Pharmacokinetic-Pharmacodynamic modelling of intracellular Mycobacterium tuberculosis growth and kill rates is predictive of clinical treatment duration

Tuberculosis (TB) treatment is long and complex, typically involving a combination of drugs taken for 6 months. Improved drug regimens to shorten and simplify treatment are urgently required, however a major challenge to TB drug development is the lack of predictive pre-clinical tools. To address this deficiency, we have adopted a new high-content imaging-based approach capable of defining the killing kinetics of first line anti-TB drugs against intracellular Mycobacterium tuberculosis (Mtb) residing inside macrophages. Through use of this pharmacokinetic-pharmacodynamic (PK-PD) approach we demonstrate that the killing dynamics of the intracellular Mtb sub-population is critical to predicting clinical TB treatment duration. Integrated modelling of intracellular Mtb killing alongside conventional extracellular Mtb killing data, generates the biphasic responses typical of those described clinically. Our model supports the hypothesis that the use of higher doses of rifampicin (35 mg/kg) will significantly reduce treatment duration. Our described PK-PD approach offers a much needed decision making tool for the identification and prioritisation of new therapies which have the potential to reduce TB treatment duration.

of therapy 9 . Generally, it is accepted that in order to understand the overall pattern of the clinical response, there is the need to understand the pharmacodynamic (PD) contribution to bacterial killing i.e. how different sub-populations of Mtb respond to specific drug treatment (e.g. refs [10][11][12], and pharmacokinetic (PK) contribution to killing dynamics i.e. the ability of a drug to reach Mtb sub-populations residing in different cells, matrices and tissues (e.g. refs 10, 13, 14).
Critically, the PK and/or PD characteristics of a drug(s) that are most relevant in predicting the clinical response of an anti-tubercular drug/drug combinations remain to be defined and validated. Currently, several pre-clinical animal and in vitro efficacy models are being evaluated to determine their value in forecasting clinical outcomes 2,3 .
It has long been recognized that intracellular Mtb growth and survival within macrophages plays a major role in TB pathogenesis 15 . Intracellular survival necessitates metabolic and physiological adaptations relative to extracellular growth. Significantly, Mtb that are genetically manipulated to lack genes required for survival within macrophages fail to establish pathogenicity in TB animal models [16][17][18][19] . Consequently, it is clear that demonstration of efficacy against intracellular Mtb must be a critical PD feature for any anti-tubercular drug under development 20 .
The importance of determining the PD response of intracellular Mtb is underscored by studies that demonstrate differential susceptibility to existing and novel anti-tubercular drugs and inhibitors against intracellular versus extracellular Mtb (e.g. refs [21][22][23]. However, to date, studies assessing intracellular Mtb sensitivity to drugs do not allow for extrapolation and prediction of the clinical potential of the developing therapy. To address this deficiency, here we describe a new high-content imaging-based, PK-PD approach that utilizes concentration and time-dependent phenotypic data of intracellular Mtb residing within macrophages exposed to first-line TB drugs. We demonstrate that the use of intracellular Mtb-derived PD data, alongside conventional extracellular Mtb PD data, results in the generation of superior clinical predictions of TB treatment duration with biphasic responses akin to those described previously in the clinic. In addition, we show that our model can be used to simulate new therapeutic regimens such as the use of higher doses of RIF (35 mg/kg) to predict the outcomes of clinical studies. We anticipate that our described high-content imaging platform and PK-PD approach will be an invaluable tool that can correctly identify new combination therapies that can genuinely reduce TB treatment duration in the clinic. Intracellular Mtb residing within macrophages are killed more slowly by first line drugs. The optimized high-content imaging platform was used to measure the pharmacodynamic response of intracellular Mtb within macrophages to first line TB drugs at concentrations spanning the pharmacological range over an exposure period up to 120 h. Optimal assay performance was assessed and confirmed by a mean Z′-factor of 0.67 for the complete data set.
RIF, INH, ETB and PZA exhibited time-and concentration-dependent anti-tubercular activity against intracellular Mtb (Fig. 2). The kill dynamics for each drug was modelled as described in eq. 2 and the resultant kinetic parameters E max (Maximum kill rate of a drug) and EC 50 (concentration required to achieve half of this maximal kill rate) are presented in Table 1. In terms of intracellular Mtb killing dynamics, RIF ranked as the most effective out of all four drugs exhibiting an E max value of 0.055 h −1 and an EC 50 value of 18.4 ng/mL, followed by ETB, PZA and then INH. The raw (Fig. 2) and simulated ( Supplementary Fig. 2) time-and concentration-dependent intracellular Mtb killing kinetics revealed that maximal killing was achieved for all drugs after an initial lag period of 20-48 h.
