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Density- and resource-dependent pharmacodynamic functions for bactericidal antibiotics. Hourly rates of population growth or death as functions of the concentration of the antibiotic are presented. Common parameters: km = 0.25, Vmax = 1.0, and Vmin = −3.0. (A) Effects of density on the PD of antibiotics. Line 1, control, with no density or resource effects (pd = pr = 0). Lines 2, 3, and 4, modest density effects (pd = 0.5, Mmax = 5.0) (line 2, n = 10⁶; line 3, n = 10⁷; line 4, n = 10⁸). Lines 5 and 6, strong density effects (pd = 0.5; Mmax = 40.0) (line 5, n = 10⁶; line 6, n = 10⁸). (B) Joint effects of resource and density levels on PD. Line 1, control, with no density or resource effect (pd = pr = 0). For the remaining lines, the resource concentration (R) was 0.25 μg/ml. Line 2, resource effect, no density effect (pr = 0.9, pd = 0). Lines 3, 4, and 5, resource and modest density effects (pr = 0.9, pd = 0.5, Mmax = 5.0) (line 3, n = 10⁶; line 4, n = 10⁷; line 5, n = 10⁸). Line 6, resource and strong density effects (pd = 0.9, pd = 0.5, Mmax = 40.0) (n = 10⁸).
Source publication
The objectives of the study were to develop a quantitative framework for generating hypotheses for and interpreting the results of time-kill and continuous-culture experiments designed to evaluate the efficacy of antibiotics and to relate the results of these experiments to MIC data. A mathematical model combining the pharmacodynamics (PD) of antib...
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Citations
... More importantly, CS can be used to design drug combinations therapy: for instance by including mutual CS drugs in drug-cycling regimen [13,28,61]. To further understand the extent of CS, laboratory evolution has been deployed to map out CS profiles between the known antibiotics for specific drug-resistant strains [36,53,35,27]; genome sequencing to characterize the components that contribute to CS [58,41,7,20]; and the development of mathematical modeling that provides insight into the collateral dynamics network and supports control strategies to reduce the growth of MDR [37,6]. Mathematical modeling establishes a high level of control involving factors such as pharmacodynamic (PD) and pharmacokinetic (PK) [65], optimal time of drug exposure [68], between others with relevance on the effects antibiotics have on bacterial growth, inhibition, killing, and mutation [60,30,9,66]. ...
The use of chemotherapeutics agents in the treatment of bacterial infections have resulted in the emergence of multidrug resistant pathogens. Clinically, with single and even multiple drug intervention strategies, pathogens have developed resistance to one or all drugs utilized. This leads to the reasonable conclusion that the primary effect of any (finite) amount of drugs is delaying resistance development as opposed to prevention. Importantly, it has been shown that in sequential exposure of pathogens to antibiotics, evolution of resistance to some drugs may increase sensitivity toward others previously used, a phenomenon known as collateral sensitivity. This suggests that multidrug resistance could be avoided by an adequate use of the available drugs. Without a framework to do this however, each bug:drugs interaction network would need to be assembled blindly, an arduous experimental process. This study develops a framework for describing qualitatively collateral sensitivity networks, accordingly the interactions between emerging drug-resistant variants are modeled and a dynamic analysis is conducted to predict failure or success of sequential drug therapies.
... Initial characterization suggested that antibiotics preferentially select for bacteria with enhanced metabolic efficiency, which may directly or indirectly contribute to resistance. To further explore this premise, we used a mathematical framework (36) to investigate the interdependent evolutionary dynamics of growth and metabolism in a microbial population under sub-inhibitory antibiotic selection. Sub-inhibitory concentrations are particularly relevant in this context since resistance evolves in increments often attributed to the stepwise accumulation of mutations (and/or acquisition of resistance genes) selected for under antibiotic treatment (37). ...
... To investigate how antibiotic selection may affect cellular metabolism, we considered the key interactions between growth, metabolism, and antibiotic-mediated lethality ( Fig. 2A). We focused on a generic bactericidal antibiotic and assume that it both inhibits the growth of, and actively kills, cells (36). Critically, increased substrate consumption not only increases growth rate but also makes cells more susceptible to drug-mediated killing-as described above, substrate consumption is a proxy for cellular metabolism, which potentiates lethality (27). ...
