Minimal Surviving Inoculum in Collective Antibiotic Resistance.

A common strategy used by bacteria to resist antibiotics is enzymatic degradation or modification. This reduces the antibiotic threat in the environment and is therefore potentially a collective mechanism that also enhances the survival of nearby cells. Collective resistance is of clinical significance, yet a quantitative understanding at the population level is still incomplete. Here, we develop a general theoretical framework of collective resistance by antibiotic degradation. Our modeling study reveals that population survival crucially depends on the ratio of timescales of two processes: the rates of population death and antibiotic removal. However, it is insensitive to molecular, biological, and kinetic details of the underlying processes that give rise to these timescales. Another important aspect of antibiotic degradation is the degree of cooperativity, related to the permeability of the cell wall to antibiotics and enzymes. These observations motivate a coarse-grained, phenomenological model, with two compound parameters representing the population's race to survival and single-cell effective resistance. We propose a simple experimental assay to measure the dose-dependent minimal surviving inoculum and apply it to Escherichia coli expressing several types of ß-lactamase. Experimental data analyzed within the theoretical framework corroborate it with good agreement. Our simple model may serve as a reference for more complex situations, such as heterogeneous bacterial communities. IMPORTANCE Collective resistance occurs when bacteria work together to decrease the concentration of antibiotics in their environment, for example, by actively breaking down or modifying them. This can help bacteria survive by reducing the effective antibiotic concentration below their threshold for growth. In this study, we used mathematical modeling to examine the factors that influence collective resistance and to develop a framework to understand the minimum population size needed to survive a given initial antibiotic concentration. Our work helps to identify generic mechanism-independent parameters that can be derived from population data and identifies combinations of parameters that play a role in collective resistance. Specifically, it highlights the relative timescales involved in the survival of populations that inactivate antibiotics, as well as the levels of cooperation versus privatization. The results of this study contribute to our understanding of population-level effects on antibiotic resistance and may inform the design of antibiotic therapies.

Ranking the effectiveness of worldwide COVID-19 government interventions.

Assessing the effectiveness of non-pharmaceutical interventions (NPIs) to mitigate the spread of SARS-CoV-2 is critical to inform future preparedness response plans. Here we quantify the impact of 6,068 hierarchically coded NPIs implemented in 79 territories on the effective reproduction number, Rt, of COVID-19. We propose a modelling approach that combines four computational techniques merging statistical, inference and artificial intelligence tools. We validate our findings with two external datasets recording 42,151 additional NPIs from 226 countries. Our results indicate that a suitable combination of NPIs is necessary to curb the spread of the virus. Less disruptive and costly NPIs can be as effective as more intrusive, drastic, ones (for example, a national lockdown). Using country-specific 'what-if' scenarios, we assess how the effectiveness of NPIs depends on the local context such as timing of their adoption, opening the way for forecasting the effectiveness of future interventions.

A structured open dataset of government interventions in response to COVID-19.

In response to the COVID-19 pandemic, governments have implemented a wide range of non-pharmaceutical interventions (NPIs). Monitoring and documenting government strategies during the COVID-19 crisis is crucial to understand the progression of the epidemic. Following a content analysis strategy of existing public information sources, we developed a specific hierarchical coding scheme for NPIs. We generated a comprehensive structured dataset of government interventions and their respective timelines of implementation. To improve transparency and motivate collaborative validation process, information sources are shared via an open library. We also provide codes that enable users to visualise the dataset. Standardization and structure of the dataset facilitate inter-country comparison and the assessment of the impacts of different NPI categories on the epidemic parameters, population health indicators, the economy, and human rights, among others. This dataset provides an in-depth insight of the government strategies and can be a valuable tool for developing relevant preparedness plans for pandemic. We intend to further develop and update this dataset until the end of December 2020.

Coexistence and cooperation in structured habitats.

BACKGROUND: Natural habitats are typically structured, imposing constraints on inhabiting populations and their interactions. Which conditions are important for coexistence of diverse communities, and how cooperative interaction stabilizes in such populations, have been important ecological and evolutionary questions. RESULTS: We investigate a minimal ecological framework of microbial population dynamics that exhibits crucial features to show coexistence: Populations repeatedly undergo cycles of separation into compartmentalized habitats and mixing with new resources. The characteristic time-scale is longer than that typical of individual growth. Using analytic approximations, averaging techniques and phase-plane methods of dynamical systems, we provide a framework for analyzing various types of microbial interactions. Population composition and population size are both dynamic variables of the model; they are found to be decoupled both in terms of time-scale and parameter dependence. We present specific results for two examples of cooperative interaction by public goods: collective antibiotics resistance, and enhanced iron-availability by pyoverdine. We find stable coexistence to be a likely outcome. CONCLUSIONS: The two simple features of a long mixing time-scale and spatial compartmentalization are enough to enable coexisting strains. In particular, costly social traits are often stabilized in such an environment-and thus cooperation established.

