An essential property of microbial communities is the ability to survive a disturbance. Survival can be achieved through resistance, the ability to absorb effects of a disturbance without a notable change, or resilience, the ability to recover after being perturbed by a disturbance. These concepts have long been applied to the analysis of ecological systems, although their interpretations are often subject to debate. Here, we show that this framework readily lends itself to the dissection of the bacterial response to antibiotic treatment, where both terms can be unambiguously defined. The ability to tolerate the antibiotic treatment in the short term corresponds to resistance, which primarily depends on traits associated with individual cells. In contrast, the ability to recover after being perturbed by an antibiotic corresponds to resilience, which primarily depends on traits associated with the population. This framework effectively reveals the phenotypic signatures of bacterial pathogens expressing extended-spectrum β-lactamases (ESBLs) when treated by a β-lactam antibiotic. Our analysis has implications for optimizing treatment of these pathogens using a combination of a β-lactam and a β-lactamase (Bla) inhibitor. In particular, our results underscore the need to dynamically optimize combination treatments based on the quantitative features of the bacterial response to the antibiotic or the Bla inhibitor.

Here, we apply these concepts to the analysis of bacterial pathogens that produce extended-spectrum β-lactamases (ESBLs), which are becoming increasingly prevalent and can degrade many β-lactam antibiotics—the most widely used class of antibiotics ( 15 ). Our results offer new insights into the design of antibacterial treatment strategies against one of the most rapidly increasing types of bacterial pathogens ( 16 – 18 ). In particular, the resistance-resilience framework reveals the phenotypic signatures of different ESBL-producing bacteria and underscores the critical need to implement adjustable formulations of combination treatments. Our framework is also potentially applicable to analysis of bacterial population-level responses to other environmental perturbations, such as other antibiotics, changes in temperature and nutrients, and xeric stress.

Each row represents a different response to an antibiotic delivered at time zero. In the first row, all individual cells can withstand the antibiotic, which results in the population growing to carrying capacity, unperturbed. In the second row, only a subpopulation of cells is killed. This result manifests as an initial decline in the population density followed by full recovery, after the antibiotic is removed in the allotted time. A third scenario entails a greater sensitivity compared with the second scenario, due to greater sensitivity of individual cells or lower capability of the population in removing the antibiotic. In this case, the population only partially recovers during the allotted time after the initial decline. In the final row, all cells are killed, leading to the population extinction. Currently, antibiotic sensitivity analyses only consider whether bacteria can recover from a set dose of antibiotic in a standard period (red dot). Bacteria that display full recovery are considered resistant, partial recovery are intermediate, and no recovery are sensitive. However, temporal dynamics (blue curve) reveal differences in how a population recovers. Living cells, blue; dead cells, gray.

Yet, this resistance-resilience framework naturally lends itself to the analysis of bacterial responses to antibiotic treatment. When running susceptibility tests, it is possible to characterize a pre-disturbance state (i.e., no exposure to antibiotic) and there are many methods to quantify the bacterial antibiotic responses (i.e., agar plates, E-test, plate reader, and microscopy) ( 9 – 11 ). Until now, resistance and resilience have not been distinguished in the context of antibiotic responses. Instead, bacteria are classified as resistant if they survive exposure to a set concentration of antibiotic after a set amount of time ( Table 1 ) ( 12 ). However, an apparently similar rate of survival can result from diverse underlying mechanisms ( 13 , 14 ): Survival can occur because individual cells withstand the treatment or because the population recovers from the initial disturbance, despite the fact that the antibiotic kills some individual bacterial cells. We term the former resistance and the latter resilience.

A disturbance is a biological, chemical, or physical event that affects a community ( 1 ). Given that the environment is constantly changing, an essential property of a community is its ability to recover after being disturbed. Responses to a disturbance include resistance, the ability to withstand perturbation in the presence of a disturbance; resilience, the ability to recover after being perturbed by a disturbance; or sensitivity, the inability to withstand or recover from a disturbance ( 2 , 3 ). Resistance and resilience have been documented in a range of systems and are often determined by different processes ( 1 , 2 , 4 ). Specifically, resistance is associated with processes that enable the tolerance of, or adaptation to, a disturbance, whereas resilience is associated with recolonization, reproduction, or rapid regrowth ( 2 ). The ability to identify the determinants for resistance versus resilience is crucial for predicting how a given community will respond to a disturbance as well as for designing strategies that will either preserve, change, or eliminate it ( 3 , 5 ). Although resistance and resilience have been defined in the literature for decades ( 6 ), the resistance-resilience framework has not been widely applied to bacterial communities. This is partially because it is often difficult to determine the pre-disturbance state of a population, definitions vary, and there is a lack of quantitative studies demonstrating how to implement these terms ( 2 , 3 , 7 , 8 ).

