Substrate geometry affects population dynamics in a bacterial biofilm.

Biofilms inhabit a range of environments, such as dental plaques or soil micropores, often characterized by noneven surfaces. However, the impact of surface irregularities on the population dynamics of biofilms remains elusive, as most experiments are conducted on flat surfaces. Here, we show that the shape of the surface on which a biofilm grows influences genetic drift and selection within the biofilm. We culture Escherichia coli biofilms in microwells with a corrugated bottom surface and observe the emergence of clonal sectors whose size corresponds to that of the corrugations, despite no physical barrier separating different areas of the biofilm. The sectors are remarkably stable and do not invade each other; we attribute this stability to the characteristics of the velocity field within the biofilm, which hinders mixing and clonal expansion. A microscopically detailed computer model fully reproduces these findings and highlights the role of mechanical interactions such as adhesion and friction in microbial evolution. The model also predicts clonal expansion to be limited even for clones with a significant growth advantage-a finding which we confirm experimentally using a mixture of antibiotic-sensitive and antibiotic-resistant mutants in the presence of sublethal concentrations of the antibiotic rifampicin. The strong suppression of selection contrasts sharply with the behavior seen in range expansion experiments in bacterial colonies grown on agar. Our results show that biofilm population dynamics can be affected by patterning the surface and demonstrate how a better understanding of the physics of bacterial growth can be used to control microbial evolution.

A Roadblock-and-Kill Mechanism of Action Model for the DNA-Targeting Antibiotic Ciprofloxacin.

Fluoroquinolones, antibiotics that cause DNA damage by inhibiting DNA topoisomerases, are clinically important, but their mechanism of action is not yet fully understood. In particular, the dynamical response of bacterial cells to fluoroquinolone exposure has hardly been investigated, although the SOS response, triggered by DNA damage, is often thought to play a key role. Here, we investigated the growth inhibition of the bacterium Escherichia coli by the fluoroquinolone ciprofloxacin at low concentrations. We measured the long-term and short-term dynamical response of the growth rate and DNA production rate to ciprofloxacin at both the population and single-cell levels. We show that, despite the molecular complexity of DNA metabolism, a simple roadblock-and-kill model focusing on replication fork blockage and DNA damage by ciprofloxacin-poisoned DNA topoisomerase II (gyrase) quantitatively reproduces long-term growth rates in the presence of ciprofloxacin. The model also predicts dynamical changes in the DNA production rate in wild-type E. coli and in a recombination-deficient mutant following a step-up of ciprofloxacin. Our work highlights that bacterial cells show a delayed growth rate response following fluoroquinolone exposure. Most importantly, our model explains why the response is delayed: it takes many doubling times to fragment the DNA sufficiently to inhibit gene expression. We also show that the dynamical response is controlled by the timescale of DNA replication and gyrase binding/unbinding to the DNA rather than by the SOS response, challenging the accepted view. Our work highlights the importance of including detailed biophysical processes in biochemical-systems models to quantitatively predict the bacterial response to antibiotics.

Predictable properties of fitness landscapes induced by adaptational tradeoffs.

Fitness effects of mutations depend on environmental parameters. For example, mutations that increase fitness of bacteria at high antibiotic concentration often decrease fitness in the absence of antibiotic, exemplifying a tradeoff between adaptation to environmental extremes. We develop a mathematical model for fitness landscapes generated by such tradeoffs, based on experiments that determine the antibiotic dose-response curves of Escherichia coli strains, and previous observations on antibiotic resistance mutations. Our model generates a succession of landscapes with predictable properties as antibiotic concentration is varied. The landscape is nearly smooth at low and high concentrations, but the tradeoff induces a high ruggedness at intermediate antibiotic concentrations. Despite this high ruggedness, however, all the fitness maxima in the landscapes are evolutionarily accessible from the wild type. This implies that selection for antibiotic resistance in multiple mutational steps is relatively facile despite the complexity of the underlying landscape.

