## Introduction

Tuberculosis (TB), caused by inhalation of Mycobacterium tuberculosis (Mtb), remains the world’s deadliest infectious disease, infecting 30% of all people world-wide and leading to ~ 1.3 million deaths annually1,2. The emergence of multidrug resistance coupled with slow progress in developing new drugs has created a pressing need to identify new approaches to treat TB. The current standard TB treatment regimen is a combination of four first-line anti-TB drugs—the antibiotics isoniazid (H), rifampicin (R), pyrazinamide (Z), and ethambutol (E). This treatment has remained unchanged over 50 years3,4,5. Typical combination therapy for TB is administered for at least six months, while treating drug-resistant strains may take up to 2 years. New drugs, such as bedaquiline, linezolid, and pretomanid, are being tested in new regimens to potentially shorten TB treatment6,7 The WHO has called for entirely new strategies to meet the goals for ‘End TB’, which aims to reduce TB deaths by 95% by 2035.

The large number of potential drug combinations greatly complicates TB treatment design8. Therapy involving drug combinations can lead to surprising non-linear effects; some drugs can enhance each other’s action leading to higher potency (synergy), or drugs can interfere with their action leading to reduced potency (antagonism)9,10. Antibiotics can interact synergistically by enhancing the uptake of other drugs or through inhibition of compensatory mechanisms. For example, ethambutol represses the levels of the enzyme inhA, the drug-target of isoniazid and enhances the bactericidal effect of isoniazid against Mtb11. Similarly, antagonistic interactions between bacteriostatic drugs and bactericidal drugs occur due to their opposing effects on cellular metabolism12. Drug interactions can impact treatment efficacy and emergence of drug resistance13. Synergistic drug combinations can also provide increased efficacy without augmenting the toxicity of individual drugs.

Such synergistic or antagonistic drug interactions can be determined using checkerboard assays by screening a panel of drug combinations in multiple doses against Mtb14. However, such experimental screening of drug interactions has limited throughput despite recent developments in reducing the number of doses required for measurement15,16,17. Designing an optimal 4-drug combination from a set of just 50 candidate drugs at a single dose requires ~ 200,000 drug interaction experiments. The dosage and dosing frequency further increase the space of possible regimens exponentially18.

Measuring in vivo drug interactions is even more challenging as it requires mice, primates, or other model organisms infected with Mtb19. Consequently, the number of drug candidates that can be screened through these model organisms is very limited. Further, current drug screening strategies for TB do not consider a patient’s immune system. Once Mtb is inhaled, it triggers a cascade of immune responses that result in the accumulation of an immune cell-rich mass around infected cells and bacteria known as a granuloma. Mtb can persist for decades within granulomas, and there are multiple granulomas within lungs of infected patients20. Granulomas also create a physical barrier altering the penetration of drugs, which can greatly impact relative drug concentrations at the site of infection and lead to effective mono-therapies in granulomas21,22,23,24. Granulomas also produce nutrient-starved and hypoxic environments that contain Mtb that are phenotypically tolerant to antibiotics, further complicating treatment25,26.

This study addresses these challenges by creating a multi-scale pipeline combining two cutting-edge computational approaches, operating at different biological scales, to evaluate combination therapies using drug transcriptomics and pharmacokinetics/pharmacodynamics (PK/PD) (Fig. 1). First, to rapidly predict drug–drug interactions (synergy/antagonism) among combinations of two or more drugs, we utilize the existing in silico tool—inferring drug interactions using chemogenomics and orthology (INDIGO) optimized for Mtb (INDIGO-MTB)8,14. INDIGO-MTB uses a training data of known drug interactions along with drug transcriptomics data as inputs. INDIGO-MTB then utilizes a machine-learning algorithm to identify gene expression patterns that are predictive of specific drug–drug interactions. Once trained, INDIGO-MTB can determine if new drugs in combination have synergistic or antagonistic interactions using transcriptomics data. We previously used INDIGO-MTB to identify synergistic drug regimens for treating TB from over a million possible drug combinations using the pathogen response transcriptome elicited by individual drugs. The INDIGO-MTB model contains 164 drugs with anti-TB activity and it accurately predicted novel interactions of two-drug and three-drug combinations in vitro8.

Next, to predict in vivo interactions and efficacy, here we integrate INDIGO-MTB predicted drug interactions within an existing multi-scale model of pathogen-immune dynamics leading to granuloma formation, known as GranSim24,28,29,30,31. GranSim integrates spatio-temporal host immunity, pathogen growth and drug PK/PD into a single computational framework. GranSim uses a hybrid agent-based model to describe interactions between immune cells and cytokines with bacteria and antibiotic delivery to granulomas, and provides a dynamic picture of pathogen clearance leading to granuloma sterilization24. Previously, we modeled PK/PD in GranSim and explored regimens with isoniazid and rifampin, three fluoroquinolones, and more recently HRZE32,33,34. An important finding from that work is that the various antibiotics have different abilities to penetrate well into the granuloma, at times reducing the number of bacteria exposed to effective concentrations34,35. However, in these studies we assumed no interaction between antibiotics. Hence, we now integrate INDIGO-MTB predictions of drug interactions within the GranSim framework, allowing the full characterization of drug interaction dynamics at the molecular and cellular scales, and verify our results against patient-level data. This allows us to evaluate how drug interactions and PK/PD at the molecular scale influence in vivo efficacy at the granuloma scale.

