Pharmacodynamic functions: a multiparameter approach to the design of antibiotic treatment regimens

ScanGrow: Deep Learning-Based Live Tracking of Bacterial Growth in Broth

Monitoring the growth of bacterial cultures is one of the most common techniques in microbiology. This is usually achieved by using expensive and bulky spectrophotometric plate readers which periodically measure the optical density of bacterial cultures during the incubation period. In this study, we present a completely novel way of obtaining bacterial growth curves based on the classification of scanned images of cultures rather than using spectrophotometric measurements. We trained a deep learning model with images of bacterial broths contained in microplates, and we integrated it into a custom-made software application that triggers a flatbed scanner to timely capture images, automatically processes the images, and represents all growth curves. The developed tool, ScanGrow, is presented as a low-cost and high-throughput alternative to plate readers, and it only requires a computer connected to a flatbed scanner and equipped with our open-source ScanGrow application. In addition, this application also assists in the pre-processing of data to create and evaluate new models, having the potential to facilitate many routine microbiological techniques.

Modeling Polygenic Antibiotic Resistance Evolution in Biofilms

The recalcitrance of biofilms to antimicrobials is a multi-factorial phenomenon, including genetic, physical, and physiological changes. Individually, they often cannot account for biofilm recalcitrance. However, their combination can increase the minimal inhibitory concentration of antibiotics needed to kill bacterial cells by three orders of magnitude, explaining bacterial survival under otherwise lethal drug treatment. The relative contributions of these factors depend on the specific antibiotics, bacterial strain, as well as environmental and growth conditions. An emerging population genetic property—increased biofilm genetic diversity—further enhances biofilm recalcitrance. Here, we develop a polygenic model of biofilm recalcitrance accounting for multiple phenotypic mechanisms proposed to explain biofilm recalcitrance. The model can be used to generate predictions about the emergence of resistance—its timing and population genetic consequences. We use the model to simulate various treatments and experimental setups. Our simulations predict that the evolution of resistance is impaired in biofilms at low antimicrobial concentrations while it is facilitated at higher concentrations. In scenarios that allow bacteria exchange between planktonic and biofilm compartments, the evolution of resistance is further facilitated compared to scenarios without exchange. We compare these predictions to published experimental observations.

Temporin B Forms Hetero-Oligomers with Temporin L, Modifies Its Membrane Activity, and Increases the Cooperativity of Its Antibacterial Pharmacodynamic Profile

The pharmacodynamic profile of antimicrobial peptides (AMPs) and their in vivo synergy are two factors that are thought to restrict resistance evolution and ensure their conservation. The frog Rana temporaria secretes a family of closely related AMPs, temporins A–L, as an effective chemical dermal defense. The antibacterial potency of temporin L has been shown to increase synergistically in combination with both temporins B and A, but this is modest. Here we show that the less potent temporin B enhances the cooperativity of the in vitro antibacterial activity of the more potent temporin L against EMRSA-15 and that this may be associated with an altered interaction with the bacterial plasma membrane, a feature critical for the antibacterial activity of most AMPs. Addition of buforin II, a histone H2A fragment, can further increase the cooperativity. Molecular dynamics simulations indicate temporins B and L readily form hetero-oligomers in models of Gram-positive bacterial plasma membranes. Patch-clamp studies show transmembrane ion conductance is triggered with lower amounts of both peptides and more quickly when used in combination, but conductance is of a lower amplitude and pores are smaller. Temporin B may therefore act by forming temporin L/B hetero-oligomers that are more effective than temporin L homo-oligomers at bacterial killing and/or by reducing the probability of the latter forming until a threshold concentration is reached. Exploration of the mechanism of synergy between AMPs isolated from the same organism may therefore yield antibiotic combinations with advantageous pharmacodynamic properties.

Allele-specific collateral and fitness effects determine the dynamics of fluoroquinolone resistance evolution

A promising strategy to overcome the evolution of antibiotic-resistant bacteria is to use collateral sensitivity-informed antibiotic treatments that rely on cycling or mixing of antibiotics, such that that resistance toward one antibiotic confers increased sensitivity to the other. Here, focusing on multistep fluoroquinolone resistance in Streptococcus pneumoniae, we show that antibiotic resistance induces diverse collateral responses whose magnitude and direction are determined by allelic identity. Using mathematical simulations, we show that these effects can be exploited via combination treatment regimens to suppress the de novo emergence of resistance during treatment.

Collateral sensitivity (CS), which arises when resistance to one antibiotic increases sensitivity toward other antibiotics, offers treatment opportunities to constrain or reverse the evolution of antibiotic resistance. The applicability of CS-informed treatments remains uncertain, in part because we lack an understanding of the generality of CS effects for different resistance mutations, singly or in combination. Here, we address this issue in the gram-positive pathogen Streptococcus pneumoniae by measuring collateral and fitness effects of clinically relevant gyrA and parC alleles and their combinations that confer resistance to fluoroquinolones. We integrated these results in a mathematical model that allowed us to evaluate how different in silico combination treatments impact the dynamics of resistance evolution. We identified common and conserved CS effects of different gyrA and parC alleles; however, the spectrum of collateral effects was unique for each allele or allelic pair. This indicated that allelic identity can impact the evolutionary dynamics of resistance evolution during monotreatment and combination treatment. Our model simulations, which included the experimentally derived antibiotic susceptibilities and fitness effects, and antibiotic-specific pharmacodynamics revealed that both collateral and fitness effects impact the population dynamics of resistance evolution. Overall, we provide evidence that allelic identity and interactions can have a pronounced impact on collateral effects to different antibiotics and suggest that these need to be considered in models examining CS-based therapies.

Lulworthinone: In Vitro Mode of Action Investigation of an Antibacterial Dimeric Naphthopyrone Isolated from a Marine Fungus

Treatment options for infections caused by antimicrobial-resistant bacteria are rendered ineffective, and drug alternatives are needed—either from new chemical classes or drugs with new modes of action. Historically, natural products have been important contributors to drug discovery. In a recent study, the dimeric naphthopyrone lulworthinone produced by an obligate marine fungus in the family Lulworthiaceae was discovered. The observed potent antibacterial activity against Gram-positive bacteria, including several clinical methicillin-resistant Staphylococcus aureus (MRSA) isolates, prompted this follow-up mode of action investigation. This paper aimed to characterize the antibacterial mode of action (MOA) of lulworthinone by combining in vitro assays, NMR experiments and microscopy. The results point to a MOA targeting the bacterial membrane, leading to improper cell division. Treatment with lulworthinone induced an upregulation of genes responding to cell envelope stress in Bacillus subtilis. Analysis of the membrane integrity and membrane potential indicated that lulworthinone targets the bacterial membrane without destroying it. This was supported by NMR experiments using artificial lipid bilayers. Fluorescence microscopy revealed that lulworthinone affects cell morphology and impedes the localization of the cell division protein FtsZ. Surface plasmon resonance and dynamic light scattering assays showed that this activity is linked with the compound‘s ability to form colloidal aggregates. Antibacterial agents acting at cell membranes are of special interest, as the development of bacterial resistance to such compounds is deemed more difficult to occur.

Kinetics of Bacterial Adaptation, Growth, and Death at Didecyldimethylammonium Chloride sub-MIC Concentrations

Minimum inhibitory concentration (MIC) and minimum bactericidal concentration (MBC) are standard indexes for determining disinfection effectiveness. Nevertheless, they are static values disregarding the kinetics at sub-MIC concentrations where adaptation, growth, stationary, and death phases can be observed. The understanding of these dynamic mechanisms is crucial to designing effective disinfection strategies. In this study, we studied the 48 h kinetics of Bacillus cereus and Escherichia coli cells exposed to sub-MIC concentrations of didecyldimethylammonium chloride (DDAC). Two mathematical models were employed to reproduce the experiments: the only-growth classical logistic model and a mechanistic model including growth and death dynamics. Although both models reproduce the lag, exponential and stationary phases, only the mechanistic model is able to reproduce the death phase and reveals the concentration dependence of the bactericidal/bacteriostatic activity of DDAC. This model could potentially be extended to study other antimicrobials and reproduce changes in optical density (OD) and colony-forming units (CFUs) with the same parameters and mechanisms of action.