Drug resistant bacteria pose a major threat to public health systems all over the world. Darwinian evolution is at the heart of this drug resistance: a mutation that allows bacteria to divide in the presence of a drug appears initially in a single cell. This mutation makes this cell and its descendants more likely to survive, so they can end up taking over the population. The evolution of resistance can be thought of in terms of 'bacterial fitness landscapes'. These landscapes visualise the relationship between the mutations present in a population of bacteria and how quickly the bacteria divide or reproduce. They are called landscapes because they can be represented as a series of mountains and valleys. The peaks of this landscape represent combinations of mutations that give bacteria the greatest chance of dividing (the greatest fitness). In a landscape with multiple peaks, some peaks will be higher than others. If the landscape is smooth, bacteria can easily acquire mutations for drug resistance. However, in a rugged landscape, bacteria may get stuck at sub-optimal peaks, because the mutations that would enable them to reach a higher peak would first lead them to losing fitness. Several studies on the evolution of antibiotic resistance exist for specific bacteria and specific drugs, but relatively little is known about the general properties of the underlying fitness landscapes. Do these landscapes have features that can help explain the rapid evolution of high levels of resistance? Antibiotic resistance often comes at a cost ­ more resistant strains of bacteria tend to grow more slowly when the drug is absent. To build a model of antibiotic resistance landscapes, Das et al. performed growth experiments on several strains of Escherichia coli exposed to a drug called ciprofloxacin. They measured how the rate at which the bacteria divided changed at different antibiotic concentrations, and combined this with the observation about resistant strains growing slower to formulate a mathematical model of antibiotic resistance landscapes. The landscapes that resulted were found to be very rugged, but unexpectedly, the bacteria could still evolve to access all fitness peaks. This means that landscape ruggedness does not constrain the evolution of resistance. Understanding how and when resistance evolves is important both for the design of new drugs and the development of treatment protocols. A specific prediction of the model is that resistance evolution in fitness landscapes where resistant strains divide more slowly is reversible. This implies that the bacteria could regain their susceptibility to treatment when the drug concentration decreases, but this would depend on the specific bacteria and drug in question. More broadly, the model provides a framework for addressing the evolution of resistance in clinical and environmental settings, where drug concentrations vary widely in time and space.

Phenotypic delay in the evolution of bacterial antibiotic resistance: Mechanistic models and their implications.

Phenotypic delay-the time delay between genetic mutation and expression of the corresponding phenotype-is generally neglected in evolutionary models, yet recent work suggests that it may be more common than previously assumed. Here, we use computer simulations and theory to investigate the significance of phenotypic delay for the evolution of bacterial resistance to antibiotics. We consider three mechanisms which could potentially cause phenotypic delay: effective polyploidy, dilution of antibiotic-sensitive molecules and accumulation of resistance-enhancing molecules. We find that the accumulation of resistant molecules is relevant only within a narrow parameter range, but both the dilution of sensitive molecules and effective polyploidy can cause phenotypic delay over a wide range of parameters. We further investigate whether these mechanisms could affect population survival under drug treatment and thereby explain observed discrepancies in mutation rates estimated by Luria-Delbrück fluctuation tests. While the effective polyploidy mechanism does not affect population survival, the dilution of sensitive molecules leads both to decreased probability of survival under drug treatment and underestimation of mutation rates in fluctuation tests. The dilution mechanism also changes the shape of the Luria-Delbrück distribution of mutant numbers, and we show that this modified distribution provides an improved fit to previously published experimental data.

Absence of MeCP2 binding to non-methylated GT-rich sequences in vivo.

MeCP2 is a nuclear protein that binds to sites of cytosine methylation in the genome. While most evidence confirms this epigenetic mark as the primary determinant of DNA binding, MeCP2 is also reported to have an affinity for non-methylated DNA sequences. Here we investigated the molecular basis and in vivo significance of its reported affinity for non-methylated GT-rich sequences. We confirmed this interaction with isolated domains of MeCP2 in vitro and defined a minimal target DNA sequence. Binding depends on pyrimidine 5' methyl groups provided by thymine and requires adjacent guanines and a correctly orientated A/T-rich flanking sequence. Unexpectedly, full-length MeCP2 protein failed to bind GT-rich sequences in vitro. To test for MeCP2 binding to these motifs in vivo, we analysed human neuronal cells using ChIP-seq and ATAC-seq technologies. While both methods robustly detected DNA methylation-dependent binding of MeCP2 to mCG and mCAC, neither showed evidence of MeCP2 binding to GT-rich motifs. The data suggest that GT binding is an in vitro phenomenon without in vivo relevance. Our findings argue that MeCP2 does not read unadorned DNA sequence and therefore support the notion that its primary role is to interpret epigenetic modifications of DNA.

