Use of multiple pharmacodynamic measures to deconstruct the Nix-TB regimen in a short-course murine model of tuberculosis

ABSTRACT A major challenge for tuberculosis (TB) drug development is to prioritize promising combination regimens from a large and growing number of possibilities. This includes demonstrating individual drug contributions to the activity of higher-order combinations. A BALB/c mouse TB infection model was used to evaluate the contributions of each drug and pairwise combination in the clinically relevant Nix-TB regimen [bedaquiline-pretomanid-linezolid (BPaL)] during the first 3 weeks of treatment at human equivalent doses. The rRNA synthesis (RS) ratio, an exploratory pharmacodynamic (PD) marker of ongoing Mycobacterium tuberculosis rRNA synthesis, together with solid culture CFU counts and liquid culture time to positivity (TTP) were used as PD markers of treatment response in lung tissue; and their time-course profiles were mathematically modeled using rate equations with pharmacologically interpretable parameters. Antimicrobial interactions were quantified using Bliss independence and Isserlis formulas. Subadditive (or antagonistic) and additive effects on bacillary load, assessed by CFU and TTP, were found for bedaquiline-pretomanid and linezolid-containing pairs, respectively. In contrast, subadditive and additive effects on rRNA synthesis were found for pretomanid-linezolid and bedaquiline-containing pairs, respectively. Additionally, accurate predictions of the response to BPaL for all three PD markers were made using only the single-drug and pairwise effects together with an assumption of negligible three-way drug interactions. The results represent an experimental and PD modeling approach aimed at reducing combinatorial complexity and improving the cost-effectiveness of in vivo systems for preclinical TB regimen development.

P ulmonary tuberculosis (TB) is treated using combinations of three or more antimicrobial drugs (higher-order drug combinations) taken daily or intermittently for at least 4-6 months (1, 2).There is a need, however, for shorter and more effective treatment regimens, especially for drug-resistant disease (3,4).Mouse TB infection models are the primary in vivo systems for assessing the efficacy of new TB drugs and regimens (5,6).They generate experimental data on pathophysiology, pharmacokinetics (PK), pharmacodynamics (PD), and relapse; and can guide allometric scaling and dose selection for early-phase clinical trials (7)(8)(9)(10)(11).Bactericidal activity of one or more drugs during early treatment is assessed by equilibrium exposure-response relationships, or by response-time profiles with sampling throughout the study duration (12,13).The sterilizing or treatment-shortening activity of regimens is typically expressed as time required to prevent relapse in 95% of mice in the relapsing mouse model which treats mice for varying durations and then quantifies microbiologic relapse after a drug holiday (12).These study types provide a basis for prioritizing promising regimens and demon strating individual drug contributions to the activity of a combination; with the latter being critical to the development of regimens that may contain multiple new investiga tional drugs (14).
While there are several established and novel methods for murine model evalu ation of TB drugs and regimens (15,16), their use for an exhaustive comparison between the hundreds of currently possible (17) higher-order combinations would be prohibitively expensive and time-consuming.Additionally, individual drug contributions to a combination are conventionally assessed by a process of single-drug additions and replacement (18,19), which only partially accounts for antimicrobial interactions.Quantitative methods that assess the effects of higher-order combinations based on their single-drug and pairwise components have been described for several types of antibiotics using in vitro systems (20,21).While these methods can be viewed as extensions of Bliss independence and Loewe additivity (as reference or null models for combined action of single drugs) (22), they have been applied in a predictive manner to reduce factorial measurements in prioritizing higher-order drug combinations (23,24).Their extension to in vivo time-kill systems could simplify combinatorial complexity in regimen-based development, and better account for the combined action of the individual drugs within a combination.
The present study describes a quantitative evaluation of early treatment response to a higher-order anti-TB combination regimen based on single-drug and pairwise combina tion effects in a murine TB model.A BALB/c mouse high-dose aerosol subacute TB infection model was used to examine the approach with the possible combinations of bedaquiline (B), pretomanid (Pa), and linezolid (L) during the first 21 days of treatment.PD response in lung tissue was assessed by solid culture CFU counts, liquid culture time to positivity (TTP), and the RS ratio-an exploratory marker that indicates the rate of bacterial rRNA synthesis; with the ratio being the amount of unstable precursor rRNA (pre-rRNA) spacer sequence to stable mature rRNA (25).While changes in CFU and TTP are commonly used to assess bactericidal activity, the change in RS ratio during the first weeks of treatment has been shown to correlate with treatment-shortening activity in BALB/c mouse experiments (16,25).The results included mathematical modeling of the time-course profiles for each PD marker, which provided for comparisons between individual drug contributions to the activity of the bedaquiline-pretomanid-linezolid (BPaL) combination; and antimicrobial interactions quantified relative to Bliss independ ence for each drug pair and an Isserlis formula for the higher-order combination (20).As the BPaL (Nix-TB) regimen was recently approved for the treatment of highly drug-resist ant TB (26,27), the results provide a clinically relevant starting point for an expanding library of single-drug and pairwise measurements from which predictions of novel higher-order combination regimens can be made and prioritized for further nonclinical or early-phase clinical testing.