Pharmacodynamic Parameters of Pharmacokinetic/Pharmacodynamic (PK/PD) Integration Models

Pharmacokinetic/pharmacodynamic (PK/PD) integration models are used to investigate the antimicrobial activity characteristics of drugs targeting pathogenic bacteria through comprehensive analysis of the interactions between PK and PD parameters. PK/PD models have been widely applied in the development of new drugs, optimization of the dosage regimen, and prevention and treatment of drug-resistant bacteria. In PK/PD analysis, minimal inhibitory concentration (MIC) is the most commonly applied PD parameter. However, accurately determining MIC is challenging and this can influence the therapeutic effect. Therefore, it is necessary to optimize PD indices to generate more rational results. Researchers have attempted to optimize PD parameters using mutant prevention concentration (MPC)-based PK/PD models, multiple PD parameter-based PK/PD models, kill rate-based PK/PD models, and others. In this review, we discuss progress on PD parameters for PK/PD models to provide a valuable reference for drug development, determining the dosage regimen, and preventing drug-resistant mutations.

Kinetics of bactericidal potency with synergistic combination of allicin and selected antibiotics

Synergistic therapy against the resurgence of bacterial pathogenesis is a modern trend for antibacterial chemotherapy. The phytochemical allicin, found in garlic extract is a commendable antimicrobial agent that can be used in synergistic combination with modern antibiotics. Determination of optimal antibacterial combination for the target species is vital for maximizing efficacy, lowering toxicity, total eradication of the bacterial cells and minimization of the risk of resistance generation. In this present investigation, Hill function-based pharmacodynamics models were employed to elaborate various time-kill kinetics parameters. The bactericidal potency of the synergistic combinations of allicin and individual antibiotic was assessed in comparison to their monotherapy application viz. using sole allicin and sole antibiotics (levofloxacin, ciprofloxacin, oxytetracycline, rifaximin, ornidazole and azithromycin) on actively growing Bacillus subtilis and Escherichia coli bacteria. Here, all the synergistic combinations showed significantly better (t-test p-value < 0.05) killing effect and biofilm reduction potential compared to their respective monotherapy application, where the highest killing effect was observed with rifaximin-allicin combination (kill rate was more than 5.5 h^-1). Moreover, the average inhibition potential to protein denaturation by the synergistic combination group was significantly higher (3.4 fold) than the sole antibiotic's group manifests reduction in the dose-related toxicity. The potential of synergism between antibiotics and allicin combination demonstrated greater killing efficiency at significantly lower concentration compared to monotherapy with increased kill rates in all cases.

Population genetics, biofilm recalcitrance, and antibiotic resistance evolution

Biofilms are communities of bacteria forming high-density sessile colonies. Such a lifestyle comes associated with costs and benefits: while the growth rate of biofilms is often lower than that of their free-living counterparts, this cost is readily repaid once the colony is subjected to antibiotics. Biofilms can grow in antibiotic concentrations a thousand times higher than planktonic bacteria. While numerous mechanisms have been proposed to explain biofilm recalcitrance towards antibiotics, little is yet known about their effect on the evolution of resistance. We synthesize the current understanding of biofilm recalcitrance from a pharmacodynamic and a population genetics perspective. Using the pharmacodynamic framework, we discuss the effects of various mechanisms and show that biofilms can either promote or impede resistance evolution.

Phage-Antibiotic Synergy Inhibited by Temperate and Chronic Virus Competition

As antibiotic resistance grows more frequent for common bacterial infections, alternative treatment strategies such as phage therapy have become more widely studied in the medical field. While many studies have explored the efficacy of antibiotics, phage therapy, or synergistic combinations of phages and antibiotics, the impact of virus competition on the efficacy of antibiotic treatment has not yet been considered. Here, we model the synergy between antibiotics and two viral types, temperate and chronic, in controlling bacterial infections. We demonstrate that while combinations of antibiotic and temperate viruses exhibit synergy, competition between temperate and chronic viruses inhibits bacterial control with antibiotics. In fact, our model reveals that antibiotic treatment may counterintuitively increase the bacterial load when a large fraction of the bacteria are antibiotic resistant, and both chronic and temperate phages are present.

Modelling the antimicrobial pharmacodynamics for bacterial strains with versus without acquired resistance to fluoroquinolones or cephalosporins

OBJECTIVES

Antimicrobial resistance threatens therapeutic options for human and animal bacterial diseases worldwide. Current antimicrobial treatment regimens were designed against bacterial strains that were fully susceptible to them. To expand the useable lifetime of existing antimicrobial drug classes by modifying treatment regimens, data are needed on the antimicrobial pharmacodynamics (PD) against strains with reduced susceptibility. In this study, we generated and mathematically modelled the PD of the fluoroquinolone ciprofloxacin and the cephalosporin ceftriaxone against non-typhoidal Salmonella enterica subsp. enterica strains with varying levels of acquired resistance.

METHODS

We included Salmonella strains across categories of reduced susceptibility to fluoroquinolones or cephalosporins reported to date, including isolates from human infections, food-animal products sold in retail, and food-animal production. We generated PD data for each drug and strain via time-kill assay. Mathematical models were compared in their fit to represent the PD. The best-fit model's parameter values across the strain susceptibility categories were compared.

RESULTS

The inhibitory baseline sigmoid I_max (or E_max) model was best fit for the PD of each antimicrobial against a majority of the strains. There were statistically significant differences in the PD parameter values across the strain susceptibility categories for each antimicrobial.

CONCLUSION

The results demonstrate predictable multiparameter changes in the PD of these first-line antimicrobials depending on the Salmonella strain's susceptibility phenotype and specific genes conferring reduced susceptibility. The generated PD parameter estimates could be used to optimise treatment regimens against infections by strains with reduced susceptibility.

Inter-species interactions alter antibiotic efficacy in bacterial communities

The efficacy of antibiotic treatments targeting polymicrobial communities is not well predicted by conventional in vitro susceptibility testing based on determining minimum inhibitory concentration (MIC) in monocultures. One reason for this is that inter-species interactions can alter the community members' susceptibility to antibiotics. Here we quantify, and identify mechanisms for, community-modulated changes of efficacy for clinically relevant antibiotics against the pathogen Pseudomonas aeruginosa in model cystic fibrosis (CF) lung communities derived from clinical samples. We demonstrate that multi-drug resistant Stenotrophomonas maltophilia can provide high levels of antibiotic protection to otherwise sensitive P. aeruginosa. Exposure protection to imipenem was provided by chromosomally encoded metallo-β-lactamase that detoxified the environment; protection was dependent upon S. maltophilia cell density and was provided by S. maltophilia strains isolated from CF sputum, increasing the MIC of P. aeruginosa by up to 16-fold. In contrast, the presence of S. maltophilia provided no protection against meropenem, another routinely used carbapenem. Mathematical ordinary differential equation modelling shows that the level of exposure protection provided against different carbapenems can be explained by differences in antibiotic efficacy and inactivation rate. Together, these findings reveal that exploitation of pre-occurring antimicrobial resistance, and inter-specific competition, can have large impacts on pathogen antibiotic susceptibility, highlighting the importance of microbial ecology for designing successful antibiotic treatments for multispecies communities.

Pharmacodynamics of Ceftriaxone, Ertapenem, Fosfomycin and Gentamicin in Neisseria gonorrhoeae

Objectives: To assess the in vitro effect of select antimicrobials on the growth of N. gonorrhoeae and its pharmacodynamic parameters. Methods: Time–kill assays were performed on two reference N. gonorrhoeae strains (ceftriaxone-resistant WHO X and ceftriaxone-susceptible WHO F) and one clinical N. gonorrhoeae strain (ceftriaxone-susceptible CS03307). Time–kill curves were constructed for each strain by measuring bacterial growth rates at doubling antimicrobial concentrations of ceftriaxone, ertapenem, fosfomycin and gentamicin. Inputs from these curves were used to estimate minimal bacterial growth rates at high antimicrobial concentrations (ψ_min), maximum bacterial growth rates in the absence of antimicrobials (ψ_max), pharmacodynamic minimum inhibitory concentrations (zMIC), and Hill’s coefficients (κ). Results: Ceftriaxone, ertapenem and fosfomycin showed gradual death overtime at higher antimicrobial concentrations with a relatively high ψ_min, demonstrating time-dependent activity. Compared to WHO F, the ψ_min for WHO X was significantly increased, reflecting decreased killing activity for ceftriaxone, ertapenem and fosfomycin. At high ceftriaxone concentrations, WHO X was still efficiently killed. CS03307 also showed a high ψ_min for ceftriaxone in spite of a low MIC and no difference in ψ_min for fosfomycin in spite of significant MIC and zMIC differences. Gentamicin showed rapid killing for all three strains at high concentrations, demonstrating concentration-dependent activity. Conclusions: Based on time–kill assays, high-dosage ceftriaxone could be used to treat N. gonorrhoeae strains with MIC above breakpoint, with gentamicin as a potential alternative. Whether ertapenem or fosfomycin would be effective to treat strains with a high MIC to ceftriaxone is questionable.

