Two-drug antimicrobial chemotherapy: a mathematical model and experiments with Mycobacterium marinum

Mathematical models of drug-resistant tuberculosis lack bacterial heterogeneity: A systematic review

Drug-resistant tuberculosis (DR-TB) threatens progress in the control of TB. Mathematical models are increasingly being used to guide public health decisions on managing both antimicrobial resistance (AMR) and TB. It is important to consider bacterial heterogeneity in models as it can have consequences for predictions of resistance prevalence, which may affect decision-making. We conducted a systematic review of published mathematical models to determine the modelling landscape and to explore methods for including bacterial heterogeneity. Our first objective was to identify and analyse the general characteristics of mathematical models of DR-mycobacteria, including M. tuberculosis. The second objective was to analyse methods of including bacterial heterogeneity in these models. We had different definitions of heterogeneity depending on the model level. For between-host models of mycobacterium, heterogeneity was defined as any model where bacteria of the same resistance level were further differentiated. For bacterial population models, heterogeneity was defined as having multiple distinct resistant populations. The search was conducted following PRISMA guidelines in five databases, with studies included if they were mechanistic or simulation models of DR-mycobacteria. We identified 195 studies modelling DR-mycobacteria, with most being dynamic transmission models of non-treatment intervention impact in M. tuberculosis (n = 58). Studies were set in a limited number of specific countries, and 44% of models (n = 85) included only a single level of "multidrug-resistance (MDR)". Only 23 models (8 between-host) included any bacterial heterogeneity. Most of these also captured multiple antibiotic-resistant classes (n = 17), but six models included heterogeneity in bacterial populations resistant to a single antibiotic. Heterogeneity was usually represented by different fitness values for bacteria resistant to the same antibiotic (61%, n = 14). A large and growing body of mathematical models of DR-mycobacterium is being used to explore intervention impact to support policy as well as theoretical explorations of resistance dynamics. However, the majority lack bacterial heterogeneity, suggesting that important evolutionary effects may be missed.

Revealing discrepancies and drivers in the impact of lomefloxacin on groundwater denitrification throughout microbial community growth and succession

The coexistence of antibiotics and nitrates has raised great concern about antibiotic's impact on denitrification. However, conflicting results in these studies are very puzzling, possibly due to differences in microbial succession stages. This study investigated the effects of the high-priority urgent antibiotic, lomefloxacin (LOM), on groundwater denitrification throughout microbial growth and succession. The results demonstrated that LOM's impact on denitrification varied significantly across three successional stages, with the most pronounced effects exhibited in the initial stage (53.8% promotion at 100 ng/L-LOM, 84.6% inhibition at 100 μg/L-LOM), followed by the decline stage (13.3-18.2% inhibition), while no effect in the stable stage. Hence, a distinct pattern encompassing susceptibility, insusceptibility, and sub-susceptibility in LOM's impact on denitrification was discovered. Microbial metabolism and environment variation drove the pattern, with bacterial numbers and antibiotic resistance as primary influencers (22.5% and 15.3%, p < 0.01), followed by carbon metabolism and microbial community (5.0% and 3.68%, p < 0.01). The structural equation model confirmed results reliability. Bacterial numbers and resistance influenced susceptibility by regulating compensation and bacteriostasis, while carbon metabolism and microbial community impacted energy, electron transfer, and gene composition. These findings provide valuable insights into the complex interplay between antibiotics and denitrification patterns in groundwater.

The pharmacokinetic-pharmacodynamic modelling framework as a tool to predict drug resistance evolution

Pharmacokinetic-pharmacodynamic (PKPD) models, which describe how drug concentrations change over time and how that affects pathogen growth, have proven highly valuable in designing optimal drug treatments aimed at bacterial eradication. However, the fast rise of antimicrobial resistance calls for increased focus on an additional treatment optimization criterion: avoidance of resistance evolution. We demonstrate here how coupling PKPD and population genetics models can be used to determine treatment regimens that minimize the potential for antimicrobial resistance evolution. Importantly, the resulting modelling framework enables the assessment of resistance evolution in response to dynamic selection pressures, including changes in antimicrobial concentration and the emergence of adaptive phenotypes. Using antibiotics and antimicrobial peptides as an example, we discuss the empirical evidence and intuition behind individual model parameters. We further suggest several extensions of this framework that allow a more comprehensive and realistic prediction of bacterial escape from antimicrobials through various phenotypic and genetic mechanisms.

Optimizing tuberculosis treatment efficacy: Comparing the standard regimen with Moxifloxacin-containing regimens

Tuberculosis (TB) continues to be one of the deadliest infectious diseases in the world, causing ~1.5 million deaths every year. The World Health Organization initiated an End TB Strategy that aims to reduce TB-related deaths in 2035 by 95%. Recent research goals have focused on discovering more effective and more patient-friendly antibiotic drug regimens to increase patient compliance and decrease emergence of resistant TB. Moxifloxacin is one promising antibiotic that may improve the current standard regimen by shortening treatment time. Clinical trials and in vivo mouse studies suggest that regimens containing moxifloxacin have better bactericidal activity. However, testing every possible combination regimen with moxifloxacin either in vivo or clinically is not feasible due to experimental and clinical limitations. To identify better regimens more systematically, we simulated pharmacokinetics/pharmacodynamics of various regimens (with and without moxifloxacin) to evaluate efficacies, and then compared our predictions to both clinical trials and nonhuman primate studies performed herein. We used GranSim, our well-established hybrid agent-based model that simulates granuloma formation and antibiotic treatment, for this task. In addition, we established a multiple-objective optimization pipeline using GranSim to discover optimized regimens based on treatment objectives of interest, i.e., minimizing total drug dosage and lowering time needed to sterilize granulomas. Our approach can efficiently test many regimens and successfully identify optimal regimens to inform pre-clinical studies or clinical trials and ultimately accelerate the TB regimen discovery process.