RESULTS

Temporal dynamics of ESBL-producing bacteria in response to β-lactam treatment The dynamics of an ESBL-producing population are uniquely suited for illustrating resistance and resilience during disturbances. In the absence of antibiotic treatment, the population grows approximately exponentially until the growth rate decreases because of the depletion of nutrients and accumulation of toxic compounds (Fig. 1A). Because of the expression of a β-lactamase (Bla) anchored in their periplasm, these bacteria can degrade the antibiotic that diffuses across the outer membrane (19). However, if Bla expression is moderate, these bacteria can still be lysed by a β-lactam antibiotic at a sufficiently high concentration (Fig. 1B). As this antibiotic effect occurs, Bla is released into the environment because of membrane leakage (from a cell not yet lysed) or cell lysis (20). If sufficient Bla (periplasmic and extracellular) is present, the antibiotic is degraded in time for the population to recover before all cells are lysed. A population’s recovery depends on collective tolerance (fig. S1): It must have a sufficiently high density when treated, so that enough Bla is collectively produced to remove the antibiotic before all bacteria are lysed. If the initial density is too low, then insufficient Bla will be produced to protect the population from antibiotic exposure. Fig. 1 Response of an ESBL-producing population to cefotaxime, a β-lactam. (A) Schematic of antibiotic response of an ESBL-producing population. In the absence of antibiotic, bacteria reproduce and consume nutrients. Upon the introduction of an antibiotic, some of the bacteria undergo lysis and release Bla and a small amount of recyclable nutrients into the environment. The released Bla degrades the antibiotic (blue inhibition arm). (B) Time course of antibiotic response. In the absence of an antibiotic (black curve), bacteria grow to a carrying capacity without any delay. In the presence of sufficient antibiotic (gray curve; A = 100 μg/ml cefotaxime), the population displays the characteristic crash, as the cells lyse, and recovery after the Bla released from lysed cells degrades the antibiotic. (C) ESBL substantially degraded cefotaxime in a short time window. The supernatant from a culture of sensitive cells still contained substantial concentrations of cefotaxime, as depicted by the zones of inhibition in the lawn of sensitive cells (strain MC4100, left column). The supernatant from the culture containing ESBL-producing bacteria did not contain substantial concentrations of cefotaxime, as depicted by the full lawns (right column). Arrows indicate where supernatant was placed on the agar plate. (D) Populations previously exposed to cefotaxime exhibited the same temporal dynamics. Culture was treated with a range of antibiotic concentrations. After 24 hours, bacteria from the recovered population were used to reinoculate fresh media with or without cefotaxime (25 μg/ml). During the second round of treatment, time courses from the populations previously exposed to cefotaxime (0, 2, or 200 μg/ml) were identical, suggesting that the population recovery was unlikely due to mutants or phenotypic variants with increased tolerance. (E) Bla production is not induced by cefotaxime. We used fluorocillin to determine that the isolate’s Bla production is not significantly increased by the addition of antibiotic. Here, the Bla activity present in a population after 3 hours of exposure to a range of antibiotic concentrations was quantified by the rate at which fluorocillin was hydrolyzed and produced green fluorescence. One-way analyses of variance (ANOVAs) indicate that the increase in fluorescence recorded was insignificant when compared to the control. Here, we showed that the population recovery was due to the Bla degrading the antibiotic, indicated by the level of antibiotic activity in the supernatant after 6 hours of exposure (Fig. 1C). Sensitive bacteria do not produce Bla and cannot break down the antibiotic; thus, the antibiotic remaining in the supernatant could inhibit the growth of sensitive bacteria. At a higher initial antibiotic concentration, the same amount of supernatant generated a larger zone of inhibition. In contrast, the bacteria producing ESBLs sufficiently degraded the antibiotic at both doses during the incubation period, as evidenced by the inability of the resulting supernatants to inhibit growth of sensitive cells. This Bla-dependent recovery was further demonstrated by the correlation between the time it takes for both sensitive and ESBL-producing bacteria to recover from antibiotic exposure and the amount of exogenous Bla present (fig. S2). To test whether the population recovery was due to the selection of a more resistant or resilient subpopulation, we collected ESBL-producing bacteria that had recovered from an antibiotic treatment and reexposed them to a range of antibiotic concentrations. The resulting antibiotic responses were similar, regardless of previous exposure concentrations (Fig. 1D). This shows that the recovery was not due to the selection of a subpopulation with enhanced tolerance, which is consistent with the notion of antibiotic degradation due to the Bla released from cell lysis. We also tested whether the antibiotic induced the production of Bla by using fluorocillin, a substrate that fluoresces green when degraded by Bla, allowing the real-time visualization of Bla activity. After incubating the isolate with different concentrations of cefotaxime for 3 hours, we added fluorocillin to the sonicated culture to quantify the total Bla present. There was no significant increase in fluorescence as a function of antibiotic concentration (Fig. 1E) at the P < 0.05 level (F 1,6 = 2.44, P = 0.17 and F 1,6 = 3.31, P = 0.12 for A = 10 and 100 μg/ml, respectively). There was a slight, but significant, decrease in fluorescence for A = 1 μg/ml (F 1,6 = 6.68, P = 0.04). Overall, Bla production is not induced by exposure to this range of antibiotic concentrations.