Collateral Sensitivity Interactions between Antibiotics Depend on Local Abiotic Conditions

Mutations conferring resistance to one antibiotic can increase (cross-resistance) or decrease (collateral sensitivity) resistance to others. Antibiotic combinations displaying collateral sensitivity could be used in treatments that slow resistance evolution. However, lab-to-clinic translation requires understanding whether collateral effects are robust across different environmental conditions. Here, we isolated and characterized resistant mutants of Escherichia coli using five antibiotics, before measuring collateral effects on resistance to other paired antibiotics. During both isolation and phenotyping, we varied conditions in ways relevant in nature (pH, temperature, and bile). This revealed that local abiotic conditions modified expression of resistance against both the antibiotic used during isolation and other antibiotics. Consequently, local conditions influenced collateral sensitivity in two ways: by favoring different sets of mutants (with different collateral sensitivities) and by modifying expression of collateral effects for individual mutants. These results place collateral sensitivity in the context of environmental variation, with important implications for translation to real-world applications. IMPORTANCE When bacteria become resistant to an antibiotic, the genetic changes involved sometimes increase (cross-resistance) or decrease (collateral sensitivity) their resistance to other antibiotics. Antibiotic combinations showing repeatable collateral sensitivity could be used in treatment to slow resistance evolution. However, collateral sensitivity interactions may depend on the local environmental conditions that bacteria experience, potentially reducing repeatability and clinical application. Here, we show that variation in local conditions (pH, temperature, and bile salts) can influence collateral sensitivity in two ways: by favoring different sets of mutants during bacterial resistance evolution (with different collateral sensitivities to other antibiotics) and by modifying expression of collateral effects for individual mutants. This suggests that translation from the lab to the clinic of new approaches exploiting collateral sensitivity will be influenced by local abiotic conditions.

Quantitative biology of survival under antibiotic treatments

The mathematical formulation for the dynamics of growth reduction and/or killing under antibiotic treatments has a long history. Even before the extensive use of antibiotics, attempts to model the killing dynamics of biocides were made [1]. Here, we review relatively simple quantitative formulations of the two main modes of survival under antibiotics, resistance and tolerance, as well as their heterogeneity in bacterial populations. We focus on the two main types of heterogeneity that have been described: heteroresistance and antibiotic persistence, each linked to the variation in a different parameter of the antibiotic response dynamics. Finally, we review the effects on survival of combining resistance and tolerance mutations as well as on the mode and tempo of evolution under antibiotic treatments.

Design principles of collateral sensitivity-based dosing strategies

Collateral sensitivity (CS)-based antibiotic treatments, where increased resistance to one antibiotic leads to increased sensitivity to a second antibiotic, may have the potential to limit the emergence of antimicrobial resistance. However, it remains unclear how to best design CS-based treatment schedules. To address this problem, we use mathematical modelling to study the effects of pathogen- and drug-specific characteristics for different treatment designs on bacterial population dynamics and resistance evolution. We confirm that simultaneous and one-day cycling treatments could supress resistance in the presence of CS. We show that the efficacy of CS-based cycling therapies depends critically on the order of drug administration. Finally, we find that reciprocal CS is not essential to suppress resistance, a result that significantly broadens treatment options given the ubiquity of one-way CS in pathogens. Overall, our analyses identify key design principles of CS-based treatment strategies and provide guidance to develop treatment schedules to suppress resistance.

The impact of the intestinal microbiota and the mucosal permeability on three different antibiotic drugs

BackgroundThe totality of bacteria, protozoa, viruses and fungi that lives in the human body is called microbiota. Human microbiota specifically colonizes the skin, the respiratory and urinary tract, the urogenital tract and the gastrointestinal system. This study focuses on the intestinal microbiota to explore the drug-microbiota relationship and, therefore, how the drug bioavailability changes in relation to the microbiota biodiversity to identify more personalized therapies, with the minimum risk of side effects. MethodsTo achieve this goal, we developed a new mathematical model with two compartments, the intestine and the blood, which takes into account the colonic mucosal permeability variation - measured by Ussing chamber system on human colonic mucosal biopsies - and the fecal microbiota composition, determined through microbiota 16S rRNA sequencing analysis. Both of the clinical parameters were evaluated in a group of Irritable Bowel Syndrome patients compared to a group of healthy controls. Key ResultsThe results show that plasma drug concentration increases as bacterial concentration decreases, while it decreases as intestinal length decreases too. ConclusionsThe study provides interesting data since in literature there are not yet mathematical models with these features, in which the importance of intestinal microbiota, the "forgotten organ", is considered both for the subject health state and in the nutrients and drugs metabolism.

Synthesis and Antimycobacterial Activity of 3-Phenyl-1H-indoles

Tuberculosis has been described as a global health crisis since the 1990s, with an estimated 1.4 million deaths in the last year. Herein, a series of 20 1H-indoles were synthesized and evaluated as in vitro inhibitors of Mycobacterium tuberculosis (Mtb) growth. Furthermore, the top hit compounds were active against multidrug-resistant strains, without cross-resistance with first-line drugs. Exposing HepG2 and Vero cells to the molecules for 72 h showed that one of the evaluated structures was devoid of apparent toxicity. In addition, this 3-phenyl-1H-indole showed no genotoxicity signals. Finally, time-kill and pharmacodynamic model analyses demonstrated that this compound has bactericidal activity at concentrations close to the Minimum Inhibitory Concentration, coupled with a strong time-dependent behavior. To the best of our knowledge, this study describes the activity of 3-phenyl-1H-indole against Mtb for the first time.

Stochastic response of bacterial cells to antibiotics: its mechanisms and implications for population and evolutionary dynamics

The effectiveness of antibiotics against bacterial infections has been declining due to the emergence of resistance. Precisely understanding the response of bacteria to antibiotics is critical to maximizing antibiotic-induced bacterial eradication while minimizing the emergence of antibiotic resistance. Cell-to-cell heterogeneity in antibiotic susceptibility is observed across various bacterial species for a wide range of antibiotics. Heterogeneity in antibiotic susceptibility is not always due to the genetic differences. Rather, it can be caused by non-genetic mechanisms such as stochastic gene expression and biased partitioning upon cell division. Heterogeneous susceptibility leads to the stochastic growth and death of individual cells and stochastic fluctuations in population size. These fluctuations have important implications for the eradication of bacterial populations and the emergence of genotypic resistance.

Prediction of Minocycline Activity in the Gut From a Pig Preclinical Model Using a Pharmacokinetic -Pharmacodynamic Approach

The increase of multidrug-resistant (MDR) bacteria has renewed interest in old antibiotics, such as minocycline, that can be active against various MDR Gram-negative pathogens. The elimination of minocycline by both kidneys and liver makes it suitable for impaired renal function patients. However, the drawback is the possible elimination of a high amount of drug in the intestines, with potential impact on the digestive microbiota during treatment. This study aimed to predict the potential activity of minocycline against Enterobacterales in the gut after parenteral administration, by combining in vivo and in vitro studies. Total minocycline concentrations were determined by UPLC-UV in the plasma and intestinal content of piglets following intravenous administration. In parallel, the in vitro activity of minocycline was assessed against two Escherichia coli strains in sterilized intestinal contents, and compared to activity in a standard broth. We found that minocycline concentrations were 6–39 times higher in intestinal contents than plasma. Furthermore, minocycline was 5- to 245-fold less active in large intestine content than in a standard broth. Using this PK-PD approach, we propose a preclinical pig model describing the link between systemic and gut exposure to minocycline, and exploring its activity against intestinal Enterobacterales by taking into account the impact of intestinal contents.

