Drug dependence in cancer is exploitable by optimally constructed treatment holidays.

Cancers with acquired resistance to targeted therapy can become simultaneously dependent on the presence of the targeted therapy drug for survival, suggesting that intermittent therapy may slow resistance. However, relatively little is known about which tumours are likely to become dependent and how to schedule intermittent therapy optimally. Here we characterized drug dependence across a panel of over 75 MAPK-inhibitor-resistant BRAFV600E mutant melanoma models at the population and single-clone levels. Melanocytic differentiated models exhibited a much greater tendency to give rise to drug-dependent progeny than their dedifferentiated counterparts. Mechanistically, acquired loss of microphthalmia-associated transcription factor in differentiated melanoma models drives ERK-JunB-p21 signalling to enforce drug dependence. We identified the optimal scheduling of 'drug holidays' using simple mathematical models that we validated across short and long timescales. Without detailed knowledge of tumour characteristics, we found that a simple adaptive therapy protocol can produce near-optimal outcomes using only measurements of total population size. Finally, a spatial agent-based model showed that optimal schedules derived from exponentially growing cells in culture remain nearly optimal in the context of tumour cell turnover and limited environmental carrying capacity. These findings may guide the implementation of improved evolution-inspired treatment strategies for drug-dependent cancers.

Modeling spatial evolution of multi-drug resistance under drug environmental gradients.

Multi-drug combinations to treat bacterial populations are at the forefront of approaches for infection control and prevention of antibiotic resistance. Although the evolution of antibiotic resistance has been theoretically studied with mathematical population dynamics models, extensions to spatial dynamics remain rare in the literature, including in particular spatial evolution of multi-drug resistance. In this study, we propose a reaction-diffusion system that describes the multi-drug evolution of bacteria, based on a rescaling approach (Gjini and Wood, 2021). We show how the resistance to drugs in space, and the consequent adaptation of growth rate is governed by a Price equation with diffusion. The covariance terms in this equation integrate features of drug interactions and collateral resistances or sensitivities to the drugs. We study spatial versions of the model where the distribution of drugs is homogeneous across space, and where the drugs vary environmentally in a piecewise-constant, linear and nonlinear manner. Applying concepts from perturbation theory and reaction-diffusion equations, we propose an analytical characterization of average mutant fitness in the spatial system based on the principal eigenvalue of our linear problem. This enables an accurate translation from drug spatial gradients and mutant antibiotic susceptibility traits, to the relative advantage of each mutant across the environment. Such a mathematical understanding allows to predict the precise outcomes of selection over space, ultimately from the fundamental balance between growth and movement traits, and their diversity in a population.

Scale-free correlations and potential criticality in weakly ordered populations of brain cancer cells.

Collective behavior spans several orders of magnitude of biological organization, from cell colonies to flocks of birds. We used time-resolved tracking of individual glioblastoma cells to investigate collective motion in an ex vivo model of glioblastoma. At the population level, glioblastoma cells display weakly polarized motion in the (directional) velocities of single cells. Unexpectedly, fluctuations in velocities are correlated over distances many times the size of a cell. Correlation lengths scale linearly with the maximum end-to-end length of the population, indicating that they are scale-free and lack a characteristic decay scale other than the size of the system. Last, a data-driven maximum entropy model captures statistical features of the experimental data with only two free parameters: the effective length scale (nc) and strength (J) of local pairwise interactions between tumor cells. These results show that glioblastoma assemblies exhibit scale-free correlations in the absence of polarization, suggesting that they may be poised near a critical point.

Antibiotic resistance in bacterial communities.

Bacteria are single-celled organisms, but the survival of microbial communities relies on complex dynamics at the molecular, cellular, and ecosystem scales. Antibiotic resistance, in particular, is not just a property of individual bacteria or even single-strain populations, but depends heavily on the community context. Collective community dynamics can lead to counterintuitive eco-evolutionary effects like survival of less resistant bacterial populations, slowing of resistance evolution, or population collapse, yet these surprising behaviors are often captured by simple mathematical models. In this review, we highlight recent progress - in many cases, advances driven by elegant combinations of quantitative experiments and theoretical models - in understanding how interactions between bacteria and with the environment affect antibiotic resistance, from single-species populations to multispecies communities embedded in an ecosystem.