Our study herein represents the first pipeline that incorporates both in vitro drug interactions and in vivo PK/PD to simulate treatment dynamics of numerous drug regimens. Our study overcomes the limitation of prior studies that have focused on variation in PK/PD parameters alone to predict treatment outcome36,37,38. Combining INDIGO-MTB with GranSim allows us to compare different regimens based on the impact of their interactions on various simulated metrics such as rate of pathogen load decline in granulomas and granuloma sterilization rates. Our approach provides a measurement of drug interactions within lung granulomas based on concentrations that different bacterial populations are experiencing in their individual granuloma environment.

## Results

### Drug interactions significantly impact in vivo treatment dynamics in GranSim

We focus on combinations of 2, 3 or 4 drugs involving the first-line antibiotics and two fluoroquinolones (Supplementary Table 1). These drugs include isoniazid (H), rifampin (R), ethambutol (E), pyrazinamide (Z), moxifloxacin (M), and levofloxacin (L). We chose these drugs as they are part of the current standard-of-care for treating TB. Further, transcriptomics and PK/PD parameters are available for these drugs for simulation using both INDIGO-MTB and GranSim.

Using INDIGO-MTB, we first predicted all possible in vitro interaction outcomes for these combinations. The combinations are predicted to have FIC values that range from synergistic (e.g. HRZ—FIC of 0.74) to antagonistic (e.g. RM—FIC of 2.31). The standard regimen (HRZE) is predicted to be synergistic (FIC—0.82) while moxifloxacin-containing regimens were mostly antagonistic (Supplementary Table 2). These predictions match the experimentally observed in vitro FIC values for these combinations from prior studies8.

Given the various factors that can impact antibiotic efficacy in vivo that are captured in GranSim, the relative impact of drug interactions on treatment outcomes is unclear. We hypothesized that analysis of various drug regimens with different drug interaction scores (FIC) can help tease out the impact on treatment outcome. Our previous studies of antibiotic treatment using GranSim did not consider drug interactions. Here we explore how either antagonistic or synergistic affects overall efficacy using GranSim.

We input FIC values into GranSim and simulated the immune response and antibiotic delivery to granulomas (“Methods”). The plasma and tissue PK parameters for these drugs within the GranSim computational framework were derived from previous studies calibrating PK parameters to experimental plasma and lesion drug concentrations (“Methods”). For each regimen tested, 100 simulated granulomas were treated for up to 180 days with daily doses of each antibiotic in the specified regimen. To compare the efficacy of each of these regimens, we evaluate three measures: the log decrease in CFU per day, percent sterilization of granulomas, and average sterilization time.

The in vitro FIC value of each combination is correlated with each of the three simulated efficacy outcomes that we calculated (Fig. 2). For our simulated log decrease in CFU per day from 0 to 14 days and the sterilization percent, we observe that both outcomes tend to decrease as FIC values go from synergistic to antagonistic (correlation R = − 0.52 and − 0.59, respectively, Fig. 2A,B). The average sterilization time is positively correlated with FIC value (correlation R = 0.59, Fig. 2C). Overall, this indicates that synergistic regimens are more likely to sterilize a greater percentage of granulomas in a shorter time at both early and later time points.

Although these relationships show moderate levels of correlation, there are a few notable deviations. Interestingly, the regimen RM (FIC = 2.31) performs better than the less antagonistic regimen HE (FIC = 1.46). The best regimen in terms of average sterilization time is HRZE (FIC = 0.82); however, the regimen RE (FIC = 0.74) has a lower FIC but does not perform as well as HRZE. These results suggest that FIC values are not the only factor impacting granuloma sterilization. Because these results are based on sterilization in granulomas, the concentrations of each antibiotic in the granuloma compartment (based on dosage and PK) also impact the ability of each regimen to sterilize.

### The in vivo drug interaction score is predictive of treatment dynamics

The antibiotic killing rate is dependent not only on the FIC value, but also on local drug concentrations within a granuloma, the subpopulation of bacteria (intracellular, extracellular replicating, extracellular non-replicating), and the specific PD parameters of antibiotics involved. Based on the definition of the FIC, synergistic or antagonistic drug combinations result in a lower or higher effective concentration to achieve the same level of bacterial killing. To evaluate the overall impact of drug interactions on the calculated killing rate constant, we evaluate an in vivo Drug Interaction Score (iDIS) for the three subpopulations of bacteria. The iDIS measures the relative increase or decrease of the antibiotic killing rate constant due to the specific drug interaction. We calculate iDIS as the ratio of the antibiotic killing rate constant evaluated in the simulation to the rate constant if the interaction is simply additive (FIC equal to 1.0). This ratio provides a measure of how much the drug interaction impacts the killing rate constant and is unique for each individual mycobacterium within GranSim as drug concentrations change over time. At each time step during treatment, the average iDIS over all Mtb by subpopulation is evaluated as a model output.