Filamentous Bacteriophages and the Competitive Interaction between Pseudomonas aeruginosa Strains under Antibiotic Treatment: a Modeling Study

Pseudomonas aeruginosa (Pa) is a major bacterial pathogen responsible for chronic lung infections in cystic fibrosis patients. Recent work has implicated Pf bacteriophages, nonlytic filamentous viruses produced by Pa, in the chronicity and severity of Pa infections. Pf phages act as structural elements in Pa biofilms and sequester aerosolized antibiotics, thereby contributing to antibiotic tolerance. Consistent with a selective advantage in this setting, the prevalence of Pf-positive (Pf+) bacteria increases over time in these patients. However, the production of Pf phages comes at a metabolic cost to bacteria, such that Pf+ strains grow more slowly than Pf-negative (Pf-) strains in vitro. Here, we use a mathematical model to investigate how these competing pressures might influence the relative abundance of Pf+ versus Pf- strains in different settings. Our model suggests that Pf+ strains of Pa cannot outcompete Pf- strains if the benefits of phage production falls onto both Pf+ and Pf- strains for a majority of parameter combinations. Further, phage production leads to a net positive gain in fitness only at antibiotic concentrations slightly above the MIC (i.e., concentrations for which the benefits of antibiotic sequestration outweigh the metabolic cost of phage production) but which are not lethal for Pf+ strains. As a result, our model suggests that frequent administration of intermediate doses of antibiotics with low decay rates and high killing rates favors Pf+ over Pf- strains. These models inform our understanding of the ecology of Pf phages and suggest potential treatment strategies for Pf+ Pa infections. IMPORTANCE Filamentous phages are a frontier in bacterial pathogenesis, but the impact of these phages on bacterial fitness is unclear. In particular, Pf phages produced by Pa promote antibiotic tolerance but are metabolically expensive to produce, suggesting that competing pressures may influence the prevalence of Pf+ versus Pf- strains of Pa in different settings. Our results identify conditions likely to favor Pf+ strains and thus antibiotic tolerance. This study contributes to a better understanding of the unique ecology of filamentous phages in both environmental and clinical settings and may facilitate improved treatment strategies for combating antibiotic tolerance.

Multi-step vs. single-step resistance evolution under different drugs, pharmacokinetics, and treatment regimens

The success of antimicrobial treatment is threatened by the evolution of drug resistance. Population genetic models are an important tool in mitigating that threat. However, most such models consider resistance emergence via a single mutational step. Here, we assembled experimental evidence that drug resistance evolution follows two patterns: (i) a single mutation, which provides a large resistance benefit, or (ii) multiple mutations, each conferring a small benefit, which combine to yield high-level resistance. Using stochastic modeling, we then investigated the consequences of these two patterns for treatment failure and population diversity under various treatments. We find that resistance evolution is substantially limited if more than two mutations are required and that the extent of this limitation depends on the combination of drug type and pharmacokinetic profile. Further, if multiple mutations are necessary, adaptive treatment, which only suppresses the bacterial population, delays treatment failure due to resistance for a longer time than aggressive treatment, which aims at eradication.

Bacteria primed by antimicrobial peptides develop tolerance and persist

Antimicrobial peptides (AMPs) are key components of innate immune defenses. Because of the antibiotic crisis, AMPs have also come into focus as new drugs. Here, we explore whether prior exposure to sub-lethal doses of AMPs increases bacterial survival and abets the evolution of resistance. We show that Escherichia coli primed by sub-lethal doses of AMPs develop tolerance and increase persistence by producing curli or colanic acid, responses linked to biofilm formation. We develop a population dynamic model that predicts that priming delays the clearance of infections and fuels the evolution of resistance. The effects we describe should apply to many AMPs and other drugs that target the cell surface. The optimal strategy to tackle tolerant or persistent cells requires high concentrations of AMPs and fast and long-lasting expression. Our findings also offer a new understanding of non-inherited drug resistance as an adaptive response and could lead to measures that slow the evolution of resistance.

Animals and plants defend themselves with ancient molecules called antimicrobial peptides (AMPs) against pathogens. As more and more bacterial diseases have become drug resistant, these AMPs are considered as promising alternatives. In natural situation such as on the skin, bacteria are often exposed to low concentrations of AMPs that do no kill. Here we show that the bacterium Escherichia coli when exposed to such low concentrations becomes recalcitrant to killing concentrations of the same AMPs. We report the ways in which the bacteria alter their surface to do so. We then use a mathematical model to show that these effects caused by low concentrations can drive the evolution of resistance. From the perspective of an organism using AMPs in self-defense, the best option is to deploy high concentrations of AMPs for long. Our findings also offer a new understanding of similar drug resistance mechanisms.

A New Method for Optimizing Sepsis Therapy by Nivolumab and Meropenem Combination: Importance of Early Intervention and CTL Reinvigoration Rate as a Response Marker

Background: Recently, there has been a growing interest in applying immune checkpoint blockers (ICBs), so far used to treat cancer, to patients with bacterial sepsis. We aimed to develop a method for predicting the personal benefit of potential treatments for sepsis, and to apply it to therapy by meropenem, an antibiotic drug, and nivolumab, a programmed cell death-1 (PD-1) pathway inhibitor.

Methods: We defined an optimization problem as a concise framework of treatment aims and formulated a fitness function for grading sepsis treatments according to their success in accomplishing the pre-defined aims. We developed a mathematical model for the interactions between the pathogen, the cellular immune system and the drugs, whose simulations under diverse combined meropenem and nivolumab schedules, and calculation of the fitness function for each schedule served to plot the fitness landscapes for each set of treatments and personal patient parameters.

Results: Results show that treatment by meropenem and nivolumab has maximum benefit if the interval between the onset of the two drugs does not exceed a dose-dependent threshold, beyond which the benefit drops sharply. However, a second nivolumab application, within 7–10 days after the first, can extinguish a pathogen which the first nivolumab application failed to remove. The utility of increasing nivolumab total dose above 6 mg/kg is contingent on the patient's personal immune attributes, notably, the reinvigoration rate of exhausted CTLs and the overall suppression rates of functional CTLs. A baseline pathogen load, higher than 5,000 CFU/μL, precludes successful nivolumab and meropenem combination therapy, whereas when the initial load is lower than 3,000 CFU/μL, meropenem monotherapy suffices for removing the pathogen.

Discussion: Our study shows that early administration of nivolumab, 6 mg/kg, in combination with antibiotics, can alleviate bacterial sepsis in cases where antibiotics alone are insufficient and the initial pathogen load is not too high. The study pinpoints the role of precision medicine in sepsis, suggesting that personalized therapy by ICBs can improve pathogen elimination and dampen immunosuppression. Our results highlight the importance in using reliable markers for classifying patients according to their predicted response and provides a valuable tool in personalizing the drug regimens for patients with sepsis.

Proximate and ultimate causes of the bactericidal action of antibiotics

During the past 85 years of antibiotic use, we have learned a great deal about how these 'miracle' drugs work. We know the molecular structures and interactions of these drugs and their targets and the effects on the structure, physiology and replication of bacteria. Collectively, we know a great deal about these proximate mechanisms of action for virtually all antibiotics in current use. What we do not know is the ultimate mechanism of action; that is, how these drugs irreversibly terminate the 'individuality' of bacterial cells by removing barriers to the external world (cell envelopes) or by destroying their genetic identity (DNA). Antibiotics have many different 'mechanisms of action' that converge to irreversible lethal effects. In this Perspective, we consider what our knowledge of the proximate mechanisms of action of antibiotics and the pharmacodynamics of their interaction with bacteria tell us about the ultimate mechanisms by which these antibiotics kill bacteria.

Fitness benefits to bacteria of carrying prophages and prophage-encoded antibiotic-resistance genes peak in different environments

Understanding the role of horizontal gene transfer (HGT) in adaptation is a key challenge in evolutionary biology. In microbes, an important mechanism of HGT is prophage acquisition (phage genomes integrated into bacterial chromosomes). Prophages can influence bacterial fitness via the transfer of beneficial genes (including antibiotic‐resistance genes, ARGs), protection from superinfecting phages, or switching to a lytic lifecycle that releases free phages infectious to competitors. We expect these effects to depend on environmental conditions because of, for example, environment‐dependent induction of the lytic lifecycle. However, it remains unclear how costs/benefits of prophages vary across environments. Here, studying prophages with/without ARGs in Escherichia coli, we disentangled the effects of prophages alone and adaptive genes they carry. In competition with prophage‐free strains, benefits from prophages and ARGs peaked in different environments. Prophages were most beneficial when induction of the lytic lifecycle was common, whereas ARGs were more beneficial upon antibiotic exposure and with reduced prophage induction. Acquisition of prophage‐encoded ARGs by competing strains was most common when prophage induction, and therefore free phages, were common. Thus, selection on prophages and adaptive genes they carry varies independently across environments, which is important for predicting the spread of mobile/integrating genetic elements and their role in evolution.