Defining resistance and resilience A population can survive a disturbance because of its resistance or its resilience (1, 2, 7). In general, resistance refers to the ability of a population (or a community) to withstand the disturbance, whereas resilience refers to the ability to recover after suffering from the disturbance. Both properties are evident in the temporal dynamics of an ESBL-producing population in response to β-lactam treatment (Fig. 1). We quantify resilience as the rate of recovery by the population after experiencing the initial crash (Fig. 1A) by using the time needed for a population to reach 50% of its carrying capacity (T50%). With increasing antibiotic concentrations, more cells will lyse in the process of degrading the antibiotic, thus increasing the resulting recovery time. The more resilient a population is, the faster it can return to a normal state after being perturbed by an antibiotic. We define resilience as the inverse of the treated population’s T50% ( ), normalized by the untreated population’s T50% ( ) (Fig. 2A and fig. S3) (1). The inverse is taken to reflect the fact that increasing the recovery time corresponds to a decrease in resilience. (1) Fig. 2 Quantifying resilience and resistance. (A) Time courses are used to quantify a population’s resilience. When no antibiotic was added (black curve), the population grew up unperturbed and reached a target threshold density (here, 50% of the carrying capacity) in time = T50%. If the antibiotic concentration added was very low (blue curve; A = 0.5 μg/ml cefotaxime), then the population reached the threshold density in a similar time to the untreated population. As the antibiotic concentration increased, the degree of lysis increased and affected the time necessary for the treated population to reach the threshold ( ). We characterized the population’s resilience for a range of antibiotic concentrations as the inverse ratio of the times to the half-maximal carrying capacity ( ). (B) Net growth rate quantifies population’s resistance. When no antibiotic was added, the population’s net growth rate decreased over time as it consumed the available nutrients and approached stationary phase. When a low dose of antibiotic was added, the net growth was not notably altered (blue curve). In this instance, the treated population’s minimum net growth rate is recorded as ρ A and compared to the untreated population’s net growth rate at the same time (ρ 0 ). As the antibiotic concentration increased, the net growth rate curve of the treated population deviated more from the untreated curve. For each antibiotic concentration, ρ A was recorded as the net growth rate at the point of maximum negative deviation from the untreated population and normalized by ρ 0 . We characterized a population’s resistance as the ratio of recovery times (ρ A /ρ 0 ). (C) Resistance and resilience as functions of the cefotaxime concentration. At low doses of cefotaxime, the population was resistant and resilient, showing little disturbance after exposure [see (A) and (B)]. As the antibiotic concentration was increased, resistance and resilience decreased due to the increase in cell lysis causing the net growth to decrease and the time to the half-maximum density increased. Once the population underwent a crash, the resistance was minimized and resilience became the dominating factor for survival. (D) The resistance-resilience map defines a phenotypic signature. Using the same data as in (A) to (C), the resistance-resilience framework can visualize the shift in a population’s antibiotic response. When the antibiotic concentration was 0 or very low, the population’s response displayed high resistance and resilience. Once the antibiotic concentration increased to 5 μg/ml, the population’s response shifted to a position where resistance was minimized and resilience dominated the antibiotic response. With further increase in antibiotic concentration, the resistance level continued to decrease. An effective treatment should minimize both resistance and resilience. Dot colors reference the antibiotic concentration used at that point, and arrows indicate the direction of increasing antibiotic concentrations. By this definition, resilience reflects a long-term response and depends primarily on population-level traits: When a single bacterium can no longer survive the effects of antibiotic, the population is initially affected; however, collective antibiotic tolerance can allow the population to outlast the disturbance and recover after being perturbed. We quantify resistance as the ability of the population to not deviate from the pre–antibiotic treatment state (as quantified by the growth rate). Mathematically, we define resistance as the ratio between the minimum net growth rate in the presence of an antibiotic in a treated population (ρ A ) and the net growth rate of an untreated population (ρ 0 ) at the same time. When dealing with the experimental data, our analysis accounts for the time delay in lysis caused by a β-lactam (21). (2) By this definition, resistance primarily reflects the instantaneous response of individual cells but manifests at the population level. In particular, the magnitude and timing of measurement of the metric depends on the probability by which an average bacterium is lysed by the antibiotic (Fig. 2B). This probability is directly determined by the expression level and activity of Bla in the bacterium, as well as the extracellular concentration of the antibiotic. For a set amount of Bla, increasing the antibiotic concentration will require more time for the Bla to degrade the antibiotic, thus delaying the time at which minimum net growth rate is observed and resulting in more lysed bacteria and a smaller minimum net growth rate. In our analysis, we use optical density (OD) as a measure of the cell density. For each bacterial strain, the degree of resistance or resilience depends on the type and dose of antibiotic used. At low antibiotic concentrations, the population experiences little or no disturbance and thus is characterized with relatively high resistance and resilience (Fig. 2C). At intermediate concentrations (A = 1.5 μg/ml), the population’s recovery displays a decline in both resistance and resilience because the antibiotic concentration is high enough to induce some lysis, slow the net growth rate, and delay the recovery time. Once the antibiotic concentration is high enough to induce a population crash (A > 5 μg/ml), the recovery of the population shifts to being dominated by resilience. If the antibiotic concentration exceeds the threshold for population recovery, the resulting resilience and resistance will be minimal. This resistance-resilience framework effectively reveals the phenotypic signature of each strain (Fig. 2D) when treated by a β-lactam. In our experiments, the OD values are sufficiently small such that they are proportional to the total biomass (21). Debris from lysed cells can also contribute to the OD values. However, this contribution is negligible except for OD values that are near the baseline (when cells are lysed). Hence, the debris of lysed cells has negligible impact on calculated values of resistance or resilience.

