Bacteriophage specificity is impacted by interactions between bacteria.

Predators play a central role in shaping community structure, function, and stability. The degree to which bacteriophage predators (viruses that infect bacteria) evolve to be specialists with a single bacterial prey species versus generalists able to consume multiple types of prey has implications for their effect on microbial communities. The presence and abundance of multiple bacterial prey types can alter selection for phage generalists, but less is known about how interactions between prey shape predator specificity in microbial systems. Using a phenomenological mathematical model of phage and bacterial populations, we find that the dominant phage strategy depends on prey ecology. Given a fitness cost for generalism, generalist predators maintain an advantage when prey species compete, while specialists dominate when prey are obligately engaged in cross-feeding interactions. We test these predictions in a synthetic microbial community with interacting strains of Escherichia coli and Salmonella enterica by competing a generalist T5-like phage able to infect both prey against P22vir, an S. enterica-specific phage. Our experimental data conform to our modeling expectations when prey species are competing or obligately mutualistic, although our results suggest that the in vitro cost of generalism is caused by a combination of biological mechanisms not anticipated in our model. Our work demonstrates that interactions between bacteria play a role in shaping ecological selection on predator specificity in obligately lytic bacteriophages and emphasizes the diversity of ways in which fitness trade-offs can manifest. IMPORTANCE: There is significant natural diversity in how many different types of bacteria a bacteriophage can infect, but the mechanisms driving this diversity are unclear. This study uses a combination of mathematical modeling and an in vitro system consisting of Escherichia coli, Salmonella enterica, a T5-like generalist phage, and the specialist phage P22vir to highlight the connection between bacteriophage specificity and interactions between their potential microbial prey. Mathematical modeling suggests that competing bacteria tend to favor generalist bacteriophage, while bacteria that benefit each other tend to favor specialist bacteriophage. Experimental results support this general finding. The experiments also show that the optimal phage strategy is impacted by phage degradation and bacterial physiology. These findings enhance our understanding of how complex microbial communities shape selection on bacteriophage specificity, which may improve our ability to use phage to manage antibiotic-resistant microbial infections.

Assisted percolation of slow-spreading mutants in heterogeneous environments.

Environmental heterogeneity can drive genetic heterogeneity in expanding populations; mutant strains may emerge that trade overall growth rate for an improved ability to survive in patches that are hostile to the wild type. This evolutionary dynamic is of practical importance when seeking to prevent the emergence of damaging traits. We show that a subcritical slow-spreading mutant can attain dominance even when the density of patches is below their percolation threshold and predict this transition using geometrical arguments. This work demonstrates a phenomenon of "assisted percolation", where one subcritical process assists another to achieve supercriticality.

Bacterial Filamentation Drives Colony Chirality.

Chirality is ubiquitous in nature, with consequences at the cellular and tissue scales. As Escherichia coli colonies expand radially, an orthogonal component of growth creates a pinwheel-like pattern that can be revealed by fluorescent markers. To elucidate the mechanistic basis of this colony chirality, we investigated its link to left-handed, single-cell twisting during E. coli elongation. While chemical and genetic manipulation of cell width altered single-cell twisting handedness, colonies ceased to be chiral rather than switching handedness, and anaerobic growth altered colony chirality without affecting single-cell twisting. Chiral angle increased with increasing temperature even when growth rate decreased. Unifying these findings, we discovered that colony chirality was associated with the propensity for cell filamentation. Inhibition of cell division accentuated chirality under aerobic growth and generated chirality under anaerobic growth. Thus, regulation of cell division is intrinsically coupled to colony chirality, providing a mechanism for tuning macroscale spatial patterning. IMPORTANCE Chiral objects, such as amino acids, are distinguishable from their mirror image. For living systems, the fundamental mechanisms relating cellular handedness to chirality at the multicellular scale remain largely mysterious. Here, we use chemical, genetic, and environmental perturbations of Escherichia coli to investigate whether pinwheel patterns in bacterial colonies are directly linked to single-cell growth behaviors. We discover that chirality can be abolished without affecting single-cell twisting; instead, the degree of chirality was linked to the proportion of highly elongated cells at the colony edge. Inhibiting cell division boosted the degree of chirality during aerobic growth and even introduced chirality to otherwise achiral colonies during anaerobic growth. These findings reveal a fascinating connection between cell division and macroscopic colony patterning.