Antibiotic resistance: turning evolutionary principles into clinical reality

Antibiotic resistance is one of the major challenges facing modern medicine worldwide. The past few decades have witnessed rapid progress in our understanding of the multiple factors that affect the emergence and spread of antibiotic resistance at the population level and the level of the individual patient. However, the process of translating this progress into health policy and clinical practice has been slow. Here, we attempt to consolidate current knowledge about the evolution and ecology of antibiotic resistance into a roadmap for future research as well as clinical and environmental control of antibiotic resistance. At the population level, we examine emergence, transmission and dissemination of antibiotic resistance, and at the patient level, we examine adaptation involving bacterial physiology and host resilience. Finally, we describe new approaches and technologies for improving diagnosis and treatment and minimizing the spread of resistance.

Quantitative modeling predicts mechanistic links between pre-treatment microbiome composition and metronidazole efficacy in bacterial vaginosis

Bacterial vaginosis is a condition associated with adverse reproductive outcomes and characterized by a shift from a Lactobacillus-dominant vaginal microbiota to a polymicrobial microbiota, consistently colonized by strains of Gardnerella vaginalis. Metronidazole is the first-line treatment; however, treatment failure and recurrence rates remain high. To understand complex interactions between Gardnerella vaginalis and Lactobacillus involved in efficacy, here we develop an ordinary differential equation model that predicts bacterial growth as a function of metronidazole uptake, sensitivity, and metabolism. The model shows that a critical factor in efficacy is Lactobacillus sequestration of metronidazole, and efficacy decreases when the relative abundance of Lactobacillus is higher pre-treatment. We validate results in Gardnerella and Lactobacillus co-cultures, and in two clinical cohorts, finding women with recurrence have significantly higher pre-treatment levels of Lactobacillus relative to bacterial vaginosis-associated bacteria. Overall results provide mechanistic insight into how personalized differences in microbial communities influence vaginal antibiotic efficacy.

Treatment timing shifts the benefits of short and long antibiotic treatment over infection

Antibiotics are the major tool for treating bacterial infections. Rising antibiotic resistance, however, calls for a better use of antibiotics. While classical recommendations favor long and aggressive treatments, more recent clinical trials advocate for moderate regimens. In this debate, two axes of 'aggression' have typically been conflated: treatment intensity (dose) and treatment duration. The third dimension of treatment timing along each individual's infection course has rarely been addressed. By using a generic mathematical model of bacterial infection controlled by immune response, we examine how the relative effectiveness of antibiotic treatment varies with its timing, duration and antibiotic kill rate. We show that short or long treatments may both be beneficial depending on treatment onset, the target criterion for success and on antibiotic efficacy. This results from the dynamic trade-off between immune response build-up and resistance risk in acute, self-limiting infections, and uncertainty relating symptoms to infection variables. We show that in our model early optimal treatments tend to be 'short and strong', while late optimal treatments tend to be 'mild and long'. This suggests a shift in the aggression axis depending on the timing of treatment. We find that any specific optimal treatment schedule may perform more poorly if evaluated by other criteria, or under different host-specific conditions. Our results suggest that major advances in antibiotic stewardship must come from a deeper empirical understanding of bacterial infection processes in individual hosts. To guide rational therapy, mathematical models need to be constrained by data, including a better quantification of personal disease trajectory in humans. Lay summary: Bacterial infections are becoming more difficult to treat worldwide because bacteria are becoming resistant to the antibiotics used. Addressing this problem requires a better understanding of how treatment along with other host factors impact antibiotic resistance. Until recently, most theoretical research has focused on the importance of antibiotic dosing on antibiotic resistance, however, duration and timing of treatment remain less explored. Here, we use a mathematical model of a generic bacterial infection to study three aspects of treatment: treatment dose/efficacy (defined by the antibiotic kill rate), duration, and timing, and their impact on several infection endpoints. We show that short and long treatment success strongly depends on when treatment begins (defined by the symptom threshold), the target criterion to optimize, and on antibiotic efficacy. We find that if administered early in an infection, "strong and short" therapy performs better, while if treatment begins at higher bacterial densities, a "mild and long" course of antibiotics is favored. In the model host immune defenses are key in preventing relapses, controlling antibiotic resistant bacteria and increasing the effectiveness of moderate intervention. In order to improve rational treatments of human infections, we call for a better quantification of individual disease trajectories in bacteria-immunity space.

Adapt or Perish: Evolutionary Rescue in a Gradually Deteriorating Environment

We investigate the evolutionary rescue of a microbial population in a gradually deteriorating environment, through a combination of analytical calculations and stochastic simulations. We consider a population destined for extinction in the absence of mutants, which can survive only if mutants sufficiently adapted to the new environment arise and fix. We show that mutants that appear later during the environment deterioration have a higher probability to fix. The rescue probability of the population increases with a sigmoidal shape when the product of the carrying capacity and of the mutation probability increases. Furthermore, we find that rescue becomes more likely for smaller population sizes and/or mutation probabilities if the environment degradation is slower, which illustrates the key impact of the rapidity of environment degradation on the fate of a population. We also show that our main conclusions are robust across various types of adaptive mutants, including specialist and generalist ones, as well as mutants modeling antimicrobial resistance evolution. We further express the average time of appearance of the mutants that do rescue the population and the average extinction time of those that do not. Our methods can be applied to other situations with continuously variable fitnesses and population sizes, and our analytical predictions are valid in the weak-to-moderate mutation regime.

Mathematical modeling of the 'inoculum effect': six applicable models and the MIC advancement point concept

Antimicrobial treatment regimens against bacterial pathogens are designed using the drug's minimum inhibitory concentration (MIC) measured at a bacterial density of 5.7 log₁₀(colony-forming units (CFU)/mL) in vitro. However, MIC changes with pathogen density, which varies among infectious diseases and during treatment. Incorporating this into treatment design requires realistic mathematical models of the relationships. We compared the MIC–density relationships for Gram-negative Escherichia coli and non-typhoidal Salmonella enterica subsp. enterica and Gram-positive Staphylococcus aureus and Streptococcus pneumonia (for n = 4 drug-susceptible strains per (sub)species and 1–8 log₁₀(CFU/mL) densities), for antimicrobial classes with bactericidal activity against the (sub)species: β-lactams (ceftriaxone and oxacillin), fluoroquinolones (ciprofloxacin), aminoglycosides (gentamicin), glycopeptides (vancomycin) and oxazolidinones (linezolid). Fitting six candidate mathematical models to the log₂(MIC) vs. log₁₀(CFU/mL) curves did not identify one model best capturing the relationships across the pathogen–antimicrobial combinations. Gompertz and logistic models (rather than a previously proposed Michaelis–Menten model) fitted best most often. Importantly, the bacterial density after which the MIC sharply increases (an MIC advancement-point density) and that density's intra-(sub)species range evidently depended on the antimicrobial mechanism of action. Capturing these dependencies for the disease–pathogen–antimicrobial combination could help determine the MICs for which bacterial densities are most informative for treatment regimen design.

Semimechanistic Modeling of Eravacycline Pharmacodynamics Using In Vitro Time-Kill Data with MIC Incorporated in an Adaptive Resistance Function

Effective bacterial infection eradication requires not only potent antibacterial agents but also proper dosing strategies. Current practices generally utilize point estimates of the effects of therapeutic agents, even though the actual kinetics of exposure are much more complex and relevant. Here, we use a full time course of the observed in vitro effects to develop a semimechanistic pharmacokinetic-pharmacodynamic model for eravacycline against multiple Gram-negative bacterial pathogens. This model incorporates components such as pharmacokinetics, bacterial life cycle, and drug effects to quantitatively describe the time course of antibacterial killing and the emergence of resistance. Model discrimination was performed by comparing goodness of fit, convergence diagnostics, and objective function values. Models were validated by assessing their abilities to describe bacterial count time courses in visual predictive checks. The final model describes 576 bacterial counts (expressed in log₁₀ CFU per milliliter) from 144 in vitro time-kill experiments with low residual error and high precision. We characterize antibacterial susceptibility as a function of the MIC and adaptive resistance. In doing so, we show that the MIC is proportional to initial susceptibility at 0 h and the development of resistance over the course of 16 h. Altogether, this model may be useful in supporting dose selection, since it incorporates in vitro pharmacodynamics and clinically observed individual drug susceptibilities.