Figure 3 shows the average iDIS for non-replicating Mtb over the first dose interval for each regimen, and its relationship to regimen outcomes. A value of 1 indicates the interaction has no impact on the killing rate constant; values greater than 1 or less than 1 indicate synergistic or antagonistic combinations, respectively.

The iDIS for each regimen is strongly correlated with the outcomes from our GranSim simulations: log decrease in CFU per day (R = 0.86), percentage of negative granulomas at eight weeks (R = 0.73), and the average sterilization time (R = − 0.73) (Fig. 3). The correlations are much stronger than those observed for FIC (Fig. 2), indicating that measuring the iDIS, which is calculated for specific granuloma environments, provides more information on regimen efficacy than examining FIC values, which are calculated based on in vitro environments.

Each combination of antibiotics has a different absolute killing rate constant based on the specific combination of PD parameters associated with that combination together with the distribution of antibiotics within a granuloma. These results suggest that iDIS provides a more accurate representation of how well a given combination of antibiotics achieves sterilization as it accounts for the unique killing rate constant that each individual Mtb experiences and measures the impact that an FIC value has on that killing rate constant.

Antibiotics are typically better at killing replicating Mtb than non-replicating Mtb. Antibiotic killing rate constants that are higher and closer to their overall Emax value are less impacted by drug interactions. We found that correlations between regimen outcomes and the average iDIS associated with replicating extracellular and intracellular Mtb are weaker than when comparing regimen outcomes to the iDIS from non-replicating Mtb (Supplementary Figs. 1 and 2). The average iDIS measurements for replicating Mtb are closer to 1.0 and weaken the correlation with regimen outcomes. Hence, the strong correlation between drug interactions and clinical outcomes are primarily driven by drug action against non-replicating bacteria.

Figure 4 shows a heat map of the mean sterilization time, iDIS and FIC for each regimen, ordered by decreasing iDIS. In general, the regimens with the fastest sterilization times also have high iDIS. The top 17 regimens, as measured by shortest average sterilization time, all contain RIF, indicating that RIF is a very important addition to regimens. Another general trend is that two-drug combinations typically perform worse than 3- or 4-drug combinations. Fluoroquinolones tend to participate in more antagonistic combinations, as measured by the iDIS. For example, 22 of the 31 MXF or LVX containing regimens are above the median iDIS of all 64 regimens. Two regimens (R23.5E45dpw2 and R23.5E90dpw1) with synergistic iDIS measurements showed slow sterilization times, as they were dosed less frequently than a day.

### INDIGO-MTB—GranSim regimen rankings are correlated with clinical rankings

To explore how our predictions of regimen efficacy compare to clinical results, we compare our INDIGO-MTB—GranSim treatment simulations to results from TB drug clinical trials. Drawing from the meta-analysis of phase II trials presented in Bonnet et al., we selected all regimens that reported sputum culture conversion in solid media40. The efficacy metric presented for Phase IIb trials is the percent of patients with negative sputum culture after 8 weeks of therapy. Since our simulations predict treatment outcomes at the granuloma scale, we estimated how sterilization at the granuloma level relates to host-level culture conversion. Figure 5A shows the comparison of the upper and lower bound estimates for percent sputum conversion from our simulation to clinical trial results for 26 regimens (“Methods”). For most regimens, estimates of sterilization percentage compare closely to clinically measured culture conversion. In general, INDIGO-MTB—GranSim simulations appear to overpredict the rates of sterilization and most incorrect predictions fall into this category (Fig. 5A). This observed overprediction is likely due to the simplification of predicting sterilization at the granuloma scale that does not include the full spectrum of complex granuloma lesions, failed adherence to regimens, and other factors that complicate TB treatment.

We next validate our simulation results by comparing the ranking of the efficacy of each of the regimens with the corresponding ranking of the efficacy from clinical trials (Fig. 6). The clinical rank is determined by ranking each regimen by the pooled culture conversion after 8 weeks, so that a ranking of 1 is the regimen with the lowest culture conversion. The simulation rank is determined by percentage of granulomas sterilized after 8 weeks. We used the Spearman ranked correlation coefficient, weighted by the number of patients in each pooled regimen result, and found a significantly strong correlation between simulations and clinical trials (R = 0.72).

