Complex interplay of physiology and selection in the emergence of antibiotic resistance

SUMMARY

Emergence of antibiotic resistance, an evolutionary process of major importance for human health [1], often occurs under changing levels of antibiotics. Selective sweeps, in which resistant cells become dominant in the population, are a critical step in this process [2]. While resistance emergence has been studied in laboratory experiments [3–8], the full progression of selective sweeps under fluctuating stress, from stochastic events in single cells to fixation in populations, has not been characterized. Here, we study fluctuating selection using Escherichia coli populations engineered with a stochastic switch controlling tetracycline resistance. Using microfluidics and live cell imaging, we treat multiple E. coli populations with the same total amount of tetracycline but administered in different temporal patterns. We find that populations exposed to either short or long antibiotic pulses are likely to develop resistance through selective sweeps, whereas intermediate pulses allow higher growth rates but suppress selective sweeps. On the basis of single-cell measurements and a dynamic growth model, we identify the major determinants of population growth and show that both physiological memory and environmental durations can strongly modulate the emergence of resistance. Our detailed quantification in a model synthetic system provides key lessons on the interaction between single cell physiology and selection that should inform the design of treatment regimens [9–12] and the analysis of phenotypically diverse populations adapting under fluctuating selection [13–17].

RESULTS AND DISCUSSION

Emergence of resistance is strongly dependent on environmental durations

To study the emergence of resistance under fluctuating antibiotic stress, we tracked a large number of E. coli populations under controlled tetracycline fluctuations and analyzed the progression of selective sweeps. To mimic the spontaneous occurrence of antibiotic resistant mutants in natural populations, we utilized the agn43 promoter driving the T7 polymerase [18, 19] to stochastically generate tetracycline resistant cells (Figure 1A). The promoter switches epigenetically between transcriptional ON and OFF states, with rate 0.1% – 1% per cell division (Table S1), which is visualized by a GFP reporter (Movie S1). The advantage of using a methylation-dependent switch is its stochastic and reversible nature, which steadily generates a low degree of heterogeneity in the population: at steady-state most cells (~95%) are in the agn43 OFF state while a small fraction is in the ON state. In our selectable strain (Sel.), the agn43 promoter drives downstream genes including the GFP reporter and tetA, a tetracycline resistance gene [20], while the control strain (Ctl.) contains the GFP reporter but lacks tetA. The selectable strain maintains heterogeneity of susceptible (tetA OFF) and resistant (tetA ON) cells (Figure 1B). In contrast, the control strain is entirely susceptible to tetracycline.

Figure 1. Stochastic expression of tetA & population dynamics in a fluctuating environment.

(A) The stochastic switch uses chromosomal agn43 promoter driving T7 RNAP [19], which activates tetA and GFP expression from plasmids. (B) Heterogeneity in agn43 promoter expression. All cells constitutively express mCherry, while the agn43 promoter state is reported by GFP. Scale bar = 5 μm. (C) Upper panel shows trajectories of 6 different populations for period duration T = 3 hr. Tetracycline (Tc) killing phases are indicated by gray shades. Growth rate is measured by the optical flow (see Experimental Procedures); growth rate in non-selective LB medium is indicated by the horizontal line. Lower panel shows dynamics of resistance sweeps tracked by the frequency of ON cells in each population. (D) Progression of resistance sweeps across all populations of the selectable (Sel.) strain for each period duration T shown in different colors. The limit of extremely short durations T corresponds to a constant, ‘average’ environment with 3 μg/ml Tc (Avg Env). (E) Progression of antibiotic killing for different period durations T using the control (Ctl.) strain; see (D) legend for period duration colors. See also Figure S1.

The selectable or control strains were cultured in a microfluidic device [21] and subjected to fluctuating selection. By periodically pulsing tetracycline (Tc) in the medium, we created environments with killing phases (6 μg/ml Tc) and recovery phases (no Tc) with a sharp transition timescale of ~5 seconds; no significant spatial effects on growth were observed in the microfluidic chambers (Movies S1–S3). In all experiments, the long-term average concentration of Tc is 3 μg/ml, which is above the minimal inhibitory concentration (MIC) of susceptible E. coli cells (1~1.5 μg/ml) [22–24]. At this concentration, susceptible cells gradually stopped growing and became filamentous after 12–18 hours of Tc exposure, and eventually lysed after 24–36 hours of Tc exposure (Movie S3, part A).

