The development of reliable methods for restoring susceptibility after antibiotic resistance arises has proven elusive. A greater understanding of the relationship between antibiotic administration and the evolution of resistance is key to overcoming this challenge. Here we present a data-driven mathematical approach for developing antibiotic treatment plans that can reverse the evolution of antibiotic resistance determinants. We have generated adaptive landscapes for 16 genotypes of the TEM β-lactamase that vary from the wild type genotype “TEM-1” through all combinations of four amino acid substitutions. We determined the growth rate of each genotype when treated with each of 15 β-lactam antibiotics. By using growth rates as a measure of fitness, we computed the probability of each amino acid substitution in each β-lactam treatment using two different models named the Correlated Probability Model (CPM) and the Equal Probability Model (EPM). We then performed an exhaustive search through the 15 treatments for substitution paths leading from each of the 16 genotypes back to the wild type TEM-1. We identified optimized treatment paths that returned the highest probabilities of selecting for reversions of amino acid substitutions and returning TEM to the wild type state. For the CPM model, the optimized probabilities ranged between 0.6 and 1.0. For the EPM model, the optimized probabilities ranged between 0.38 and 1.0. For cyclical CPM treatment plans in which the starting and ending genotype was the wild type, the probabilities were between 0.62 and 0.7. Overall this study shows that there is promise for reversing the evolution of resistance through antibiotic treatment plans.

Most studies on the evolution of antibiotic resistance are focused on selection for resistance at lethal antibiotic concentrations, which has allowed the detection of mutant strains that show strong phenotypic traits. However, solely focusing on lethal concentrations of antibiotics narrowly limits our perspective of antibiotic resistance evolution. New high-resolution competition assays have shown that resistant bacteria are selected at relatively low concentrations of antibiotics. This finding is important because sublethal concentrations of antibiotics are found widely in patients undergoing antibiotic therapies, and in nonmedical conditions such as wastewater treatment plants, and food and water used in agriculture and farming. To understand the impacts of sublethal concentrations on selection, we measured 30 adaptive landscapes for a set of TEM β-lactamases containing all combinations of the four amino acid substitutions that exist in TEM-50 for 15 β-lactam antibiotics at multiple concentrations. We found that there are many evolutionary pathways within this collection of landscapes that lead to nearly every TEM-genotype that we studied. While it is known that the pathways change depending on the type of β-lactam, this study demonstrates that the landscapes including fitness optima also change dramatically as the concentrations of antibiotics change. Based on these results we conclude that the presence of multiple concentrations of β-lactams in an environment result in many different adaptive landscapes through which pathways to nearly every genotype are available. Ultimately this may increase the diversity of genotypes in microbial populations.

Growth rates are an important tool in microbiology because they provide high throughput fitness measurements. The release of GrowthRates, a program that uses the output of plate reader files to automatically calculate growth rates, has facilitated experimental procedures in many areas. However, many sources of variation within replicate growth rate data exist and can decrease data reliability. We have developed a new statistical package, CompareGrowthRates (CGR), to enhance the program GrowthRates and accurately measure variation in growth rate data sets. We define a metric, Variability-score (V-score), that can help determine if variation within a data set might result in false interpretations. CGR also uses the bootstrap method to determine the fraction of bootstrap replicates in which a strain will grow the fastest. We illustrate the usage of CGR with growth rate data sets similar to those in Mira, Meza, et al. (Adaptive landscapes of resistance genes change as antibiotic concentrations change. Mol Biol Evol. 32(10): 2707-2715). These statistical methods are compatible with the analytic methods described in Growth Rates Made Easy and can be used with any set of growth rate output from GrowthRates.

The spectrophotometer has been used for decades to measure the density of bacterial populations as the turbidity expressed as optical density–OD. However, the OD alone is an unreliable metric and is only proportionately accurate to cell titers to about an OD of 0.1. The relationship between OD and cell titer depends on the configuration of the spectrophotometer, the length of the light path through the culture, the size of the bacterial cells, and the cell culture density. We demonstrate the importance of plate reader calibration to identify the exact relationship between OD and cells/mL. We use four bacterial genera and two sizes of micro-titer plates (96-well and 384-well) to show that the cell/ml per unit OD depends heavily on the bacterial cell size and plate size. We applied our calibration curve to real growth curve data and conclude the cells/mL–rather than OD–is a metric that can be used to directly compare results across experiments, labs, instruments, and species.