The collective effect of finite-sized inhomogeneities on the spatial spread of populations in two dimensions.

The dynamics of a population expanding into unoccupied habitat has been primarily studied for situations in which growth and dispersal parameters are uniform in space or vary in one dimension. Here, we study the influence of finite-sized individual inhomogeneities and their collective effect on front speed if randomly placed in a two-dimensional habitat. We use an individual-based model to investigate the front dynamics for a region in which dispersal or growth of individuals is reduced to zero (obstacles) or increased above the background (hotspots), respectively. In a regime where front dynamics is determined by a local front speed only, a principle of least time can be employed to predict front speed and shape. The resulting analytical solutions motivate an event-based algorithm illustrating the effects of several obstacles or hotspots. We finally apply the principle of least time to large heterogeneous environments by solving the Eikonal equation numerically. Obstacles lead to a slow-down that is dominated by the number density and width of obstacles, but not by their precise shape. Hotspots result in a speed-up, which we characterize as function of hotspot strength and density. Our findings emphasize the importance of taking the dimensionality of the environment into account.

The spatial and metabolic basis of colony size variation.

Spatial structure impacts microbial growth and interactions, with ecological and evolutionary consequences. It is therefore important to quantitatively understand how spatial proximity affects interactions in different environments. We tested how proximity influences colony size when either Escherichia coli or Salmonella enterica are grown on various carbon sources. The importance of colony location changed with species and carbon source. Spatially explicit, genome-scale metabolic modeling recapitulated observed colony size variation. Competitors that determine territory size, according to Voronoi diagrams, were the most important drivers of variation in colony size. However, the relative importance of different competitors changed through time. Further, the effect of location increased when colonies took up resources quickly relative to the diffusion of limiting resources. These analyses made it apparent that the importance of location was smaller than expected for experiments with S. enterica growing on glucose. The accumulation of toxic byproducts appeared to limit the growth of large colonies and reduced variation in colony size. Our work provides an experimentally and theoretically grounded understanding of how location interacts with metabolism and diffusion to influence microbial interactions.

Genetic drift and selection in many-allele range expansions.

We experimentally and numerically investigate the evolutionary dynamics of four competing strains of E. coli with differing expansion velocities in radially expanding colonies. We compare experimental measurements of the average fraction, correlation functions between strains, and the relative rates of genetic domain wall annihilations and coalescences to simulations modeling the population as a one-dimensional ring of annihilating and coalescing random walkers with deterministic biases due to selection. The simulations reveal that the evolutionary dynamics can be collapsed onto master curves governed by three essential parameters: (1) an expansion length beyond which selection dominates over genetic drift; (2) a characteristic angular correlation describing the size of genetic domains; and (3) a dimensionless constant quantifying the interplay between a colony's curvature at the frontier and its selection length scale. We measure these parameters with a new technique that precisely measures small selective differences between spatially competing strains and show that our simulations accurately predict the dynamics without additional fitting. Our results suggest that the random walk model can act as a useful predictive tool for describing the evolutionary dynamics of range expansions composed of an arbitrary number of genotypes with different fitnesses.

Allele surfing promotes microbial adaptation from standing variation.