Comparison of intracellular and extracellular killing dynamics for all drugs show that intracellular Mtb residing inside macrophages exhibited much slower E max values compared to kill rates shown previously in liquid cultures 24,25 and parameterised in Table 1.
To facilitate the comparison, concentration-kill rate relationship plots were performed for each drug (Fig. 3). A comparison of the concentration-intracellular kill rate relationship for all 4 drugs reveals the superiority of RIF over the other drugs, displaying the highest achievable E max and a low EC 50 (Fig. 3a). Plots comparing concentration-kill rate relationships for extracellular 25 versus intracellular Mtb, show that despite broadly comparable EC 50 levels, RIF, ETB and INH all display accelerated kill rates in the liquid assay compared to kill rates for intracellular Mtb (Fig. 3b-d).
PK-PD modelling using macrophage intracellular Mtb kill rates is predictive of treatment duration. To determine whether the PD data acquired from the intracellular macrophage high content platform has value in forecasting clinical TB treatment scenarios, Monte-Carlo PK-PD simulations for RIF, ETB, INH and PZA were conducted based on 1,000 theoretical subjects. Using published clinical PK parameters 26-31 , simulations were performed for different treatment regimens using either intracellular or extracellular Mtb PD data, or a combination of both.
A simulation of the recommended WHO treatment regimen of an intensive 8 week treatment phase of RIF, ETB, INH and PZA followed by a 16 week continuation phase of RIF, INH using PD parameters taken from extracellular (liquid culture) Mtb data, reveal that median clearance time to achieve a 10 7 Mtb/ml log drop would take 16 days (Fig. 4a). This predicted rapid clearance contrasts with the simulations using intracellular Mtb PD parameters (Table 1 and Fig. 3) which predict a median clearance time of 56 days to achieve the same reduction of Mtb as predicted based on liquid culture (Fig. 4b). Significantly, simulations that combine both extracellular and intracellular Mtb PD parameters, result in a biphasic response for Mtb clearance, the intersection of which is dependent on the starting proportions of the two populations (Fig. 4c). The majority of Mtb in advanced disease states are found to be extracellular 32,33 . Simulations of a standard 6 month treatment as per WHO recommendations, assuming that 95% of Mtb is extracellular and the rest 5% intracellular, results in 83% of patients achieving cure whilst the 17% remaining would be predicted to fail treatment (Fig. 4d). Notably, it is the killing dynamics of the intracellular Mtb population that predominantly determine the treatment duration. Sensitivity analysis across a wide range of intracellular:extracellular ratio fractions (1%:99%-99%:1%) results in minimal variation (<8%) in total population achieving cure at the end of standard therapy whilst variation in median time to achieve cure changes by no more than 13 days (22%) regardless of assumed initial intracellular/extracellular ratio at the beginning of the simulation ( Supplementary Fig. 3). We conducted a further comparison of our simulated standard 6 month treatment with clinical data obtained from the control arm of a recent Phase 3 trial (REMoxTB 7 ). Kaplan-Meier estimates showing the time until conversion to culture-negative status, show that our simulations using growth and kill curves from 95:5% extracellular: intracellular Mtb-based PK-PD modelling compare very favourably with the clinical scenario (Fig. 4e). Using our models, it is possible to make predictions of the clinical outcomes of proposed trials using the drugs we have investigated such as proposed high dose rifampicin 34,35 . Simulations using high dose RIF (35 mg/kg) exposures again show a biphasic response due to differential killing dynamics of extracellular and intracellular Mtb (Fig. 4f). Significantly, assuming a 95:5%, extracellular:intracellular ratio of Mtb, simulations predict that only 12 weeks (~3 months) of a high dose RIF-containing treatment should deliver a clinical outcome equivalent to a 6 month HRZE standard course (87% cure and 13% failure rate, Fig. 4f). A predicted reduced time until conversion to culture-negative status for high dose RIF compared to standard treatment is further illustrated in Kaplan-Meier simulations (Fig. 4e).

