Building Optimal Three-Drug Combination Chemotherapy Regimens

Multidrug therapy is often required. Examples include antiviral therapy, nosocomial infections, and, most commonly, anti-Mycobacterium tuberculosis therapy. Our laboratory previously identified a mathematical approach to identify 2-drug regimens with a synergistic or additive interaction using a full factorial study design. Our objective here was to generate a method to identify an optimal 3-drug therapy. We studied M. tuberculosis isolate H37Rv in log-phase growth in flasks.

ABSTRACT

Multidrug therapy is often required. Examples include antiviral therapy, nosocomial infections, and, most commonly, anti-Mycobacterium tuberculosis therapy. Our laboratory previously identified a mathematical approach to identify 2-drug regimens with a synergistic or additive interaction using a full factorial study design. Our objective here was to generate a method to identify an optimal 3-drug therapy. We studied M. tuberculosis isolate H37Rv in log-phase growth in flasks. Pretomanid and moxifloxacin were chosen as the base 2-drug regimen. Bedaquiline (plus M2 metabolite) was chosen as the third drug for evaluation. Total bacterial burden and bacterial burden less-susceptible to study drugs were enumerated. A large mathematical model was fit to all the data. This allowed extension to evaluation of the 3-drug regimen by employing a Monte Carlo simulation. Pretomanid plus moxifloxacin demonstrated excellent bacterial kill and suppressed amplification of less-susceptible pathogens. Total bacterial burden was driven to extinction in 3 weeks in 6 of 9 combination therapy evaluations. Only the lowest pretomanid/moxifloxacin exposures in combination did not extinguish the bacterial burden. No combination regimen allowed resistance amplification. Generation of 95% credible intervals about estimates of the interaction parameters α (α_s, α_r-p, and α_r-m) by bootstrapping showed the interaction was near synergistic. The addition of bedaquiline/M2 metabolite was evaluated by forming a 95% confidence interval regarding the decline in bacterial burden. The addition of bedaquiline/M2 metabolite shortened the time to eradication by 1 week and was significantly different. A model-based system approach to evaluating combinations of 3 agents shows promise to rapidly identify the most promising combinations that can then be trialed.

INTRODUCTION

Identifying combination therapy regimens that achieve the dual goals of improved bacterial cell kill and suppressed amplification of less-susceptible bacterial subpopulations can be challenging. Generally, we seek two-drug regimens to accomplish these aims. Our group has described a high-dimensional system of inhomogeneous differential equations that allows simultaneous modeling of five system outputs (each drug, the total bacterial burden, and the bacterial burdens resistant to drug 1 and sensitive to drug 2 as well as the burden resistant to drug 2 and sensitive to drug 1). The model system is structured to allow estimation of effect parameters (kill rate constant, 50% concentration [C₅₀], and Hill’s constant) for each drug as well as the interaction of these agents (α interaction parameters). This allows a statistically robust determination of the manner in which these two agents interact (synergy, additivity, and antagonism) for the susceptible population as well as for the two less-susceptible populations (1). We have published several examples of applying this approach to Mycobacterium tuberculosis, Pseudomonas aeruginosa, and hepatitis C virus (1–4). A full factorial study design allows the rapid identification of optimal regimens and the observation of the interaction of one intervention with another (5). We have performed such a study design in vitro for M. tuberculosis, hepatitis C virus, and P. aeruginosa (1, 3, 4).

There are times, however, where a two-drug combination is not optimal, particularly for suppressing the amplification of less-susceptible subpopulations. Examples are seen in M. tuberculosis (1) as well as in nosocomial pathogens (6, 7).

If we attempt to apply the same approach to a 3-drug regimen, we have substantial difficulty achieving a full factorial study design. This is mainly due to the number of regimens that must be examined. In a 2-drug experiment, we study three exposures to drug 1 and 3 exposures to drug 2 (6 total regimens for single-agent therapy). We then examine all possible 2-drug regimens (9 regimens [3 × 3]) and a no-treatment control (NTC) for a total of 16 regimens.

With a 3-drug experimental design with three levels of exposure for each drug, we have 9 1-drug regimens. We need 27 regimens to study all possible 2-drug combinations for 3 drugs. We need another 27 regimens for all possible 3-drug combination (3 × 3 × 3) plus an NTC for a total of 64 regimens. Technically, this is an overwhelming challenge, requiring a very large number of personnel, supplies, and computer support.

