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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