Pharmacodynamics and Bactericidal Activity of Combination Regimens in Pulmonary Tuberculosis: Application to Bedaquiline-Pretomanid-Pyrazinamide

A critical barrier to codevelopment of tuberculosis (TB) regimens is a limited ability to identify optimal drug and dose combinations in early-phase clinical testing. While pharmacokinetic-pharmacodynamic (PKPD) target attainment is the primary tool for exposure-response optimization of TB drugs, the PD target is a static index that does not distinguish individual drug contributions to the efficacy of a multidrug combination. A PKPD model of bedaquiline-pretomanid-pyrazinamide (BPaZ) for the treatment of pulmonary TB was developed as part of a dynamic exposure-response approach to regimen development. The model describes a time course relationship between the drug concentrations in plasma and their individual as well as their combined effect on sputum bacillary load assessed by solid culture CFU counts and liquid culture time to positivity (TTP). The model parameters were estimated using data from the phase 2A studies NC-001-(J-M-Pa-Z) and NC-003-(C-J-Pa-Z). The results included a characterization of BPaZ activity as the most and least sensitive to changes in pyrazinamide and bedaquiline exposures, respectively, with antagonistic activity of BPa compensated by synergistic activity of BZ and PaZ. Simulations of the NC-003 study population with once-daily bedaquiline at 200 mg, pretomanid at 200 mg, and pyrazinamide at 1,500 mg showed BPaZ would require 3 months to attain liquid culture negativity in 90% of participants. These results for BPaZ were intended to be an example application with the general approach aimed at entirely novel drug combinations from a growing pipeline of new and repurposed TB drugs.

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.

Disparity in socio-economic status explains the pattern of self-medication of antibiotics in India: understanding from game-theoretic perspective

The emergence of antimicrobial resistance has raised great concern for public health in many lower-income countries including India. Socio-economic determinants like poverty, health expenditure and awareness accelerate this emergence by influencing individuals' attitudes and healthcare practices such as self-medication. This self-medication practice is highly prevalent in many countries, where antibiotics are available without prescriptions. Thus, complex dynamics of drug- resistance driven by economy, human behaviour, and disease epidemiology poses a serious threat to the community, which has been less emphasized in prior studies. Here, we formulate a game-theoretic model of human choices in self-medication integrating economic growth and disease transmission processes. We show that this adaptive behaviour emerges spontaneously in the population through a self-reinforcing process and continual feedback from the economy, resulting in the emergence of resistance as externalities of human choice under resource constraints situations. We identify that the disparity between social-optimum and individual interest in self-medication is primarily driven by the effectiveness of treatment, health awareness and public health interventions. Frequent multiple-peaks of resistant strains are also observed when individuals imitate others more readily and self-medication is more likely. Our model exemplifies that timely public health intervention for financial risk protection, and antibiotic stewardship policies can improve the epidemiological situation and prevent economic collapse.

vCOMBAT: a novel tool to create and visualize a computational model of bacterial antibiotic target-binding

Background

As antibiotic resistance creates a significant global health threat, we need not only to accelerate the development of novel antibiotics but also to develop better treatment strategies using existing drugs to improve their efficacy and prevent the selection of further resistance. We require new tools to rationally design dosing regimens from data collected in early phases of antibiotic and dosing development. Mathematical models such as mechanistic pharmacodynamic drug-target binding explain mechanistic details of how the given drug concentration affects its targeted bacteria. However, there are no available tools in the literature that allow non-quantitative scientists to develop computational models to simulate antibiotic-target binding and its effects on bacteria.

Results

In this work, we have devised an extension of a mechanistic binding-kinetic model to incorporate clinical drug concentration data. Based on the extended model, we develop a novel and interactive web-based tool that allows non-quantitative scientists to create and visualize their own computational models of bacterial antibiotic target-binding based on their considered drugs and bacteria. We also demonstrate how Rifampicin affects bacterial populations of Tuberculosis bacteria using our vCOMBAT tool.

Conclusions

The vCOMBAT online tool is publicly available at https://combat-bacteria.org/.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-021-04536-3.

Interaction Tolerance Detection Test for Understanding the Killing Efficacy of Directional Antibiotic Combinations

Combination treatments are commonly prescribed for enhancing drug efficacy, as well as for preventing the evolution of resistance. The interaction between drugs is typically evaluated near the MIC, using growth rate as a measure of treatment efficacy. However, for infections in which the killing activity of the treatment is important, measurements far above the MIC are needed. In this regime, the killing rate often becomes weakly concentration dependent, and a different metric is needed to characterize drug interactions. We evaluate the interaction metric on killing using an easy visual assay, the interaction tolerance detection test (iTDtest), that estimates the survival of bacteria under antibiotic combinations. We identify antibiotic combinations that enable the eradication of tolerant bacteria. Furthermore, the visualization of the antibiotic interactions reveals directional drug interactions and enables predicting high-order combination outcomes, therefore facilitating the determination of optimal treatments. IMPORTANCE The killing efficacy of antibiotic combinations is rarely measured in the clinical setting. However, in cases where the treatment is required to kill the infecting organism and not merely arrest its growth, the information on the killing efficacy is important, especially when tolerant strains are implicated. Here, we report on an easy method for the determination of the killing efficacy of antibiotic combinations which enabled to reveal combinations effective against tolerant bacteria. The results could be generally used to guide antimicrobial therapy in life-threatening infections.

Mathematical model and tool to explore shorter multi-drug therapy options for active pulmonary tuberculosis

Standard treatment for active tuberculosis (TB) requires drug treatment with at least four drugs over six months. Shorter-duration therapy would mean less need for strict adherence, and reduced risk of bacterial resistance. A system pharmacology model of TB infection, and drug therapy was developed and used to simulate the outcome of different drug therapy scenarios. The model incorporated human immune response, granuloma lesions, multi-drug antimicrobial chemotherapy, and bacterial resistance. A dynamic population pharmacokinetic/pharmacodynamic (PK/PD) simulation model including rifampin, isoniazid, pyrazinamide, and ethambutol was developed and parameters aligned with previous experimental data. Population therapy outcomes for simulations were found to be generally consistent with summary results from previous clinical trials, for a range of drug dose and duration scenarios. An online tool developed from this model is released as open source software. The TB simulation tool could support analysis of new therapy options, novel drug types, and combinations, incorporating factors such as patient adherence behavior.

A comprehensive in-silico model of pulmonary tuberculosis successfully predicted previous clinical trials and could simulate future therapeutics.

Head and neck surgical antibiotic prophylaxis in resource-constrained settings

PURPOSE OF REVIEW

Antimicrobial resistance represents a global threat and causes almost 700 000 deaths per year. The rapid dissemination of resistant bacteria is occurring globally, turning this into the primary threat to public health in the 21st century and forcing organizations around the globe to take urgent action.

RECENT FINDINGS

About risks related to surgical site infection (SSI) in head and neck surgery, surgical limitations in resource-constrained settings, comorbidities and the risk of SSI, evidence about surgical prophylaxis from low and middle-income countries, SSI gap between the developed and developing worlds and how to reduce resistance.