In the manuscript, we set forth a statistically robust approach that allows inferences to be drawn to identify optimal 3-drug regimens that most rapidly kill M. tuberculosis and also suppress amplification of less-susceptible subpopulations. We chose to examine M. tuberculosis in log phase, as this is the largest population. We previously demonstrated that the combination of pretomanid plus moxifloxacin is an attractive 2-drug combination for M. tuberculosis (8). We also examined bedaquiline alone and in combination and wished to look at this agent as a potential third drug for the combination (27). We chose a static time-kill assay to examine the drug regimens, as this was an initial examination. We can also perform this approach in a hollow-fiber infection model or in animal models. Our novel method can be used to statistically determine if the addition of another drug to a two-drug regimen incrementally improves the antimicrobial kill and/or resistance prevention activity of any drug combination against any microbe.

RESULTS

Bacterial isolates.

The H37Rv strain of Mycobacterium tuberculosis was used for these studies. The pretomanid, moxifloxacin, bedaquiline, and M2 metabolite MIC values for strain H37Rv were obtained from duplicates and were as follows: pretomanid, ≤0.06 mg/liter (agar) and 0.125 mg/liter (broth); moxifloxacin, 0.25 mg/liter (agar) and 0.50 mg/liter (broth); bedaquiline, 0.06 mg/liter (agar) and 0.25 mg/liter (broth). The mutational frequencies to resistance were 1/4.495 log₁₀ CFU/ml, 1/6.684 log₁₀ CFU/ml, and 1/6.000 log₁₀ CFU/ml, respectively.

Drug concentrations in the static time-kill curves.

The pharmacokinetic parameter values were taken from prior publications (9–11). We chose to examine the time-kill and resistance emergence from 3 concentrations for each agent. These were maximum concentration of drug (C_max), the average concentration (C_avg) (determined as area under the concentration-time curve from 0 to 24 h [AUC_0–24-SS]/24), and the trough concentration (C_trough). The nominal values for the three drugs are displayed in Table 1.

TABLE 1.

Nominal concentrations of pretomanid, moxifloxacin, and bedaquiline in the static time-kill study

Drug	C (mg/liter)
	Maximum	Average	Trough
Pretomanid	1.70	1.26	0.535
Moxifloxacin	1.44	0.792	0.380
Bedaquiline/M2a
Wk 1		3.37/0.674
Wk 2		5.83/1.17
Wk 3		2.80/0.560
Wk 4		2.66/0.532

^aM2, the metabolite was calculated to have 20% of the AUC of the parent compound bedaquiline in humans.

Protein binding.

Preliminary data (not shown) demonstrated that if pretomanid, bedaquiline, and M2 metabolite concentrations were corrected for protein binding, no microbiological activity was generated. Consequently, in the absence of an understanding how binding affected microbiological activity for these agents, we decided to employ total drug concentrations. We used a value of 50% protein binding for moxifloxacin (12).

Antibacterial activity and resistance emergence in the static time-kill assay for 1-drug and 2-drug regimens.

The antimicrobial effects of the drugs alone for pretomanid and moxifloxacin are displayed in Fig. 1A to G. In Fig. 1A, the no-treatment control is displayed. This control was used for Fig. 1 (see also Fig. 3). There is concentration-dependent killing for pretomanid as a single agent that ranges from 0.85 to 0.36 log₁₀ CFU/ml as concentrations ranged from C_max to C_trough. There was amplification of a less-susceptible population by day 7 that truncated the killing effect of pretomanid alone. For the C_max and C_avg, there was complete takeover of the total population by day 14. There was major amplification of the less-susceptible population for C_trough, but the takeover was never complete because of the lesser selective pressure.

FIG 1.

(A to G) Anti-Mycobacterium tuberculosis activity of pretomanid and moxifloxacin alone. Both total bacterial burden and less-susceptible bacterial burden plots are displayed.

FIG 3.

(A to I) Combination chemotherapy of pretomanid plus moxifloxacin in all combinations of C_max, C_avg, and C_trough. Both total bacterial burden and less-susceptible bacterial burden plots are displayed.