In each experiment, we exposed replicate populations of 100–150 cells to a given periodic antibiotic regimen, and measured the progression of selective sweeps by the fraction of resistant cells (tetA ON). Period durations T ranged from 6 minutes to 6 hours (Movies S2, S3). In Figure 1C (lower panel), we show six representative populations observed for T = 3hr. Populations may exhibit an early resistance sweep (e.g. blue & purple) or take longer to complete a sweep (red), while other populations do not exhibit sweeps within 48 hrs of observation (green, cyan & yellow). Once a resistance sweep completed, population growth rate increased significantly (Figure 1C, upper panel) and no longer oscillated with the environment. While resistant cells have a selective advantage in the antibiotic phase, they sustain a mild fitness cost in the recovery phase (Table S1), and incomplete sweeps can be interrupted or even reversed as environments change (e.g. red population at times t = 15–21 hr), driven by standing ON/OFF diversity within the population.

Dynamics were qualitatively different under shorter antibiotic periods. For an intermediate period (T = 30min), resistance sweeps were frequently interrupted since recovery phases can recurrently “rescue” susceptible individuals (Figure S1B). Under short periods (T = 6min), environments change so rapidly that cells perceive a mixture of recovery and killing during their cell cycle. In this case, resistant cells had an overall selective advantage (Figure S1C), since the long-term average antibiotic concentration (3 μg/ml Tc) is above the MIC. We plotted the percentage of populations (n=40–80 for each duration T) that were fixed for resistance as a function of time (Figure 1D). Despite the fact that the same total amount of tetracycline was delivered in all experiments, the adaptive consequences were strikingly different: after 48 hrs, short Tc periods (≤ 12min) promoted resistance sweeps more effectively (>40% of the populations) than longer periods. The reduced occurrence of selective sweeps for longer periods is due neither to a lack of ON cells, which are steadily produced in all fluctuating conditions (Figure S1F), nor to a reduced population size.

We repeated the same set of experiments using the Ctl. strain, which lacks resistant cells. Unexpectedly, even though all cells are susceptible to Tc, the Ctl. strain was only killed under short Tc periods (≤ 15 min) and was able to survive under longer periods (Figure 1E). Although tetracycline is a bacteriostatic antibiotic, under long-term exposure to short Tc periods, or under constant 3 ug/ml Tc, all susceptible cells eventually become filamented and lyse after 24–48 hours (Movie S3A), indicating that resistance caused by de novo mutations does not play a role over our experimental timespan. For comparison, Sel. populations could survive under all periods, due to their resistant cells (Figure S1E). These results indicate that short pulses effectively exert stronger time-averaged selective pressures, which drive the Sel. populations toward resistance and the Ctl. populations to extinction.

The growth advantage of resistant cells is minimized under intermediate pulse durations

To understand the basis of these strong period dependencies, we analyzed population growth rates across experiments. First, we examined whether the population growth rate was correlated with the fraction of ON cells (Figure 2A). Short and long periods exhibited significant positive correlations, while intermediate periods had no correlation, suggesting that resistant cells have a significant advantage over susceptible cells under short and long, but not intermediate, periods. We quantified this by linear regression of population growth rate versus the fraction of ON cells (see Experimental Procedures), yielding for each duration T an effective long-term growth rate of ON and OFF cells. ON and OFF cells had significantly different growth rate profiles over T (p-val < 10⁻⁷, for interaction between cell state and T in a two-way ANOVA), with ON cells having similar effective growth rates across T, while OFF cells exhibited a peak at T = 30min (Figure 2B). The selective coefficient s of resistant cells is calculated in Figure 2C. Resistant cells have a pronounced selective advantage for either short or long T, with a minimum benefit at T =30min where they are nearly equivalent to OFF cells.

Figure 2. Long-term growth rates, ON cell frequency, & efficacy of selection.

(A) Correlation between ON cell frequency (x-axis) and population long-term growth rate (y-axis) for different T. Each point represents a population. Red and blue dots represent data averaged over time intervals 0–12 hr and 24–36 hr, respectively, from experiments using the Sel. strain. Purple dashed lines: growth rate in non-selective LB medium. (B) Effective growth rates G_on and G_off for ON (green) and OFF (black) cells at different T obtained by linear regression of ON cell frequency vs. growth rate; error bars correspond to the standard deviation estimated from the regression model. Purple dashed line: growth rate in non-selective LB medium. Single-cell measurement yields similar results (Figure S1D). (C) Selective coefficient of ON vs. OFF cells for Sel. and Ctl. strains, using s = (G_on − G_off)/G_off. Values for Sel. indicate the advantage of resistant ON cells. Ctl. strains go extinct under fast fluctuations, hence no data is shown for T < 30min. (D) Progression of resistance sweeps between 0–48 hr shown as distribution of ON cell frequency across populations. Frequency of ON cells (avg. over 12hr bins) increases over time for short durations T indicating effectiveness of selective sweeps. (E) Long-term growth rates (avg. over 12hr bins) show significant increase over time for T = 6, 12min but not for longer durations.

