacts (between 0% and 100%), the thresholds for initiating local measures (between 5 and 20 active infections per 100,000 inhabitants) as well as their duration after infection numbers have returned below the threshold (between 7 and 28 days). We compare performance across the five different countries and test how further subdivision of large counties into independently controlled regions of up to 100,000 or 200,000 inhabitants affects the results. FINDINGS: Our numerical simulations show a substantially reduced restriction time for regional containment, if the effective reproduction number of SARS-CoV-2 without restrictions, R 0, is only slightly larger than 1 and the proportion of cross-regional contacts (the so-called leakiness) is low. In Germany, specifically, for R 0=1.14, a leakiness of 1% is sufficiently low to reduce the mean restriction time from 468 days (s.d. 3 days) for the national containment strategy to 43 days (s.d. 3 days across simulations) for the regional strategy, when local measures are initiated at 10 infections per 100,000 inhabitants in the past 7 days. For R 0=1.28, the allowed leakiness for minimal restriction time reduces to approximately 0.3%. The dependence of the restriction time on the leakiness is threshold-like only for regional containment, due to cooperative effects. It rises to levels similar to the national containment strategy for a leakiness > 10% (517 days national vs. 486 days regional for leakiness 32% and R 0=1.14). We find a strong correlation between the population size of each region and the experienced restriction time. For countries with large counties, this can result in only a mild reduction in restriction time for regional containment, which can only be partly compensated by lower thresholds for initiating local measures and increasing their duration. In contrast, further subdividing large counties into smaller units can ensure a strong reduction of the restriction time for the regional strategy. INTERPRETATION: The leakiness, i.e. the proportion of cross-regional contacts, and the regional structure itself were crucial parameters for the performance of the regional strategy. Therefore, regional strategies could offer an adaptive way to contain the epidemic with fewer overall restrictions, if cross-regional infections can be kept below the critical level, which could be achieved without affecting local socioeconomic freedom. Maintaining general hygiene and contact tracing, testing should be intensified to ensure regional measures can be initiated at low infection thresholds, preventing the spread of the disease to other regions before local elimination. While such tight control could lead to more restrictions in the short run, restrictions necessary for long-term containment could be reduced by up to a factor of 10. Our open-source simulation code is freely available and can be readily adapted to other countries. FUNDING: This work was supported by the Max Planck Society.

Stochastic effects on the dynamics of an epidemic due to population subdivision.

Using a stochastic susceptible-infected-removed meta-population model of disease transmission, we present analytical calculations and numerical simulations dissecting the interplay between stochasticity and the division of a population into mutually independent sub-populations. We show that subdivision activates two stochastic effects-extinction and desynchronization-diminishing the overall impact of the outbreak even when the total population has already left the stochastic regime and the basic reproduction number is not altered by the subdivision. Both effects are quantitatively captured by our theoretical estimates, allowing us to determine their individual contributions to the observed reduction of the peak of the epidemic.

Publisher's Note: Suppression of Beneficial Mutations in Dynamic Microbial Populations [Phys. Rev. Lett. 118, 028102 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.118.028102.

Genetically engineered control of phenotypic structure in microbial colonies.

Rapid advances in cellular engineering1,2 have positioned synthetic biology to address therapeutic3,4 and industrial5 problems, but a substantial obstacle is the myriad of unanticipated cellular responses in heterogeneous real-world environments such as the gut6,7, solid tumours8,9, bioreactors10 or soil11. Complex interactions between the environment and cells often arise through non-uniform nutrient availability, which generates bidirectional coupling as cells both adjust to and modify their local environment through phenotypic differentiation12,13. Although synthetic spatial gene expression patterns14-17 have been explored under homogeneous conditions, the mutual interaction of gene circuits, growth phenotype and the environment remains a challenge. Here, we design gene circuits that sense and control phenotypic structure in microcolonies containing both growing and dormant bacteria. We implement structure modulation by coupling different downstream modules to a tunable sensor that leverages Escherichia coli's stress response and is activated on growth arrest. One is an actuator module that slows growth and thereby alters nutrient gradients. Environmental feedback in this circuit generates robust cycling between growth and dormancy in the interior of the colony, as predicted by a spatiotemporal computational model. We also use the sensor to drive an inducible gating module for selective gene expression in non-dividing cells, which allows us to radically alter population structure by eliminating the dormant phenotype with a 'stress-gated lysis circuit'. Our results establish a strategy to leverage and control microbial colony structure for synthetic biology applications in complex environments.

Divergent Aging of Isogenic Yeast Cells Revealed through Single-Cell Phenotypic Dynamics.

Although genetic mutations that alter organisms' average lifespans have been identified in aging research, our understanding of the dynamic changes during aging remains limited. Here, we integrate single-cell imaging, microfluidics, and computational modeling to investigate phenotypic divergence and cellular heterogeneity during replicative aging of single S. cerevisiae cells. Specifically, we find that isogenic cells diverge early in life toward one of two aging paths, which are characterized by distinct age-associated phenotypes. We captured the dynamics of single cells along the paths with a stochastic discrete-state model, which accurately predicts both the measured heterogeneity and the lifespan of cells on each path within a cell population. Our analysis suggests that genetic and environmental factors influence both a cell's choice of paths and the kinetics of paths themselves. Given that these factors are highly conserved throughout eukaryotes, divergent aging might represent a general scheme in cellular aging of other organisms.