Discussion
Survival of Mtb within macrophages is a critical aspect of TB pathogenicity 15 . TB drug discovery efforts that have failed to simulate physiological growth conditions have resulted in the identification of false positive hits in drug screening and discovery programmes that have translated poorly to in vivo models (and man) and that are therefore not developable 3,36 . The intracellular macrophage environment offers the ability to measure Mtb drug dynamics within an environment that better reflects the common niche of this pathogen. Reflecting the nutritionally-constrained environment of the intracellular macrophage milieu 37 , the population growth of intracellular Mtb residing within macrophages was much slower (~21 h doubling time, Table 1 and Supplementary  Fig. 1) compared with Mtb grown in stirred liquid culture which has a doubling time of approximately 9 h 24, 25 (Table 1 and Supplementary Fig. 1).
Drug susceptibility of Mtb residing within macrophages has previously been shown to correlate poorly with that of extracellular Mtb. This has been explained by invoking selective inhibition of pathways essential for intracellular metabolism 21,23 or poor permeability/altered drug transport 38 Figs 2 and 3). Significantly, the inability to increase the E max using super-pharmacological concentrations of drug, suggests that this phenomenon is not solely linked to intracellular drug availability which has been linked to altered RIF susceptibility when measured using static assays 38 . Instead, we hypothesise that the kill rate (E max ) of RIF, INH and ETB (a comparison of PZA cannot be made using the standard liquid culture conditions used here) is intimately linked to the inherent growth rate of the intracellular Mtb residing within the nutritionally-constrained environment of the macrophage (the same logic would apply to Mtb in any intracellular/compartmental niche that constrains growth dynamics). A link between growth-rate and kill rate for antibiotics that target the replication machinery of the cell has been described for many years (e.g. refs  (c) Predicted dynamics of total TB in patients receiving HRZE combination for 6 months based on the assumption that extracellular TB constitutes 95% and intracellular 5% of total TB (1-month view). (d) Predicted dynamics of total TB in patients receiving HRZE combination for 6 months based on the assumption that extracellular TB constitutes 95% and intracellular 5% of total TB (6-month view). (e) Probability of sputum sample conversion to Mtb culture-positive status over time as observed in TB patients receiving standard HRZE treatment in a previous clinical study 7 (solid black line) compared to the predicted probabilities over time using our novel PK-PD model (dashed red line). Dashed green line shows our PK-PD prediction when using a standard HRZE regimen but with an elevated dose of RIF (35 mg/kg). The comparison assumes that the limit of detection for positive culture conversion is 10 CFU/mL when using Löwenstein-Jensen medium culture assays 67 which have been implemented in the comparator clinical study. (f) Predicted dynamics of total TB in patients receiving HRZE with a high dose of RIF (35 mg/kg) for 3 months on the assumption that extracellular TB constitutes 95% and intracellular 5% of total TB (6-month view). [39][40][41]. The mechanisms underpinning growth-rate dependent killing of some antibiotics are beginning to be understood. Antibiotics targeting the ribosome for example, growth-rate-dependent killing is explained by the growth rate-dependent partitioning of the cell's translational resources between production of new ribosomes and production of other proteins 40,42,43 . Single-cell studies have also recently confirmed that phenotypic antibiotic tolerance, often described as persistence, can be demonstrated in actively growing bacteria 44 , including Mycobacterium species 45 and is not therefore wholly dependent on rare stochastic non-dividing (also known as dormant) populations 46 .
The significance of reduced kill rate (E max ) values for RIF, INH and ETB in intracellular Mtb experiments relative to kill rate (E max ) values derived from liquid culture experiments of extracellular Mtb, is that PK-PD predictions of clinical scenarios can be radically skewed from clinical reality. This is illustrated in the PK-PD simulations performed using extracellular (Fig. 4a) and intracellular (Fig. 4b) Mtb drug dynamic parameters, resulting in dramatically different times to culture conversion. The majority of Mtb in advance disease state are found to be extracellular 32,33 , assuming a ratio of 95% extracellular to 5% intracellular Mtb following treatment results in biphasic TB elimination profiles (Fig. 4c) that are similar to the treatment responses reported clinically following short-course regimens 47,48 . It is noteworthy that treatment response in terms of both duration and cure (%) displayed only minimal variation in sensitivity analyses performed across a wide range of intracellular:extracellular ratio fractions (1%:99%-99%:1%, Supplementary Fig. 3).