... To capture these core interactions, we modified a previously described populationlevel model consisting of two ordinary differential equations that capture cell density (N) and substrate concentration (S) over time (36). For this full model, cells (N) grow accord ing to classical Monod kinetics, which are described by three parameters: the substrate conversion constant (which describes the fraction of substrate converted into biomass [e]), the maximal growth rate (μ M ), and the half-maximal substrate concentration (K S ). ...
Bacterial growth and metabolic rates are often closely related. However, under antibiotic selection, a paradox in this relationship arises: antibiotic efficacy decreases when bacteria are metabolically dormant, yet antibiotics select for resistant cells that grow fastest during treatment. That is, antibiotic selection counterintuitively favors bacteria with fast growth but slow metabolism. Despite this apparent contradiction, antibiotic resistant cells have historically been characterized primarily in the context of growth, whereas the extent of analogous changes in metabolism is comparatively unknown. Here, we observed that previously evolved antibiotic-resistant strains exhibited a unique relationship between growth and metabolism whereby nutrient utilization became more efficient, regardless of the growth rate. To better understand this unexpected phenomenon, we used a simplified model to simulate bacterial populations adapting to sub-inhibitory antibiotic selection through successive bottlenecking events. Simulations predicted that sub-inhibitory bactericidal antibiotic concentrations could select for enhanced metabolic efficiency, defined based on nutrient utilization: drug-adapted cells are able to achieve the same biomass while utilizing less substrate, even in the absence of treatment. Moreover, simulations predicted that restoring metabolic efficiency would re-sensitize resistant bacteria exhibiting metabolic-dependent resistance; we confirmed this result using adaptive laboratory evolutions of Escherichia coli under carbenicillin treatment. Overall, these results indicate that metabolic efficiency is under direct selective pressure during antibiotic treatment and that differences in evolutionary context may determine both the efficacy of different antibiotics and corresponding re-sensitization approaches.
IMPORTANCE
The sustained emergence of antibiotic-resistant pathogens combined with the stalled drug discovery pipelines highlights the critical need to better understand the underlying evolution mechanisms of antibiotic resistance. To this end, bacterial growth and metabolic rates are often closely related, and resistant cells have historically been characterized exclusively in the context of growth. However, under antibiotic selection, antibiotics counterintuitively favor cells with fast growth, and slow metabolism. Through an integrated approach of mathematical modeling and experiments, this study thereby addresses the significant knowledge gap of whether antibiotic selection drives changes in metabolism that complement, and/or act independently, of antibiotic resistance phenotypes.
... This will be relevant if, before treatment begins, the microbial load reaches a level which is close to the environmental carrying capacity, so that resource limitation leads to significant reduction of the growth rate. Several published models have included this mechanism, either by replacing the constant per capita growth term in (3) by a nonlinear (typically logistic) term (Bhagunde et al. 2015;Geli et al. 2012;Kesisoglou et al 2022;Nikolaou and Tam 2006;Paterson et al. 2016;Tindall et al. 2022), or by explicitly modelling the resource dynamics (Ali et al. 2022;Khan and Imran 2018;Levin and Udekwu 2010;Zilonova et al. 2016). We expect that when density-dependent growth is included in the model, the 'ideal' concentration profile (the solution of Problem 1) will no longer be constant in time. ...
This work studies fundamental questions regarding the optimal design of antimicrobial treatment protocols, using pharmacodynamic and pharmacokinetic mathematical models. We consider the problem of designing an antimicrobial treatment schedule to achieve eradication of a microbial infection, while minimizing the area under the time-concentration curve (AUC), which is equivalent to minimizing the cumulative dosage. We first solve this problem under the assumption that an arbitrary antimicrobial concentration profile may be chosen, and prove that the ideal concentration profile consists of a constant concentration over a finite time duration, where explicit expressions for the optimal concentration and the time duration are given in terms of the pharmacodynamic parameters. Since antimicrobial concentration profiles are induced by a dosing schedule and the antimicrobial pharmacokinetics, the ‘ideal’ concentration profile is not strictly feasible. We therefore also investigate the possibility of achieving outcomes which are close to those provided by the ‘ideal’ concentration profile, using a bolus+continuous dosing schedule, which consists of a loading dose followed by infusion of the antimicrobial at a constant rate. We explicitly find the optimal bolus+continuous dosing schedule, and show that, for realistic parameter ranges, this schedule achieves results which are nearly as efficient as those attained by the ‘ideal’ concentration profile. The optimality results obtained here provide a baseline and reference point for comparison and evaluation of antimicrobial treatment plans.