Finding the right sequence of drugs.

Rapidly switching between similar antibiotics may help to slow down the evolution of resistance.

Price equation captures the role of drug interactions and collateral effects in the evolution of multidrug resistance.

Bacterial adaptation to antibiotic combinations depends on the joint inhibitory effects of the two drugs (drug interaction [DI]) and how resistance to one drug impacts resistance to the other (collateral effects [CE]). Here we model these evolutionary dynamics on two-dimensional phenotype spaces that leverage scaling relations between the drug-response surfaces of drug-sensitive (ancestral) and drug-resistant (mutant) populations. We show that evolved resistance to the component drugs - and in turn, the adaptation of growth rate - is governed by a Price equation whose covariance terms encode geometric features of both the two-drug-response surface (DI) in ancestral cells and the correlations between resistance levels to those drugs (CE). Within this framework, mean evolutionary trajectories reduce to a type of weighted gradient dynamics, with the drug interaction dictating the shape of the underlying landscape and the collateral effects constraining the motion on those landscapes. We also demonstrate how constraints on available mutational pathways can be incorporated into the framework, adding a third key driver of evolution. Our results clarify the complex relationship between drug interactions and collateral effects in multidrug environments and illustrate how specific dosage combinations can shift the weighting of these two effects, leading to different and temporally explicit selective outcomes.

Spatial segregation and cooperation in radially expanding microbial colonies under antibiotic stress.

Antibiotic resistance in microbial communities reflects a combination of processes operating at different scales. In this work, we investigate the spatiotemporal dynamics of bacterial colonies comprised of drug-resistant and drug-sensitive cells undergoing range expansion under antibiotic stress. Using the opportunistic pathogen Enterococcus faecalis with plasmid-encoded ß-lactamase, we track colony expansion dynamics and visualize spatial patterns in fluorescently labeled populations exposed to antibiotics. We find that the radial expansion rate of mixed communities is approximately constant over a wide range of drug concentrations and initial population compositions. Imaging of the final populations shows that resistance to ampicillin is cooperative, with sensitive cells surviving in the presence of resistant cells at otherwise lethal concentrations. The populations exhibit a diverse range of spatial segregation patterns that depend on drug concentration and initial conditions. Mathematical models indicate that the observed dynamics are consistent with global cooperation, despite the fact that ß-lactamase remains cell-associated. Experiments confirm that resistant colonies provide a protective effect to sensitive cells on length scales multiple times the size of a single colony, and populations seeded with (on average) no more than a single resistant cell can produce mixed communities in the presence of the drug. While biophysical models of drug degradation suggest that individual resistant cells offer only short-range protection to neighboring cells, we show that long-range protection may arise from synergistic effects of multiple resistant cells, providing surprisingly large protection zones even at small population fractions.

Roadmap on biology in time varying environments.

Biological organisms experience constantly changing environments, from sudden changes in physiology brought about by feeding, to the regular rising and setting of the Sun, to ecological changes over evolutionary timescales. Living organisms have evolved to thrive in this changing world but the general principles by which organisms shape and are shaped by time varying environments remain elusive. Our understanding is particularly poor in the intermediate regime with no separation of timescales, where the environment changes on the same timescale as the physiological or evolutionary response. Experiments to systematically characterize the response to dynamic environments are challenging since such environments are inherently high dimensional. This roadmap deals with the unique role played by time varying environments in biological phenomena across scales, from physiology to evolution, seeking to emphasize the commonalities and the challenges faced in this emerging area of research.

Evolution in alternating environments with tunable interlandscape correlations.