Recent phase III clinical trials have investigated the impact of introducing fluoroquinolones into treatment regimens to treat drug-susceptible TB, some with the additional intent of shortening treatment time from six months to four. Many of these trials have failed to show improvement in TB treatment, and often led to higher rates of unfavorable outcomes at the trial’s endpoints41,42,43. These trends are reflected in our analysis of the drug interactions for various drug combinations. The control regimen, HRZE, is strongly synergistic as measured by iDIS, and we predict short average sterilization times (14 days, Fig. 4). In contrast, fluoroquinolone containing regimens, such as HRMZ and RMZE, are closer to additive, and are predicted to have longer sterilization times of 41 and 21 days, respectively. These trends indicate that our simulation predictions are consistent with phase III clinical trial observations. Thus INDIGO-MTB—GranSim simulations provide strong predictive measures of clinical outcome for different regimens.

Both iDIS and INDIGO-MTB FIC predictions for these regimens are also significantly correlated with their clinical ranking (Fig. 5B,C). These simulated results are consistent with the correlation observed in a prior study between INDIGO-MTB FIC scores and percentage of patients with negative culture after treatment from 57 randomized clinical trials8. Based on these results, both interaction measurements have the potential to help predict the clinical efficacy of drug combination regimens.

The FIC value is one measure of drug interactions in vitro; however, there are many factors that impact regimen efficacy in vivo that FIC alone does not capture. Measuring the iDIS can incorporate changes in concentration due to PK variability, changes to dosing regimens, and heterogeneous antibiotic concentrations due to granuloma structure and the varying environments where bacteria reside. It also includes effects of the immune responses occurring with granulomas.

### Spatial variation in drug concentration influences iDIS in granulomas

Nonuniform drug distributions within granulomas arise due to barriers to diffusion that the cellular structure of granulomas creates22,23,24,32. The spatial variation in antibiotic concentrations within a granuloma leads to variations in local effective concentrations, and ultimately antibiotic killing rates and iDIS. The free drug concentrations available to induce bactericidal activity against Mtb are also influenced by binding to extracellular matrix as well as partitioning into macrophages44. Hence, we next focused on the contribution of the drug spatial variation to iDIS.

Figure 7 shows the spatial variation of both effective drug concentrations and iDIS for each of the four regimens simulated: HRZE, RE, HE and RM. Overall, when antibiotics in a regimen are present in the granuloma at similar relative concentrations, the in vitro interaction is maintained in vivo. Interactions can also be strong in caseated regions of the granuloma, where non-replicating Mtb are typically located. Because iDIS tends to be higher in locations that contain more non-replicating Mtb, this may contribute to synergistic combinations performing better than antagonistic combinations.

An additional aspect that influences the iDIS is the relative contribution of each antibiotic in the combinations (Fig. 7, column 1). Antibiotic combinations that contribute more equally to the effective concentration deviate more from additivity than combinations of antibiotic concentrations in which contributions are uneven (i.e. when one antibiotic has a much higher adjusted concentration than the other antibiotics). Although RE has a more synergistic FIC than HRZE, the iDIS against non-replicating Mtb for HRZE is higher than RE, and HRZE has better efficacy than RE. This is partially due to R and Z contributing to the effective concentration in the granuloma evenly (R ~ 50% contribution, Z ~ 40% contribution). The contributions from R and E in RE, however, are more disproportionate, with > 90% of the effective concentration due to R and < 10% of the effective concentration from E.

A similar situation occurs with the two antagonistic combinations HE and RM. Although RM is predicted to be strongly antagonistic, its efficacy is still average compared across all regimens tested. HE, on the other hand, has a less antagonistic FIC, but performs more poorly than RM. When looking at both antibiotic contributions for these two regimens and the iDIS against non-replicating Mtb, we see that H accounts for ~ 75% of the effective concentration and E accounts for ~ 25%. Although not equal contributions, this still allows for an antagonistic interaction to occur. With the RM combination, R accounts for almost all of the contribution to the effective concentration because its levels are higher relative to its own $${C}_{50}$$, resulting in almost no antagonistic interaction to occur with M, despite the high FIC. For antagonistic combinations, uneven contributions from the different antibiotics in the combination can mitigate the effect of the antagonistic interaction.

Due to this dependence on drug concentrations, the predicted iDIS varies for different doses and regimens of the same drug combination (Supplementary Fig. 3). In contrast, the FIC interaction score is fixed for a combination irrespective of the dosage. As doses vary in vivo, the strength of the synergistic or antagonistic interactions can either increase or decrease, depending on the specific combination of antibiotics. One common trend is less frequent dosing tends to decrease the interaction strength, which we observe for both the HRZE and RE combinations.