SUMMARY

Antibiotic protocols can be adjusted to local and regional bacterial resistance profiles, taking into account the availability of antibiotics and cost limitations on each country in order to decrease the SSI risk.

Antibiotic drug-resistance as a complex system driven by socio-economic growth and antibiotic misuse

Overwhelming antibiotic use poses a serious challenge today to the public-health policymakers worldwide. Many empirical studies pointed out this ever-increasing antibiotic consumption as primary driver of the community-acquired antibiotic drug-resistance, especially in the middle- and lower-income countries. The association is well documented across spatio-temporal gradients in many parts of the world, but there is rarely any study that emphasizes the mechanism of the association, which is important for combating drug-resistance. Formulating a mathematical model of emergence and transmission of drug-resistance, we in this paper, present how amalgamating three components: socio-economic growth, population ecology of infectious disease, and antibiotic misuse can instinctively incite proliferation of resistance in the society. We show that combined impact of economy, infections, and self-medication yield synergistic interactions through feedbacks on each other, presenting the emergence of drug-resistance as a self-reinforcing cycle in the population. Analysis of our model not only determines the threshold of antibiotic use beyond which the emergence of resistance may occur, but also characterizes how fast it develops depending on economic growth, and lack of education and awareness of the population. Our model illustrates that proper and timely government aid in population health can break the self-reinforcing process and reduce the burden of drug-resistance in the community.

Association of anti-tuberculosis drug concentrations in hair and treatment outcomes in MDR- and XDR-TB

Therapeutic drug monitoring for drug-resistant tuberculosis (TB) is likely to improve treatment outcomes. While assessments of plasma drug levels can explain pharmacokinetic variability among trial participants, these measures require phlebotomy and a cold chain, and are generally not repeated frequently enough to characterise drug exposure over time. Using a novel multi-analyte assay, we found evidence that higher anti-TB drug concentrations in hair, a non-biohazardous and noninvasively collected biomatrix, predict extensively-drug resistant-TB clinical outcomes in a high-burden setting.

In Silico Exploration of Aryl Halides Analogues as Checkpoint Kinase 1 Inhibitors by Using 3D QSAR, Molecular Docking Study, and ADMET Screening

Purpose: In this review, a set of aryl halides analogs were identified as potent checkpoint kinase 1 (Chk1) inhibitors through a series of computer-aided drug design processes, to develop models with good predictive ability, highlight the important interactions between the ligand and the Chk1 receptor protein and determine properties of the new proposed drugs as Chk1 inhibitors agents.

Methods: Three-dimensional quantitative structure–activity relationship (3D-QSAR) modeling, molecular docking and absorption, distribution, metabolism, excretion and toxicity (ADMET) approaches are used to determine structure activity relationship and confirm the stable conformation on the receptor pocket.

Results: The statistical analysis results of comparative -molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA) models that employed for a training set of 24 compounds gives reliable values of Q² (0.70 and 0.94, respectively) and R² (0.68 and 0.96, respectively).

Conclusion: Computer–aided drug design tools used to develop models that possess good predictive ability, and to determine the stability of the observed and predicted molecules in the receptor pocket, also in silico of pharmacokinetic (ADMET) results shows good properties and bioavailability for these new proposed Chk1 inhibitors agents.

Emergence and selection of isoniazid and rifampin resistance in tuberculosis granulomas

Drug resistant tuberculosis is increasing world-wide. Resistance against isoniazid (INH), rifampicin (RIF), or both (multi-drug resistant TB, MDR-TB) is of particular concern, since INH and RIF form part of the standard regimen for TB disease. While it is known that suboptimal treatment can lead to resistance, it remains unclear how host immune responses and antibiotic dynamics within granulomas (sites of infection) affect emergence and selection of drug-resistant bacteria. We take a systems pharmacology approach to explore resistance dynamics within granulomas. We integrate spatio-temporal host immunity, INH and RIF dynamics, and bacterial dynamics (including fitness costs and compensatory mutations) in a computational framework. We simulate resistance emergence in the absence of treatment, as well as resistance selection during INH and/or RIF treatment. There are four main findings. First, in the absence of treatment, the percentage of granulomas containing resistant bacteria mirrors the non-monotonic bacterial dynamics within granulomas. Second, drug-resistant bacteria are less frequently found in non-replicating states in caseum, compared to drug-sensitive bacteria. Third, due to a steeper dose response curve and faster plasma clearance of INH compared to RIF, INH-resistant bacteria have a stronger influence on treatment outcomes than RIF-resistant bacteria. Finally, under combination therapy with INH and RIF, few MDR bacteria are able to significantly affect treatment outcomes. Overall, our approach allows drug-specific prediction of drug resistance emergence and selection in the complex granuloma context. Since our predictions are based on pre-clinical data, our approach can be implemented relatively early in the treatment development process, thereby enabling pro-active rather than reactive responses to emerging drug resistance for new drugs. Furthermore, this quantitative and drug-specific approach can help identify drug-specific properties that influence resistance and use this information to design treatment regimens that minimize resistance selection and expand the useful life-span of new antibiotics.

Assessing the Combined Antibacterial Effect of Isoniazid and Rifampin on Four Mycobacterium tuberculosis Strains Using In Vitro Experiments and Response-Surface Modeling

While isoniazid and rifampin have been the cornerstone of tuberculosis therapy caused by drug-susceptible Mycobacterium tuberculosis for more than 40 years, their combined action has never been thoroughly assessed by modern quantitative pharmacology approaches. The aims of this work were to perform in vitro experiments and mathematical modeling of the antibacterial effect of isoniazid and rifampin alone and in combination against various strains of Mycobacterium tuberculosis After MIC determination of H37Rv and three strains belonging to the Beijing, Euro-American, and Indo-Oceanic lineages, the antibacterial effects of isoniazid and rifampin alone and in combination were studied in static time-kill experiments. A sigmoidal maximum effect model (Hill equation) and a response-surface model were used to describe the effect of the drugs alone and in combination, respectively. The killing effect of isoniazid and rifampin alone were well described by the Hill equation. Rifampin displayed a more concentration-dependent effect than isoniazid around the MIC. The pharmacodynamics parameters of each drug (maximal effect, median effect concentration, and coefficient of sigmoidicity) were quite similar between the four strains. The response-surface model from Minto et al. fit data of combined effect very well with low bias and imprecision (C. F. Minto, T. W. Schnider, T. G. Short, K. M. Gregg, A. Gentilini, Anesthesiology 92:1603-1616, 2000, https://doi.org/10.1097/00000542-200006000-00017). Response-surface modeling showed that the combined action of isoniazid and rifampin was synergistic for the H37Rv, Beijing, and Euro-American strains but only additive for the Indo-Oceanic strain. This study can serve as a motivating example for preclinical evaluation of combined action of antituberculous drugs.