We characterized the progress of population adaptation by averaging the data in 12-hour bins, and examining the changes in growth rate and ON cell frequency. Consistent with the results from Figure 1, short periods (T = 6,12 min) showed a significant increase of growth rate along with increasing numbers of ON cells (Figure 2D, E). Longer periods have an overall increase of ON cell frequency, while some variability is observed at the longest periods (T = 180,360 min) due to incomplete sweeps. Intriguingly, populations at the intermediate period (T = 30min) had the highest growth rate (Figure 2E) while their ON cell frequency remained low (<10%). Similar analysis for Ctl. populations shows that the population growth rate also peaks for the 30min period (Figure S3A). These results indicate that population growth rate is determined not only by the ON cell frequency but also by physiological factors in OFF cells.

Single cells respond to antibiotics differently depending on how they are presented temporally

To investigate physiological responses to tetracycline fluctuations, we tracked populations at single-cell resolution (see Experimental Procedures) and analyzed the behavior of susceptible and resistant subpopulations separately. We focused on surviving susceptible cells, which are the major source of differences in selective efficacy. Under long period durations, susceptible cells gradually decreased their elongation rates in the killing phases and gradually recovered in recovery phases (Figure 3A). The cell division rate, in contrast, quickly decreased to zero in the killing phase and recovered slowly in the recovery phases. The lack of coordination between elongation and division resulted in a change of cell sizes: in killing phases, elongation rate remained positive while cell division was arrested in most cells, causing a net increase of cell size. Cells returned to normal sizes (~ 0.9 μm²) during the recovery phases. For intermediate periods, the physiological response was substantially different. Cell elongation and division rates oscillated with the environment and did not drop to zero (Figure 3B). After 4 hrs of transient response to antibiotic stress, the two processes became largely synchronized, and cell size remained within a narrow range between 1 – 1.2 μm². For short periods, cells’ elongation rate decreased toward zero, cell division was arrested, and cells gradually filamented, indicating a significant antibiotic stress (Figure 3C). Eventually, filamentous cells either lysed, ceased dividing, or were washed out of the chambers, all of which resulted in population extinction. Susceptible cells in the Sel. strain (Figure 3A–C) and Ctl. strain (Figure S2A–C) have similar growth behaviors, indicating that cooperative interactions between ON and OFF cells are not a major determinant of these physiological responses.

Figure 3. Single-cell analysis of susceptible cells under fluctuating selection.

(A–C) Single-cell measurement of susceptible (OFF) cells in the Sel. strain for (A) T = 3hr, (B) T = 30min, and (C) T = 6min. Data shown from a typical chamber in each experiment. Error bars show standard error among multiple independent populations. Antibiotic killing phases are represented by gray shades. Purple dashed lines: growth rate in non-selective LB medium. Image panels (mCherry channel) show cell morphology after 12 hours of fluctuating selection. Populations in these images have not acquired resistant ON cells, thus all cells shown here are susceptible OFF cells. (D–E) Autocorrelation of elongation rate (D) and cell division rate (E) computed for susceptible cells as the Pearson correlation of measurements at times t and t + τ, shown as a function of τ. Periodicities of both elongation rate and cell division rate vanish for short periods. See also Figure S2.

On the basis of these observations, we conclude that susceptible cells perceive distinct types of stress across temporal fluctuation regimes. We hypothesized that under fast fluctuations (short periods), cells perceived an essentially uniform, time-averaged environment, integrated over the cell cycle, and did not have time to react differently during the killing and recovery phases. To verify this, we computed the autocorrelation function of elongation rate and cell division rate (Figure 3D,E). If cells behave differently under killing and recovery phases, the autocorrelation function should reveal periodic patterns. Indeed, periodic autocorrelation occurs for T ≥ 30min, but not for shorter periods, indicating that cells perceive a time-averaged environment under fast fluctuations. Since the time-averaged dose (3 μg/ml Tc) is above the MIC, susceptible cells are at a significant disadvantage compared with resistant cells.

A cell growth model identifies role of physiological memory and predicts long-term growth rates under fluctuating stress