CRISPR-based herd immunity can limit phage epidemics in bacterial populations.

Herd immunity, a process in which resistant individuals limit the spread of a pathogen among susceptible hosts has been extensively studied in eukaryotes. Even though bacteria have evolved multiple immune systems against their phage pathogens, herd immunity in bacteria remains unexplored. Here we experimentally demonstrate that herd immunity arises during phage epidemics in structured and unstructured Escherichia coli populations consisting of differing frequencies of susceptible and resistant cells harboring CRISPR immunity. In addition, we develop a mathematical model that quantifies how herd immunity is affected by spatial population structure, bacterial growth rate, and phage replication rate. Using our model we infer a general epidemiological rule describing the relative speed of an epidemic in partially resistant spatially structured populations. Our experimental and theoretical findings indicate that herd immunity may be important in bacterial communities, allowing for stable coexistence of bacteria and their phages and the maintenance of polymorphism in bacterial immunity.

Cooperative stochastic binding and unbinding explain synaptic size dynamics and statistics.

Synapses are dynamic molecular assemblies whose sizes fluctuate significantly over time-scales of hours and days. In the current study, we examined the possibility that the spontaneous microscopic dynamics exhibited by synaptic molecules can explain the macroscopic size fluctuations of individual synapses and the statistical properties of synaptic populations. We present a mesoscopic model, which ties the two levels. Its basic premise is that synaptic size fluctuations reflect cooperative assimilation and removal of molecules at a patch of postsynaptic membrane. The introduction of cooperativity to both assimilation and removal in a stochastic biophysical model of these processes, gives rise to features qualitatively similar to those measured experimentally: nanoclusters of synaptic scaffolds, fluctuations in synaptic sizes, skewed, stable size distributions and their scaling in response to perturbations. Our model thus points to the potentially fundamental role of cooperativity in dictating synaptic remodeling dynamics and offers a conceptual understanding of these dynamics in terms of central microscopic features and processes.

Collective Fluctuations in the Dynamics of Adaptation and Other Traveling Waves.

The dynamics of adaptation are difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from random genetic drift arising in a vanguard of particularly fit individuals of the population. Several approaches have been developed to analyze the crucial role of genetic drift on the expected dynamics of adaptation, including the mean fitness of the entire population, or the fate of newly arising beneficial deleterious mutations. However, little is known about how genetic drift causes fluctuations to emerge on the population level, where it becomes palpable as variations in the adaptation speed and the fitness distribution. Yet these phenomena control the decay of genetic diversity and variability in evolution experiments and are key to a truly predictive understanding of evolutionary processes. Here, we show that correlations induced by these emergent fluctuations can be computed at any arbitrary order by a suitable choice of a dynamical constraint. The resulting linear equations exhibit fluctuation-induced terms that amplify short-distance correlations and suppress long-distance ones. These terms, which are in general not small, control the decay of genetic diversity and, for wave-tip dominated ("pulled") waves, lead to anticorrelations between the tip of the wave and the lagging bulk of the population. While it is natural to consider the process of adaptation as a branching random walk in fitness space subject to a constraint (due to finite resources), we show that other traveling wave phenomena in ecology and evolution likewise fall into this class of constrained branching random walks. Our methods, therefore, provide a systematic approach toward analyzing fluctuations in a wide range of population biological processes, such as adaptation, genetic meltdown, species invasions, or epidemics.

Deep sequencing of a genetically heterogeneous sample: local haplotype reconstruction and read error correction.

We present a computational method for analyzing deep sequencing data obtained from a genetically diverse sample. The set of reads obtained from a deep sequencing experiment represents a statistical sample of the underlying population. We develop a generative probabilistic model for assigning observed reads to unobserved haplotypes in the presence of sequencing errors. This clustering problem is solved in a Bayesian fashion using the Dirichlet process mixture to define a prior distribution on the unknown number of haplotypes in the mixture. We devise a Gibbs sampler for sampling from the joint posterior distribution of haplotype sequences, assignment of reads to haplotypes, and error rate of the sequencing process, to obtain estimates of the local haplotype structure of the population. The method is evaluated on simulated data and on experimental deep sequencing data obtained from HIV samples.