Simulations of a standard 6 month treatment as per WHO recommendations, assuming that 95% of TB is extracellular and the rest 5% intracellular, results in 83% of patients achieving cure whilst the 17% remaining would be predicted to fail treatment (Fig. 4d). This agrees with literature data relating to relapse rates after standard 6 month TB treatment 49 . Simulations of standard WHO treatment duration lasting 2 months are predicted to result in a 50% cure rate, this is again in agreement with clinical studies 50,51 52 .
The described high-content imaging platform makes possible the dynamic measurement of intracellular Mtb in response to any drug. By linking the intracellular kill kinetics with drug exposure, and in this regard we underline the importance of acquiring accurate drug measurements in relevant compartments/tissues (e.g. ref. 13), it is possible to simulate clinical scenarios that can be validated against actual trial data. Here, we described this approach for high dose RIF trials (35 mg/kg) which are currently under clinical evaluation (e.g. refs 34, 35). Strikingly, simulations using PD data from intracellular Mtb exposed to high RIF concentrations (Fig. 2a) predict that clinical outcome equivalent to a 6 month HRZE standard course (83% cure and 17% failure rate, Fig. 4e) would occur within a significantly shorter time period (12 weeks) of a high dose RIF-containing treatment, reducing treatment therefore by approximately a half of the usual length. Our simulations are consistent with clinical data from Phase II studies in which rate increases in the dose of RIF result in an accelerate rate of decline in bacterial load 34,[53][54][55][56] .
Mtb within macrophages play a critical role in the life history of TB infection. The dynamic drug response of intracellular Mtb residing inside macrophages is dramatically different to that of extracellular Mtb. In essence, for drugs affecting the replication machinery, maximum kill kinetics are intimately linked with compartmentalized growth dynamics. The critical importance of this observation is that the dynamic intracellular Mtb drug response (compared to extracellular killing) provides the most predictive estimates of clinical treatment response. The described dynamic high-content imaging platform offers a new tool to aid decision-making and is recommended for incorporation as an essential assay for compound progression within the TCP (target candidate profiles) of future TB drug discovery programmes aiming to identify therapies that reduce treatment duration.  Aliquots of 1.5 mL of bacterial culture with magnetic stirrers was incubated aerobically at 37 °C in the presence or absence of drug. At three time points per day for up to 7 days, optical density (600 nm) was measured (beginning from day 0). In experiments in which colony forming units (CFUs) were measured, aliquots of culture were withdrawn at periodic intervals and pelleted material washed in drug-free Middlebrook 7H9 media before CFU/ mL determination by colony counting on solid growth media containing Middlebrook 7H11 agar plates supplemented with 10% oleic acid-albumin-dextrose-catalase solution (Becton Dickinson), 0.2% (v/v) glycerol and 0.05% (v/v) Tween 80.

Methods
Scientific RepoRts | 7: 502 | DOI:10.1038/s41598-017-00529-6 Macrophage Infection Assay in 96-Well Plates, High-content Image Acquisition and Analysis. THP-1 cells were routinely cultured in RPMI 1640 with L-Glutamine and NaHCO 3 (Gibco) supplemented with 10% heat-inactivated foetal bovine serum (FBS; Gibco), at 37 °C, 5% CO 2 . For the infection assay THP-1 cells were differentiated in 96-well Matriplate plates (MGB096-1-2-LG-L Black 0.17 low glass; Brooks). THP-1 cells were seeded at 5 × 10 5 cells per well and differentiated for 72 h in RPMI 1640 with L-Glutamine and NaHCO 3 supplemented with 10% heat-inactivated FBS and 100 ng/ml phorbol 12-myristate 13-acetate (PMA; Sigma) at 37 °C, 5% CO 2 . The medium was removed after 72 h and THP-1 cells incubated for a further 24 h in RPMI 1640 with L-Glutamine and NaHCO 3 supplemented with 10% FBS at 37 °C, 5% CO 2 . Differentiated THP-1 cells were infected with H37Rv-GFP in suspension at a multiplicity of infection (MOI) of 1:5 in RPMI 1640 with L-Glutamine and NaHCO 3 supplemented with 10% heat-inactivated FBS for 24 h at 37 °C. After 24 h the cells were washed and the drugs at the required concentrations added. Infected cells were incubated for up to 5 days at 37 °C, 5% CO 2 . At each time point, plates were fixed with 5% paraformaldehyde (PFA) (Sigma) for 2 h before staining. Macrophages were