Natural populations are often exposed to temporally varying environments. Evolutionary dynamics in varying environments have been extensively studied, although understanding the effects of varying selection pressures remains challenging. Here, we investigate how cycling between a pair of statistically related fitness landscapes affects the evolved fitness of an asexually reproducing population. We construct pairs of fitness landscapes that share global fitness features but are correlated with one another in a tunable way, resulting in landscape pairs with specific correlations. We find that switching between these landscape pairs, depending on the ruggedness of the landscape and the interlandscape correlation, can either increase or decrease steady-state fitness relative to evolution in single environments. In addition, we show that switching between rugged landscapes often selects for increased fitness in both landscapes, even in situations where the landscapes themselves are anticorrelated. We demonstrate that positively correlated landscapes often possess a shared maximum in both landscapes that allows the population to step through sub-optimal local fitness maxima that often trap single landscape evolution trajectories. Finally, we demonstrate that switching between anticorrelated paired landscapes leads to ergodic-like dynamics where each genotype is populated with nonzero probability, dramatically lowering the steady-state fitness in comparison to single landscape evolution.

Fluorescent reporter plasmids for single-cell and bulk-level composition assays in E. faecalis.

Fluorescent reporters are an important tool for monitoring dynamics of bacterial populations at the single cell and community level. While there are a large range of reporter constructs available-particularly for common model organisms like E. coli-fewer options exist for other species, including E. faecalis, a gram-positive opportunistic pathogen. To expand the potential toolkit available for E. faecalis, we exchanged the original fluorescent reporter in a previously developed plasmid (pBSU101) with one of eight fluorescent reporters and confirmed that all constructs exhibited detectable fluorescence in single E. faecalis cells and mixed biofilm communities. To identify promising constructs for bulk-level experiments, we then measured the fluorescence spectra from E. faecalis populations in microwell plate (liquid) cultures during different phases of aerobic growth. Cultures showed density- and reporter-specific variations in fluorescent signal, though spectral signatures of all reporters become clear in late-exponential and stationary-phase populations. Based on these results, we identified six pairs of reporters that can be combined with simple spectral unmixing to accurately estimate population composition in 2-strain mixtures at or near stationary phase. This approach offers a simple and scalable method for selection and competition experiments in simple two-species populations under aerobic growth conditions. Finally, we incorporated codon-optimized variants of blue (BFP) and red (RFP) reporters and show that they lead to increased fluorescence in exponentially growing cells. As a whole, the results inform the scope of application of different reporters and identify both single reporters and reporter pairs that are promising for fluorescence-based assays at bulk and single-cell levels in E. faecalis.

Antibiotics can be used to contain drug-resistant bacteria by maintaining sufficiently large sensitive populations.

Standard infectious disease practice calls for aggressive drug treatment that rapidly eliminates the pathogen population before resistance can emerge. When resistance is absent, this elimination strategy can lead to complete cure. However, when resistance is already present, removing drug-sensitive cells as quickly as possible removes competitive barriers that may slow the growth of resistant cells. In contrast to the elimination strategy, a containment strategy aims to maintain the maximum tolerable number of pathogens, exploiting competitive suppression to achieve chronic control. Here, we combine in vitro experiments in computer-controlled bioreactors with mathematical modeling to investigate whether containment strategies can delay failure of antibiotic treatment regimens. To do so, we measured the "escape time" required for drug-resistant Escherichia coli populations to eclipse a threshold density maintained by adaptive antibiotic dosing. Populations containing only resistant cells rapidly escape the threshold density, but we found that matched resistant populations that also contain the maximum possible number of sensitive cells could be contained for significantly longer. The increase in escape time occurs only when the threshold density-the acceptable bacterial burden-is sufficiently high, an effect that mathematical models attribute to increased competition. The findings provide decisive experimental confirmation that maintaining the maximum number of sensitive cells can be used to contain resistance when the size of the population is sufficiently large.

Delayed antibiotic exposure induces population collapse in enterococcal communities with drug-resistant subpopulations.