For moxifloxacin alone, the killing effect was more pronounced than for pretomanid. This is likely because of a slight delay in amplification of the less-susceptible population. Eventually, all three concentrations studied resulted in complete takeover of the total population with less-susceptible isolates by day 14. At day 7, moxifloxacin bacterial cell kill ranged from 3.58 (C_max) to 3.25 (C_trough) log₁₀ CFU/ml. At day 7, there was less-susceptible subpopulation amplification for C_avg and C_trough but not for C_max. This did occur for C_max by day 14.

We also examined bedaquiline alone and bedaquiline plus its M2 metabolite. This is displayed in Fig. 2. We evaluated bedaquiline alone and bedaquiline plus its M2 metabolite at the C_avg concentration, as for the reasons stated above, generating a full factorial design was not possible, given the resources available. Furthermore, bedaquiline has an exceptionally long terminal elimination half-life, and is an AUC/MIC-driven agent for bacterial kill; thus, examining the C_avg (C_avg = AUC/dosing interval) makes the most sense.

FIG 2.

Anti-Mycobacterium tuberculosis activity of bedaquiline alone (A) and bedaquiline plus its M2 metabolite (B). Both total bacterial burden and less-susceptible bacterial burden plots are displayed.

For bedaquiline alone, there was minimal amplification of a less-susceptible population at day 7 (0.15 log₁₀ CFU/ml) and the bacterial kill was 1.45 log₁₀ CFU/ml. At day 14, there was substantial amplification for the less-susceptible population, but the bacterial kill still reached 3.06 log₁₀ CFU/ml. After day 14, there was virtually complete replacement of the total population by less-susceptible organisms.

For bedaquiline plus M2 metabolite, there was a 1.68 log₁₀ CFU/ml bacterial kill and no amplification of less-susceptible organisms at day 7. By day 14, there was minimal amplification of the less-susceptible subpopulation, and the overall bacterial kill was 3.36 log₁₀ CFU/ml. The addition of the M2 metabolite added 0.22 (day 7) to 0.30 log₁₀ CFU/ml to the bacterial kill and delayed resistance amplification by 7 days.

Combination therapy with pretomanid plus moxifloxacin is displayed in Fig. 3A to I. In all panels, we should note that all less-susceptible populations for both pretomanid and moxifloxacin were cleared by day 7. In Fig. 3A, B, D, E, G, and H, the total bacterial burden was cleared by day 21. In Fig. 3C, F, and I, where different concentrations of pretomanid were paired with the C_trough of moxifloxacin, there was still clearance of less-susceptible organisms by day 7, but the total burdens were cleared for Fig. 3C and F by day 28. For Fig. 3I, where the two drugs are combined at C_trough values, there were still 1.18 log₁₀ CFU/ml present at day 28. For all but one of the regimens, there was a 7.46 log₁₀ CFU/ml kill over the observation period.

Examining 3-drug combinations.

While the combination of pretomanid plus moxifloxacin is a potent and resistance-suppressing regimen, there are clinical circumstances where patients will have very large bacterial burdens from greater infection site involvement. At the beginning of therapy, the large baseline burden indicates that there will be a larger than normal number of less-susceptible organisms in the total population and, hence, a larger likelihood of resistance emergence. For this reason, it may be prudent to start therapy with a three-drug regimen.

We previously saw that bedaquiline was quite active against log-phase, acid-phase, and nonreplicating persister (NRP)-phase M. tuberculosis (8). This, along with a mutational frequency to resistance of 1/10⁶, made it an attractive candidate for the third drug.

Pretomanid plus bedaquiline plus M2 metabolite (Fig. 4A) and pretomanid plus moxifloxacin plus bedaquiline with M2 metabolite (Fig. 4C) both eradicated the bacterial burden by day 14 and suppressed amplification of less-susceptible populations. The combination of moxifloxacin plus bedaquiline with M2 metabolite did not demonstrate an advantage over pretomanid plus moxifloxacin with all drugs at C_avg but did eradicate the bacterial burden at day 28. Again, all resistant subpopulations were cleared.

FIG 4.

Pretomanid and moxifloxacin at C_avg combined with bedaquiline plus M2 metabolite at C_avg (A and B) and pretomanid plus moxifloxacin plus bedaquiline with M2 metabolite at C_avg (C).

Population modeling of the 16 regimens for pretomanid plus moxifloxacin plus a no-treatment control.