On measuring selection in cancer from subclonal mutation frequencies.

Recently available cancer sequencing data have revealed a complex view of the cancer genome containing a multitude of mutations, including drivers responsible for cancer progression and neutral passengers. Measuring selection in cancer and distinguishing drivers from passengers have important implications for development of novel treatment strategies. It has recently been argued that a third of cancers are evolving neutrally, as their mutational frequency spectrum follows a 1/f power law expected from neutral evolution in a particular intermediate frequency range. We study a stochastic model of cancer evolution and derive a formula for the probability distribution of the cancer cell frequency of a subclonal driver, demonstrating that driver frequency is biased towards 0 and 1. We show that it is difficult to capture a driver mutation at an intermediate frequency, and thus the calling of neutrality due to a lack of such driver will significantly overestimate the number of neutrally evolving tumors. Our approach provides quantification of the validity of the 1/f statistic across the entire range of relevant parameter values. We also show that our conclusions remain valid for non-exponential models: spatial 3d model and sigmoidal growth, relevant for early- and late stages of cancer growth.

Quantitative modelling predicts the impact of DNA methylation on RNA polymerase II traffic.

Patterns of gene expression are primarily determined by proteins that locally enhance or repress transcription. While many transcription factors target a restricted number of genes, others appear to modulate transcription levels globally. An example is MeCP2, an abundant methylated-DNA binding protein that is mutated in the neurological disorder Rett syndrome. Despite much research, the molecular mechanism by which MeCP2 regulates gene expression is not fully resolved. Here, we integrate quantitative, multidimensional experimental analysis and mathematical modeling to indicate that MeCP2 is a global transcriptional regulator whose binding to DNA creates "slow sites" in gene bodies. We hypothesize that waves of slowed-down RNA polymerase II formed behind these sites travel backward and indirectly affect initiation, reminiscent of defect-induced shockwaves in nonequilibrium physics transport models. This mechanism differs from conventional gene-regulation mechanisms, which often involve direct modulation of transcription initiation. Our findings point to a genome-wide function of DNA methylation that may account for the reversibility of Rett syndrome in mice. Moreover, our combined theoretical and experimental approach provides a general method for understanding how global gene-expression patterns are choreographed.

Spatiotemporal regulation of clonogenicity in colorectal cancer xenografts.

Cancer evolution is predominantly studied by focusing on differences in the genetic characteristics of malignant cells within tumors. However, the spatiotemporal dynamics of clonal outgrowth that underlie evolutionary trajectories remain largely unresolved. Here, we sought to unravel the clonal dynamics of colorectal cancer (CRC) expansion in space and time by using a color-based clonal tracing method. This method involves lentiviral red-green-blue (RGB) marking of cell populations, which enabled us to track individual cells and their clonal outgrowth during tumor initiation and growth in a xenograft model. We found that clonal expansion largely depends on the location of a clone, as small clones reside in the center and large clones mostly drive tumor growth at the border. These dynamics are recapitulated in a computational model, which confirms that the clone position within a tumor rather than cell-intrinsic features, is crucial for clonal outgrowth. We also found that no significant clonal loss occurs during tumor growth and clonal dispersal is limited in most models. Our results imply that, in addition to molecular features of clones such as (epi-)genetic differences between cells, clone location and the geometry of tumor growth are crucial for clonal expansion. Our findings suggest that either microenvironmental signals on the tumor border or differences in physical properties within the tumor, are major contributors to explain heterogeneous clonal expansion. Thus, this study provides further insights into the dynamics of solid tumor growth and progression, as well as the origins of tumor cell heterogeneity in a relevant model system.