Determinants of resistance and resilience To help further our investigation, we developed a kinetic model to describe the temporal response of a bacterial population constitutively expressing Bla to a β-lactam antibiotic. When no antibiotic is present, the population grows to carrying capacity without delay; however, once the antibiotic concentration is high enough, the population density undergoes a crash as a substantial portion of the population is lysed by the antibiotic, and a recovery as the released Bla degrades the antibiotic (Fig. 3A and fig. S4). We chose to simplify the system by lumping the activity of intra- and extracellular Bla, based on direct measurements that suggest that extracellular Bla plays a much greater role once substantial lysis has occurred (fig. S5). Fig. 3 Modeling reveals key determinants of resistance and resilience. (A) Simulated time courses of an ESBL-producing isolate with and without an antibiotic. The characteristic “crash and recovery” is generated once the antibiotic concentration is high enough. (B) Sensitivity analysis reveals determinants of resistance and resilience. Total effect indices (ST) for resistance and resilience are reported for each parameter (a = 100 μg/ml). Resistance is most affected by the lysis rate (γ). The remaining parameters did not substantially affect the system’s resistance but did affect resilience. The most influential parameters included the maximum lysis rate (γ), Bla activity (κ b ), the turnover rate of Bla (d b ), and the amount of nutrients released during lysis (ξ). (C) Modulating resistance and resilience by tuning Bla activity. We altered Bla activity in the model (left column) or experimentally added clavulanic acid (right column) in combination with a range of antibiotic concentrations. Here, a low Bla activity corresponds to κ b = 0 in the model or clavulanic acid (0.005 μg/ml) in the experiment. A high Bla activity corresponds to κ b = 0. 35 in the model or no clavulanic acid in the experiment. Reducing Bla activity increased the population’s sensitivity, causing both resistance and resilience to decrease at lower concentrations of antibiotic. Global sensitivity analysis was used to determine which parameters influenced resistance and resilience under a range of antibiotic concentrations. Briefly, the Sobol method calculates resilience and resistance for a range of parameter values and breaks down the variation for each into fractions that can be attributed to one or more parameters (22). Here, we reported the total effect index, ST, which reflects how much a parameter and all its interactions with any other parameters contributes to the variation in resistance and resilience at a particular antibiotic concentration (Fig. 3B and fig. S6). Comparing the ST for each parameter when a = 100 μg/ml reveals that resistance is only sensitive to the maximum lysis rate (ST γ = 1 ± 0.02). The sensitivity analysis revealed that all parameters affect resilience to varying degrees, depending on the antibiotic concentration. Resilience is sensitive to the maximum lysis rate (ST γ = 0.9 ± 0.02), Bla activity ( = 0.13 ± 0.01), the turnover rate of Bla ( = 0.05 ± 0.003), and the amount of nutrients recycled from cell lysis (ST ξ = 0. 03 ± 0.01). These parameters determine the collective ability of the population to remove the antibiotic, underscoring the notion that resilience is a population-level trait. We tested the influence of Bla activity computationally by varying κ b and experimentally by using clavulanic acid, a well-characterized Bla inhibitor (Fig. 3C and fig. S7). With increased Bla inhibition, the population became more sensitive to the antibiotic, thus resulting in the antibiotic response shifting from relying on both resistance and resilience to just resilience at a lower concentration of antibiotic. Furthermore, the population with substantially reduced Bla activity did not survive exposure to the higher concentrations of antibiotic (resistance and resilience were both reduced).