### Plasma clearance rates correlate with in vivo drug interaction score

Even for a given simulated granuloma and drug regimen, antibiotic concentrations can vary due to host-to-host PK variability34. This can also result in changes in iDIS. We picked four different regimens, ranging from synergistic to antagonistic (HRZE, RE, HE, RM) to exhaustively explore the impact of various PK parameters. The plasma clearance rate constant for many of the antibiotics in these regimens is significantly correlated with predicted iDIS, particularly the clearance rate constants for R, E and M (Table 1). A more detailed analysis of correlations between plasma PK parameters and iDIS is shown in Supplementary Table 3. The R clearance rate constant is strongly correlated with iDIS, with coefficients between 0.8 and 0.9, depending on the regimen. The correlation coefficients for the clearance rate constant for R are positive for synergistic combinations (HRZE, RE), and negative for antagonistic combinations (RM). Because iDIS values that deviate further from 1 imply a stronger interaction, this means that faster clearance rates for R tend to increase the interaction strength. The opposite is true for the clearance rate constant of E. The correlation coefficient between the clearance rate constant for E and predicted iDIS is negative in synergistic combinations (HRZE, RE), and positive in the antagonistic combination (HE). While this may seem counterintuitive, it supports the idea that the iDIS value is dependent on relative in vivo drug concentrations. Faster clearance rates generally result in lower concentrations in plasma, and consequently lower concentrations in the granuloma. Because R tends to contribute more to effective concentrations than other antibiotics, increasing the clearance rates for R will strengthen the interaction by decreasing R concentration and allow for more similar antibiotic contributions. For E, whose contribution to effective concentration tends to be lower, increasing clearance rates result in lower E concentrations and contributions, and scenarios of even more lopsided contributions and less interaction. Relative drug concentrations inside the granuloma affect the strength of drug interactions, and these strong correlations indicate that interactions may be stronger or weaker for certain combinations depending on an individual’s PK34.

We see a similar trend to plasma PK when analyzing the impact that lung tissue PK parameters have on iDIS. Sensitivity analysis on the tissue PK parameters for different regimens shows that some have a positive correlation and some have a negative correlation with iDIS. Tissue PK parameters that lead to more similar concentrations and contributions of antibiotics results in stronger interactions (Supplementary Table 4). As an example, for the RE regimen, vascular permeability for R is negatively correlated with iDIS of the regimen while vascular permeability for E is positively correlated.

## Discussion

There is an urgent need for multi-drug regimens to treat TB, the world’s deadliest disease. In particular, understanding the role of synergistic or antagonistic interactions between anti-TB drugs in vivo may provide a more rational approach to choosing novel combinations that have greater clinical efficacy. However, measuring drug interactions in vivo is challenging due to the limited throughput, cost, and time involved in testing drugs in model organisms. In this study, we introduce a computational pipeline that can simulate in vivo interactions by using datasets derived from individual drug-response transcriptomes and PK/PD, thereby greatly reducing cost and time. Our approach integrates interaction scores of combinations of antibiotics into a computational model that simulates drug delivery into the lung, spatial concentrations of drugs and pharmacodynamic effects within TB granulomas.

To evaluate drug regimens, we introduce a new metric called the in vivo drug interaction score (iDIS) that is dynamic and unique for each mycobacterium based on its location and metabolic state (i.e. replicating/non-replicating) within a granuloma. Unlike the in vitro drug interaction scores derived from checkerboard assays and INDIGO-MTB, which are fixed for given drug combinations, the in vivo score can provide a more nuanced impact of drug interactions on pathogen clearance. This allowed us to compare various drug regimens and rank them based on their in vivo interactions. We found that our ranking of regimens is highly concordant with clinically observed efficacy of various drug combinations40. In Fig. 5, we compare the percentage of simulated granulomas that were sterilized after 8 weeks of treatment for 26 different antibiotic regimens, and compared those results to 8-week sputum culture conversion from clinical trials of those same regimens. For regimens where our predicted sterilization does not agree with clinical results, we tend to overpredict sterilization. This could partially be explained by the fact that while we compare sterilization at the granuloma scale, culture conversion reflects a host-level outcome that involves treating and sterilizing multiple granulomas and lesions. Additionally, accounting for different drug–drug interactions depending on a heterogeneous granuloma environment (such as in the caseum) could further improve our ability to accurately predict clinical results46.

When simulating all regimens considered in this study, the FIC alone does correlate with the simulated and predicted outcomes from our model. However, there are a handful of regimens that do not fit the trend. Measuring the iDIS, which evaluates the relative increase or decrease in killing rate due to the interaction within the complex granuloma environment, provides a complementary measure of regimen outcome. This is because the effect that drug interactions have on killing rate constants is dependent on the balance of contributions from each single antibiotic. Combinations with highly synergistic or antagonistic FIC values may be closer to additive if only one antibiotic is present in sufficient quantities within a granuloma.

Our analysis of various drug regimens revealed ways of amplifying synergy as well mechanisms to mitigate antagonism in vivo. We found that some combinations with in vitro antagonism perform well clinically due to the distinct spatial distribution of the underlying drugs. Antagonistic interactions can be mitigated if the drugs have uneven distributions and effective concentrations or through less frequent dosing. Overall, we find that combinations with strong in vitro synergy remain synergistic or additive in vivo. Hence screening for synergy in vitro can be a useful strategy for identifying regimens with strong in vivo activity. In a minority of cases, this synergy may not be achieved in vivo; nevertheless, synergistic combinations generally outperform antagonistic regimens.