Antimicrobial combinations: Bliss independence and Loewe additivity derived from mechanistic multi-hit models

Antimicrobial peptides (AMPs) and antibiotics reduce the net growth rate of bacterial populations they target. It is relevant to understand if effects of multiple antimicrobials are synergistic or antagonistic, in particular for AMP responses, because naturally occurring responses involve multiple AMPs. There are several competing proposals describing how multiple types of antimicrobials add up when applied in combination, such as Loewe additivity or Bliss independence. These additivity terms are defined ad hoc from abstract principles explaining the supposed interaction between the antimicrobials. Here, we link these ad hoc combination terms to a mathematical model that represents the dynamics of antimicrobial molecules hitting targets on bacterial cells. In this multi-hit model, bacteria are killed when a certain number of targets are hit by antimicrobials. Using this bottom-up approach reveals that Bliss independence should be the model of choice if no interaction between antimicrobial molecules is expected. Loewe additivity, on the other hand, describes scenarios in which antimicrobials affect the same components of the cell, i.e. are not acting independently. While our approach idealizes the dynamics of antimicrobials, it provides a conceptual underpinning of the additivity terms. The choice of the additivity term is essential to determine synergy or antagonism of antimicrobials.This article is part of the themed issue 'Evolutionary ecology of arthropod antimicrobial peptides'.

Comparing efficacies of moxifloxacin, levofloxacin and gatifloxacin in tuberculosis granulomas using a multi-scale systems pharmacology approach

Granulomas are complex lung lesions that are the hallmark of tuberculosis (TB). Understanding antibiotic dynamics within lung granulomas will be vital to improving and shortening the long course of TB treatment. Three fluoroquinolones (FQs) are commonly prescribed as part of multi-drug resistant TB therapy: moxifloxacin (MXF), levofloxacin (LVX) or gatifloxacin (GFX). To date, insufficient data are available to support selection of one FQ over another, or to show that these drugs are clinically equivalent. To predict the efficacy of MXF, LVX and GFX at a single granuloma level, we integrate computational modeling with experimental datasets into a single mechanistic framework, GranSim. GranSim is a hybrid agent-based computational model that simulates granuloma formation and function, FQ plasma and tissue pharmacokinetics and pharmacodynamics and is based on extensive in vitro and in vivo data. We treat in silico granulomas with recommended daily doses of each FQ and compare efficacy by multiple metrics: bacterial load, sterilization rates, early bactericidal activity and efficacy under non-compliance and treatment interruption. GranSim reproduces in vivo plasma pharmacokinetics, spatial and temporal tissue pharmacokinetics and in vitro pharmacodynamics of these FQs. We predict that MXF kills intracellular bacteria more quickly than LVX and GFX due in part to a higher cellular accumulation ratio. We also show that all three FQs struggle to sterilize non-replicating bacteria residing in caseum. This is due to modest drug concentrations inside caseum and high inhibitory concentrations for this bacterial subpopulation. MXF and LVX have higher granuloma sterilization rates compared to GFX; and MXF performs better in a simulated non-compliance or treatment interruption scenario. We conclude that MXF has a small but potentially clinically significant advantage over LVX, as well as LVX over GFX. We illustrate how a systems pharmacology approach combining experimental and computational methods can guide antibiotic selection for TB.

Tuberculosis (TB) is caused by infection with the bacterium Mycobacterium tuberculosis (Mtb) and kills 1.5 million people each year. TB requires at least 6 months of treatment with up to four drugs, and is characterized by formation of granulomas in patient lungs. Granulomas are spherical collections of host cells and bacteria. Fluoroquinolones (FQs) are a class of drug that could help shorten TB treatment. Three FQs that are used to treat TB are: moxifloxacin (MXF), levofloxacin (LVX) or gatifloxacin (GFX). To date, it is unclear if one FQ is better than the others at treating TB, in part because little is known about how these drugs distribute and work inside the lung granulomas. We use computer simulations of Mtb infection and FQ treatment within granulomas to predict which FQ is better and why. Our computer model is calibrated to multiple experimental data sets. We compare the three FQs by multiple metrics, and predict that MXF is better than LVX and GFX because it kills bacteria more quickly, and it works better when patients miss doses. However, all three FQs are unable to kill a part of the bacterial population living in the center of granulomas. Our results can now inform future experimental studies.

Bacteriocin-Antimicrobial Synergy: A Medical and Food Perspective

The continuing emergence of multi-drug resistant pathogens has sparked an interest in seeking alternative therapeutic options. Antimicrobial combinatorial therapy is one such avenue. A number of studies have been conducted, involving combinations of bacteriocins with other antimicrobials, to circumvent the development of antimicrobial resistance and/or increase antimicrobial potency. Such bacteriocin-antimicrobial combinations could have tremendous value, in terms of reducing the likelihood of resistance development due to the involvement of two distinct mechanisms of antimicrobial action. Furthermore, antimicrobial synergistic interactions may also have potential financial implications in terms of decreasing the costs of treatment by reducing the concentration of an expensive antimicrobial and utilizing it in combination with an inexpensive one. In addition, combinatorial therapies with bacteriocins can broaden antimicrobial spectra and/or result in a reduction in the concentration of an antibiotic required for effective treatments to the extent that potentially toxic or adverse side effects can be reduced or eliminated. Here, we review studies in which bacteriocins were found to be effective in combination with other antimicrobials, with a view to targeting clinical and/or food-borne pathogens. Furthermore, we discuss some of the bottlenecks which are currently hindering the development of bacteriocins as viable therapeutic options, as well as addressing the need to exercise caution when attempting to predict clinical outcomes of bacteriocin-antimicrobial combinations.

A review of computational and mathematical modeling contributions to our understanding of Mycobacterium tuberculosis within-host infection and treatment

Tuberculosis (TB) is an ancient and deadly disease characterized by complex host-pathogen dynamics playing out over multiple time and length scales and physiological compartments. Computational modeling can be used to integrate various types of experimental data and suggest new hypotheses, mechanisms, and therapeutic approaches to TB. Here, we offer a first-time comprehensive review of work on within-host TB models that describe the immune response of the host to infection, including the formation of lung granulomas. The models include systems of ordinary and partial differential equations and agent-based models as well as hybrid and multi-scale models that are combinations of these. Many aspects of M. tuberculosis infection, including host dynamics in the lung (typical site of infection for TB), granuloma formation, roles of cytokine and chemokine dynamics, and bacterial nutrient availability have been explored. Finally, we survey applications of these within-host models to TB therapy and prevention and suggest future directions to impact this global disease.