A Roadblock-and-Kill Mechanism of Action Model for the DNA-Targeting Antibiotic Ciprofloxacin

Fluoroquinolones, antibiotics that cause DNA damage by inhibiting DNA topoisomerases, are clinically important, but their mechanism of action is not yet fully understood. In particular, the dynamical response of bacterial cells to fluoroquinolone exposure has hardly been investigated, although the SOS response, triggered by DNA damage, is often thought to play a key role. Here, we investigated the growth inhibition of the bacterium Escherichia coli by the fluoroquinolone ciprofloxacin at low concentrations. We measured the long-term and short-term dynamical response of the growth rate and DNA production rate to ciprofloxacin at both the population and single-cell levels. We show that, despite the molecular complexity of DNA metabolism, a simple roadblock-and-kill model focusing on replication fork blockage and DNA damage by ciprofloxacin-poisoned DNA topoisomerase II (gyrase) quantitatively reproduces long-term growth rates in the presence of ciprofloxacin. The model also predicts dynamical changes in the DNA production rate in wild-type E. coli and in a recombination-deficient mutant following a step-up of ciprofloxacin. Our work highlights that bacterial cells show a delayed growth rate response following fluoroquinolone exposure. Most importantly, our model explains why the response is delayed: it takes many doubling times to fragment the DNA sufficiently to inhibit gene expression. We also show that the dynamical response is controlled by the timescale of DNA replication and gyrase binding/unbinding to the DNA rather than by the SOS response, challenging the accepted view. Our work highlights the importance of including detailed biophysical processes in biochemical-systems models to quantitatively predict the bacterial response to antibiotics.

Drug-target binding quantitatively predicts optimal antibiotic dose levels in quinolones

Antibiotic resistance is rising and we urgently need to gain a better quantitative understanding of how antibiotics act, which in turn would also speed up the development of new antibiotics. Here, we describe a computational model (COMBAT-COmputational Model of Bacterial Antibiotic Target-binding) that can quantitatively predict antibiotic dose-response relationships. Our goal is dual: We address a fundamental biological question and investigate how drug-target binding shapes antibiotic action. We also create a tool that can predict antibiotic efficacy a priori. COMBAT requires measurable biochemical parameters of drug-target interaction and can be directly fitted to time-kill curves. As a proof-of-concept, we first investigate the utility of COMBAT with antibiotics belonging to the widely used quinolone class. COMBAT can predict antibiotic efficacy in clinical isolates for quinolones from drug affinity (R2>0.9). To further challenge our approach, we also do the reverse: estimate the magnitude of changes in drug-target binding based on antibiotic dose-response curves. We overexpress target molecules to infer changes in antibiotic-target binding from changes in antimicrobial efficacy of ciprofloxacin with 92-94% accuracy. To test the generality of our approach, we use the beta-lactam ampicillin to predict target molecule occupancy at MIC from antimicrobial action with 90% accuracy. Finally, we apply COMBAT to predict antibiotic concentrations that can select for resistance due to novel resistance mutations. Using ciprofloxacin and ampicillin as well defined test cases, our work demonstrates that drug-target binding is a major predictor of bacterial responses to antibiotics. This is surprising because antibiotic action involves many additional effects downstream of drug-target binding. In addition, COMBAT provides a framework to inform optimal antibiotic dose levels that maximize efficacy and minimize the rise of resistant mutants.

Human antimicrobial peptide, LL-37, induces non-inheritable reduced susceptibility to vancomycin in Staphylococcus aureus

Antimicrobial peptides (AMPs) are central components of the innate immune system providing protection against pathogens. Yet, serum and tissue concentrations vary between individuals and with disease conditions. We demonstrate that the human AMP LL-37 lowers the susceptibility to vancomycin in the community-associated methicillin-resistant S. aureus (CA-MRSA) strain FPR3757 (USA300). Vancomycin is used to treat serious MRSA infections, but treatment failures occur despite MRSA strains being tested susceptible according to standard susceptibility methods. Exposure to physiologically relevant concentrations of LL-37 increased the minimum inhibitory concentration (MIC) of S. aureus towards vancomycin by 75%, and resulted in shortened lag-phase and increased colony formation at sub-inhibitory concentrations of vancomycin. Computer simulations using a mathematical antibiotic treatment model indicated that a small increase in MIC might decrease the efficacy of vancomycin in clearing a S. aureus infection. This prediction was supported in a Galleria mellonella infection model, where exposure of S. aureus to LL-37 abolished the antimicrobial effect of vancomycin. Thus, physiological relevant concentrations of LL-37 reduce susceptibility to vancomycin, indicating that tissue and host specific variations in LL-37 concentrations may influence vancomycin susceptibility in vivo.

Eco-evolutionary control of pathogens

Vaccinations and therapies targeting evolving pathogens aim to curb the pathogen and to steer it toward a controlled evolutionary state. Control is leveraged against the pathogen’s intrinsic evolutionary forces, which in turn, can drive an escape from control. Here, we analyze a simple model of control, in which a host produces antibodies that bind the pathogen. We show that the leverages of host (or external intervention) and pathogen are often highly imbalanced: an error threshold separates parameter regions of efficient control from regions of compromised control, where the pathogen retains the upper hand. Because control efficiency can be predicted from few measurable fitness parameters, our results establish a proof of principle how control theory can guide interventions against evolving pathogens.

Control can alter the eco-evolutionary dynamics of a target pathogen in two ways, by changing its population size and by directed evolution of new functions. Here, we develop a payoff model of eco-evolutionary control based on strategies of evolution, regulation, and computational forecasting. We apply this model to pathogen control by molecular antibody–antigen binding with a tunable dosage of antibodies. By analytical solution, we obtain optimal dosage protocols and establish a phase diagram with an error threshold delineating parameter regimes of successful and compromised control. The solution identifies few independently measurable fitness parameters that predict the outcome of control. Our analysis shows how optimal control strategies depend on mutation rate and population size of the pathogen, and how monitoring and computational forecasting affect protocols and efficiency of control. We argue that these results carry over to more general systems and are elements of an emerging eco-evolutionary control theory.

A data-based mathematical modelling study to quantify the effects of ciprofloxacin and ampicillin on the within-host dynamics of Salmonella enterica during treatment and relapse

Antibiotic therapy has drastically reduced the mortality and sequelae of bacterial infections. From naturally occurring to chemically synthesized, different classes of antibiotics have been successfully used without detailed knowledge of how they affect bacterial dynamics in vivo. However, a proportion of patients receiving antimicrobial therapy develop recrudescent infections post-treatment. Relapsing infections are attributable to incomplete clearance of bacterial populations following antibiotic administration; the metabolic profile of this antibiotic-recalcitrant bacterial subpopulation, the spatio-temporal context of its emergence and the variance of antibiotic-bacterial interactions in vivo remain unclear. Here, we develop and apply a mechanistic mathematical model to data from a study comparing the effects of ciprofloxacin and ampicillin on the within-host dynamics of Salmonella enterica serovar Typhimurium in murine infections. Using the inferential capacity of our model, we show that the antibiotic-recalcitrant bacteria following ampicillin, but not ciprofloxacin, treatment belong to a non-replicating phenotype. Aligning with previous studies, we independently estimate that the lymphoid tissues and spleen are important reservoirs of non-replicating bacteria. Finally, we predict that post-treatment, the progenitors of the non-growing and growing bacterial populations replicate and die at different rates. Ultimately, the liver, spleen and mesenteric lymph nodes are all repopulated by progenitors of the previously non-growing phenotype in ampicillin-treated mice.

A survey of within-host and between-hosts modelling for antibiotic resistance

Antibiotic resistance is a global public health problem which has the attention of many stakeholders including clinicians, the pharmaceutical industry, researchers and policy makers. Despite the existence of many studies, control of resistance transmission has become a rather daunting task as the mechanisms underlying resistance evolution and development are not fully known. Here, we discuss the mechanisms underlying antibiotic resistance development, explore some treatment strategies used in the fight against antibiotic resistance and consider recent findings on collateral susceptibilities amongst antibiotic classes. Mathematical models have proved valuable for unravelling complex mechanisms in biology and such models have been used in the quest of understanding the development and spread of antibiotic resistance. While assessing the importance of such mathematical models, previous systematic reviews were interested in investigating whether these models follow good modelling practice. We focus on theoretical approaches used for resistance modelling considering both within and between host models as well as some pharmacodynamic and pharmakokinetic approaches and further examine the interaction between drugs and host immune response during treatment with antibiotics. Finally, we provide an outlook for future research aimed at modelling approaches for combating antibiotic resistance.