HRZE stands out among the regimens we tested because it has a synergistic interaction (FIC) which is maintained in vivo (iDIS) due to the similar penetration and distribution of the four drugs in the regimen. In contrast, regimens such as RE and RM have dissimilar drug distributions and their in vitro interactions are not observed in vivo. The RE regimen has a synergistic FIC but the dissimilar drug distributions lead to a reduced iDIS. Similarly, RM has a strongly antagonistic FIC but the dissimilar drug distributions lead to reduced antagonism in vivo.

The clinical relationship between plasma PK and regimen efficacy is well established, and can impact the treatment outcomes and the development of resistance38,47,48. Measuring PK parameters in patients can help to predict sterilization rates49. While the impact of PK on individual drugs can be straightforward to interpret, the relationship between measured PK and efficacy can be complex for multidrug regimens. Our study suggests that changes in interactions likely occur in vivo due to PK variability. Studies that involve measuring variability in PK and the effect on drug interactions could be the subject of future research.

As part of this study, we wanted to determine which combinations of antibiotics are predicted to have strong synergy and antagonism, as well as which combinations are predicted to have high efficacy. We screened 64 combinations and regimens of front-line regimens (HRZE) along with M and L. The clinically used HRZE regimen does outperform other screened combinations, which highlights the need for new drugs to achieve the aim of improving TB treatment. Based on the INDIGO-MTB model, we previously identified drug combinations involving new TB drugs such as bedaquiline that have better synergy than HRZE. Given the concordance between INDIGO-MTB FIC and various clinical metrics observed in this study, the synergistic combinations identified by INDIGO-MTB may be promising leads for further optimization using GranSim for reducing treatment time18.

A limitation to our computational model is that the same FIC value is applied to all Mtb within a simulation, regardless of its environment or metabolic state. It is likely that the strength of a given interaction, or even whether it is synergistic or antagonistic, is dependent on the bacterium’s microenvironment in the granuloma46,50. Additionally, these simulations represent treatment of primary granulomas in TB disease, and do not necessarily reflect the true and enormous complexity of granuloma lesions that occur during TB disease. Further, as the simulations are at the granuloma scale, relating the outcomes measured by the simulation to clinical outcomes is difficult. The final limitation is that we only considered combinations of six different antibiotics. There are many other antibiotics in use or in development for use to treat TB. Expanding our ability to accurately simulate the PK/PD of additional antibiotics will greatly increase our ability to answer how important drug interactions are in determining regimen efficacy.

In summary, our study addresses an important gap in current methods for identifying promising drug combinations for TB treatment by presenting a new pipeline for evaluating interactions between drugs in vivo. This pipeline provides an additional metric with which to evaluate novel combinations of antibiotics, explain mechanisms of failed regimens, and assist in optimization regimens as we expand our list of potential antibiotics.

## Methods

### INDIGO-MTB model for predicting drug interactions

INDIGO-MTB identifies interactions between drugs in a combination regimen by utilizing pathogen transcriptomics in response to individual drugs. INDIGO-MTB was built using drug response transcriptome data for 164 drugs, including well known drugs rifampicin, isoniazid, streptomycin, and several fluoroquinolones8. The model first generates a drug–gene association network using the transcriptomics data, and the machine-learning algorithm, Random Forest. The algorithm identifies genes that are predictive of drug interaction outcomes using a training data set of known interactions27. This trained network model is used to predict interactions for novel drug combinations and provides the Fractional Inhibitory Concentration (FIC) as an output (Fig. 1a). The model can identify all possible 2-way, 3-way, 4-way and 5-way synergistic, additive and antagonistic drug interactions after in silico screening of more than 1 million potential drug combinations. INDIGO-MTB predicted FIC scores to be integrated within GranSim were generated for all possible combinations of the first line drugs and two fluoroquinolones (H, R, Z, E, Levofloxacin (L) and Moxifloxacin (M)), as listed in Supplementary Table 1.

### GranSim model of granuloma formation and function

GranSim is a well-established agent-based model of granuloma formation and function24,28,29,30,31. It simulates the spatial heterogeneity and bacterial burden of primary TB lesions by simulating the immune response to infection with Mtb in a computational grid representing a small section of lung tissue, with formation of a granuloma as an emergent behavior (Fig. 1b,c). The simulation begins with a single infected macrophage at the center of the grid, and macrophages and T cells are recruited to the site of infection and interact with each other according to immunology-based rules that describe cell movement, activation, cytokine secretion, and killing of bacteria (for a full list of rules see referenced webpage51). Bacteria are tracked individually and modeled as individual agents in the simulation, existing in three distinct subpopulations: intracellular (inside macrophages), extracellular replicating and extracellular non-replicating. The effective growth rates of extracellular bacteria are modulated by the number of bacteria in a given grid compartment. The growth rate becomes zero when the carrying capacity for that compartment is reached to reflect the relative availability of nutrients and physical space limitations30. Growth rates of extracellular Mtb are also slowed by the presence of caseum (dead cell debris), as a way to estimate the effect of lack of oxygen52. The parameter values describing rules and interactions are based on previous GranSim studies and evidence from experimental literature and datasets on non-human primates24,34,53.