The model system that our laboratory developed for 2-drug combinations was employed to model the full factorial experiment for pretomanid plus moxifloxacin (1). Table 2 displays the mean and median parameter vectors from the analysis as well as estimates of standard deviations and shrinkage. The model fit the data acceptably well. Figure 5 displays the predicted-observed plots for the pre-Bayesian (population) regression as well as the Bayesian (individual) regression. Measures of bias and imprecision are also displayed. All are acceptable. One of the reasons to perform a population analysis is to identify unambiguously the interaction of the two agents for the susceptible population and the populations resistant to one of the two agents in the combination. This information is given by the α term. A bootstrap analysis demonstrates (Table 3) that for the susceptible population the 95% credible interval overlaps zero, indicating an additive interaction. For the pretomanid-resistant population and moxifloxacin-resistant population, the lower bound of the 95% credible interval remains positive, indicating significant synergistic interactions.

TABLE 2.

Population pharmacokinetic/pharmacodynamic parameter values for the combination of pretomanid plus moxifloxacin plus no-treatment control in a full factorial design

Parametera	Value
	Mean	Median	SD	Shrinkage (%)
Kg-s	1.6	1.6	0.02	60.41
Kk-s	2.46	2.5	0.1	43.05
E50-Pret-s	0.33	0.34	0.22	58.45
E50-Mox-s	0.25	0.27	0.26	58.44
αs	0.56	0.21	0.99	42.58
Kg-r-Pret	0.79	0.79	0.02	55.67
Kk-r-Pret	2.52	2.61	0.36	56.88
E50-Pret-r-Pret	4.35	3.25	3.36	40.64
αr-Pret	10.43	9.93	2.72	61.06
Kg-r-Mox	0.74	0.74	0.1	60.1
Kk-r-Mox	10.0	10.0	0.0	62.17
E50-Mox-r-Mox	63.41	65.36	50.93	60.18
αr-Mox	6.26	7.51	3.93	49.9
HPret-s	1.07	1.08	0.07	58.79
HMox-s	10.62	10.13	2.41	60.17
HPret-r-Pret	7.32	5.95	3.98	45.49
HMox-r-Mox	3.15	3.32	2.0	57.95

^aS, susceptible population; r-Pret, less susceptible (i.e., resistant) population to pretomanid; r-Mox, less-susceptible (i.e., resistant) population to moxifloxacin; K_g-s, growth rate constant of the population S; K_k-s, decay rate constant of the population S; E_50-Pret-s, concentration of pretomanid for which the population S is half maximal; E_50-Mox-s, concentration of moxifloxacin for which the population S is half maximal; α_s, interaction parameter for population S; K_g-r-Pret, growth rate constant of the population r-Pret; K_k-r-Pret, decay rate constant of the population r-Pret; E_{50-Pret-r-Pret}, concentration of pretomanid for which the population r-Pret is half maximal; α_r-Pret, interaction parameter for population r-Pret; K_g-r-Mox, growth rate constant of the population r-Mox; K_k-r-Mox, decay rate constant of the population r-Mox; E_50-Mox-r-Mox, concentration of moxifloxacin for which the population r-Mox is half maximal; α_r-Mox, interaction parameter for population r-Mox; H_Pret-s, Hill’s constant susceptible for pretomanid; H_Mox-s, Hill’s constant susceptible for moxifloxacin; H_Pret-r-Pret, Hill’s constant resistant for pretomanid; and H_Mox-r-Mox, Hill’s constant resistant for moxifloxacin.

FIG 5.

Goodness-of-fit plots for the population analysis. Observed data versus population or pre-Bayesian (left) and individual or Bayesian (right) predictions are presented as blue circles. The red solid lines are linear regressions of the blue circles. The dotted lines represent the reference line of y = x. Each point is an observation of colony counts (total counts or counts resistant to either pretomanid or moxifloxacin). Units are log₁₀ CFU/ml.

TABLE 3.

Bootstrap 95% credible intervals for α interaction parameters for populations susceptible to both drugs and sensitive/resistant to each drug

Parameter	95% CI	Type of pharmacodynamic interaction
αs (susceptible)	–0.012 ~ 1.87	Additive
αr1 (resistant to pretomanid)	7.288 ~ 13.06	Synergistic
αr2 (resistant to moxifloxacin)	1.101 ~ 9.827	Synergistic

Determination of the effect on bacterial kill by adding bedaquiline with its M2 metabolite to the pretomanid/moxifloxacin regimen.