The highly synergistic, broad spectrum, antibacterial activity of organic acids and transition metals

For millennia, transition metals have been exploited to inhibit bacterial growth. We report here the potentiation of the anti-bacterial activity of transition metals by organic acids. Strong synergy between low, non-toxic concentrations of transition metals and organic acids was observed with up to ~1000-fold higher inhibitory effect on bacterial growth. We show that organic acids shuttle transition metals through the permeability barrier of the bacterial membrane, leading to increased influx of transition metals into bacterial cells. We demonstrate that this synergy can be effectively used to inhibit the growth of a broad range of plant and human bacterial pathogens, and suggest that a revision of food preservation and crop protection strategies may be in order. These findings bear significant biomedical, agricultural, financial and environmental opportunities.

Mathematical modeling of herpes simplex virus-2 suppression with pritelivir predicts trial outcomes

Pharmacokinetic and pharmacodynamic models estimate the potency of antiviral agents but do not capture viral and immunologic factors that drive the natural dynamics of infection. We designed a mathematical model that synthesizes pharmacokinetics, pharmacodynamics, and viral pathogenesis concepts to simulate the activity of pritelivir, a DNA helicase-primase inhibitor that targets herpes simplex virus. Our simulations recapitulate detailed viral kinetic shedding features in five dosage arms of a phase 2 clinical trial. We identify that in vitro estimates of median effective concentration (EC50) are lower than in vivo values for the drug. Nevertheless, pritelivir potently decreases shedding at appropriate doses based on its mode of action and long half-life. Although pritelivir directly inhibits replication in epithelial cells, our model indicates that pritelivir also indirectly limits downstream viral spread from neurons to genital keratinocytes, within genital ulcers, and from ulcer to new mucosal sites of infection. We validate our model based on its ability to predict outcomes in a subsequent trial with a higher dose. The model can therefore be used to optimize dose selection in clinical practice.

Time-kill curve analysis and pharmacodynamic modelling for in vitro evaluation of antimicrobials against Neisseria gonorrhoeae

BACKGROUND

Gonorrhoea is a sexually transmitted infection caused by the Gram-negative bacterium Neisseria gonorrhoeae. Resistance to first-line empirical monotherapy has emerged, so robust methods are needed to evaluate the activity of existing and novel antimicrobials against the bacterium. Pharmacodynamic models describing the relationship between the concentration of antimicrobials and the minimum growth rate of the bacteria provide more detailed information than the MIC only.

RESULTS

In this study, a novel standardised in vitro time-kill curve assay was developed. The assay was validated using five World Health Organization N. gonorrhoeae reference strains and a range of ciprofloxacin concentrations below and above the MIC. Then the activity of nine antimicrobials with different target mechanisms was examined against a highly antimicrobial susceptible clinical strain isolated in 1964. The experimental time-kill curves were analysed and quantified with a previously established pharmacodynamic model. First, the bacterial growth rates at each antimicrobial concentration were estimated with linear regression. Second, we fitted the model to the growth rates, resulting in four parameters that describe the pharmacodynamic properties of each antimicrobial. A gradual decrease of bactericidal effects from ciprofloxacin to spectinomycin and gentamicin was found. The beta-lactams ceftriaxone, cefixime and benzylpenicillin showed bactericidal and time-dependent properties. Chloramphenicol and tetracycline were purely bacteriostatic as they fully inhibited the growth but did not kill the bacteria. We also tested ciprofloxacin resistant strains and found higher pharmacodynamic MICs (zMIC) in the resistant strains and attenuated bactericidal effects at concentrations above the zMIC.

CONCLUSIONS

N. gonorrhoeae time-kill curve experiments analysed with a pharmacodynamic model have potential for in vitro evaluation of new and existing antimicrobials. The pharmacodynamic parameters based on a wide range of concentrations below and above the MIC provide information that could support improving future dosing strategies to treat gonorrhoea.

Multistrain models predict sequential multidrug treatment strategies to result in less antimicrobial resistance than combination treatment

Background

Combination treatment is increasingly used to fight infections caused by bacteria resistant to two or more antimicrobials. While multiple studies have evaluated treatment strategies to minimize the emergence of resistant strains for single antimicrobial treatment, fewer studies have considered combination treatments. The current study modeled bacterial growth in the intestine of pigs after intramuscular combination treatment (i.e. using two antibiotics simultaneously) and sequential treatments (i.e. alternating between two antibiotics) in order to identify the factors that favor the sensitive fraction of the commensal flora.

Growth parameters for competing bacterial strains were estimated from the combined in vitro pharmacodynamic effect of two antimicrobials using the relationship between concentration and net bacterial growth rate. Predictions of in vivo bacterial growth were generated by a mathematical model of the competitive growth of multiple strains of Escherichia coli.

Results

Simulation studies showed that sequential use of tetracycline and ampicillin reduced the level of double resistance, when compared to the combination treatment. The effect of the cycling frequency (how frequently antibiotics are alternated in a sequential treatment) of the two drugs was dependent upon the order in which the two drugs were used.

Conclusion

Sequential treatment was more effective in preventing the growth of resistant strains when compared to the combination treatment. The cycling frequency did not play a role in suppressing the growth of resistant strains, but the specific order of the two antimicrobials did. Predictions made from the study could be used to redesign multidrug treatment strategies not only for intramuscular treatment in pigs, but also for other dosing routes.

Electronic supplementary material

The online version of this article (doi:10.1186/s12866-016-0724-5) contains supplementary material, which is available to authorized users.