Evolutionary Rescue and Drug Resistance on Multicopy Plasmids

Bacteria often carry "extra DNA" in the form of plasmids in addition to their chromosome. Many plasmids have a copy number greater than one such that the genes encoded on these plasmids are present in multiple copies per cell. This has evolutionary consequences by increasing the mutational target size, by prompting the (transitory) co-occurrence of mutant and wild-type alleles within the same cell, and by allowing for gene dosage effects. We develop and analyze a mathematical model for bacterial adaptation to harsh environmental change if adaptation is driven by beneficial alleles on multicopy plasmids. Successful adaptation depends on the availability of advantageous alleles and on their establishment probability. The establishment process involves the segregation of mutant and wild-type plasmids to the two daughter cells, allowing for the emergence of mutant homozygous cells over the course of several generations. To model this process, we use the theory of multitype branching processes, where a type is defined by the genetic composition of the cell. Both factors-the availability of advantageous alleles and their establishment probability-depend on the plasmid copy number, and they often do so antagonistically. We find that in the interplay of various effects, a lower or higher copy number may maximize the probability of evolutionary rescue. The decisive factor is the dominance relationship between mutant and wild-type plasmids and potential gene dosage effects. Results from a simple model of antibiotic degradation indicate that the optimal plasmid copy number may depend on the specific environment encountered by the population.

Theoretical investigation of stochastic clearance of bacteria: first-passage analysis

Understanding mechanisms of bacterial eradication is critically important for overcoming failures of antibiotic treatments. Current studies suggest that the clearance of large bacterial populations proceeds deterministically, while for smaller populations, the stochastic effects become more relevant. Here, we develop a theoretical approach to investigate the bacterial population dynamics under the effect of antibiotic drugs using a method of first-passage processes. It allows us to explicitly evaluate the most important characteristics of bacterial clearance dynamics such as extinction probabilities and extinction times. The new meaning of minimal inhibitory concentrations for stochastic clearance of bacterial populations is also discussed. In addition, we investigate the effect of fluctuations in population growth rates on the dynamics of bacterial eradication. It is found that extinction probabilities and extinction times generally do not correlate with each other when random fluctuations in the growth rates are taking place. Unexpectedly, for a significant range of parameters, the extinction times increase due to these fluctuations, indicating a slowing in the bacterial clearance dynamics. It is argued that this might be one of the initial steps in the pathway for the development of antibiotic resistance. Furthermore, it is suggested that extinction times is a convenient measure of bacterial tolerance.

Predictable properties of fitness landscapes induced by adaptational tradeoffs

Fitness effects of mutations depend on environmental parameters. For example, mutations that increase fitness of bacteria at high antibiotic concentration often decrease fitness in the absence of antibiotic, exemplifying a tradeoff between adaptation to environmental extremes. We develop a mathematical model for fitness landscapes generated by such tradeoffs, based on experiments that determine the antibiotic dose-response curves of Escherichia coli strains, and previous observations on antibiotic resistance mutations. Our model generates a succession of landscapes with predictable properties as antibiotic concentration is varied. The landscape is nearly smooth at low and high concentrations, but the tradeoff induces a high ruggedness at intermediate antibiotic concentrations. Despite this high ruggedness, however, all the fitness maxima in the landscapes are evolutionarily accessible from the wild type. This implies that selection for antibiotic resistance in multiple mutational steps is relatively facile despite the complexity of the underlying landscape.

Resist or perish: Fate of a microbial population subjected to a periodic presence of antimicrobial

The evolution of antimicrobial resistance can be strongly affected by variations of antimicrobial concentration. Here, we study the impact of periodic alternations of absence and presence of antimicrobial on resistance evolution in a microbial population, using a stochastic model that includes variations of both population composition and size, and fully incorporates stochastic population extinctions. We show that fast alternations of presence and absence of antimicrobial are inefficient to eradicate the microbial population and strongly favor the establishment of resistance, unless the antimicrobial increases enough the death rate. We further demonstrate that if the period of alternations is longer than a threshold value, the microbial population goes extinct upon the first addition of antimicrobial, if it is not rescued by resistance. We express the probability that the population is eradicated upon the first addition of antimicrobial, assuming rare mutations. Rescue by resistance can happen either if resistant mutants preexist, or if they appear after antimicrobial is added to the environment. Importantly, the latter case is fully prevented by perfect biostatic antimicrobials that completely stop division of sensitive microorganisms. By contrast, we show that the parameter regime where treatment is efficient is larger for biocidal drugs than for biostatic drugs. This sheds light on the respective merits of different antimicrobial modes of action.

Coexistence and cooperation in structured habitats

Background

Natural habitats are typically structured, imposing constraints on inhabiting populations and their interactions. Which conditions are important for coexistence of diverse communities, and how cooperative interaction stabilizes in such populations, have been important ecological and evolutionary questions.

Results

We investigate a minimal ecological framework of microbial population dynamics that exhibits crucial features to show coexistence: Populations repeatedly undergo cycles of separation into compartmentalized habitats and mixing with new resources. The characteristic time-scale is longer than that typical of individual growth. Using analytic approximations, averaging techniques and phase-plane methods of dynamical systems, we provide a framework for analyzing various types of microbial interactions. Population composition and population size are both dynamic variables of the model; they are found to be decoupled both in terms of time-scale and parameter dependence. We present specific results for two examples of cooperative interaction by public goods: collective antibiotics resistance, and enhanced iron-availability by pyoverdine. We find stable coexistence to be a likely outcome.

Conclusions

The two simple features of a long mixing time-scale and spatial compartmentalization are enough to enable coexisting strains. In particular, costly social traits are often stabilized in such an environment—and thus cooperation established.

Resistance Evolution Against Antimicrobial Peptides in Staphylococcus aureus Alters Pharmacodynamics Beyond the MIC

Antimicrobial peptides (AMPs) have been proposed as a promising class of new antimicrobials partly because they are less susceptible to bacterial resistance evolution. This is possibly caused by their mode of action but also by their pharmacodynamic characteristics, which differ significantly from conventional antibiotics. Although pharmacodynamics of antibiotic resistant strains have been studied, such data are lacking for AMP resistant strains. Here, we investigated if the pharmacodynamics of the Gram-positive human pathogen Staphylococcous aureus evolve under antimicrobial peptide selection. Interestingly, the Hill coefficient (kappa κ) evolves together with the minimum inhibition concentration (MIC). Except for one genotype, strains harboring mutations in menF and atl, all mutants had higher kappa than the non-selected sensitive controls. Higher κ results in steeper pharmacodynamic curve and, importantly, in a narrower mutant selection window. S. aureus selected for resistance to melittin displayed cross resistant against pexiganan and had as steep pharmacodynamic curves (high κ) as pexiganan-selected lines. By contrast, the pexiganan-sensitive tenecin-selected lines displayed lower κ. Taken together, our data demonstrate that pharmacodynamic parameters are not fixed traits of particular drug/strain interactions but actually evolve under drug treatment. The contribution of factors such as κ and the maximum and minimum growth rates on the dynamics and probability of resistance evolution are open questions that require urgent attention.

Quantitative Models of Phage-Antibiotic Combination Therapy

This work develops and analyzes a novel model of phage-antibiotic combination therapy, specifically adapted to an in vivo context. The objective is to explore the underlying basis for clinical application of combination therapy utilizing bacteriophage that target antibiotic efflux pumps in Pseudomonas aeruginosa. In doing so, the paper addresses three key questions. How robust is combination therapy to variation in the resistance profiles of pathogens? What is the role of immune responses in shaping therapeutic outcomes? What levels of phage and antibiotics are necessary for curative success? As we show, combination therapy outperforms either phage or antibiotic alone, and therapeutic effectiveness is enhanced given interaction with innate immune responses. Notably, therapeutic success can be achieved even at subinhibitory concentrations of antibiotic. These in silico findings provide further support to the nascent application of combination therapy to treat MDR bacterial infections, while highlighting the role of system-level feedbacks in shaping therapeutic outcomes.

The spread of multidrug-resistant (MDR) bacteria is a global public health crisis. Bacteriophage therapy (or “phage therapy”) constitutes a potential alternative approach to treat MDR infections. However, the effective use of phage therapy may be limited when phage-resistant bacterial mutants evolve and proliferate during treatment. Here, we develop a nonlinear population dynamics model of combination therapy that accounts for the system-level interactions between bacteria, phage, and antibiotics for in vivo application given an immune response against bacteria. We simulate the combination therapy model for two strains of Pseudomonas aeruginosa, one which is phage sensitive (and antibiotic resistant) and one which is antibiotic sensitive (and phage resistant). We find that combination therapy outperforms either phage or antibiotic alone and that therapeutic effectiveness is enhanced given interaction with innate immune responses. Notably, therapeutic success can be achieved even at subinhibitory concentrations of antibiotics, e.g., ciprofloxacin. These in silico findings provide further support to the nascent application of combination therapy to treat MDR bacterial infections, while highlighting the role of innate immunity in shaping therapeutic outcomes.