Observed data: PD response-time profiles in BALB/c mice
The time course of PD response for each drug (B, Pa, L), drug pair (BPa, BL, PaL), and the three-drug BPaL combination was assessed by RS ratio, CFU, and TTP, from terminal sampling of lung tissue collected on treatment days 0 (baseline), 2, 4, 7, 11, 14, and 21; and for an untreated (UNTx) control group, on days 2, 4, and 7. Scatter plots of group mean and standard deviation (SD) values for each PD marker versus time are shown in Fig. 1.The general pattern of activity for log 10 CFU and TTP showed an inverse relation ship, with monophasic decreases in the former matching corresponding increases in the latter; and which varied uniformly across the treatment groups.The RS ratio profiles showed a biphasic response with an initial rapid reduction that slowed toward a plateau by the end of the first week.For PaL, however, there was a slower rate of reduction without a clear inflection point; and for linezolid monotherapy, there was a pronounced increase from baseline to day 4 followed by a variable but downward trend.

PD modeling: characterization of drug activity
The PD response profiles were parameterized using rate equations based on synthe sis and degradation of pre-rRNA spacer sequences assessed by RS ratio, and bacte rial population growth and drug-killing effect assessed by CFU and TTP.The model parameters were estimated as probability distributions conditioned on the baseline-nor malized group mean values of each PD marker and are summarized by their distribution mean and SD in Table 1.The rate and extent of drug effect on RS ratio were characterized by a degradation half-life, t 1/2 RS , and an equilibration value, RS ss , respectively.The half-life characterizes the initial treatment effect and depends inversely on the degradation rate, while the equilibration value represents the long-term equilibrium state.Bactericidal activity was characterized by the drug kill rate constant, k drug , which represents the rate of log 10 CFU/lung decrease or TTP increase; together with a solid-liquid culture conversion factor, τ, where the liquid culture was a mycobacteria growth indicator tube (MGIT) system.For a particular liquid culture inoculum with matching solid culture CFU, smaller and larger values of τ represent, respectively, larger and smaller rates of oxygen consumption yielding corresponding smaller and larger TTP values.The mean (SD) values for the bacterial population growth rate constant, µ = 0.72 (0.043)/day, and carrying capacity, K = 9.34 × 10 7 (5.83 × 10 6 ) CFU/lung in the absence of drug were determined from the untreated group data (Fig. S1).Model simulations of the baselinenormalized PD profiles as fractional effects, E/E 0 , are shown together with the observed data in Fig. 2; where E = E(t) is the PD response at elapsed time, t, from the first dose, and E 0 = E(t = 0) is the baseline value.The fractional effect for TTP was defined using the reciprocal values, TTP −1 .
As single drugs, the effects of B, Pa, and L were distinguished by differences in their PD parameter values and by their profile shapes, with bedaquiline monotherapy   showing the largest kill rate, and the most rapid and extensive reduction in RS ratio.While the kill rate constants and overall time course for decline in bacillary burden in the lungs were similar for B, BPa, BL, and BPaL, they show pronounced differences in their effect on RS ratio degradation rate and equilibration values with BPaL showing the smallest equilibration value.The most rapid effect on RS ratio was observed for mice treated with BPa, which was antagonistic by CFU and TTP measures relative to bedaqui line given as monotherapy.Overall, the RS ratio parameter values and time-course profiles exhibited more clearly defined differences between the various tested regimens that were less apparent based on CFU and TTP kill curves alone.While the PD model assumptions provided an explanatory representation of basic processes and features of the observed profiles for each PD marker, the relatively small but visually apparent errors, or differences between model simulation and observed data, in the first week of treatment indicate transitory drug effect processes that were not accounted for in the model equations.While not especially large, the deviations between model output and observation indicate delayed onset in bactericidal activity in the first-week CFU data for Pa, L, and PaL.Similarly, differences between modeled and observed RS ratios for B, BL, and BPaL on day 2 and day 4 indicate a possible additional early-phase synthesis-degradation process for bedaquiline exposure.The largest deviation from the modeling assumptions is seen for the RS ratio response to linezolid monotherapy, with the first-week increase from baseline indicating a delayed onset of degradation.The errors in the first week of treatment for TTP indicate possible limits on the assumption of similarity between the viable bacilli in the two culture media; such differences in mycobacterial cell populations have been characterized for rifampicin in human early bactericidal activity (EBA) studies (28).After the first week of treatment, however, the modeling errors are smaller and less informative for drug effect processes that deviate from the modeling assumptions.This suggests the attainment of equilibrium in drug effects after the first week with response profiles accounted for by simple assumptions of first-order drug kill rates, equivalence between bactericidal activity assessed by log 10 CFU and TTP, and a balance between synthesis and degradation of precursor rRNA.