The molecular underpinnings of antibiotic resistance are increasingly understood, but less is known about how these molecular events influence microbial dynamics on the population scale. Here, we show that the dynamics of E. faecalis communities exposed to antibiotics can be surprisingly rich, revealing scenarios where increasing population size or delaying drug exposure can promote population collapse. Specifically, we demonstrate how density-dependent feedback loops couple population growth and antibiotic efficacy when communities include drug-resistant subpopulations, leading to a wide range of behavior, including population survival, collapse, or one of two qualitatively distinct bistable behaviors where survival is favored in either small or large populations. These dynamics reflect competing density-dependent effects of different subpopulations, with growth of drug-sensitive cells increasing but growth of drug-resistant cells decreasing effective drug inhibition. Finally, we demonstrate how populations receiving immediate drug influx may sometimes thrive, while identical populations exposed to delayed drug influx collapse.

Antibiotic resistance is a threat to human and animal health worldwide. Although we rely on antibiotics to treat diseases caused by bacteria, such as tuberculosis, some bacteria are already resistant to many of the drugs available. Understanding the basis of resistance is crucial for developing new antibiotics, and for using current drugs more efficiently. One way that bacteria resist antibiotics is by producing enzymes that inactivate specific drugs. If a community of bacteria contains both vulnerable and resistant cells, this can lead to a phenomenon called 'cooperative resistance'. When treated with antibiotics, vulnerable cells within the group are shielded by their resistant neighbors, which effectively remove the drugs from the environment. Cooperative resistance can make it difficult for researchers to understand how resistance develops in different bacterial populations. This is because a large group of cells may collectively behave in a different way than individual cells. This means that bacterial populations are a more realistic model for 'real-world' infections and disease than studies of single cells. Now, Hallinen, Karslake and Wood show how cooperation between cells affects the way bacterial communities respond to beta-lactams, the most commonly prescribed class of antibiotic drugs. Experiments using cultures of Enterococcus faecalis, a bacterium that often causes hospital infections, revealed that the density of different bacterial populations changes the effectiveness of drugs. Although increased cell density had a protective effect on populations containing only resistant bacteria, it made non-resistant populations even more vulnerable. Mathematical modelling using information from the culture experiments predicted that interactions between vulnerable and resistant bacteria within a mixed community can determine how populations change over time. For example, if the number of antibiotic-sensitive cells is too high, this can cause the entire population to collapse. These predictions contradict the conventional understanding of how antibiotic resistance spreads, where small numbers of resistant cells multiply rapidly at the expense of vulnerable ones. These results shed new light on the complex dynamics of antibiotic resistance within bacterial populations as a whole. In the future, they may inspire new ecology-based strategies for slowing the spread of resistance, ultimately helping reduce the burden of disease.

Antibiotic interactions shape short-term evolution of resistance in E. faecalis.

Antibiotic combinations are increasingly used to combat bacterial infections. Multidrug therapies are a particularly important treatment option for E. faecalis, an opportunistic pathogen that contributes to high-inoculum infections such as infective endocarditis. While numerous synergistic drug combinations for E. faecalis have been identified, much less is known about how different combinations impact the rate of resistance evolution. In this work, we use high-throughput laboratory evolution experiments to quantify adaptation in growth rate and drug resistance of E. faecalis exposed to drug combinations exhibiting different classes of interactions, ranging from synergistic to suppressive. We identify a wide range of evolutionary behavior, including both increased and decreased rates of growth adaptation, depending on the specific interplay between drug interaction and drug resistance profiles. For example, selection in a dual ß-lactam combination leads to accelerated growth adaptation compared to selection with the individual drugs, even though the resulting resistance profiles are nearly identical. On the other hand, populations evolved in an aminoglycoside and ß-lactam combination exhibit decreased growth adaptation and resistant profiles that depend on the specific drug concentrations. We show that the main qualitative features of these evolutionary trajectories can be explained by simple rescaling arguments that correspond to geometric transformations of the two-drug growth response surfaces measured in ancestral cells. The analysis also reveals multiple examples where resistance profiles selected by drug combinations are nearly growth-optimized along a contour connecting profiles selected by the component drugs. Our results highlight trade-offs between drug interactions and resistance profiles during the evolution of multi-drug resistance and emphasize evolutionary benefits and disadvantages of particular drug pairs targeting enterococci.