Transitioning from First Drug Use to Dependence Onset: Illustration of a Multiparametric Approach for Comparative Epidemiology

Studying transitions from first drug use (DU) to drug dependence (DD) onset, we estimate a parsimonious set of parameters based on epidemiological data, with plans for future longitudinal research on newly incident drug users and with tracking of self-administration frequencies and DD clinical features. Our expectation is a distinctive sigmoid pattern with one asymptote for lower DD probability (when DU is insubstantial), upturning slopes of DD risk beyond a middle value (PD50), and eventual higher DD risk asymptotes at higher DU frequencies. We illustrate this novel approach using cross-sectional data from the United States National Surveys on Drug Use and Health, 2002-2011. Empirical DD probabilities observed soon after newly incident use are estimated across DU frequency values, using parametric Hill functions and four governing parameters for differential comparison across drugs and DU subgroups. Among drug subtypes considered, cocaine shows larger estimates, especially among females (estimated P(min)=7% for females vs 3% for males; p<0.001), for whom PD50 is shorter by 8 days of use (p=0.027), conditional on the same rate of use in the past 30 days. Clear alcohol male-female differences also are observed (eg, female PD50 < male PD50; p=0.002). Although based on cross-sectional snapshots soon after DU onset, this novel multiparametric statistical approach for comparative epidemiological DD research creates new opportunities in planned studies with prospectively gathered longitudinal data. The cross-sectional estimates provide starting values needed to plan future longitudinal research programs on transitions from initial DU until formation of a DD syndrome.

Combination Effects of Antimicrobial Peptides

Antimicrobial peptides (AMPs) are ancient and conserved across the tree of life. Their efficacy over evolutionary time has been largely attributed to their mechanisms of killing. Yet, the understanding of their pharmacodynamics both in vivo and in vitro is very limited. This is, however, crucial for applications of AMPs as drugs and also informs the understanding of the action of AMPs in natural immune systems. Here, we selected six different AMPs from different organisms to test their individual and combined effects in vitro. We analyzed their pharmacodynamics based on the Hill function and evaluated the interaction of combinations of two and three AMPs. Interactions of AMPs in our study were mostly synergistic, and three-AMP combinations displayed stronger synergism than two-AMP combinations. This suggests synergism to be a common phenomenon in AMP interaction. Additionally, AMPs displayed a sharp increase in killing within a narrow dose range, contrasting with those of antibiotics. We suggest that our results could lead a way toward better evaluation of AMP application in practice and shed some light on the evolutionary consequences of antimicrobial peptide interactions within the immune system of organisms.

Pharmacodynamic modelling of in vitro activity of tetracycline against a representative, naturally occurring population of porcine Escherichia coli

Background

The complex relationship between drug concentrations and bacterial growth rates require not only the minimum inhibitory concentration but also other parameters to capture the dynamic nature of the relationship. To analyse this relationship between tetracycline concentration and growth of Escherichia coli representative of those found in the Danish pig population, we compared the growth of 50 randomly selected strains. The observed net growth rates were used to describe the in vitro pharmacodynamic relationship between drug concentration and net growth rate based on E_max model with three parameters: maximum net growth rate (α_max); concentration for a half-maximal response (E_max); and the Hill coefficient (γ).

Results

The net growth rate in the absence of antibiotic did not differ between susceptible and resistant isolates (P = 0.97). The net growth rate decreased with increasing tetracycline concentrations, and this decline was greater in susceptible strains than resistant strains. The lag phase, defined as the time needed for the strain to reach an OD₆₀₀ value of 0.01, increased exponentially with increasing tetracycline concentration. The pharmacodynamic parameters confirmed that the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \alpha_{max} $$\end{document}αmax between susceptible and resistant strains in the absence of a drug was not different. EC₅₀ increased linearly with MIC on a log–log scale, and γ was different between susceptible and resistant strains.

Conclusions

The in vitro model parameters described the inhibition effect of tetracycline on E. coli when strains were exposed to a wide range of tetracycline concentrations. These parameters, along with in vivo pharmacokinetic data, may be useful in mathematical models to predict in vivo competitive growth of many different strains and for development of optimal dosing regimens for preventing selection of resistance.

Quantifying the impact of drug combination regimens on TB treatment efficacy and multidrug resistance probability

OBJECTIVES

TB patients' non-adherence to the multidrug treatment regimen is thought to be the main cause of the emergence of drug resistance. The purpose of this study was to quantify the impacts of two-drug combination regimens and non-adherence to these regimens on treatment efficacy and drug resistance probability.

METHODS

A drug treatment modelling strategy was developed by incorporating a pharmacokinetic/pharmacodynamic model into a bacterial population dynamic model to explore the dynamics of TB bacilli and evolution of resistance during multidrug combination therapy, with an emphasis on non-adherence. A Hill-equation-based pharmacodynamic model was used to assess the bactericidal efficacy of single drugs and to estimate drug interactions.

RESULTS

Non-adherence to the treatment regimen increased treatment duration by nearly 1.6- and 3.4-fold relative to compliance with treatment. Symptom-based intermittent treatment, a form of non-adherence, might lead to treatment failure and accelerated growth and evolution of resistant mutants, resulting in a dramatically higher probability of 4.17 × 10(-3) (95% CI 2.10 × 10(-4)-1.28 × 10(-2)) for the emergence of MDR TB. Overall, determination of the optimal treatment regimen depended on the different types of medication adherence.

CONCLUSIONS

Our model not only predicts evolutionary dynamics, but also quantifies treatment efficacy. More broadly, our model provides a quantitative framework for improving treatment protocols and establishing an emergence threshold of resistance that can be used to prevent drug resistance.

Antibiotic efficacy is linked to bacterial cellular respiration

Bacteriostatic and bactericidal antibiotic treatments result in two fundamentally different phenotypic outcomes--the inhibition of bacterial growth or, alternatively, cell death. Most antibiotics inhibit processes that are major consumers of cellular energy output, suggesting that antibiotic treatment may have important downstream consequences on bacterial metabolism. We hypothesized that the specific metabolic effects of bacteriostatic and bactericidal antibiotics contribute to their overall efficacy. We leveraged the opposing phenotypes of bacteriostatic and bactericidal drugs in combination to investigate their activity. Growth inhibition from bacteriostatic antibiotics was associated with suppressed cellular respiration whereas cell death from most bactericidal antibiotics was associated with accelerated respiration. In combination, suppression of cellular respiration by the bacteriostatic antibiotic was the dominant effect, blocking bactericidal killing. Global metabolic profiling of bacteriostatic antibiotic treatment revealed that accumulation of metabolites involved in specific drug target activity was linked to the buildup of energy metabolites that feed the electron transport chain. Inhibition of cellular respiration by knockout of the cytochrome oxidases was sufficient to attenuate bactericidal lethality whereas acceleration of basal respiration by genetically uncoupling ATP synthesis from electron transport resulted in potentiation of the killing effect of bactericidal antibiotics. This work identifies a link between antibiotic-induced cellular respiration and bactericidal lethality and demonstrates that bactericidal activity can be arrested by attenuated respiration and potentiated by accelerated respiration. Our data collectively show that antibiotics perturb the metabolic state of bacteria and that the metabolic state of bacteria impacts antibiotic efficacy.