PD interactions
Time-course profiles of the PD interactions were determined using the fractional effect profiles for RS ratio, log 10 CFU, and TTP −1 .A basic difference between the methods of Loewe and Bliss is the requirement of dose-response curves for the former, while the latter requires only single-dose measurements.As such, Bliss independence and its statistical interpretation could be applied directly to our single-dose kinetic profiles for the drug pairs.Figure 3 shows the observed and modeled PD marker data for each drug pair and the pointwise product of the modeled single-drug profiles, where the latter corresponds to an additive effect relative to Bliss independence (statistical independence).Also shown are the interactions calculated as the difference between the two PD response curves, or deviation from additivity, together with the corresponding observed data.Positive deviations represent subadditive (or antagonistic) interactions, resulting from a smaller effect observed for the drug pair than expected by the product of their single-drug profiles.Subadditive interactions were found for the BPa CFU and TTP profiles, and for PaL in the RS ratio.All other pairwise effects were found to be approximately additive, without substantive differences between the observed values and those predicted from an independent product assumption.For BPa, the interactions exhibited an initial increasing and variable response that became stable by day 11.
The extension of Bliss independence to three drugs becomes the triple product of the single-drug effects, which does not account for mutual interactions.The Isserlis formula includes the measured pairwise effects without assumptions on the type or magnitude of their interactions.Figure 4 shows the observed BPaL data and PD model fits together with the model-predicted Isserlis and Bliss formulas.Relative to Bliss independence, the combination was found to be subadditive with respect to CFU and TTP, and except for the day 2 value, additive with respect to RS ratio.In contrast, and again with the exception of the day 2 RS ratio value, there were no significant three-way interactions for BPaL when the mutual interactions were accounted for by the Isserlis formula.The absence of three-way interactions used as an assumption (20) provided accurate predictions of BPaL response for all three PD markers based on the responses of the single-drug and pairwise components.