Using Selection by Nonantibiotic Stressors to Sensitize Bacteria to Antibiotics.

Evolutionary adaptation of bacteria to nonantibiotic selective forces, such as osmotic stress, has been previously associated with increased antibiotic resistance, but much less is known about potentially sensitizing effects of nonantibiotic stressors. In this study, we use laboratory evolution to investigate adaptation of Enterococcus faecalis, an opportunistic bacterial pathogen, to a broad collection of environmental agents, ranging from antibiotics and biocides to extreme pH and osmotic stress. We find that nonantibiotic selection frequently leads to increased sensitivity to other conditions, including multiple antibiotics. Using population sequencing and whole-genome sequencing of single isolates from the evolved populations, we identify multiple mutations in genes previously linked with resistance to the selecting conditions, including genes corresponding to known drug targets or multidrug efflux systems previously tied to collateral sensitivity. Finally, we hypothesized based on the measured sensitivity profiles that sequential rounds of antibiotic and nonantibiotic selection may lead to hypersensitive populations by harnessing the orthogonal collateral effects of particular pairs of selective forces. To test this hypothesis, we show experimentally that populations evolved to a sequence of linezolid (an oxazolidinone antibiotic) and sodium benzoate (a common preservative) exhibit increased sensitivity to more stressors than adaptation to either condition alone. The results demonstrate how sequential adaptation to drug and nondrug environments can be used to sensitize bacteria to antibiotics and highlight new potential strategies for exploiting shared constraints governing adaptation to diverse environmental challenges.

Pervasive and diverse collateral sensitivity profiles inform optimal strategies to limit antibiotic resistance.

Evolved resistance to one antibiotic may be associated with "collateral" sensitivity to other drugs. Here, we provide an extensive quantitative characterization of collateral effects in Enterococcus faecalis, a gram-positive opportunistic pathogen. By combining parallel experimental evolution with high-throughput dose-response measurements, we measure phenotypic profiles of collateral sensitivity and resistance for a total of 900 mutant-drug combinations. We find that collateral effects are pervasive but difficult to predict because independent populations selected by the same drug can exhibit qualitatively different profiles of collateral sensitivity as well as markedly different fitness costs. Using whole-genome sequencing of evolved populations, we identified mutations in a number of known resistance determinants, including mutations in several genes previously linked with collateral sensitivity in other species. Although phenotypic drug sensitivity profiles show significant diversity, they cluster into statistically similar groups characterized by selecting drugs with similar mechanisms. To exploit the statistical structure in these resistance profiles, we develop a simple mathematical model based on a stochastic control process and use it to design optimal drug policies that assign a unique drug to every possible resistance profile. Stochastic simulations reveal that these optimal drug policies outperform intuitive cycling protocols by maintaining long-term sensitivity at the expense of short-term periods of high resistance. The approach reveals a new conceptual strategy for mitigating resistance by balancing short-term inhibition of pathogen growth with infrequent use of drugs intended to steer pathogen populations to a more vulnerable future state. Experiments in laboratory populations confirm that model-inspired sequences of four drugs reduce growth and slow adaptation relative to naive protocols involving the drugs alone, in pairwise cycles, or in a four-drug uniform cycle.

Tuning Spatial Profiles of Selection Pressure to Modulate the Evolution of Drug Resistance.

