The MIC of an antibiotic required to prevent replication is used both as a measure of the susceptibility/resistance of bacteria to that drug and as the single pharmacodynamic parameter for the rational design of antibiotic treatment regimes. MICs are experimentally estimated in vitro under conditions optimal for the action of the antibiotic. However, bacteria rarely grow in these optimal conditions. Using a mathematical model of the pharmacodynamics of antibiotics, we make predictions about the nutrient dependency of bacterial growth in the presence of antibiotics. We test these predictions with experiments in broth and a glucose-limited minimal media with Escherichia coli and eight different antibiotics. Our experiments question the sufficiency of using MICs and simple pharmacodynamic functions as measures of the pharmacodynamics of antibiotics under the nutritional conditions of infected tissues. To an extent that varies among drugs: (i) the estimated MICs obtained in rich media are greater than those estimated in minimal media; (ii) exposure to these drugs increases the time before logarithmic growth starts, their lag; and (iii) the stationary-phase density of E. coli populations declines with greater sub-MIC antibiotic concentrations. We postulate a mechanism to account for the relationship between sub-MICs of antibiotics and these growth parameters. This study is limited to a single bacterial strain and two types of culture media with different nutritive content. These limitations aside, the results of our study clearly question the use of MIC as the unique pharmacodynamic parameter to develop therapeutically oriented protocols. IMPORTANCE For studies of antibiotics and how they work, the most-often used measurement of drug efficacy is the MIC. The MIC is the concentration of an antibiotic needed to inhibit bacterial growth. This parameter is critical to the design and implementation of antibiotic therapy. We provide evidence that the use of MIC as the sole measurement for antibiotic efficacy ignores important aspects of bacterial growth dynamics. Before now, there has not been a nexus between bacteria, the conditions in which they grow, and the MIC. Most importantly, few studies have considered sub-MICs of antibiotics, despite their clinical importance. Here, we explore these concentrations in-depth, and we demonstrate MIC to be an incomplete measure of how an infection will interact with a specific antibiotic. Understanding the critiques of MIC is the first of many steps needed to improve infectious disease treatment.

The dynamics of growth of bacterial populations has been extensively studied for planktonic cells in well-agitated liquid culture, in which all cells have equal access to nutrients. In the real world, bacteria are more likely to live in physically structured habitats as colonies, within which individual cells vary in their access to nutrients. The dynamics of bacterial growth in such conditions is poorly understood, and, unlike that for liquid culture, there is not a standard broadly used mathematical model for bacterial populations growing in colonies in three dimensions (3-d). By extending the classic Monod model of resource-limited population growth to allow for spatial heterogeneity in the bacterial access to nutrients, we develop a 3-d model of colonies, in which bacteria consume diffusing nutrients in their vicinity. By following the changes in density of E. coli in liquid and embedded in glucose-limited soft agar, we evaluate the fit of this model to experimental data. The model accounts for the experimentally observed presence of a sub-exponential, diffusion-limited growth regime in colonies, which is absent in liquid cultures. The model predicts and our experiments confirm that, as a consequence of inter-colony competition for the diffusing nutrients and of cell death, there is a non-monotonic relationship between total number of colonies within the habitat and the total number of individual cells in all of these colonies. This combined theoretical-experimental study reveals that, within 3-d colonies, E. coli cells are loosely packed, and colonies produce about 2.5 times as many cells as the liquid culture from the same amount of nutrients. We verify that this is because cells in liquid culture are larger than in colonies. Our model provides a baseline description of bacterial growth in 3-d, deviations from which can be used to identify phenotypic heterogeneities and inter-cellular interactions that further contribute to the structure of bacterial communities.

Retrons were described in 1984 as DNA sequences that code for a reverse transcriptase and a unique single-stranded DNA/RNA hybrid called multicopy single-stranded DNA (msDNA). It would not be until 2020 that a function was shown for retrons, when compelling evidence was presented that retrons activate an abortive infection pathway in response to bacteriophage (phage) infection. When infected with the virulent mutant of the phage lambda, λVIR, and to a lesser extent, other phages, a retron designated Ec48 is activated, the Escherichia coli bearing this retron element dies, and the infecting phage is lost. With the aid of a mathematical model, we explore the a priori conditions under which retrons will protect bacterial populations from predation by phage and the conditions under which retron-bearing bacteria will evolve in populations without this element. Using isogenic E. coli with and without Ec48 and λVIR, we estimated the parameters of our model and tested the hypotheses generated from our analysis of its properties. Our models and experiments demonstrate that cells expressing a retron-mediated abortive infection system can protect bacterial populations. Our results demonstrate that retron bearing bacteria only have a competitive advantage under a limited set of conditions.