DISCUSSION
While murine models provide a critical assessment of new TB drugs and treatment regimens leading up to clinical testing, they can be costly and labor-intensive, which limits their use as high-throughput screens for the large numbers of possible higherorder combination regimens generated from the current drug pipeline (29,30).The purpose of this study was to examine the use of single-drug and pairwise combinations as a reduced set of targeted drug effect measurements to predict the outcomes of higher-order drug combinations and to demonstrate the component drug contributions  to the PD responses of the regimen as a whole.A standard mouse TB infection model with three different PD markers, and the BPaL regimen, was used as a test case.The most common methods for predicting higher-order antibiotic combination effects are based on in vitro equilibrium studies measuring bacterial population growth under subinhibi tory drug concentrations (20,21,24,31).Here, these methods were adapted to an in vivo system with PD response-time profiles and bactericidal concentrations.The results included accurate predictions of BPaL effects on the kinetic profiles of the three PD markers, the characterization of BPaL component drug contributions to the combination based on a minimal set of pharmacologically interpretable parameters, and quantitative measures of drug interactions using two different models for additivity.These results show a potential for single-drug and pairwise measurements to predict higher-order combination effects as an experimentally feasible approach to prioritizing large numbers of novel TB regimens for further nonclinical and early-phase clinical testing; including combinations that would otherwise remain untested.
Demonstration of the individual drug contributions to the activity of a combination is a basic task for the development of novel TB regimens (14).For mouse TB models, such demonstration is typically conducted one drug at a time, where efficacy of the combination is assessed with and without each tested drug (18,19,32).Separate from investigation of its predictive capacity, the Isserlis formula provided a deconstruction of the PD effects of BPaL as a sum of effects arising from single-drug and pairwise products.The PD effects were also characterized for each drug component by a kill rate constant for bactericidal activity, and RS ratio half-life and equilibration as a measure of rRNA synthesis (16,25).The interactions were quantified over time as deviations from Bliss and Isserlis formulas, with the latter including mutual interactions in contrast to the former which did not.Pretomanid was the only substantively interacting drug, with subadditive effects on bacillary load in combination with bedaquiline, and on rRNA synthesis in combination with linezolid.There were no substantive interactions among the three PD markers for the BL pair, nor any that emerged from all three drugs acting together when mutual interactions were accounted for.The different characterizations of BPaL as subadditive by Bliss independence and additive by the Isserlis formula illustrate the dependence of such classification on how combined action without interaction is defined.The difference in this case is illustrated by the predictive accuracy of the Isserlis formula compared to Bliss independence.Additionally, such interactions were found to differ depending on the type of PD response, which shows the utility of including multiple PD markers, in this case for rRNA synthesis using the RS ratio and burden using CFU and TTP.
Beyond the methodological limitations in data handling, modeling assumptions, and the sensitivity to variability and error, the main limitation to generalizing the results of this study is the narrow scope, with only one drug combination, one dosage regimen, and one M. tuberculosis strain; where strain differences, in particular, may result in different outcomes for the PD interactions as have been observed for BALB/c TB-infection models (33).Evaluation of a wider range of drug classes, including dose ranging for at least the single-drug measurements, would better establish a basic pattern of outcomes from this experimental system.While available mouse studies of BPaL have not included possible PK drug-drug interactions (18,34), the absence of such PK measurements is a limitation on understanding sources of error in the observed PD interactions.Application of the Isserlis formula for prediction required an assumption of negligible higher-order interactions and was based on previous observation of such effects from in vitro antibiotic combination studies including antimycobacterial drugs (20,21,24), and from theoretical considerations of locality (35) that might apply to drug-mediated interactions in biochemical processes.While the accuracy of the BPaL results across disparate PD markers may indicate a more general application, there are examples of higher-order or emergent effects that challenge this assumption (31,36).For example, factorial measurements of in vitro antibiotic growth inhibition of Escherichia coli identified emergent interactions in 17% of 1,512 three-drug combinations with the proportion increasing with the number of drugs (37).A comparison between growth inhibition and bactericidal activity of these combinations could improve understanding of the limitations on predictive capacity of pairwise interactions.Although the combina tion of CFU and RS ratio reduction has been shown to correlate with treatment-shorten ing ability for several different combination regimens (16,25), the absence of selection criteria beyond that of maximum observed effect is another limitation.For example, possible relationships between PD interactions and acquired drug resistance may require a more detailed understanding of resistance mechanisms and longer treatment duration to assess (18,38).Application of this analysis to other PD markers such as lipoarabino mannan (39) and 16S rRNA (40) remains untested.
This study combined in vivo measurements of drug effect with mathematical modeling as a potential method of prioritizing novel TB regimens for further nonclinical and clinical evaluation.The experimental design was similar to phase 2a EBA studies (41) and could be further combined with similarly designed in vitro time-kill studies to identify translatable elements across the preclinical and early-phase clinical develop ment stages.Consideration of the planned evaluation of novel TB regimens by the UNITE4TB consortium (42) provides an example of how the approach developed here could be applied.There are eleven planned phase 2b/c studies of mostly four-drug combinations assembled from eight individual drugs assessed in phase 2a monotherapy testing.In total, 19 phase 2 studies will yield an evaluation of 11 combination regimens.Using Isserlis formulas based on single-drug and pairwise outcomes (20), an alternative approach could first measure the 8 single-drug and 28 pairwise combinations of the 8 drugs, which would then yield predictions for 56 three-drug, 70 four-drug, and 56 five-drug combinations.A ranking of promising regimens could be made from compar isons among predicted outcomes for early bactericidal activity using CFU or TTP and treatment-shortening using the combined CFU and RS ratio (16,25), to provide a basis for additional nonclinical testing.Such an approach could provide a more thorough and systematic prioritization of combination regimens for early-phase clinical trials, and the flexibility to incorporate new drugs with minimal experimental testing.