### Simulation of antibiotic delivery and concentrations within granuloma

We simulate antibiotic delivery within the GranSim computational framework as previously described24,32,34. Briefly, a plasma PK model simulates absorption into plasma following an oral dose, exchange with peripheral tissue, and first-order elimination from plasma. Flux of antibiotics into the simulation grid is based on the local gradient between the average drug concentration surrounding vascular sources on the agent-based grid and the plasma concentration. Here we use a 200 × 200 grid representing a 4 mm × 4 mm lung section. The flux is calculated over time as plasma concentrations change within and around each vascular source and allows for delivery or subtraction from the computational lung environment, depending on the direction of the concentration gradient. Once on the grid, antibiotics diffuse, bind to extracellular material (epithelial tissue and caseum), partition within macrophages and degrade (Fig. 1b,c). Based on relative binding and partitioning rates into macrophages, concentrations of intracellular and bound antibiotic are modeled at pseudo-steady state for isoniazid, rifampin, ethambutol and pyrazinamide. The drugs moxifloxacin and levofloxacin exhibit slower rates of binding and partitioning relative to diffusion. Hence the dynamic binding and partitioning of these drugs are modeled using ordinary differential equations32. We determined plasma PK parameters by calibration to human data as previously described22,34,54. We calibrated tissue PK parameters based on concentrations in rabbit or human lesions22,32,34,44. Parameters are listed in Supplementary Tables 5 and 6.

### Calculation of antibiotic killing rate and in vivo drug interaction

We calculate the antibiotic killing rate constant using an Emax model (Hill equation) as we have done previously24, with parameters listed in Supplementary Table 7. This antibiotic killing rate constant is evaluated at each time step for every Mtb in the simulation based on the local grid concentrations as they change over time. The antibiotic killing rate constant ($$k$$) is evaluated as

$$k(t)={E}_{max}\frac{{{C}_{eff}(t)}^{h}}{{{C}_{eff}(t)}^{h}+{{C}_{50}}^{h}}$$
(1)

where $${E}_{max}$$ is the maximal killing rate constant, $${C}_{50}$$ is the concentration at which half maximal killing is achieved, h is the Hill coefficient, and $${C}_{eff}$$ is the effective concentration of the antibiotic (or combination of antibiotics). To reflect each antibiotic’s unique levels of activity against different sub-populations of bacteria, the PD parameters $${C}_{50}, {E}_{max}$$ and h vary depending on the location of the bacteria within the granuloma (intracellular, extracellular replicating, or extracellular non-replicating).The relationship between a combination of drug concentrations and pharmacodynamic effect (such as killing and inhibition) is described using the Loewe Additivity model16,55. In the Loewe additivity model, a simply additive interaction between two antibiotics is described by

$$\frac{{C}_{1}}{{IC}_{x,1}}+\frac{{C}_{2}}{{IC}_{x,2}}=1$$
(2)

where $${IC}_{x,1}$$ and $${IC}_{x,2}$$ are the inhibitory concentrations of drugs 1 and 2 that achieve x% inhibition on their own, and $${C}_{1}$$ and $${C}_{2}$$ are the concentrations that achieve the same level of inhibition in combination. We can convert the concentration of drug 2 to an equipotent concentration of drug 1, shown in Fig. 8 and denoted $${C}_{2,adj}$$. This gives the concentration of drug 1 that results in the same antibiotic killing rate constant as the given concentration of drug 2 ($${C}_{2}$$), which we define as the adjusted concentration for drug 2 ($${C}_{2,adj}$$)

$${{C}_{1} =C}_{2,adj}={\left(\frac{{{C}_{\mathrm{1,50}}}^{{h}_{1}}{{C}_{2}}^{{h}_{2}}}{\frac{{E}_{max,1}}{{E}_{max,2}}\left({{C}_{2}}^{{h}_{2}}+{{C}_{\mathrm{50,2}}}^{{h}_{2}}\right)-{{C}_{2}}^{{h}_{2}}}\right)}^{1/{h}_{1}},$$
(3)

The corresponding inhibitory concentrations for a given x% inhibition for drugs 1 and 2 are now both equivalent to $${IC}_{x,1}$$, because both $${C}_{1}$$ and $${C}_{2,adj}$$ are expressed in terms of concentration of drug 1. Substituting $${C}_{2,adj}$$ for $${C}_{2}$$ and $${IC}_{x,2}$$ for $${IC}_{x,1}$$, Equation (2) can be rewritten as

$${{C}_{1}+C}_{2,adj}= {IC}_{x,1}.$$
(4)

If there are three or more drugs under consideration, we define this sum of concentrations as the effective concentration ($${C}_{eff}$$) of a combination of n antibiotics:

$${C}_{eff}={\sum }_{i=1}^{n}{C}_{i,adj}$$
(5)