Rational engineering of synthetic microbial systems: from single cells to consortia.

One promise of synthetic biology is to provide solutions for biomedical and industrial problems by rational design of added functionality in living systems. Microbes are at the forefront of this biological engineering endeavor due to their general ease of handling and their relevance in many potential applications from fermentation to therapeutics. In recent years, the field has witnessed an explosion of novel regulatory tools, from synthetic orthogonal transcription factors to posttranslational mechanisms for increased control over the behavior of synthetic circuits. Tool development has been paralleled by the discovery of principles that enable increased modularity and the management of host-circuit interactions. Engineered cell-to-cell communication bridges the scales from intracellular to population-level coordination. These developments facilitate the translation of more than a decade of circuit design into applications.

Complex restitution behavior and reentry in a cardiac tissue model for neonatal mice.

Spatiotemporal dynamics in cardiac tissue emerging from the coupling of individual cardiomyocytes underlie the heart's normal rhythm as well as undesired and possibly life-threatening arrhythmias. While single cells and their transmembrane currents have been studied extensively, systematically investigating spatiotemporal dynamics is complicated by the nontrivial relationship between single-cell and emergent tissue properties. Mathematical models have been employed to bridge this gap and contribute to a deepened understanding of the onset, development, and termination of arrhythmias. However, no such tissue-level model currently exists for neonatal mice. Here, we build on a recent single-cell model of neonatal mouse cardiomyocytes by Wang and Sobie (Am. J. Physiol. Heart Circ. Physiol 294:H2565) to predict properties that are commonly used to gauge arrhythmogenicity of cardiac substrates. We modify the model to yield well-defined behavior for common experimental protocols and construct a spatially extended version to study emergent tissue dynamics. We find a complex action potential duration (APD) restitution behavior characterized by a nonmonotonic dependence on pacing frequency. Electrotonic coupling in tissue leads not only to changes in action potential morphology but can also induce spatially concordant and discordant alternans not observed in the single-cell model. In two-dimensional tissue, our results show that the model supports stable functional reentry, whose frequency is in good agreement with that observed in adult mice. Our results can be used to further constrain and validate the mathematical model of neonatal mouse cardiomyocytes with future experiments.

Multigenerational silencing dynamics control cell aging.

Cellular aging plays an important role in many diseases, such as cancers, metabolic syndromes, and neurodegenerative disorders. There has been steady progress in identifying aging-related factors such as reactive oxygen species and genomic instability, yet an emerging challenge is to reconcile the contributions of these factors with the fact that genetically identical cells can age at significantly different rates. Such complexity requires single-cell analyses designed to unravel the interplay of aging dynamics and cell-to-cell variability. Here we use microfluidic technologies to track the replicative aging of single yeast cells and reveal that the temporal patterns of heterochromatin silencing loss regulate cellular life span. We found that cells show sporadic waves of silencing loss in the heterochromatic ribosomal DNA during the early phases of aging, followed by sustained loss of silencing preceding cell death. Isogenic cells have different lengths of the early intermittent silencing phase that largely determine their final life spans. Combining computational modeling and experimental approaches, we found that the intermittent silencing dynamics is important for longevity and is dependent on the conserved Sir2 deacetylase, whereas either sustained silencing or sustained loss of silencing shortens life span. These findings reveal that the temporal patterns of a key molecular process can directly influence cellular aging, and thus could provide guidance for the design of temporally controlled strategies to extend life span.

Gene Conversion Facilitates Adaptive Evolution on Rugged Fitness Landscapes.

Gene conversion is a ubiquitous phenomenon that leads to the exchange of genetic information between homologous DNA regions and maintains coevolving multi-gene families in most prokaryotic and eukaryotic organisms. In this paper, we study its implications for the evolution of a single functional gene with a silenced duplicate, using two different models of evolution on rugged fitness landscapes. Our analytical and numerical results show that, by helping to circumvent valleys of low fitness, gene conversion with a passive duplicate gene can cause a significant speedup of adaptation, which depends nontrivially on the frequency of gene conversion and the structure of the landscape. We find that stochastic effects due to finite population sizes further increase the likelihood of exploiting this evolutionary pathway. A universal feature appearing in both deterministic and stochastic analysis of our models is the existence of an optimal gene conversion rate, which maximizes the speed of adaptation. Our results reveal the potential for duplicate genes to act as a "scratch paper" that frees evolution from being limited to strictly beneficial mutations in strongly selective environments.

Emergent dynamics of spatio-temporal chaos in a heterogeneous excitable medium.