Bacterial growth: a statistical physicist's guide.

Bacterial growth presents many beautiful phenomena that pose new theoretical challenges to statistical physicists, and are also amenable to laboratory experimentation. This review provides some of the essential biological background, discusses recent applications of statistical physics in this field, and highlights the potential for future research.

Phenotypic Switching Can Speed up Microbial Evolution.

Stochastic phenotype switching has been suggested to play a beneficial role in microbial populations by leading to the division of labour among cells, or ensuring that at least some of the population survives an unexpected change in environmental conditions. Here we use a computational model to investigate an alternative possible function of stochastic phenotype switching: as a way to adapt more quickly even in a static environment. We show that when a genetic mutation causes a population to become less fit, switching to an alternative phenotype with higher fitness (growth rate) may give the population enough time to develop compensatory mutations that increase the fitness again. The possibility of switching phenotypes can reduce the time to adaptation by orders of magnitude if the "fitness valley" caused by the deleterious mutation is deep enough. Our work has important implications for the emergence of antibiotic-resistant bacteria. In line with recent experimental findings, we hypothesise that switching to a slower growing - but less sensitive - phenotype helps bacteria to develop resistance by providing alternative, faster evolutionary routes to resistance.

Erratum: An exactly solvable, spatial model of mutation accumulation in cancer.

This corrects the article DOI: 10.1038/srep39511.

Mechanical interactions in bacterial colonies and the surfing probability of beneficial mutations.

Bacterial conglomerates such as biofilms and microcolonies are ubiquitous in nature and play an important role in industry and medicine. In contrast to well-mixed cultures routinely used in microbial research, bacteria in a microcolony interact mechanically with one another and with the substrate to which they are attached. Here, we use a computer model of a microbial colony of rod-shaped cells to investigate how physical interactions between cells determine their motion in the colony and how this affects biological evolution. We show that the probability that a faster-growing mutant 'surfs' at the colony's frontier and creates a macroscopic sector depends on physical properties of cells (shape, elasticity and friction). Although all these factors contribute to the surfing probability in seemingly different ways, their effects can be summarized by two summary statistics that characterize the front roughness and cell alignment. Our predictions are confirmed by experiments in which we measure the surfing probability for colonies of different front roughness. Our results show that physical interactions between bacterial cells play an important role in biological evolution of new traits, and suggest that these interactions may be relevant to processes such as de novo evolution of antibiotic resistance.

Beyond the Hypercube: Evolutionary Accessibility of Fitness Landscapes with Realistic Mutational Networks.

Evolutionary pathways describe trajectories of biological evolution in the space of different variants of organisms (genotypes). The probability of existence and the number of evolutionary pathways that lead from a given genotype to a better-adapted genotype are important measures of accessibility of local fitness optima and the reproducibility of evolution. Both quantities have been studied in simple mathematical models where genotypes are represented as binary sequences of two types of basic units, and the network of permitted mutations between the genotypes is a hypercube graph. However, it is unclear how these results translate to the biologically relevant case in which genotypes are represented by sequences of more than two units, for example four nucleotides (DNA) or 20 amino acids (proteins), and the mutational graph is not the hypercube. Here we investigate accessibility of the best-adapted genotype in the general case of K > 2 units. Using computer generated and experimental fitness landscapes we show that accessibility of the global fitness maximum increases with K and can be much higher than for binary sequences. The increase in accessibility comes from the increase in the number of indirect trajectories exploited by evolution for higher K. As one of the consequences, the fraction of genotypes that are accessible increases by three orders of magnitude when the number of units K increases from 2 to 16 for landscapes of size N ∼ 106 genotypes. This suggests that evolution can follow many different trajectories on such landscapes and the reconstruction of evolutionary pathways from experimental data might be an extremely difficult task.

An exactly solvable, spatial model of mutation accumulation in cancer.