Imperfect drug penetration leads to spatial monotherapy and rapid evolution of multidrug resistance

Infections with rapidly evolving pathogens are often treated using combinations of drugs with different mechanisms of action. One of the major goal of combination therapy is to reduce the risk of drug resistance emerging during a patient's treatment. Although this strategy generally has significant benefits over monotherapy, it may also select for multidrug-resistant strains, particularly during long-term treatment for chronic infections. Infections with these strains present an important clinical and public health problem. Complicating this issue, for many antimicrobial treatment regimes, individual drugs have imperfect penetration throughout the body, so there may be regions where only one drug reaches an effective concentration. Here we propose that mismatched drug coverage can greatly speed up the evolution of multidrug resistance by allowing mutations to accumulate in a stepwise fashion. We develop a mathematical model of within-host pathogen evolution under spatially heterogeneous drug coverage and demonstrate that even very small single-drug compartments lead to dramatically higher resistance risk. We find that it is often better to use drug combinations with matched penetration profiles, although there may be a trade-off between preventing eventual treatment failure due to resistance in this way and temporarily reducing pathogen levels systemically. Our results show that drugs with the most extensive distribution are likely to be the most vulnerable to resistance. We conclude that optimal combination treatments should be designed to prevent this spatial effective monotherapy. These results are widely applicable to diverse microbial infections including viruses, bacteria, and parasites.

Bacterial responses to antibiotics and their combinations

Antibiotics affect bacterial cell physiology at many levels. Rather than just compensating for the direct cellular defects caused by the drug, bacteria respond to antibiotics by changing their morphology, macromolecular composition, metabolism, gene expression and possibly even their mutation rate. Inevitably, these processes affect each other, resulting in a complex response with changes in the expression of numerous genes. Genome-wide approaches can thus help in gaining a comprehensive understanding of bacterial responses to antibiotics. In addition, a combination of experimental and theoretical approaches is needed for identifying general principles that underlie these responses. Here, we review recent progress in our understanding of bacterial responses to antibiotics and their combinations, focusing on effects at the levels of growth rate and gene expression. We concentrate on studies performed in controlled laboratory conditions, which combine promising experimental techniques with quantitative data analysis and mathematical modeling. While these basic research approaches are not immediately applicable in the clinic, uncovering the principles and mechanisms underlying bacterial responses to antibiotics may, in the long term, contribute to the development of new treatment strategies to cope with and prevent the rise of resistant pathogenic bacteria.

Evolutionary rescue: linking theory for conservation and medicine

Evolutionary responses that rescue populations from extinction when drastic environmental changes occur can be friend or foe. The field of conservation biology is concerned with the survival of species in deteriorating global habitats. In medicine, in contrast, infected patients are treated with chemotherapeutic interventions, but drug resistance can compromise eradication of pathogens. These contrasting biological systems and goals have created two quite separate research communities, despite addressing the same central question of whether populations will decline to extinction or be rescued through evolution. We argue that closer integration of the two fields, especially of theoretical understanding, would yield new insights and accelerate progress on these applied problems. Here, we overview and link mathematical modelling approaches in these fields, suggest specific areas with potential for fruitful exchange, and discuss common ideas and issues for empirical testing and prediction.

What should be considered in the treatment of bacterial infections by multi-drug therapies: a mathematical perspective?

Bacterial infections are a global health concern with high levels of mortality and morbidity associated. The resistance of pathogens to drugs is one leading cause of this problem, being common the administration of multiple drugs to improve the therapeutic effects. This review critically explores diverse aspects involved in the treatment of bacterial infections through multi-drug therapies, from a mathematical and within-host perspectives. Five recent models were selected and are reviewed. These models fall into the following question: which drugs to select, the respective dose, the administration period to effectively eradicate the infection in the shortest period of time and with reduced side effects? In this analysis, three groups of variables were considered: pharmacokinetics, pharmacodynamics and disturbance variables. To date, there is no model that fully answers to this issue for a living organism and it is questionable whether this would be possible for any case of infection.

A model-guided analysis and perspective on the evolution and epidemiology of antibiotic resistance and its future

A simple epidemiological model is used as a framework to explore the potential efficacy of measures to control antibiotic resistance in community-based self-limiting human infections. The analysis of the properties of this model predict that resistance can be maintained at manageable levels if: first, the rates at which specific antibiotics are used declines with the frequency of resistance to these drugs; second, resistance rarely emerges during therapy; and third, external sources rarely contribute to the entry of resistant bacteria into the community. We discuss the feasibility and limitations of these measures to control the rates of antibiotic resistance and the potential of advances in diagnostic procedures to facilitate this endeavor.

Exploring the collaboration between antibiotics and the immune response in the treatment of acute, self-limiting infections

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.

In silico models of M. tuberculosis infection provide a route to new therapies

Tuberculosis (TB) is a global health problem responsible for ~2 million deaths per year. Current antibiotic treatments are lengthy and fraught with compliance and resistance issues. There is a crucial need for additional approaches to provide a cost-effective means of exploring the design space for potential therapies. We discuss the use of mathematical and computational models in virtual experiments and virtual clinical trials both to develop new hypotheses regarding the disease and to provide a cost-effective means of discovering new treatment strategies.

Fitness landscapes emerging from pharmacodynamic functions in the evolution of multidrug resistance

Adaptive evolution often involves beneficial mutations at more than one locus. In this case, the trajectory and rate of adaptation is determined by the underlying fitness landscape, that is, the fitness values and mutational connectivity of all genotypes under consideration. Drug resistance, especially resistance to multiple drugs simultaneously, is also often conferred by mutations at several loci so that the concept of fitness landscapes becomes important. However, fitness landscapes underlying drug resistance are not static but dependent on drug concentrations, which means they are influenced by the pharmacodynamics of the drugs administered. Here, I present a mathematical framework for fitness landscapes of multidrug resistance based on Hill functions describing how drug concentrations affect fitness. I demonstrate that these 'pharmacodynamic fitness landscapes' are characterized by pervasive epistasis that arises through (i) fitness costs of resistance (even when these costs are additive), (ii) nonspecificity of resistance mutations to drugs, in particular cross-resistance, and (iii) drug interactions (both synergistic and antagonistic). In the latter case, reciprocal drug suppression may even lead to reciprocal sign epistasis, so that the doubly resistant genotype occupies a local fitness peak that may be difficult to access by evolution. Simulations exploring the evolutionary dynamics on some pharmacodynamic fitness landscapes with both constant and changing drug concentrations confirm the crucial role of epistasis in determining the rate of multidrug resistance evolution.