We define synergy or antagonism between two or more drugs based on deviations from simple additivity, as assumed above. This deviation is represented using the Fractional Inhibitory Concentration (FIC)56:

$$FIC=\frac{{C}_{o}}{{C}_{e}}$$
(6)

where $${C}_{o}$$ represents the observed combined drug concentration to yield a given level of inhibition, and $${C}_{e}$$ is the expected combined drug concentration to yield the same level of inhibition if the two drugs or more drugs were simply additive16. The FIC measures changes in potency, i.e. how much drug is needed to produce a certain pharmacodynamic effect. Based on the value of FIC, synergistic or antagonistic combinations result in a lower or higher effective drug concentration to achieve the same level of killing. To incorporate drug interactions into our model, we assume the effective concentration for a combination of $$n$$ drugs is adjusted from Eq. (5) based on the FIC value:

$${C}_{eff}={\left({\sum }_{i=1}^{n}{{C}_{i,adj}}^{FIC}\right)}^{1/FIC}$$
(7)

Equation (7) adjusts effective concentration so that synergistic combinations (FIC < 1) result in a higher effective concentration, and antagonistic combinations (FIC > 1) result in a lower effective concentration. Using our defined effective concentration, we substitute Eq. (7) into Eq. (1) to evaluate the antibiotic killing rate constant for combinations of antibiotics while also accounting for drug interactions. Our drug interaction model and effective concentration formulae accurately recreate in vitro drug interaction behavior observed in checkerboard assays (Fig. 8)16.

To evaluate the impact that each drug interaction has on the calculated killing rate constant (Eq. 1) for a given combination of antibiotics in our in vivo simulation, we define an in vivo Drug Interaction Score (iDIS). The iDIS is the ratio of the bacterial killing rate constant with a predicted FIC to the killing rate constant if FIC was equal to 1, i.e. no or additive drug interactions. This allows us to quantify the impact that drug interactions have on bacterial killing for each individual Mtb at each time step during simulated treatment.

### Antibiotic treatment simulations and calculation of regimen efficacy

To simulate treatment with different antibiotic combinations, we first created an in silico granuloma library to generate a set of granulomas. Each library consists of 500 granulomas simulations, generated from 100 parameter sets sampled with Latin Hypercube Sampling (LHS), and each parameter set was replicated five times57,58. Supplementary Table 2 lists the parameters varied and their ranges, which have been established in previous work24,34. Parameter ranges capture natural variability in the immune response and lung environment, such as differences in cellular recruitment and immune cell activation. In addition, replicating simulations with the same parameter set incorporates variability due to stochasticity in the simulations. Granulomas are simulated for 300 days in the absence of antibiotics. At day 300, a random sample of 100 unsterilized granulomas is selected from the relevant library for treatment. The prescribed regimens are simulated for 180 days or until the granuloma is sterilized. See Supplementary Table 1 for the full list of regimens tested.

We evaluate three metrics from our simulations to assess the efficacy of each regimen tested: log decrease in CFU per day, percent of simulated granulomas that are sterilized after 8 weeks of treatment (sterilization percent), and average time at which those granulomas become sterile (sterilization time). For each regimen, 100 granulomas are simulated and results from those simulations are used to calculate three outcomes measures: simulated log decrease in CFU per day, sterilization percent, and sterilization time.

### Comparison to clinical trials

To validate our model results, we compared our treatment simulation outcomes to Phase IIb clinical trial data40. We compared the clinical datasets outcomes for each regimen with our simulated granuloma sterilizations after 8 weeks of treatment. We used the percent of granulomas that are completely sterilized at 8 weeks as a lower bound estimate. Our upper bound estimate is the percentage of granulomas with fewer than 10 CFU after 8 weeks. We chose this value as these granulomas with low bacterial load would not be detectable in sputum. Additionally, we compared the rank of clinically tested regimens, ranked by sputum conversion, to the rank of regimens based on simulation results. Simulated regimen rankings were ranked by average sterilization time, FIC, and average iDIS for non-replicating Mtb. Further, we compared our predicted treatment sterilization times for fluoroquinolone-containing regimens with clinical endpoints (up to 6 months) from recent phase III clinical trials that include fluoroquinolones for treating drug-susceptible TB41,42,43.

### Plasma and tissue PK sensitivity analysis on interaction strength

We performed a sensitivity analysis to evaluate how PK parameters impact the predicted iDIS for regimens with different levels of synergy. For four regimens (HRZE, RE, HE, RM), we selected a single granuloma to simulate treatment for 1 day to measure an iDIS. For each regimen, we simulated the granuloma 500 times with different plasma PK parameters sampled using LHS. For each plasma PK parameter set, we calculated the average iDIS over the first day of dosing over all non-replicating Mtb. We repeated this process for sensitivity analysis on tissue PK parameter, simulating the granuloma 500 times with different tissue PK parameters sampled using LHS. Finally, we evaluated the partial ranked correlation coefficient (PRCC) between each PK parameter and the predicted iDIS to determine the impact each parameter has on the drug interactions58,59.