One of the hallmarks of cancer is the accumulation of driver mutations which increase the net reproductive rate of cancer cells and allow them to spread. This process has been studied in mathematical models of well mixed populations, and in computer simulations of three-dimensional spatial models. But the computational complexity of these more realistic, spatial models makes it difficult to simulate realistically large and clinically detectable solid tumours. Here we describe an exactly solvable mathematical model of a tumour featuring replication, mutation and local migration of cancer cells. The model predicts a quasi-exponential growth of large tumours, even if different fragments of the tumour grow sub-exponentially due to nutrient and space limitations. The model reproduces clinically observed tumour growth times using biologically plausible rates for cell birth, death, and migration rates. We also show that the expected number of accumulated driver mutations increases exponentially in time if the average fitness gain per driver is constant, and that it reaches a plateau if the gains decrease over time. We discuss the realism of the underlying assumptions and possible extensions of the model.

Antibiotic resistance: a physicist's view.

The problem of antibiotic resistance poses challenges across many disciplines. One such challenge is to understand the fundamental science of how antibiotics work, and how resistance to them can emerge. This is an area where physicists can make important contributions. Here, we highlight cases where this is already happening, and suggest directions for further physics involvement in antimicrobial research.

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.

Lower glycolysis carries a higher flux than any biochemically possible alternative.

The universality of many pathways of core metabolism suggests a strong role for evolutionary selection, but it remains unclear whether existing pathways have been selected from a large or small set of biochemical possibilities. To address this question, we construct in silico all possible biochemically feasible alternatives to the trunk pathway of glycolysis and gluconeogenesis, one of the most highly conserved pathways in metabolism. We show that, even though a large number of alternative pathways exist, the alternatives carry lower flux than the real pathway under typical physiological conditions. We also find that if physiological conditions were different, different pathways could outperform those found in nature. Together, our results demonstrate how thermodynamic and biophysical constraints restrict the biochemical alternatives that are open to evolution, and suggest that the existing trunk pathway of glycolysis and gluconeogenesis may represent a maximal flux solution.

A spatial model predicts that dispersal and cell turnover limit intratumour heterogeneity.

Most cancers in humans are large, measuring centimetres in diameter, and composed of many billions of cells. An equivalent mass of normal cells would be highly heterogeneous as a result of the mutations that occur during each cell division. What is remarkable about cancers is that virtually every neoplastic cell within a large tumour often contains the same core set of genetic alterations, with heterogeneity confined to mutations that emerge late during tumour growth. How such alterations expand within the spatially constrained three-dimensional architecture of a tumour, and come to dominate a large, pre-existing lesion, has been unclear. Here we describe a model for tumour evolution that shows how short-range dispersal and cell turnover can account for rapid cell mixing inside the tumour. We show that even a small selective advantage of a single cell within a large tumour allows the descendants of that cell to replace the precursor mass in a clinically relevant time frame. We also demonstrate that the same mechanisms can be responsible for the rapid onset of resistance to chemotherapy. Our model not only provides insights into spatial and temporal aspects of tumour growth, but also suggests that targeting short-range cellular migratory activity could have marked effects on tumour growth rates.

The role of mechanical forces in the planar-to-bulk transition in growing Escherichia coli microcolonies.

Mechanical forces are obviously important in the assembly of three-dimensional multicellular structures, but their detailed role is often unclear. We have used growing microcolonies of the bacterium Escherichia coli to investigate the role of mechanical forces in the transition from two-dimensional growth (on the interface between a hard surface and a soft agarose pad) to three-dimensional growth (invasion of the agarose). We measure the position within the colony where the invasion transition happens, the cell density within the colony and the colony size at the transition as functions of the concentration of the agarose. We use a phenomenological theory, combined with individual-based computer simulations, to show how mechanical forces acting between the bacterial cells, and between the bacteria and the surrounding matrix, lead to the complex phenomena observed in our experiments-in particular the observation that agarose concentration non-trivially affects the colony size at transition. Matching these approaches leads to a prediction for how the friction between the bacteria and the agarose should vary with agarose concentration. Our experimental conditions mimic numerous clinical and environmental scenarios in which bacteria invade soft matrices, as well as shedding more general light on the transition between two- and three-dimensional growth in multicellular assemblies.