A novel molecular typing method of Mycobacteria based on DNA barcoding visualization

Different subtypes of Mycobacterium tuberculosis (MTB) may induce diverse severe human infections, and some of their symptoms are similar to other pathogenes, e.g. Nontuberculosis mycobacteria (NTM). So determination of mycobacterium subtypes facilitates the effective control of MTB infection and proliferation. This study exploits a novel DNA barcoding visualization method for molecular typing of 17 mycobacteria genomes published in the NCBI prokaryotic genome database. Three mycobacterium genes (Rv0279c, Rv3508 and Rv3514) from the PE/PPE family of MT Band were detected to best represent the inter-strain pathogenetic variations. An accurate and fast MTB substrain typing method was proposed based on the combination of the aforementioned three biomarker genes and the 16S rRNA gene. The protocol of establishing a bacterial substrain typing system used in this study may also be applied to the other pathogenes.

Resource competition may lead to effective treatment of antibiotic resistant infections

Drug resistance is a common problem in the fight against infectious diseases. Recent studies have shown conditions (which we call antiR) that select against resistant strains. However, no specific drug administration strategies based on this property exist yet. Here, we mathematically compare growth of resistant versus sensitive strains under different treatments (no drugs, antibiotic, and antiR), and show how a precisely timed combination of treatments may help defeat resistant strains. Our analysis is based on a previously developed model of infection and immunity in which a costly plasmid confers antibiotic resistance. As expected, antibiotic treatment increases the frequency of the resistant strain, while the plasmid cost causes a reduction of resistance in the absence of antibiotic selection. Our analysis suggests that this reduction occurs under competition for limited resources. Based on this model, we estimate treatment schedules that would lead to a complete elimination of both sensitive and resistant strains. In particular, we derive an analytical expression for the rate of resistance loss, and hence for the time necessary to turn a resistant infection into sensitive (tclear). This time depends on the experimentally measurable rates of pathogen division, growth and plasmid loss. Finally, we estimated tclear for a specific case, using available empirical data, and found that resistance may be lost up to 15 times faster under antiR treatment when compared to a no treatment regime. This strategy may be particularly suitable to treat chronic infection. Finally, our analysis suggests that accounting explicitly for a resistance-decaying rate may drastically change predicted outcomes in host-population models.

The pharmaco -, population and evolutionary dynamics of multi-drug therapy: experiments with S. aureus and E. coli and computer simulations

There are both pharmacodynamic and evolutionary reasons to use multiple rather than single antibiotics to treat bacterial infections; in combination antibiotics can be more effective in killing target bacteria as well as in preventing the emergence of resistance. Nevertheless, with few exceptions like tuberculosis, combination therapy is rarely used for bacterial infections. One reason for this is a relative dearth of the pharmaco-, population- and evolutionary dynamic information needed for the rational design of multi-drug treatment protocols. Here, we use in vitro pharmacodynamic experiments, mathematical models and computer simulations to explore the relative efficacies of different two-drug regimens in clearing bacterial infections and the conditions under which multi-drug therapy will prevent the ascent of resistance. We estimate the parameters and explore the fit of Hill functions to compare the pharmacodynamics of antibiotics of four different classes individually and in pairs during cidal experiments with pathogenic strains of Staphylococcus aureus and Escherichia coli. We also consider the relative efficacy of these antibiotics and antibiotic pairs in reducing the level of phenotypically resistant but genetically susceptible, persister, subpopulations. Our results provide compelling support for the proposition that the nature and form of the interactions between drugs of different classes, synergy, antagonism, suppression and additivity, has to be determined empirically and cannot be inferred from what is known about the pharmacodynamics or mode of action of these drugs individually. Monte Carlo simulations of within-host treatment incorporating these pharmacodynamic results and clinically relevant refuge subpopulations of bacteria indicate that: (i) the form of drug-drug interactions can profoundly affect the rate at which infections are cleared, (ii) two-drug therapy can prevent treatment failure even when bacteria resistant to single drugs are present at the onset of therapy, and (iii) this evolutionary virtue of two-drug therapy is manifest even when the antibiotics suppress each other's activity.

In this study, we combine pharmacodynamic experiments using pathogenic strains of E. coli and S. aureus with mathematical and computer simulation models to explore the relative efficacies of two-drug antibiotic combinations in clearing infections and preventing the emergence of resistance. We develop a pharmacodynamic method that provides a convenient way to determine whether drug combinations will interact synergistically, antagonistically, additively or suppressively. We find that it is not possible to predict the nature and form of drug interactions based on what is known about the mode of action of individual drugs, thus illustrating the necessity of assessing the efficacy of drug combinations empirically. Our simulations of the within-host population and evolutionary dynamics of bacteria undergoing multi-drug treatment indicate that the form of the interaction between drugs observed experimentally can substantially affect the rate of clearance of the infection. On the other hand, the form of these interactions plays a minimal role in the emergence of resistance. Even when antibiotics are suppressive, two-drug therapy can prevent the ascent of bacteria resistant to single drugs that are present at the start of therapy and/or generated during the course of the infection.

Antibiotic transport in resistant bacteria: synchrotron UV fluorescence microscopy to determine antibiotic accumulation with single cell resolution

A molecular definition of the mechanism conferring bacterial multidrug resistance is clinically crucial and today methods for quantitative determination of the uptake of antimicrobial agents with single cell resolution are missing. Using the naturally occurring fluorescence of antibacterial agents after deep ultraviolet (DUV) excitation, we developed a method to non-invasively monitor the quinolones uptake in single bacteria. Our approach is based on a DUV fluorescence microscope coupled to a synchrotron beamline providing tuneable excitation from 200 to 600 nm. A full spectrum was acquired at each pixel of the image, to study the DUV excited fluorescence emitted from quinolones within single bacteria. Measuring spectra allowed us to separate the antibiotic fluorescence from the autofluorescence contribution. By performing spectroscopic analysis, the quantification of the antibiotic signal was possible. To our knowledge, this is the first time that the intracellular accumulation of a clinical antibiotic could be determined and discussed in relation with the level of drug susceptibility for a multiresistant strain. This method is especially important to follow the behavior of quinolone molecules at individual cell level, to quantify the intracellular concentration of the antibiotic and develop new strategies to combat the dissemination of MDR-bacteria. In addition, this original approach also indicates the heterogeneity of bacterial population when the same strain is under environmental stress like antibiotic attack.