BALB/c mouse high-dose aerosol infection model
All animal studies were performed at Colorado State University in a certified animal biosafety level III facility, and conducted in accordance with guidelines of the Colorado State University Institutional Animal Care and Use Committee (reference number: 1212).Six-to eight-week-old female pathogen-free BALB/c mice (Jackson Laboratories) were exposed to high-dose aerosol (Glas-Col) of M. tuberculosis Erdman from broth culture (optical density at 600 nm of ∼0.8) to achieve deposition of ∼4.0 log 10 CFU in the lungs of each mouse (43).Mice were sacrificed for lung CFU counts 1 day after infection (day −10) and at day 0 to determine the number of CFU implanted in lungs and the number of bacilli present at the start of treatment, respectively.

Antibiotic treatment
Mice were randomized to the different treatment groups.Treatments were initiated 11 days post-aerosol (day 0) and were given once daily by oral gavage, 7 days per week, for the duration of the study.Bedaquiline fumarate was administered at 25 mg/kg.Linezolid was administered at 100 mg/kg.Pretomanid was administered at 50 mg/kg.Bedaquiline fumarate was formulated in 20% hydroxypropyl-b-cyclodextrin solution acidified with 1.5% 1N HCl.Pretomanid was prepared in the CM-2 formula tion as previously described (43).Linezolid was prepared in 5% polyethylene glycol (PEG)-200/95% (0.5%, wt:vol) methyl-cellulose.In cases of drug combinations, bedaqui line was administered first, followed 1 h later by pretomanid and/or 4 h later by linezolid.Each drug was administered in 0.2 mL volume.

Evaluation of drug activity
Drug bactericidal activity was assessed by lung CFU reductions and TTP increases, and by RS ratio turnover.Groups of five mice each were humanely euthanized 1 day following 2, 4, 7, 11, 14, or 21 consecutive days of drug treatment.At each time point, lung lobes were removed aseptically.The superior and middle lobes (roughly one-third of the lung by mass) were immediately flash frozen under liquid nitrogen for RNA preservation.The remaining two-thirds of the lung were used for CFU and TTP assessments.Details on RS ratio assessment were described previously (25).For CFU plating and TTP assessments, previously frozen lungs were homogenized using the Bertin Precellys CKMix50-7 mL lysis kit [in 4.5 mL phosphate-buffered saline (PBS) with 10% bovine serum albumin (BSA)].Lung homogenates were plated in serial dilutions on 0.4% charcoal-supplemented 7H11 agar supplemented with 10% oleic acid, BSA, dextrose, and catalase (OADC) and with selective antibiotics, including cycloheximide (10 mg/L) and carbenicillin (50 mg/L).
For TTP assessments, lung homogenates were diluted fivefold in 7H9 media supplemented with 10% OADC and 0.05% Tween80, placed in a 2 mL screw-cap tube containing sterile 2 mm beads and bead-beat at 2,800 rpm for 10 s.Homogenates were then inoculated into 7 mL MGITs containing 7H9 media supplemented with 10% OADC, 0.05% Tween80, 0.4% charcoal, and BD MGIT PANTA antibiotic mixture (polymyxin B, amphotericin B, nalidixic acid, trimethoprim and azlocillin), per the manufacturer's instructions.Finally, MGITs were incubated in the BD BACTEC MGIT 320 system for at least 42 days at 37°C.TTP was recorded as the time (in h) for cultures to turn positive.Cultures that were assayed in the MGIT system but remained negative up to day 42 (the accepted cutoff) were recorded as negative.