The most significant difference between bacteriophages functionally and ecologically is whether they are purely lytic (virulent) or temperate. Virulent phages can only be transmitted horizontally by infection, most commonly with the death of their hosts. Temperate phages can also be transmitted horizontally, but upon infection of susceptible bacteria, their genomes can be incorporated into that of their host's as a prophage and be transmitted vertically in the course of cell division by their lysogenic hosts. From what we know from studies with the temperate phage Lambda and other temperate phages, in laboratory culture, lysogenic bacteria are protected from killing by the phage coded for by their prophage by immunity; where upon infecting lysogens, the free temperate phage coded by their prophage is lost. Why are lysogens resistant and not only immune to the phage coded by their prophage since immunity does not confer protection against virulent phages? To address this question, we used a mathematical model and performed experiments with temperate and virulent mutants of the phage Lambda in laboratory culture. Our models predict and experiments confirm that selection would favor the evolution of resistant and immune lysogens, particularly if the environment includes virulent phage that shares the same receptors as the temperate. To explore the validity and generality of this prediction, we examined 10 lysogenic Escherichia coli from natural populations. All 10 were capable of forming immune lysogens, but their original hosts were resistant to the phage coded by their prophage.

The successful treatment of bacterial infections is the product of a collaboration between antibiotics and the host’s immune defenses. Nevertheless, in the design of antibiotic treatment regimens, few studies have explored the combined action of antibiotics and the immune response to clearing infections. Here, we use mathematical models to examine the collective contribution of antibiotics and the immune response to the treatment of acute, self-limiting bacterial infections. Our models incorporate the pharmacokinetics and pharmacodynamics of the antibiotics, the innate and adaptive immune responses, and the population and evolutionary dynamics of the target bacteria. We consider two extremes for the antibiotic-immune relationship: one in which the efficacy of the immune response in clearing infections is directly proportional to the density of the pathogen; the other in which its action is largely independent of this density. We explore the effect of antibiotic dose, dosing frequency, and term of treatment on the time before clearance of the infection and the likelihood of antibiotic-resistant bacteria emerging and ascending. Our results suggest that, under most conditions, high dose, full-term therapy is more effective than more moderate dosing in promoting the clearance of the infection and decreasing the likelihood of emergence of antibiotic resistance. Our results also indicate that the clinical and evolutionary benefits of increasing antibiotic dose are not indefinite. We discuss the current status of data in support of and in opposition to the predictions of this study, consider those elements that require additional testing, and suggest how they can be tested.

For many bacterial infections, noninherited mechanisms of resistance are responsible for extending the term of treatment and in some cases precluding its success. Among the most important of these noninherited mechanisms of resistance is the ability of bacteria to form biofilms. There is compelling evidence that bacteria within biofilms are more refractory to antibiotics than are planktonic cells. Not so clear, however, is the extent to which this resistance can be attributed to the structure of biofilms rather than the physiology and density of bacteria within them. To explore the contribution of the structure of biofilms to resistance in a quantitative way, we developed an assay that compares the antibiotic sensitivity of bacteria in biofilms to cells mechanically released from these structures. Our method, which we apply to Escherichia coli and Staphylococcus aureus each with antibiotics of five classes, controls for the density and physiological state of the treated bacteria. For most of the antibiotics tested, the bacteria in biofilms were no more resistant than the corresponding populations of planktonic cells of similar density. Our results, however, suggest that killing by gentamicin, streptomycin, and colistin is profoundly inhibited by the structure of biofilms; these drugs are substantially more effective in killing bacteria released from biofilms than cells within these structures.

