Statistical Package for Growth Rates Made Easy

A stochastic programming approach to the antibiotics time machine problem

Antibiotics Time Machine is an important problem to understand antibiotic resistance and how it can be reversed. Mathematically, it can be modeled as follows: Consider a set of genotypes, each of which contain a set of mutated and unmutated genes. Suppose that a set of growth rate measurements of each genotype under a set of antibiotics is given. The transition probabilities of a 'realization' of a Markov chain associated with each arc under each antibiotic are computable via a predefined function given the growth rate realizations. The aim is to maximize the expected probability of reaching to the genotype with all unmutated genes given the initial genotype in a predetermined number of transitions, considering the following two sources of uncertainties: (i) the randomness in growth rates, (ii) the randomness in transition probabilities, which are functions of growth rates. We develop stochastic mixed-integer linear programming and dynamic programming approaches to solve static and dynamic versions of the Antibiotics Time Machine Problem under the aforementioned uncertainties. We adapt a Sample Average Approximation approach that exploits the special structure of the problem and provide accurate solutions that perform very well in an out-of-sample analysis.

Estimating microbial population data from optical density

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.

Possible Role for Allelic Variation in Yeast MED15 in Ecological Adaptation

The propensity for Saccharomyces cerevisiae yeast to ferment sugars into ethanol and CO₂ has long been useful in the production of a wide range of food and drink. In the production of alcoholic beverages, the yeast strain selected for fermentation is crucial because not all strains are equally proficient in tolerating fermentation stresses. One potential mechanism by which domesticated yeast may have adapted to fermentation stresses is through changes in the expression of stress response genes. MED15 is a general transcriptional regulator and RNA Pol II Mediator complex subunit which modulates the expression of many metabolic and stress response genes. In this study, we explore the role of MED15 in alcoholic fermentation. In addition, we ask whether MED15 alleles from wine, sake or palm wine yeast improve fermentation activity and grape juice fermentation stress responses. And last, we investigate to what extent any differences in activity are due to allelic differences in the lengths of three polyglutamine tracts in MED15. We find that strains lacking MED15 are deficient in fermentation and fermentation stress responses and that MED15 alleles from alcoholic beverage yeast strains can improve both the fermentation capacity and the response to ethanol stresses when transplanted into a standard laboratory strain. Finally, we find that polyglutamine tract length in the Med15 protein is one determinant in the efficiency of the alcoholic fermentation process. These data lead to a working model in which polyglutamine tract length and other types of variability within transcriptional hubs like the Mediator subunit, Med15, may contribute to a reservoir of transcriptional profiles that may provide a fitness benefit in the face of environmental fluctuations.

Adaptive Processes Change as Multiple Functions Evolve

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 bla _TEM-50 confer both cephalosporin and β-lactamase inhibitor resistance. We wanted to compare the evolution of bla _TEM-50 with that of another variant, bla _TEM-85, which differs in that bla _TEM-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 bla _TEM-50 would result in more epistatic interactions than for bla _TEM-85 As expected, we found more epistatic interactions between the substitutions present in bla _TEM-50 than in bla _TEM-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 bla _TEM-85 precursor genotypes but not the bla _TEM-50 variants. This result further suggests that 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.

Exploiting evolutionary trade-offs for posttreatment management of drug-resistant populations

Antibiotic resistance frequently evolves through fitness trade-offs in which the genetic alterations that confer resistance to a drug can also cause growth defects in resistant cells. Here, through experimental evolution in a microfluidics-based turbidostat, we demonstrate that antibiotic-resistant cells can be efficiently inhibited by amplifying the fitness costs associated with drug-resistance evolution. Using tavaborole-resistant Escherichia coli as a model, we show that genetic mutations in leucyl-tRNA synthetase (that underlie tavaborole resistance) make resistant cells intolerant to norvaline, a chemical analog of leucine that is mistakenly used by tavaborole-resistant cells for protein synthesis. We then show that tavaborole-sensitive cells quickly outcompete tavaborole-resistant cells in the presence of norvaline due to the amplified cost of the molecular defect of tavaborole resistance. This finding illustrates that understanding molecular mechanisms of drug resistance allows us to effectively amplify even small evolutionary vulnerabilities of resistant cells to potentially enhance or enable adaptive therapies by accelerating posttreatment competition between resistant and susceptible cells.

Clinical Mutations That Partially Activate the Stringent Response Confer Multidrug Tolerance in Staphylococcus aureus

Antibiotic tolerance is an underappreciated antibiotic escape strategy that is associated with recurrent and relapsing infections, as well as acting as a precursor to resistance. Tolerance describes the ability of a bacterial population to survive transient exposure to an otherwise lethal concentration of antibiotic without exhibiting an elevated MIC. It is detected in time-kill assays as a lower rate of killing than a susceptible strain and can be quantified by the metric minimum duration for killing (MDK). The molecular mechanisms behind tolerance are varied, but activation of the stringent response (SR) via gene knockouts and/or chemical induction has long been associated with tolerance. More recently, two Gram-positive clinical isolates from persistent bacteremias were found to bear mutations in the SR controller, Rel, that caused elevated levels of the alarmone (p)ppGpp. Here, we show that introduction of either of these mutations into Staphylococcus aureus confers tolerance to five different classes of antibiotic as a result of (p)ppGpp-mediated growth defects (longer lag time and/or lower growth rate). The degree of tolerance is related to the severity of the growth defect and ranges from a 1.5- to 3.1-fold increase in MDK. Two classes of proposed SR inhibitor were unable to reverse or reduce this tolerance. Our findings reveal the significance of SR-activating mutations in terms of tolerance and clinical treatment failures. The panel of strains reported here provide a clinically relevant model of tolerance for further investigation of its link to resistance development, as well as potential validation of high-throughput tolerance screens.