Figure 6 displays the decline of the susceptible population when pretomanid/moxifloxacin is administered (Fig. 6A). In Fig. 6B, this decline plus its 95% confidence interval is displayed along with the decline caused by the combination of pretomanid/moxifloxacin plus bedaquiline with its M2 metabolite. The counts hit an estimate of zero colonies at day 14. This is 7 days earlier than for the pretomanid/moxifloxacin combination. At days 14 and 21, the observed colony counts are below the 95% confidence interval, indicating that the addition of bedaquiline with its M2 metabolite generates significantly faster bacterial kill. In Fig. 6C, the combination of moxifloxacin plus bedaquiline with its M2 metabolite does not generate faster kill. It achieves an estimate of zero colonies at day 28, a week later than seen with pretomanid/moxifloxacin, but the decline remains within the 95% confidence interval, indicating that the bacterial kill is not significantly different from pretomanid/moxifloxacin. In all three evaluations, the less-susceptible populations hit an estimated zero colonies at day 7.

FIG 6.

Monte Carlo simulation from the median parameter vector showing the decline of the total population burden (A), the decline of the pretomanid plus moxifloxacin plus bedaquiline with M2 metabolite (B), and moxifloxacin plus bedaquiline with M2 metabolite (C) along with a predicted 95% confidence interval for the moxifloxacin plus pretomanid regimen alone for the log₁₀ CFU/ml bacterial load decline.

DISCUSSION

Combination chemotherapy is of great utility in some but not all circumstances. In traditional chemotherapy for organisms of nosocomial origin, combination therapy is of greatest use in patients with large bacterial burdens, such as those with ventilator-associated bacterial pneumonia.

With the introduction of streptomycin for the therapy of Mycobacterium tuberculosis (13), it became rapidly obvious that combination therapy was generally a necessity for patients with established infection with this pathogen. Early trials were dominated by 2-drug regimens, as the number of agents available was small. Examining the clinical and resistance suppression outcomes from the patients in the Medical Research Council (MRC) trial comparing para-aminosalicylic acid alone, streptomycin alone, and the combination (13), it is clear that the combination allowed patients to fare better. However, there were still failures and resistance emergence. Indeed, using a more modern drug set of linezolid plus rifampin, we demonstrated that not all 2-drug regimens are successful (1).

We previously studied the combination of pretomanid plus moxifloxacin in a 96-well plate assay (8). Both agents had good single-agent activity, and the combination was shown to be additive for bacterial cell kill. It is important to recognize that these evaluations in 96-well plate assays do not probe issues regarding the amplification of less-susceptible bacterial populations.

We also examined bedaquiline and linezolid alone and in combination in this 96-well plate assay (27). These agents are also impressive. Other laboratories have demonstrated that these agents are promising drugs for inclusion in multiagent regimens (14, 15). We decided to evaluate the 2-drug combination of pretomanid plus moxifloxacin in a full factorial design in a static time-kill experiment in flasks.

As can be seen in Fig. 1, both pretomanid and moxifloxacin produced some bacterial kill as single agents, although these cell kills were larger with moxifloxacin. This is likely because of resistance emergence. The mutational frequency to resistance was slightly more than 2 logs greater (easier to emerge resistant) for pretomanid relative to that for moxifloxacin. Both drugs had relatively rapid and complete resistance emergence, and the less-susceptible populations took over virtually the whole population for both agents.

We also examined bedaquiline and its M2 metabolite in this system (Fig. 2) and, as described above, there was log bacterial kill observed, but amplification of less-susceptible populations occurred because of the monotherapy. It should be noted that the addition of the M2 metabolite provided some extra bacterial kill and delayed, but did not prevent, resistance emergence. As this is a metabolite, it is likely that the same mechanism would mediate an increased MIC for both bedaquiline and its M2 metabolite. This would explain the slight increase in bacterial killing and, with this, the delay in resistance emergence (further out on the “inverted U” plot) (16, 17).

