The adaptation rate of a quantitative trait in an environmental gradient

Bacterial motility can govern the dynamics of antibiotic resistance evolution

Spatial heterogeneity in antibiotic concentrations is thought to accelerate the evolution of antibiotic resistance, but current theory and experiments have overlooked the effect of cell motility on bacterial adaptation. Here, we study bacterial evolution in antibiotic landscapes with a quantitative model where bacteria evolve under the stochastic processes of proliferation, death, mutation and migration. Numerical and analytical results show that cell motility can both accelerate and decelerate bacterial adaptation by affecting the degree of genotypic mixing and ecological competition. Moreover, we find that for sufficiently high rates, cell motility can limit bacterial survival, and we derive conditions for all these regimes. Similar patterns are observed in more complex scenarios, namely where bacteria can bias their motion in chemical gradients (chemotaxis) or switch between motility phenotypes either stochastically or in a density-dependent manner. Overall, our work reveals limits to bacterial adaptation in antibiotic landscapes that are set by cell motility.

Role of a Concentration Gradient in Malaria Drug Resistance Evolution: A Combined within- and between-Hosts Modelling Approach

Resistance to antimalarial drugs is currently a growing public health problem, resulting in more cases with treatment failure. Although previous studies suggested that a concentration gradient facilitates the antibiotic resistance evolution in bacteria, no attempt has been made to investigate the roles of a concentration gradient in malaria drug resistance. Unlike the person-to-person mode of transmission of bacteria, the malaria parasites need to switch back and forth between the human and mosquito hosts to complete the life cycle and to spread the resistant alleles. Here we developed a stochastic combined within- and between-hosts evolutionary dynamics model specific to malaria parasites in order to investigate the influence of an antimalarial concentration gradient on the evolutionary dynamics of malaria drug resistance. Every stage of malaria development in both human and mosquito hosts are individually modelled using the tau-leaping algorithm. We found that the concentration gradient can accelerate antimalarial resistance evolution. The gain in resistance evolution was improved by the increase in the parasite mutation rate and the mosquito biting rate. In addition, even though the rate of resistance evolution is not sensitive to the changes in parasite reduction ratios (PRRs) of antimalarial drugs, the probability of finding the antimalarial drug resistant parasites decreases when the PRR increases.

The effect of spatiotemporal antibiotic inhomogeneities on the evolution of resistance

Combating the evolution of widespread antibiotic resistance is one of the most pressing challenges facing modern medicine. Recent research has demonstrated that the evolution of pathogens with high levels of resistance can be accelerated by spatial and temporal inhomogeneities in antibiotic concentration, which frequently arise in patients and the environment. Strategies to predict and counteract the effects of such inhomogeneities will be critical in the fight against resistance. In this paper we develop a mechanistic framework for modelling the adaptive evolution of resistance in the presence of spatiotemporal antibiotic concentrations, which treats the adaptive process as an interaction between two mutually orthogonal forces; the first returns cells to their wild-type state in the absence of antibiotic selection, and the second selects for increased coping ability in the presence of an antibiotic. We apply our model to investigate laboratory adaptation experiments, and then extend it to consider the case in which multiple strategies for resistance undergo competitive evolution.

Growth-dependent drug susceptibility can prevent or enhance spatial expansion of a bacterial population

As a population wave expands, organisms at the tip typically experience plentiful nutrients while those behind the front become nutrient-depleted. If the environment also contains a gradient of some inhibitor (e.g. a toxic drug), a tradeoff exists: the nutrient-rich tip is more exposed to the inhibitor, while the nutrient-starved region behind the front is less exposed. Here we show that this can lead to complex dynamics when the organism's response to the inhibitory substance is coupled to nutrient availability. We model a bacterial population which expands in a spatial gradient of antibiotic, under conditions where either fast-growing bacteria at the wave's tip, or slow-growing, resource-limited bacteria behind the front are more susceptible to the antibiotic. We find that growth-rate dependent susceptibility can have strong effects on the dynamics of the expanding population. If slow-growing bacteria are more susceptible, the population wave advances far into the inhibitory zone, leaving a trail of dead bacteria in its wake. In contrast, if fast-growing bacteria are more susceptible, the wave is blocked at a much lower concentration of antibiotic, but a large population of live bacteria remains behind the front. Our results may contribute to understanding the efficacy of different antimicrobials for spatially structured microbial populations such as biofilms, as well as the dynamics of ecological population expansions more generally.

Environmental heterogeneity can tip the population genetics of range expansions

The population genetics of most range expansions is thought to be shaped by the competition between Darwinian selection and random genetic drift at the range margins. Here, we show that the evolutionary dynamics during range expansions is highly sensitive to additional fluctuations induced by environmental heterogeneities. Tracking mutant clones with a tunable fitness effect in bacterial colonies grown on randomly patterned surfaces we found that environmental heterogeneity can dramatically reduce the efficacy of selection. Time-lapse microscopy and computer simulations suggest that this effect arises generically from a local 'pinning' of the expansion front, whereby stretches of the front are slowed down on a length scale that depends on the structure of the environmental heterogeneity. This pinning focuses the range expansion into a small number of 'lucky' individuals with access to expansion paths, altering the neutral evolutionary dynamics and increasing the importance of chance relative to selection.

Convection shapes the trade-off between antibiotic efficacy and the selection for resistance in spatial gradients

Since penicillin was discovered about 90 years ago, we have become used to using drugs to eradicate unwanted pathogenic cells. However, using drugs to kill bacteria, viruses or cancer cells has the serious side effect of selecting for mutant types that survive the drug attack. A crucial question therefore is how one could eradicate as many cells as possible for a given acceptable risk of drug resistance evolution. We address this general question in a model of drug resistance evolution in spatial drug gradients, which recent experiments and theories have suggested as key drivers of drug resistance. Importantly, our model takes into account the influence of convection, resulting for instance from blood flow. Using stochastic simulations, we study the fates of individual resistance mutations and quantify the trade-off between the killing of wild-type cells and the rise of resistance mutations: shallow gradients and convection into the antibiotic region promote wild-type death, at the cost of increasing the establishment probability of resistance mutations. We can explain these observed trends by modeling the adaptation process as a branching random walk. Our analysis reveals that the trade-off between death and adaptation depends on the relative length scales of the spatial drug gradient and random dispersal, and the strength of convection. Our results show that convection can have a momentous effect on the rate of establishment of new mutations, and may heavily impact the efficiency of antibiotic treatment.