The objectives of the study were to develop a quantitative framework for generating hypotheses for and interpreting the results of time-kill and continuous-culture experiments designed to evaluate the efficacy of antibiotics and to relate the results of these experiments to MIC data. A mathematical model combining the pharmacodynamics (PD) of antibiotics with the population dynamics of bacteria exposed to these drugs in batch and continuous cultures was developed, and its properties were analyzed numerically (using computer simulations). These models incorporate details of (i) the functional form of the relationship between the concentrations of the antibiotics and rates of kill, (ii) the density of the target population of bacteria, (iii) the growth rate of the bacteria, (iv) byproduct resources generated from dead bacteria, (v) antibiotic-refractory subpopulations, persistence, and wall growth (biofilms), and (vi) density-independent and -dependent decay in antibiotic concentrations. Each of the factors noted above can profoundly affect the efficacy of antibiotics. Consequently, if the traditional (CLSI) MICs represent the sole pharmacodynamic parameter, PK/PD indices can fail to predict the efficacy of antibiotic treatment protocols. More comprehensive pharmacodynamic data obtained with time-kill and continuous-culture experiments would improve the predictive value of these indices. The mathematical model developed here can facilitate the design and interpretation of these experiments. The validity of the assumptions behind the construction of these models and the predictions (hypotheses) generated from the analysis of their properties can be tested experimentally. These hypotheses are presented, suggestions are made about how they can be tested, and the existing statuses of these tests are briefly discussed.

We used mathematical models to address several questions concerning the epidemiologic and evolutionary future of HIV/AIDS in human populations. Our analysis suggests that 1) when HIV first enters a human population, and for many subsequent years, the epidemic is driven by early transmissions, possibly occurring before donors have seroconverted to HIV-positive status; 2) new HIV infections in a subpopulation (risk group) may decline or level off due to the saturation of the susceptible hosts rather than to evolution of the virus or to the efficacy of intervention, education, and public health measures; 3) evolution in humans for resistance to HIV infection or for the infection to engender a lower death rate will require thousands of years and will be achieved only after vast numbers of persons die of AIDS; 4) evolution is unlikely to increase the virulence of HIV; and 5) if HIV chemotherapy reduces the transmissibility of the virus, treating individual patients can reduce the frequency of HIV infections and AIDS deaths in the general population.

Plasmids are key drivers of bacterial evolution because they are crucial agents for the horizontal transfer of adaptive traits, such as antibiotic resistance. Most plasmids entail a metabolic burden that reduces the fitness of their host if there is no selection for plasmid-encoded genes. It has been hypothesized that the translational demand imposed by plasmid-encoded genes is a major mechanism driving the fitness cost of plasmids. Plasmid-encoded genes typically present a different codon usage from host chromosomal genes. As a consequence, the translation of plasmid-encoded genes might sequestrate ribosomes on plasmid transcripts, overwhelming the translation machinery of the cell. However, the pervasiveness and origins of the translation-derived costs of plasmids are yet to be assessed. Here, we systematically altered translation efficiency in the host cell to disentangle the fitness effects produced by six natural antibiotic resistance plasmids. We show that limiting translation efficiency either by reducing the number of available ribosomes or their processivity does not increase plasmid costs. Overall, our results suggest that ribosomal paucity is not a major contributor to plasmid fitness costs. This article is part of the theme issue 'The secret lives of microbial mobile genetic elements'.

In the course of liquid culture, serial passage experiments with Escherichia coli K-12 bearing a mutator gene deletion (ΔmutS) we observed the evolution of strains that appeared to kill or inhibit the growth of the bacteria from where they were derived, their ancestors. We demonstrate that this inhibition occurs after the cells stop growing and requires physical contact between the evolved and ancestral bacteria. Thereby, it is referred to as stationary phase contact-dependent inhibition (SCDI). The evolution of this antagonistic relationship is not anticipated from existing theory and experiments of competition in mass (liquid) culture. Nevertheless, it occurred in the same way (parallel evolution) in the eight independent serial transfer cultures, through different single base substitutions in a gene in the glycogen synthesis pathway, glgC. We demonstrate that the observed mutations in glgC, which codes for ADP-glucose pyrophosphorylase, are responsible for both the ability of the evolved bacteria to inhibit or kill their ancestors and their immunity to that inhibition or killing. We present evidence that without additional evolution, mutator genes, or known mutations in glgC, other strains of E. coli K-12 are also capable of SCDI or sensitive to this inhibition. We interpret this, in part, as support for the generality of SCDI and also as suggesting that the glgC mutations responsible for the SCDI, which evolved in our experiments, may suppress the action of one or more genes responsible for the sensitivity of E. coli to SCDI. Using numerical solutions to a mathematical model and in vitro experiments, we explore the population dynamics of SCDI and postulate the conditions responsible for its evolution in mass culture. We conclude with a brief discussion of the potential ecological significance of SCDI and its possible utility for the development of antimicrobial agents, which unlike existing antibiotics, can kill or inhibit the growth of bacteria that are not growing.