IMPORTANCE This work develops and analyzes a novel model of phage-antibiotic combination therapy, specifically adapted to an in vivo context. The objective is to explore the underlying basis for clinical application of combination therapy utilizing bacteriophage that target antibiotic efflux pumps in Pseudomonas aeruginosa. In doing so, the paper addresses three key questions. How robust is combination therapy to variation in the resistance profiles of pathogens? What is the role of immune responses in shaping therapeutic outcomes? What levels of phage and antibiotics are necessary for curative success? As we show, combination therapy outperforms either phage or antibiotic alone, and therapeutic effectiveness is enhanced given interaction with innate immune responses. Notably, therapeutic success can be achieved even at subinhibitory concentrations of antibiotic. These in silico findings provide further support to the nascent application of combination therapy to treat MDR bacterial infections, while highlighting the role of system-level feedbacks in shaping therapeutic outcomes.

Stochastic Gene Expression Influences the Selection of Antibiotic Resistance Mutations

Bacteria can resist antibiotics by expressing enzymes that remove or deactivate drug molecules. Here, we study the effects of gene expression stochasticity on efflux and enzymatic resistance. We construct an agent-based model that stochastically simulates multiple biochemical processes in the cell and we observe the growth and survival dynamics of the cell population. Resistance-enhancing mutations are introduced by varying parameters that control the enzyme expression or efficacy. We find that stochastic gene expression can cause complex dynamics in terms of survival and extinction for these mutants. Regulatory mutations, which augment the frequency and duration of resistance gene transcription, can provide limited resistance by increasing mean expression. Structural mutations, which modify the enzyme or efflux efficacy, provide most resistance by improving the binding affinity of the resistance protein to the antibiotic; increasing the enzyme's catalytic rate alone may contribute to resistance if drug binding is not rate limiting. Overall, we identify conditions where regulatory mutations are selected over structural mutations, and vice versa. Our findings show that stochastic gene expression is a key factor underlying efflux and enzymatic resistances and should be taken into consideration in future antibiotic research.

Modulation of Streptomycin Killing Rate against Mature Escherichia Coli Biofilms in the Presence of Medicinal Plant Extracts

Background. Medicinal plant extracts exhibiting pro- and antioxidant properties may affect antibiotic-induced killing of biofilm-producing bacteria in both synergistic and antagonistic modes. Better understanding of these alternations is required to adjust antibiotic therapy and herbal medicine in order to exclude unwanted losses of antibiotic efficiency.Aim: to study modulation modes of streptomycin killing rate against mature biofilms of Escherichia coli in the presence of different doses of commonly used medicinal plant extracts.Materials and methods. Pharmacodynamic parameter killing rate and mass biofilm formation were determined in the presence of streptomycin and medicinal plant extracts.Results. Synergism was found between 100 mg/ml streptomycin and low doses (0.83 mg of dry herb/ml) of green, black tea, Arctostaphylos uva-ursi, Betula pendula and Laminaria japonica against killing mature biofilms. Alternatively, high doses (6.64 mg of dry herb/ml) of green, black tea and Vaccinium vitis-ideae demonstrated antagonism, decreasing killing rate and enhancing biofilm formation. Presumably, high doses of the extracts were sufficient to enhance biofilm formation blocking penetration of streptomycin through enlarged biofilm matrix and diminishing the killing rate.Conclusions. Widely consumed as soft beverages or for prophylactic purposes green, black tea and V. vitis-ideae could promote strong antagonistic effects with streptomycin. These extracts can stimulate biofilm production, making benefit for commensal microbiota, but have clinical relevance due to a significant reduction in the lethal efficiency of streptomycin in biofilms of pathogenic strains. This highlights the need of careful antibiotic prescription scheme adjustment when choosing appropriate combinations of plant extracts and antibiotics to achieve a synergistic effect.

Microbial phenotypic heterogeneity in response to a metabolic toxin: Continuous, dynamically shifting distribution of formaldehyde tolerance in Methylobacterium extorquens populations

While microbiologists often make the simplifying assumption that genotype determines phenotype in a given environment, it is becoming increasingly apparent that phenotypic heterogeneity (in which one genotype generates multiple phenotypes simultaneously even in a uniform environment) is common in many microbial populations. The importance of phenotypic heterogeneity has been demonstrated in a number of model systems involving binary phenotypic states (e.g., growth/non-growth); however, less is known about systems involving phenotype distributions that are continuous across an environmental gradient, and how those distributions change when the environment changes. Here, we describe a novel instance of phenotypic diversity in tolerance to a metabolic toxin within wild-type populations of Methylobacterium extorquens, a ubiquitous phyllosphere methylotroph capable of growing on the methanol periodically released from plant leaves. The first intermediate in methanol metabolism is formaldehyde, a potent cellular toxin that is lethal in high concentrations. We have found that at moderate concentrations, formaldehyde tolerance in M. extorquens is heterogeneous, with a cell's minimum tolerance level ranging between 0 mM and 8 mM. Tolerant cells have a distinct gene expression profile from non-tolerant cells. This form of heterogeneity is continuous in terms of threshold (the formaldehyde concentration where growth ceases), yet binary in outcome (at a given formaldehyde concentration, cells either grow normally or die, with no intermediate phenotype), and it is not associated with any detectable genetic mutations. Moreover, tolerance distributions within the population are dynamic, changing over time in response to growth conditions. We characterized this phenomenon using bulk liquid culture experiments, colony growth tracking, flow cytometry, single-cell time-lapse microscopy, transcriptomics, and genome resequencing. Finally, we used mathematical modeling to better understand the processes by which cells change phenotype, and found evidence for both stochastic, bidirectional phenotypic diversification and responsive, directed phenotypic shifts, depending on the growth substrate and the presence of toxin.

Scientists tend to appreciate microbes for their simplicity and predictability: a population of genetically identical cells inhabiting a uniform environment is expected to behave in a uniform way. However, counter-examples to this assumption are frequently being discovered, forcing a re-examination of the relationship between genotype and phenotype. In most such examples, bacterial cells are found to split into two discrete populations, for instance growing and non-growing. Here, we report the discovery of a novel example of microbial phenotypic heterogeneity in which cells are distributed along a gradient of phenotypes, ranging from low to high tolerance of a toxic chemical. Furthermore, we demonstrate that the distribution of phenotypes changes in different growth conditions, and we use mathematical modeling to show that cells may change their phenotype either randomly or in a particular direction in response to the environment. Our work expands our understanding of how a bacterial cell's genome, family history, and environment all contribute to its behavior, with implications for the diverse situations in which we care to understand the growth of any single-celled populations.

A Whole-Body Mathematical Model of Sepsis Progression and Treatment Designed in the BioGears Physiology Engine

Sepsis is a debilitating condition associated with a high mortality rate that greatly strains hospital resources. Though advances have been made in improving sepsis diagnosis and treatment, our understanding of the disease is far from complete. Mathematical modeling of sepsis has the potential to explore underlying biological mechanisms and patient phenotypes that contribute to variability in septic patient outcomes. We developed a comprehensive, whole-body mathematical model of sepsis pathophysiology using the BioGears Engine, a robust open-source virtual human modeling project. We describe the development of a sepsis model and the physiologic response within the BioGears framework. We then define and simulate scenarios that compare sepsis treatment regimens. As such, we demonstrate the utility of this model as a tool to augment sepsis research and as a training platform to educate medical staff.

Diffusion-driven enhancement of the antibiotic resistance selection window

The current crisis of antimicrobial resistance in clinically relevant pathogens has highlighted our limited understanding of the ecological and evolutionary forces that drive drug resistance adaptation. For instance, although human tissues are highly heterogeneous, most of our mechanistic understanding about antibiotic resistance evolution is based on constant and well-mixed environmental conditions. A consequence of considering spatial heterogeneity is that, even if antibiotics are prescribed at high dosages, the penetration of drug molecules through tissues inevitably produces antibiotic gradients, exposing bacterial populations to a range of selective pressures and generating a dynamic fitness landscape that changes in space and time. In this paper, we will use a combination of mathematical modelling and computer simulations to study the population dynamics of susceptible and resistant strains competing for resources in a network of micro-environments with varying degrees of connectivity. Our main result is that highly connected environments increase diffusion of drug molecules, enabling resistant phenotypes to colonize a larger number of spatial locations. We validated this theoretical result by culturing fluorescently labelled Escherichia coli in 3D-printed devices that allow us to control the rate of diffusion of antibiotics between neighbouring compartments and quantify the spatio-temporal distribution of resistant and susceptible bacterial cells.