... Some of the works on dynamical modelling of microbial dynamics under the effect of antimicrobials, in particular the more theoretical studies, include mechanisms which are absent from the basic model considered here. One such mechanism is density-dependence of the microbial population growth, which will be relevant if this population reaches a size at which resource limitation reduces its growth rate [1,3,12,15,16,18,29,33,41,46]. Another element which influences microbial dynamics is immune response, and if the strength of immune supression is comparable to that of the antimicrobial, it might be important to include an immune system component in the model [12,13,14,41]. ...
This work studies fundamental questions regarding the optimal design of antimicrobial treatment protocols, using standard pharmacodynamic and pharmacokinetic mathematical models. We consider the problem of designing an antimicrobial treatment schedule to achieve eradication of a microbial infection, while minimizing the area under the time-concentration curve (AUC). We first solve this problem under the assumption that an arbitrary antimicrobial concentration profile may be chosen, and prove that the 'ideal' concentration profile consists of a constant concentration over a finite time duration, where explicit expressions for the optimal concentration and the time duration are given in terms of the pharmacodynamic parameters. Since antimicrobial concentration profiles are induced by a dosing schedule and the antimicrobial pharmacokinetics, the ideal concentration profile is not strictly feasible. We therefore also investigate the possibility of achieving outcomes which are close to those provided by the ideal concentration profile,using a bolus+continuous dosing schedule, which consists of a loading dose followed by infusion of the antimicrobial at a constant rate. We explicitly find the optimal bolus+continuous dosing schedule, and show that, for realistic parameter ranges, this schedule achieves results which are nearly as efficient as those attained by the ideal concentration profile. The optimality results obtained here provide a baseline and reference point for comparison and evaluation of antimicrobial treatment plans.
... This allows us to generalise our conclusions as these parameters likely vary for different combinations of phage, antibiotics and bacteria. The ranges evaluated are shown in Table 1, and are either derived from our initial parameterisation of the model [28], or from other studies [50,51]. ...
... Importantly, our results similarly suggest that higher decay rates for antibiotics present alongside phage would reduce bacteria remaining after 48h, at the cost of a higher peak concentration of multidrug-resistant bacteria, since this decay would allow bacteria to reach the proliferation threshold sooner (Fig 6C, S7 Fig). This knowledge may be further useful in the context of phage therapy, to select the antibiotics that will be given alongside phage [51]. ...
Bacteriophage (phage) are bacterial predators that can also spread antimicrobial resistance (AMR) genes between bacteria by generalised transduction. Phage are often present alongside antibiotics in the environment, yet evidence of their joint killing effect on bacteria is conflicted, and the dynamics of transduction in such systems are unknown. Here, we combine in vitro data and mathematical modelling to identify conditions where phage and antibiotics act in synergy to remove bacteria or drive AMR evolution. We adapt a published model of phage-bacteria dynamics, including transduction, to add the pharmacodynamics of erythromycin and tetracycline, parameterised from new in vitro data. We simulate a system where two strains of Staphylococcus aureus are present at stationary phase, each carrying either an erythromycin or tetracycline resistance gene, and where multidrug-resistant bacteria can be generated by transduction only. We determine rates of bacterial clearance and multidrug-resistant bacteria appearance, when either or both antibiotics and phage are present at varying timings and concentrations. Although phage and antibiotics act in synergy to kill bacteria, by reducing bacterial growth antibiotics reduce phage production. A low concentration of phage introduced shortly after antibiotics fails to replicate and exert a strong killing pressure on bacteria, instead generating multidrug-resistant bacteria by transduction which are then selected for by the antibiotics. Multidrug-resistant bacteria numbers were highest when antibiotics and phage were introduced simultaneously. The interaction between phage and antibiotics leads to a trade-off between a slower clearing rate of bacteria (if antibiotics are added before phage), and a higher risk of multidrug-resistance evolution (if phage are added before antibiotics), exacerbated by low concentrations of phage or antibiotics. Our results form hypotheses to guide future experimental and clinical work on the impact of phage on AMR evolution, notably for studies of phage therapy which should investigate varying timings and concentrations of phage and antibiotics.
... It is thought that drug levels must exceed at least 8-10 times the MIC to prevent the emergence of a resistant population, which can be seen with the use of such drugs as a single daily dose of fluoroquinolones [28]. In clinical practice, in antibiotic therapy, to minimize the increase in the size of the pathogen inoculum, antibiotic therapy in the shortest possible time is required using MSW [29]. ...