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In bacteria, evolution of resistance to one antibiotic is frequently associated with increased resistance (cross‐resistance) or increased susceptibility (collateral sensitivity) to other antibiotics. Cross‐resistance and collateral sensitivity are typically evaluated at the minimum inhibitory concentration (MIC). However, these susceptibility changes are not well characterized with respect to the mutant prevention concentration (MPC), the antibiotic concentration that prevents a single‐step mutation from occurring. We measured the MIC and the MPC for Staphylococcus epidermidis and 14 single‐drug resistant strains against seven antibiotics. We found that the MIC and the MPC were positively correlated but that this correlation weakened if cross‐resistance did not evolve. If any type of resistance did evolve, the range of concentrations between the MIC and the MPC tended to shift right and widen. Similar patterns of cross‐resistance and collateral sensitivity were observed at the MIC and MPC levels, though more symmetry was observed at the MIC level. Whole‐genome sequencing revealed mutations in both known‐target and nontarget genes. Moving forward, examining both the MIC and the MPC may lead to better predictions of evolutionary trajectories in antibiotic‐resistant bacteria.

Nosocomial outbreaks of bacteria are well documented. Based on these incidents, and the heavy usage of antibiotics in hospitals, it has been assumed that antibiotic resistance evolves in hospital environments. To test this assumption, we studied resistance phenotypes of bacteria collected from patient isolates at a community hospital over a 2.5-year period. A graphical model analysis shows no association between resistance and patient information other than time of arrival. This allows us to focus on time-course data. We introduce a hospital transmission model, based on negative binomial delay. Our main contribution is a statistical hypothesis test called the Nosocomial Evolution of Resistance Detector (NERD). It calculates the significance of resistance trends occurring in a hospital. It can inform hospital staff about the effects of various practices and interventions, can help detect clonal outbreaks, and is available as an R package. We applied the NERD method to each of the 16 antibiotics in the study via 16 hypothesis tests. For 13 of the antibiotics, we found that the hospital environment had no significant effect on the evolution of resistance; the hospital is merely a piece of the larger picture. The p-values obtained for the other three antibiotics (cefepime, ceftazidime, and gentamicin) indicate that particular care should be taken in hospital practices with these antibiotics. One of the three, ceftazidime, was significant after accounting for multiple hypotheses, indicating a trend of decreased resistance for this drug.

Epistasis influences the gene-environment interactions that shape bacterial fitness through antibiotic exposure which can ultimately affect the availability of certain resistance phenotypes to bacteria. The substitutions present within blaTEM-50 confer both cephalosporin and β-lactamase inhibitor resistance. We wanted to compare the evolution of blaTEM-50 with another variant, blaTEM-85, which differs in that blaTEM-85 contains only substitutions that contribute to cephalosporin resistance. Differences between the landscapes and epistatic interactions of these TEM variants are important for understanding their separate evolutionary responses to antibiotics. We hypothesized the substitutions within blaTEM-50 would result in more epistatic interactions than blaTEM-85. As expected, we found more epistatic interactions between the substitutions present in blaTEM-50 than in blaTEM-85. Our results suggest that selection from many cephalosporins is required to achieve the full potential resistance to cephalosporins, but that a single β-lactam and inhibitor combination will drive evolution of the full potential resistance phenotype. Surprisingly, we also found significantly positive increases in growth rates as antibiotic concentration increased for some of the strains expressing blaTEM-85 precursor genotypes but not the blaTEM-50 variants. This result further suggests additive interactions more effectively optimize phenotypes than epistatic interactions which means that exposure to numerous cephalosporins actually increases the ability of a TEM enzyme to confer resistance to any single cephalosporin.