Spatial heterogeneity plays an important role in the evolution of drug resistance. While recent studies have indicated that spatial gradients of selection pressure can accelerate resistance evolution, much less is known about evolution in more complex spatial profiles. Here we use a stochastic toy model of drug resistance to investigate how different spatial profiles of selection pressure impact the time to fixation of a resistant allele. Using mean first passage time calculations, we show that spatial heterogeneity accelerates resistance evolution when the rate of spatial migration is sufficiently large relative to mutation but slows fixation for small migration rates. Interestingly, there exists an intermediate regime-characterized by comparable rates of migration and mutation-in which the rate of fixation can be either accelerated or decelerated depending on the spatial profile, even when spatially averaged selection pressure remains constant. Finally, we demonstrate that optimal tuning of the spatial profile can dramatically slow the spread and fixation of resistant subpopulations, even in the absence of a fitness cost for resistance. Our results may lay the groundwork for optimized, spatially resolved drug dosing strategies for mitigating the effects of drug resistance.

Interplay between Antibiotic Efficacy and Drug-Induced Lysis Underlies Enhanced Biofilm Formation at Subinhibitory Drug Concentrations.

Subinhibitory concentrations of antibiotics have been shown to enhance biofilm formation in multiple bacterial species. While antibiotic exposure has been associated with modulated expression of many biofilm-related genes, the mechanisms of drug-induced biofilm formation remain a focus of ongoing research efforts and may vary significantly across species. In this work, we investigate antibiotic-induced biofilm formation in Enterococcus faecalis, a leading cause of nosocomial infections. We show that biofilm formation is enhanced by subinhibitory concentrations of cell wall synthesis inhibitors but not by inhibitors of protein, DNA, folic acid, or RNA synthesis. Furthermore, enhanced biofilm is associated with increased cell lysis, increases in extracellular DNA (eDNA) levels, and increases in the density of living cells in the biofilm. In addition, we observe similar enhancement of biofilm formation when cells are treated with nonantibiotic surfactants that induce cell lysis. These findings suggest that antibiotic-induced biofilm formation is governed by a trade-off between drug toxicity and the beneficial effects of cell lysis. To understand this trade-off, we developed a simple mathematical model that predicts changes in antibiotic-induced biofilm formation due to external perturbations, and we verified these predictions experimentally. Specifically, we demonstrate that perturbations that reduce eDNA (DNase treatment) or decrease the number of living cells in the planktonic phase (a second antibiotic) decrease biofilm induction, while chemical inhibitors of cell lysis increase relative biofilm induction and shift the peak to higher antibiotic concentrations. Overall, our results offer experimental evidence linking cell wall synthesis inhibitors, cell lysis, increased eDNA levels, and biofilm formation in E. faecalis while also providing a predictive quantitative model that sheds light on the interplay between cell lysis and antibiotic efficacy in developing biofilms.

Population Density Modulates Drug Inhibition and Gives Rise to Potential Bistability of Treatment Outcomes for Bacterial Infections.

The inoculum effect (IE) is an increase in the minimum inhibitory concentration (MIC) of an antibiotic as a function of the initial size of a microbial population. The IE has been observed in a wide range of bacteria, implying that antibiotic efficacy may depend on population density. Such density dependence could have dramatic effects on bacterial population dynamics and potential treatment strategies, but explicit measures of per capita growth as a function of density are generally not available. Instead, the IE measures MIC as a function of initial population size, and population density changes by many orders of magnitude on the timescale of the experiment. Therefore, the functional relationship between population density and antibiotic inhibition is generally not known, leaving many questions about the impact of the IE on different treatment strategies unanswered. To address these questions, here we directly measured real-time per capita growth of Enterococcus faecalis populations exposed to antibiotic at fixed population densities using multiplexed computer-automated culture devices. We show that density-dependent growth inhibition is pervasive for commonly used antibiotics, with some drugs showing increased inhibition and others decreased inhibition at high densities. For several drugs, the density dependence is mediated by changes in extracellular pH, a community-level phenomenon not previously linked with the IE. Using a simple mathematical model, we demonstrate how this density dependence can modulate population dynamics in constant drug environments. Then, we illustrate how time-dependent dosing strategies can mitigate the negative effects of density-dependence. Finally, we show that these density effects lead to bistable treatment outcomes for a wide range of antibiotic concentrations in a pharmacological model of antibiotic treatment. As a result, infections exceeding a critical density often survive otherwise effective treatments.