PD modeling and antimicrobial interactions
The PD response profiles for each treatment group were modeled as functions of elapsed time, t, from the start of treatment using PD rate equations (44,45).The PD response for RS ratio was represented by a turnover equation: where R = R(t) is the RS ratio with initial condition, R(0) = R 0 .The rate constants for apparent production, k prod , and fractional loss, k loss , were expressed as a half-life, t 1/2 RS = ln (2)/k loss , and an equilibration (or steady state) value, RS ss = k prod /k loss .The CFU and TTP profiles were modeled using logistic growth with constant drug-killing effect as follows: where N = N(t) represents the CFU/lung and T = T(t) is the TTP.The initial conditions were specified as N(0) =N 0 and T(0) =T 0 .The parameter, µ, is the bacterial growth rate constant; K, the carrying capacity; k drug , the drug kill rate constant; and τ, a solid-liquid culture conversion factor between CFU and TTP with a detailed derivation previously described (46).The model parameters were estimated from the observed data using Bayes' theorem and Markov chain Monte Carlo (MCMC) simulation (47).The MCMC simulations consisted of 10 independent sampling chains of 100,000 iterations each; with every 10th iteration of the last 10,000 retained and aggregated into a final 10,000 iteration sample.
The PD interactions were characterized as functions of time using the fractional response (or survival fraction), u = u(t), for each drug alone, u i , the pairs, u ij , and the three-drug combination, u ijk , where i, j, k are drug labels.Pairwise interactions were quantified as the deviation from Bliss independence, β ij = u ij − u i u j , and three-way interactions as deviations from an Isserlis formula (20), β ijk = u ijk − (u i u jk + u j u ki + u k u ij − 2u i u j u k ).
In the absence of pairwise interactions, the Isserlis formula reduces to a Bliss independence formula with deviations β ijk = u ijk − u i u j u k .Interactions were specified relative to zero deviation (additive) as subadditive (or antagonistic) for positive deviation or superadditive (or synergistic) for negative deviation.

Data handling and limitations
The observed mouse efficacy data were obtained as terminal samples, which precluded individual PD response-time profiles.The PD profiles used for model parameter estimates were constructed as population summaries from the group mean values calculated with missing data ignored.Negative cultures were treated as missing.The mathematical models were constructed as simple representations of the basic biological processes underlying the observed PD responses during early treatment.Additional features or distinguishing factors related to drug mechanisms of action, such as delays in onset of activity, multiple subpopulations of bacilli, or features that may become evident with longer-duration treatments such as a possibly vanishing RS ratio, were not included in the PD modeling assumptions.The relationship between CFU and TTP included an assumption of similarity between the viable bacillary populations that are detected in the two different culture media, and that this relationship did not change over time.The Isserlis and Bliss formulas are sensitive to measurement uncertainty and variability due to multiplication of error (48).

FIG 2
FIG 2 Fractional effect (E/E 0 ) profiles of M. tuberculosis RS ratio, solid culture CFU (log 10 CFU), and reciprocal of the liquid culture TTP −1 from BALB/c mouse lungs.Data are model simulations of the predicted mean (solid line with shaded 95% confidence interval) together with observed group mean (points) and SD (error bars) for each treatment group versus time.The observed day 4 RS ratio mean (SD) value for L not shown in the plot was equal to 1.46 (0.25).B, bedaquiline; Pa, pretomanid; L, linezolid; BPa, bedaquiline-pretomanid; BL, bedaquiline-linezolid; PaL, pretomanid-linezolid; and BPaL, bedaquiline-pretomanid-linezolid.

FIG 3
FIG 3 Pairwise PD response profiles and interactions as a deviation from Bliss independence.(A) PD marker fractional effect (E/E 0 ) for bedaquiline-pretomanid (BPa), bedaquiline-linezolid (BL), and pretomanid-linezolid (PaL) combinations.Observed data (OBS) group mean (points) and SD (error bars), together with model simulations for the pair (dashed lines) and Bliss independence as pointwise products of single-drug model fits.(B) Interactions as deviations from Bliss independence.Values are shown for each PD marker for the observed mean values (point symbols) and model predictions (lines).

FIG 4
FIG 4 BPaL PD response profiles and interactions as deviations from Bliss and Isserlis formulas.(A) PD marker fractional effect (E/E 0 ) for BPaL.Observed data (OBS) group mean (points) and SD (error bars), together with model simulations for the combination (dashed lines) and Bliss independence (top row) and Isserlis formula predictions (bottom row).(B) Interactions as deviations from Bliss independence (top row) and Isserlis formula (bottom row).Values are shown for each PD marker for the observed mean values (point symbols) and model predictions (lines).