Background
Antibiotic resistance is closely related to therapy failure. Most antibiotic resistance is caused by delays in determining antibiotic agents, low administration doses, long periods between doses (inadequate pharmacokinetics) and single drug administration in infections caused by more than one pathogen. Treatment of Pseudomonas aeruginosa (P. aeruginosa) with ciprofloxacin, levofloxacin, and ofloxacin as monotherapy can lead to drug resistance, although combination therapy also does not provide a better outcome.
Objective
To analyze the time-kill curve for P. aeruginosa and Multidrug resistance (MDR) P. aeruginosa.
Methods
This research is a case control study using isolates of P. aeruginosa ATCC 27853, clinical isolates of P. aeruginosa and MDR P. aeruginosa. Exposure of ciprofloxacin, levofloxacin, and ofloxacin to isolates with 1MIC, 2MIC, and 4MIC were then cultured at 0, 2, 4, 6, 8, 24 h of testing, then counting the number of colonies that grew and then analyzed by time-kill curve and statistical tests. The statistical test used in this study was the ANOVA and Mann-Whitney test with p < 0.05.
Results
Ciprofloxacin and ofloxacin achieved bactericidal activity, especially at a concentration of 4MIC. Levofloxacin ultimately achieved bactericidal activity at all concentrations. Statistical analysis showed there were significant differences in the number of colonies p < 0.001 in the second, fourth, sixth, and eighth hour between the three isolates, p < 0.001 in the sixth and second 4 h between 1MIC and 4MIC, p = 0.012 in the second 4 h between levofloxacin and ofloxacin antibiotics.
Conclusion
Levofloxacin has shown to have better bactericidal activity than ciprofloxacin, and ciprofloxacin has almost the same bactericidal activity as ofloxacin in vitro tests seen from the time-kill curve.
... The effect of mutations on bacterial growth can be modeled by adjusting the pharmacodynamic function: fitness costs are represented by the reduction of the maximum growth rate Ψ max , while an increase in the minimum inhibitory concentration (MIC) needed to stop the bacterial growth captures the benefit. Therefore, the shape of the growth-defining function is changed: the curve typically starts at a lower growth rate and is shifted to the right [39], compared with the sensitive strain ( Figure 1, Key figure). ...
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.
... Here, w is the growth rate when positive and kill rate when negative (42)(43)(44), c is the drug concentration, MDK 99 is the minimum duration for 99% killing, and k is the Hill coefficient. The effect of a drug becomes concentration insensitive when the concentration is much higher than the MIC (12). ...
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.
... Second, antibiotic resistant bacteria are not killed directly by the antibiotics [24][25][26], but antibiotic susceptible bacteria are killed at a rate proportional to the antibiotic concentration: κ a(t) [35]. ...
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 develop antibiotic-resistance.
... Efficacious antibiotics, by definition, reduce within-host pathogen density [Levin and Udekwu 2010]; for some infections, antibiotics consequently increase host survival. ...
... That is, the per unit density bacterial mortality effected by a given antibiotic concentration declines as bacterial density increases [Levin and Udekwu 2010]. ...
Humans, domestic animals, orchard crops, and ornamental plants are commonly treated with antibiotics in response to bacterial infection. By curing infectious individuals, antibiotic therapy might limit the spread of contagious disease among hosts. But an antibiotic`s suppression of within-host pathogen density might also reduce the probability that the host is otherwise removed from infectious status prior to therapeutic recovery. When rates of both recovery via treatment and other removal events (e.g., isolation or mortality) depend directly on within-host pathogen density, antibiotic treatment can relax the overall removal rate sufficiently to increase between-host disease transmission. To explore this dependence, a deterministic within-host dynamics drives the infectious host's time-dependent probability of disease transmission, as well as the probabilistic duration of the infectious period. At the within-host scale, the model varies (1) inoculum size, (2) bacterial self-regulation, (3) the time between infection and initiation of therapy, and (4) antibiotic efficacy. At the between-host scale the model varies (5) the size/susceptibility of groups randomly encountered by an infectious host. Results identify conditions where antibiotic treatment can increase duration of a host`s infectiousness, and consequently increase the expected number of new infections. At lower antibiotic efficacy, treatment might convert a rare, serious bacterial disease into a common, but treatable infection.