stained with Hoechst 3442 (Invitrogen) at 2 µg/mL in PBS for 30 min at 37 °C. Image acquisition was performed with an Operetta (PerkinElmer) using a 60x High NA objective. H37Rv-GFP were detected using 460/490 nm excitation coupled with a 500/550 nm detection filter and Hoechst 3442 labeled cells were detected using excitation at 360/400 nm laser coupled with a 410/480 nm detection filter. Fourteen fields and a Z stack of 6 intervals over 0-6 µm were recorded for each plate well. Each image was processed using Harmony 3.5.1 analysis software (PerkinElmer). Briefly, the cell nucleus was segmented using detection of Hoechst 3442. From this the cell area was defined again using Hoechst 3442 (due to cellular RNA staining). Within each macrophage the spot finding algorithm was utilised to detect the area of H37Rv-GFP in each cell. The output parameter deduced from the images was the bacterial load, which refers to the total surface area of all the green objects that reside within the macrophages, as a ratio of total cell area. Data were generated from multiple independent experiments (n ≥ 3) performed in triplicate. Assay performance was measured using Z′-factor determination 57 .
Pharmacodynamic data analysis. The growth dynamics of Mtb were calculated according to an exponential, capacity saturated model which takes into account the saturation of growth that was observed at day 5 with control experiments. The growth rate was calculated according to Eq. 1 taken from 58 : where Mtb represents the total Mtb count in the well at any given time (t), Kg max represents the maximal growth rate per unit time and POPMAX represents the maximum capacity of the Mtb population in a well, in other words the maximum limit of Mtb number per well. A model that calculates the kill dynamics of drugs over multiple time points was developed based on previous work 58 , in contrast to calculating fixed time point MIC or IC 50 values. The kill dynamics for each drug in the assay were modelled simultaneously over 5 days with all the tested concentrations (a gradient of 12 concentrations per drug ranging from 0.5 ng/mL to 32 µg/mL). We use the term 'kill rate' to describe the rate of reduction of Mtb growth per unit time, e.g. when the kill rate is equal to the growth rate, the number of Mtb will remain constant and when the kill rate exceeds the growth rate, the number of Mtb will decline over time, and vice versa. The model calculates the most likely values of E max (Maximum possible kill rate of a drug per unit time) and C 50 (concentration required to achieve half of this maximal kill rate) based on all the available data from all the tested drug concentrations according to Eq. 2: (2) max max 50 Using Eq. 2 the model calculates the maximal kill rate of each drug per unit time as well as the C 50 value that is required to achieve half of that rate.
For extracellular Mtb growth and kill dynamics, we used a combination of in-house data of Mtb grown (planktonic) in liquid media as well as previously published kill dynamic data of first-line drugs published by our laboratory 24 and that of other groups e.g. ref. 25 using the same model to allow for intracellular-extracellular dynamics comparisons.
Monte-Carlo Simulations. The growth and kill parameters estimated from the intracellular and extracellular assays were used to predict the PK-PD relationship in a clinical context. The PK parameters of all four drugs were taken from the literature 26,27,30,31,[59][60][61][62][63][64][65][66] . The PK-PD model linked the PK to the PD component by using the simulated dynamic drug concentrations in a patient to represent 'conc' . In Eq. 2. When combining multiple drugs it was assumed that the rate of kill is equal to that of the drug that achieves the higher kill rate based on its concentration and kill rate (based on the argument that you can only kill once and there is no underlying synergy/antagonism between the drugs). This was achieved by using IF statements in the Pmetrics model file that are applied at each time step. The simulation was then run assuming that all four drugs are administered concomitantly once daily for a period of 8 weeks followed by RIF and INH for a further period of 18 weeks, as per standard WHO treatment recommendations. The simulation is aimed at identifying the time it takes to achieve a 7 log reduction of Mtb, as such a drop is correlated with a cure in clinical studies 48 . Variability was set at 30% for the PK parameters whilst the variability and limits of the PD parameters were set according to the modelling of the in-vitro data.