The full factorial design outcomes for the combination of pretomanid plus moxifloxacin are seen in Fig. 3. In general, six of the nine combination regimens resulted in probable eradication by day 21 and eradication of the less-susceptible populations by day 7. In the remaining three, the less-susceptible populations reach undetectable levels by day 7; in two of the remaining three, probable eradication was attained at day 28. For the flask where both pretomanid and moxifloxacin were at the minimum concentration (C_min), there was slightly >1 log CFU/ml organisms present at day 28.

We applied the high-dimensional mathematical model our group previously described (1) to all the data simultaneously. The mean and median parameter vectors are shown in Table 2. The dynamic parameters are of interest. The drug concentrations at which the kill rate is half maximal (E₅₀s) for both pretomanid and moxifloxacin for the fully susceptible population are modest and consistent with the bacterial load decline observed. For the less-susceptible populations, the E₅₀ values are beyond the clinically achievable range. However, these isolates remain fully susceptible to the companion drug, and given the modest size of the less-susceptible populations at baseline and that the α value was significantly synergistic for both less-susceptible populations, it is not surprising that these could be controlled rapidly (day 7).

The other factor of major interest is how the two drugs interact pharmacodynamically. This information is provided by the α terms. To ascertain the statistical significance of the interaction, it is necessary to construct a 95% credible interval about the estimate of α. This was done by a 1,000-iterate bootstrap procedure. When the lower bound of the credible interval is positive, this indicates significant synergy. When the upper bound is negative, this indicates significant antagonism. In any instance where the credible interval crosses zero, the interaction is deemed additive. In Table 3, we see that the α for the susceptible population has a credible interval that crosses zero and is deemed additive. For reasons that are mechanistically unclear, the α values for the pretomanid-resistant and moxifloxacin-resistant populations have a lower bound that is positive and, therefore, is significantly synergistic. These additive and synergistic interactions may also have contributed to the ability of the regimen to rapidly control the less-susceptible populations.

Obviously, the pretomanid/moxifloxacin combination is an impressive regimen. However, there are true between-patient differences in bacterial burden, in disease processes, and pharmacokinetic parameter values, so that the full concentration time-profile of drugs is likely not attained at the effect site in a portion of instances. Consequently, we felt that it would be prudent to develop a 3-drug regimen. We chose bedaquiline for this. As noted above, the practical difficulties with achieving a full factorial design are considerable for a 3-drug regimen. We decided to take a different route. By identifying the parameters of a model that examined the bacterial kill for the susceptible population and the two less-susceptible populations, we could generate a 1,000-iterate Monte Carlo simulation. This allows construction of 95% confidence bounds around the mean bacterial burden decline.

The third agent (bedaquiline with its active M2 metabolite) was then studied at C_avg along with pretomanid and moxifloxacin at C_avg. C_avg was chosen because bedaquiline, moxifloxacin, and pretomanid have AUC/MIC as a driver (18–20). Pretomanid has the AUC/MIC ratio as a driver when the agent is dosed daily or half of the dose is given twice daily (19).

The 3-drug regimen cleared the bacterial load more quickly that the 2-drug regimen (Fig. 4). As the less-susceptible populations were cleared by day 7, the first sampling time, we could not evaluate the impact of the third agent on this endpoint.

Figure 6A shows the bacterial load decline from the raw data. In Fig. 6B, the Monte Carlo simulation-generated 95% confidence intervals are displayed around the rate of bacterial decline for the 3-drug combination. The 3-drug regimen cleared the bacterial burden by day 14, a week earlier than the 2-drug regimen, and was outside the lower 95% confidence interval at day 14, indicating that the increase in rate of bacterial decline was statistically significant. Of interest, a regimen of moxifloxacin plus bedaquiline with its M2 metabolite did not accelerate the kill rate. It did, however, remain inside the 95% confidence interval, and so the change in rate was not significant.

Identifying new regimens for the therapy of tuberculosis is difficult. This difficulty is increasing. We are fortunate to have a reasonable number of new and repurposed agents that are coming to the armamentarium of the clinician. Having a reasonable number of new agents makes identifying optimal regimens difficult, expensive, and time consuming.

We should do our utmost to avoid combinations that are antagonistic. We have previously shown that a drug pair (rifampin plus moxifloxacin) that was synergistic for bacterial resistance suppression in log-phase organisms but antagonistic for bacterial load reduction in NRP phase missed its clinical endpoint of shortening therapy (21).