Self-organized activation patterns in excitable media such as spiral waves and spatio-temporal chaos underlie dangerous cardiac arrhythmias. While the interaction of single spiral waves with different types of heterogeneity has been studied extensively, the effect of heterogeneity on fully developed spatio-temporal chaos remains poorly understood. We investigate how the complexity and stability properties of spatio-temporal chaos in the Bär-Eiswirth model of excitable media depend on the heterogeneity of the underlying medium. We employ different measures characterizing the chaoticity of the system and find that the spatial arrangement of multiple discrete lower excitability regions has a strong impact on the complexity of the dynamics. Varying the number, shape, and spatial arrangement of the heterogeneities, we observe strong emergent effects ranging from increases in chaoticity to the complete cessation of chaos, contrasting the expectation from the homogeneous behavior. The implications of our findings for the development and treatment of arrhythmias in the heterogeneous cardiac muscle are discussed.

A stabilized microbial ecosystem of self-limiting bacteria using synthetic quorum-regulated lysis.

Microbial ecologists are increasingly turning to small, synthesized ecosystems1-5 as a reductionist tool to probe the complexity of native microbiomes6,7. Concurrently, synthetic biologists have gone from single-cell gene circuits8-11 to controlling whole populations using intercellular signalling12-16. The intersection of these fields is giving rise to new approaches in waste recycling17, industrial fermentation18, bioremediation19 and human health16,20. These applications share a common challenge7 well-known in classical ecology21,22-stability of an ecosystem cannot arise without mechanisms that prohibit the faster-growing species from eliminating the slower. Here, we combine orthogonal quorum-sensing systems and a population control circuit with diverse self-limiting growth dynamics to engineer two 'ortholysis' circuits capable of maintaining a stable co-culture of metabolically competitive Salmonella typhimurium strains in microfluidic devices. Although no successful co-cultures are observed in a two-strain ecology without synthetic population control, the 'ortholysis' design dramatically increases the co-culture rate from 0% to approximately 80%. Agent-based and deterministic modelling reveal that our system can be adjusted to yield different dynamics, including phase-shifted, antiphase or synchronized oscillations, as well as stable steady-state population densities. The 'ortholysis' approach establishes a paradigm for constructing synthetic ecologies by developing stable communities of competitive microorganisms without the need for engineered co-dependency.

Suppression of Beneficial Mutations in Dynamic Microbial Populations.

Quantitative predictions for the spread of mutations in bacterial populations are essential to interpret evolution experiments and to improve the stability of synthetic gene circuits. We derive analytical expressions for the suppression factor for beneficial mutations in populations that undergo periodic dilutions, covering arbitrary population sizes, dilution factors, and growth advantages in a single stochastic model. We find that the suppression factor grows with the dilution factor and depends nontrivially on the growth advantage, resulting in the preferential elimination of mutations with certain growth advantages. We confirm our results by extensive numerical simulations.

Requirement analysis for an electronic laboratory notebook for sustainable data management in biomedical research.

Sustainable data management in biomedical research requires documentation of metadata for all experiments and results. Scientists usually document research data and metadata in laboratory paper notebooks. An electronic laboratory notebook (ELN) can keep metadata linked to research data resulting in a better understanding of the research results, meaning a scientific benefit [1]. Besides other challenges [2], the biggest hurdles for introducing an ELN seem to be usability, file formats, and data entry mechanisms [3] and that many ELNs are assigned to specific research fields such as biology, chemistry, or physics [4]. We aimed to identify requirements for the introduction of ELN software in a biomedical collaborative research center [5] consisting of different scientific fields and to find software fulfilling most of these requirements.

Negative curvature boundaries as wave emitting sites for the control of biological excitable media.

Understanding the interaction of electric fields with the complex anatomy of biological excitable media is key to optimizing control strategies for spatiotemporal dynamics in those systems. On the basis of a bidomain description, we provide a unified theory for the electric-field-induced depolarization of the substrate near curved boundaries of generalized shapes, resulting in the localized recruitment of control sites. Our findings are confirmed in experiments on cardiomyocyte cell cultures and supported by two-dimensional numerical simulations on a cross section of a rabbit ventricle.

Low-energy control of electrical turbulence in the heart.

Controlling the complex spatio-temporal dynamics underlying life-threatening cardiac arrhythmias such as fibrillation is extremely difficult, because of the nonlinear interaction of excitation waves in a heterogeneous anatomical substrate. In the absence of a better strategy, strong, globally resetting electrical shocks remain the only reliable treatment for cardiac fibrillation. Here we establish the relationship between the response of the tissue to an electric field and the spatial distribution of heterogeneities in the scale-free coronary vascular structure. We show that in response to a pulsed electric field, E, these heterogeneities serve as nucleation sites for the generation of intramural electrical waves with a source density ρ(E) and a characteristic time, τ, for tissue depolarization that obeys the power law τ ∝ E(α). These intramural wave sources permit targeting of electrical turbulence near the cores of the vortices of electrical activity that drive complex fibrillatory dynamics. We show in vitro that simultaneous and direct access to multiple vortex cores results in rapid synchronization of cardiac tissue and therefore, efficient termination of fibrillation. Using this control strategy, we demonstrate low-energy termination of fibrillation in vivo. Our results give new insights into the mechanisms and dynamics underlying the control of spatio-temporal chaos in heterogeneous excitable media and provide new research perspectives towards alternative, life-saving low-energy defibrillation techniques.