The coupling of ecology and evolution during range expansions enables mutations to establish at expanding range margins and reach high frequencies. This phenomenon, called allele surfing, is thought to have caused revolutions in the gene pool of many species, most evidently in microbial communities. It has remained unclear, however, under which conditions allele surfing promotes or hinders adaptation. Here, using microbial experiments and simulations, we show that, starting with standing adaptive variation, range expansions generate a larger increase in mean fitness than spatially uniform population expansions. The adaptation gain results from 'soft' selective sweeps emerging from surfing beneficial mutations. The rate of these surfing events is shown to sensitively depend on the strength of genetic drift, which varies among strains and environmental conditions. More generally, allele surfing promotes the rate of adaptation per biomass produced, which could help developing biofilms and other resource-limited populations to cope with environmental challenges.

How Obstacles Perturb Population Fronts and Alter Their Genetic Structure.

As populations spread into new territory, environmental heterogeneities can shape the population front and genetic composition. We focus here on the effects of an important building block of heterogeneous environments, isolated obstacles. With a combination of experiments, theory, and simulation, we show how isolated obstacles both create long-lived distortions of the front shape and amplify the effect of genetic drift. A system of bacteriophage T7 spreading on a spatially heterogeneous Escherichia coli lawn serves as an experimental model system to study population expansions. Using an inkjet printer, we create well-defined replicates of the lawn and quantitatively study the population expansion of phage T7. The transient perturbations of the population front found in the experiments are well described by a model in which the front moves with constant speed. Independent of the precise details of the expansion, we show that obstacles create a kink in the front that persists over large distances and is insensitive to the details of the obstacle's shape. The small deviations between experimental findings and the predictions of the constant speed model can be understood with a more general reaction-diffusion model, which reduces to the constant speed model when the obstacle size is large compared to the front width. Using this framework, we demonstrate that frontier genotypes just grazing the side of an isolated obstacle increase in abundance, a phenomenon we call 'geometry-enhanced genetic drift', complementary to the founder effect associated with spatial bottlenecks. Bacterial range expansions around nutrient-poor barriers and stochastic simulations confirm this prediction. The effect of the obstacle on the genealogy of individuals at the front is characterized by simulations and rationalized using the constant speed model. Lastly, we consider the effect of two obstacles on front shape and genetic composition of the population illuminating the effects expected from complex environments with many obstacles.

Physical and Mathematical Modeling in Experimental Papers.

An increasing number of publications include modeling. Often, such studies help us to gain a deeper insight into the phenomena studied and break down barriers between experimental and theoretical communities. However, combining experimental and theoretical work is challenging for authors, reviewers, and readers. To help maximize the usefulness and impact of combined theoretical and experimental research, this Primer describes the purpose, usefulness, and different types of models and addresses the practical aspect of integrated publications by outlining characteristics of good modeling, presentation, and fruitful collaborations.

Toward a unified physical model of nucleosome patterns flanking transcription start sites.

Recent genome-wide maps of nucleosome positions in different eukaryotes revealed patterns around transcription start sites featuring a nucleosome-free region flanked by a periodic modulation of the nucleosome density. For Saccharomyces cerevisiae, the average in vivo pattern was previously shown to be quantitatively described by a "nucleosome gas" model based on the statistical positioning mechanism. However, this simple physical description is challenged by the fact that the pattern differs quantitatively between species and by recent experiments that appear incompatible with statistical positioning, indicating important roles for chromatin remodelers. We undertake a data-driven search for a unified physical model to describe the nucleosome patterns of 12 yeast species and also consider an extension of the model to capture remodeling effects. We are led to a nucleosome gas that takes into account nucleosome breathing, i.e., transient unwrapping of nucleosomal DNA segments. This known biophysical property of nucleosomes rationalizes a "pressure"-induced dependence of the effective nucleosome size that is suggested by the data. By fitting this model to the data, we find an average energy cost for DNA unwrapping consistent with previous biophysical experiments. Although the available data are not sufficient to reconstruct chromatin remodeling mechanisms, a minimal model extension by one mechanism yields an "active nucleosome gas" that can rationalize the behavior of systems with reduced histone-DNA ratio and remodeler knockouts. We therefore establish a basis for a physical description of nucleosome patterns that can serve as a null model for sequence-specific effects at individual genes and in models of transcription regulation.