We started our search for a 2-drug regimen using a 96-well plate screening approach to identify regimens that were not antagonistic (8). This allowed us to perform a full factorial design experiment, where the bacterial kill and resistance suppression were shown to be exceptional in a time-kill assay.

Again, the third agent was identified in a 96-well assay (27). The key to generating a statistically robust way to evaluate the third agent requires a fully parametric analysis of the full factorial design experiment. Using the parameter vector to generate a Monte Carlo simulation allows evaluation of different third agents. The approach worked for identifying better 3-drug regimens as well as for identifying a regimen that was not significantly better than the original two-drug regimen. The combination of these approaches may be a path forward to rapidly identifying optimal regimens, where we can then take them into intact animal model systems and finally validate the promise in humans.

The approach outlined here needs to have its limitations pointed out. First, it is a static time-kill assay, and so it does not have the full dynamics of the agents as seen in animals and humans. Second, it does not evaluate the penetration of the agents into lung lesions and, especially, into caseum (22, 23). This may have a major impact on regimen effectiveness. Nonetheless, a multidrug regimen that is relatively ineffective in vitro is somewhat unlikely to achieve the clinical goals of resistance suppression and regimen shortening in a large portion of those treated for M. tuberculosis. Finally, the work here reflects activity against log-phase organisms. It is important to also evaluate regimen activity against acid-phase and NRP-phase organisms. These evaluations are currently ongoing.

With the advent of new agents, we need to focus resources on regimens that have a high likelihood of achieving these goals. The approaches described here may provide a way forward to rapidly develop the most promising new regimens.

MATERIALS AND METHODS

Bacteria.

M. tuberculosis strain H37Rv (ATCC 27294) was used. Stocks of the bacteria were stored at −80°C. For each experiment, an aliquot of the bacterial stock was inoculated into filter-capped T-flasks containing 7H9 Middlebrook broth that was supplemented with 0.05% Tween 80 and 10% albumin, dextrose, and catalase (ADC). The culture was incubated at 37°C and 5% CO₂ on a rocker platform for 4 to 5 days to achieve log-phase growth.

Drugs.

Pretomanid was kindly supplied by the Global Alliance for TB Drug Development. Moxifloxacin was purchased from BOC Sciences (Shirley, NY), as was bedaquiline. Moxifloxacin was dissolved in sterile water; pretomanid was dissolved in dimethyl sulfoxide (DMSO). Subsequent dilutions were performed in TB medium. The final concentration of DMSO was 0.5%.

Susceptibility testing and mutation frequency determination.

Susceptibility studies for all agents were conducted with log-growth-phase H37Rv M. tuberculosis using the agar proportional method described by the CLSI (24) and the absolute serial dilution method on 7H10 agar with 10% oleic acid, albumin, dextrose, and catalase (OADC). Briefly, a 10⁴-CFU volume of H37Rv in log-phase growth was plated on Middlebrook 7H10 agar (Becton, Dickinson Microbiology Systems, Sparks, MD) supplemented with 10% OADC (Becton, Dickinson Microbiology Systems) containing 2-fold dilutions of the agents. The cultures were incubated at 37°C and 5% CO₂. After 4 weeks of incubation, the MICs were determined by identifying the lowest drug concentration at which there was no bacterial growth on the agar plate. For the agar proportional method, the lowest concentration of a drug that provided a 99% reduction in the bacterial density relative to the no-drug control was read as the MIC. For the absolute serial dilution method, the MIC was read as the lowest concentration of drug for which there was no growth on the agar plate.

The mutation frequency of the H37Rv strain was evaluated using methods that are described elsewhere (17). Briefly, H37Rv cultures in log-phase growth were inoculated onto plates containing Middlebrook 7H10 agar plus 10% Middlebrook OADC with either pretomanid, moxifloxacin or bedaquiline at a concentration equivalent to 3.0× the baseline MIC. The mutation frequency was identified after 4 weeks of incubation at 37°C and 5% CO₂.

Flask experiments for 2- and 3-drug regimens for pretomanid, moxifloxacin, and bedaquiline/M2 metabolite.