As indicated by these results, cell growth in a fluctuating environment is significantly more complex than the exponential elongation process that has been observed under constant conditions [25], since the elongation rate itself can change substantially over a single cell cycle. Indeed, simple models using constant single-cell elongation rates and tuned to our data fail to predict any of the observed trends (Figure S3A). We now introduce a minimal model that captures most of the behaviors we have measured, and predicts long-term growth rates over changing environments. At the single cell level, we model a changing growth rate (g) by an ordinary differential equation: $\frac{dg}{dt}=a_0+a_{1}g+a_2{g}^2$, where a_j are fixed parameters that depend on the environment but not on the duration T. We obtained parameter sets for killing and recovery environments separately by fitting the experimental results (see Experimental Procedures). The solution converges to stable periodic trajectories (Figure 4A, dot-dashed lines), and correctly captures the measured trends of susceptible cell growth of Ctl. strains across a range of periods T (Figure 4A, open circles). Interestingly, the model indicates that killing and recovery processes are not symmetric. For susceptible cells, the change of growth rate (dg/dt) in the recovery phase is unimodal (Figure 4B, inset, black line): it is low at high growth rate (as the growth rate reaches its maximal value) as well as at low growth rate (likely indicating physiologically stressed states). In contrast, dg/dt in the killing phase decreases monotonically as growth rate increases (Figure 4B, inset, red line). Direct single-cell measurement of dg/dt yielded similar unimodal and monotonic dependencies (Figure S2E).

Figure 4. Modeling cellular growth physiology & memory in a changing environment.

(A) Periodic average of population growth over all populations for each value of T, using experimental data of Ctl. strains (circles) and model fit (dot-dashed lines). Purple horizontal dashed lines: growth rate in non-selective LB medium. (B) Long-term growth rates measured (circles) and predicted by different models (curves). Magenta circles: time-averaged g from Figure 4A. Blue circles: effective growth rate of OFF cells from Figure 2B. For the model with memory, a memory kernel timescale of t_m = 1min was used, comparable with timescales for tetracycline to cross cell membranes [31] and for binding/unbinding to ribosomes [32, 33] (see Supplemental Information). Inset: Dependence of dg/dt (min⁻²) on g (min⁻¹) in ODE model for killing (red) and recovery (black) phases. (C) Simulated population dynamics of selective sweeps based on the single-cell physiological model (see Supplemental Information). See also Figures S3 and S4.

Instructively, the above model yields correct predictions of growth dynamics and long-term growth rates for long T, but fails to predict the growth rate drop for short periods (dot-dashed line in Figure 4B). However, we have assumed that cell growth can respond instantaneously when environments change, an approximation that becomes problematic for short T. A more reasonable assumption is that cells retain physiological memory of the recent past (e.g. due to retaining ribosome-bound tetracycline or other metabolites), and that their instantaneous growth rate reflects a temporally-integrated cellular state. We modified our model to allow dg/dt to be a weighted average of past environments, using a memory kernel that decays exponentially in time over a timescale t_m (see Supplemental Information). Overall, the physiological memory model (solid line in Figure 4B, AIC=66.12) performs much better than the model without memory (dot-dashed line in Figure 4B, AIC=414.5), and recapitulates the highly non-trivial trend of long-term growth rates across all periods T. As periods become shorter, due to memory the cells behave increasingly as though they experience the time-averaged antibiotic dose rather than distinct growth and recovery environments (see Figure S3C for full model behavior). To further test the predictive power of the model, we performed population dynamics simulations that either included (Figure 4C) or excluded (Figure S3D) the physiological response. Comparison with experimental results (Figure 1D) indicates that accounting for the physiological response is crucial for predicting how environmental durations influence resistance sweeps.

Our results show that susceptible cells exhibit highest long-term growth rate at T = 30min, and several, possibly interrelated determinants might underlie this critical timescale, including cell cycle time, ribosomal synthesis/turnover rate, and transcriptional regulation. We measured killing-recovery dynamics in MOPS minimal medium, and the results were consistent with cell cycle time being one important timescale (see Figure S4A,B). To test whether a growth-rate peak at intermediate duration is unique to tetracycline, we measured susceptible cell growth under fluctuations of kanamycin (a bactericidal ribosome-inhibiting antibiotic) and found similar results, i.e. higher growth is observed at an intermediate duration (Figure S4C–E). While our model correctly predicts the duration T at the peak it underestimates its magnitude (Figure 4B), indicating that elongation rate dynamics are insufficient to fully account for cellular growth in fluctuating environments, and additional variables will need to be assessed in future work.

The experiments we presented here, utilizing tetracycline resistance in a synthetic system, allow the interactions of single cell physiology and selection to be directly quantified, revealing several key principles. We demonstrated experimentally that selection under fluctuating environments is strongly modulated by physiological responses. Our modeling results showed how a physiological memory timescale dictates a cutoff frequency on environmental fluctuations above which cells perceive a time-averaged environment. We established that detailed measurements of the characteristic curves for speed of killing and recovery are essential for predicting population growth dynamics. We anticipate that our quantitative approach will be similarly fruitful across a wide range of research involving adaptation of heterogeneous populations in fluctuating conditions [15, 26–29], from cancer therapy [10] to applied microbiology [30].

Experimental Procedures

See Supplemental Information for the detailed procedures of experiments and data analysis.