Quantitative test of the barrier nucleosome model for statistical positioning of nucleosomes up- and downstream of transcription start sites.

The positions of nucleosomes in eukaryotic genomes determine which parts of the DNA sequence are readily accessible for regulatory proteins and which are not. Genome-wide maps of nucleosome positions have revealed a salient pattern around transcription start sites, involving a nucleosome-free region (NFR) flanked by a pronounced periodic pattern in the average nucleosome density. While the periodic pattern clearly reflects well-positioned nucleosomes, the positioning mechanism is less clear. A recent experimental study by Mavrich et al. argued that the pattern observed in Saccharomyces cerevisiae is qualitatively consistent with a "barrier nucleosome model," in which the oscillatory pattern is created by the statistical positioning mechanism of Kornberg and Stryer. On the other hand, there is clear evidence for intrinsic sequence preferences of nucleosomes, and it is unclear to what extent these sequence preferences affect the observed pattern. To test the barrier nucleosome model, we quantitatively analyze yeast nucleosome positioning data both up- and downstream from NFRs. Our analysis is based on the Tonks model of statistical physics which quantifies the interplay between the excluded-volume interaction of nucleosomes and their positional entropy. We find that although the typical patterns on the two sides of the NFR are different, they are both quantitatively described by the same physical model with the same parameters, but different boundary conditions. The inferred boundary conditions suggest that the first nucleosome downstream from the NFR (the +1 nucleosome) is typically directly positioned while the first nucleosome upstream is statistically positioned via a nucleosome-repelling DNA region. These boundary conditions, which can be locally encoded into the genome sequence, significantly shape the statistical distribution of nucleosomes over a range of up to approximately 1,000 bp to each side.

Freely relaxing polymers remember how they were straightened.

The relaxation of initially straight semiflexible polymers has been discussed mainly with respect to the longest relaxation time. The biologically relevant nonequilibrium dynamics on shorter times is comparatively poorly understood, partly because "initially straight" can be realized in manifold ways. Combining Brownian dynamics simulations and systematic theory, we demonstrate how different experimental preparations give rise to specific short-time and universal long-time dynamics. We also discuss boundary effects and the onset of the stretch-coil transition.

Spontaneous unknotting of a polymer confined in a nanochannel.

We study the dynamics of a knot in a semiflexible polymer confined to a narrow channel of width comparable to the polymers' persistence length. Using a combination of Brownian dynamics simulations and a coarse-grained stochastic model, we characterize the coupled dynamics of knot size variation and knot diffusion along the polymer, which ultimately leads to spontaneous unknotting. We find that the knot grows to macroscopic size before disappearing. Interestingly, an external force applied to the ends of the confined polymer speeds up spontaneous unknotting.

Optimal flexibility for conformational transitions in macromolecules.

Conformational transitions in macromolecular complexes often involve the reorientation of leverlike structures. Using a simple theoretical model, we show that the rate of such transitions is drastically enhanced if the lever is bendable, e.g., at a localized hinge. Surprisingly, the transition is fastest with an intermediate flexibility of the hinge. In this intermediate regime, the transition rate is also least sensitive to the amount of "cargo" attached to the lever arm, which could be exploited by molecular motors. To explain this effect, we generalize the Kramers-Langer theory for multidimensional barrier crossing to configuration-dependent mobility matrices.

Kinetic accessibility of buried DNA sites in nucleosomes.

Using a theoretical model for spontaneous partial DNA unwrapping from histones, we study the transient exposure of protein-binding DNA sites within nucleosomes. We focus on the functional dependence of the rates for site exposure and reburial on the site position, which is measurable experimentally and pertinent to gene regulation. We find the dependence to be roughly described by a random walker model. Close inspection reveals a surprising physical effect of flexibility-assisted barrier crossing, which we characterize within a toy model, the "semiflexible Brownian rotor."