Experiments were carried out in Corning 75-cm² cell culture flasks (vented cap). Each flask held 40 ml of organisms in medium. The stability of each drug was checked at 0.1 mg/liter, 1.0 mg/liter, and 10.0 mg/liter in 7H9 broth plus 10% ADC plus 0.2% glycerol plus 0.05% Tween. Storage conditions were at −80°C, 4°C, room temperature, and 35°C. Samples were taken at 0, 2, 8, 24, 32, 48, and 120 h. Moxifloxacin, bedaquiline, and the M2 metabolite were stable. Pretomanid showed degradation with 49.9%, 50.2%, and 44.2% remaining for concentrations of 0.1, 1.0, and 10.0 mg/liter, respectively, at 120 h at 35°C. For this reason, samples for drug concentration were taken thrice weekly. Also, bedaquiline concentrations changed according to the clinical dosing schedule over time. In addition, pH and glucose were checked weekly. Organisms were spun down weekly without washing and resuspended in fresh medium and drugs.

Samples were taken on a weekly basis, were washed and then quantitatively plated onto antibiotic-free agar and antibiotic-supplemented agar to characterize the effect of each treatment regimen on the total bacterial and less-susceptible bacterial populations. A volume of 200 μl was removed from the flask and was streaked onto the zero-dilution plate. Another 100-μl sample was used to perform serial 10-fold dilutions to obtain accurate countable numbers. This was conducted both for antibiotic-free plates (total bacterial burden) and antibiotic-containing plates (drug-less-susceptible organisms). For detection of mutants less susceptible to drugs, the agar (pH 7.0) was supplemented with 10% OADC. The agar plates were read after 6 weeks of incubation at 37°C in a 5% CO₂ atmosphere. Drug concentrations incorporated into the agar were 3.0× the baseline MIC value.

Assays of pretomanid, moxifloxacin, bedaquiline, and M2 metabolite.

Pretomanid, bedaquiline, the bedaquiline M2 metabolite, and moxifloxacin each were validated in 7H9 broth using liquid chromatography-tandem mass spectrometry (LC-MS/MS). The equipment included a Thermo Endura tandem mass spectrometer with a Dionex Ultimate 3000 ultrahigh-performance liquid chromatography (UHPLC) system. The pretomanid calibration curve was 0.01 to 5.00 mg/liter. Within-day precision across the curve was 0.52% to 7.16% coefficient of variation (CV). Overall 3-day precision across the 6 curves was 0.72% to 7.03% CV. Within-sample precision across 6 injections was 5.87% CV. The bedaquiline calibration curve was 0.01 to 5.00 mg/liter. Within-day precision across the curve was 0.70% to 11.97% CV. Overall 3-day precision across the 6 curves was 2.63% to 7.54% CV. Within-sample precision across 6 injections was 5.52% CV. The M2 metabolite of bedaquiline performed similarly to the parent drug. The moxifloxacin calibration curve was 0.20 to 15.00 mg/liter. Within-day precision across the curve was 0.47% to 5.32% CV. Overall 3-day precision across the 6 curves was 1.61% to 4.66% CV. Within sample precision across 6 injections was 2.61% CV.

Population pharmacokinetic/pharmacodynamic mathematical model, bootstrap procedure, and Monte Carlo simulation.

Population modeling was performed employing the nonparametric adaptive grid (NPAG) program of Leary et al. (25) and Neely et al. (26). Modeling choices (weighting, etc.) and goodness-of-fit evaluations were performed as previously published (17). Both the bootstrap procedure for generation of the 95% credible intervals about the α terms and the Monte Carlo simulation for generating the 95% confidence bounds for the bacterial load decline were performed within Pmetrics.

The population analysis for pretomanid and moxifloxacin generated a median parameter vector. This vector was employed to generate a 1,000-iterate Monte Carlo simulation for the total bacterial burden (after day 7, the total burden was identical to the drug-susceptible burden). This allowed construction of a 95% confidence interval. Examining the bacterial kill of the multidrug regimens (pretomanid, moxifloxacin, bedaquiline, and its M2 metabolite as well as moxifloxacin, bedaquiline, and M2 metabolite) allowed determination of whether the new regimens were better, the same, or worse than the pretomanid plus moxifloxacin regimen as a function of whether the new regimen bacterial kill was below the 95% confidence interval (better at the P value of 0.05), within it (not different), or above it (worse at the P value of 0.05).