Abstract
Warfarin is well recognized for its high-affinity and capacity-limited binding to the pharmacological target and undergoes target-mediated drug disposition. Here, we developed a physiologically based pharmacokinetic (PBPK) model that incorporated saturable target binding and other reported hepatic disposition components of warfarin. The PBPK model parameters were optimized by fitting to the reported blood pharmacokinetic (PK) profiles of warfarin with no stereoisomeric separation after oral dosing of racemic warfarin (0.1, 2, 5, or 10 mg) using the Cluster Gauss-Newton method (CGNM). The CGNM-based analysis yielded multiple “accepted” sets for six optimized parameters, which were then used to simulate the warfarin blood PK and in vivo target occupancy (TO) profiles. When further analyses examined the impact of dose selection on uncertainty in parameter estimation by the PBPK modeling, the PK data from 0.1 mg dose (well below target saturation) was important in practically identifying the target binding-related parameters in vivo. When stereoselective differences were incorporated for both hepatic disposition and target interactions, our PBPK modeling predicted that R-warfarin (of slower clearance and lower target affinity than S-warfarin) contributes to TO prolongation after oral dosing of racemic warfarin. Our results extend the validity of the approach by which the PBPK-TO modeling of blood PK profiles can yield TO prediction in vivo (applicable to the drugs with targets of high affinity and abundance and limited distribution volume via nontarget interactions). Our findings support that model-informed dose selection and PBPK-TO modeling may aid in TO and efficacy assessment in preclinical and clinical phase 1 studies.
SIGNIFICANCE STATEMENT The current physiologically based pharmacokinetic modeling incorporated the reported hepatic disposition components and target binding of warfarin and analyzed the blood pharmacokinetic (PK) profiles from varying warfarin doses, practically identifying target binding-related parameters in vivo. By implementing the stereoselective differences between R- and S-warfarin, our analysis predicted the role of R-warfarin in prolonging overall target occupancy. Our results extend the validity of analyzing blood PK profiles to predict target occupancy in vivo, which may guide efficacy assessment.
Introduction
Target-mediated drug disposition (TMDD) refers to the phenomenon in which the saturable binding of drugs to their pharmacological targets leads to nonlinear pharmacokinetic (PK) behaviors (Levy, 1994). TMDD has been frequently considered for biologics, which typically interact with their targets of high specificity and affinity. Once the formation of the drug-target complex reaches saturation with either high doses or repeated dosing, the fraction of the dose binding to the target becomes disproportionately small. As such, systemic drug exposure can increase much more than expected from a single low dose, leading to dose-dependent PK profiles that are nonlinear at low doses but linear at high doses. Compared with biologics, TMDD occurrence is less common among small-molecule drugs. Yet, TMDD cases have been increasingly reported among small-molecule drugs in recent years (An, 2017).
To enhance our mechanistic understanding of the TMDD among small-molecule drugs, it is important to tease out the relative contribution of saturable target binding to nonlinear PK profiles compared with other components in drug disposition (e.g., saturable metabolism/transport in the liver or intestine). By applying the physiologically based pharmacokinetic (PBPK) modeling with target binding, our group recently reported that target binding, albeit not a major contributor to the nonlinear bosentan PKs, is important in capturing the observed PK profiles at low concentration ranges (Koyama et al., 2021). We also noted that the analysis of blood bosentan PK profiles obtained from a wide range of doses via PBPK modeling with target binding could practically identify target binding-related parameters of bosentan, thereby predicting the target occupancy (TO) profiles in vivo. These findings prompted us to pursue additional cases that may expand the validity of our approach of analyzing the blood PK profiles toward the prediction of the TO in vivo.
Approved for medical use in 1954, warfarin, a racemic mixture of R- and S-enantiomers, is still considered the mainstay of oral anticoagulant treatment of patients with various cardiovascular diseases. However, the safe use of warfarin remains challenging due to its narrow therapeutic window and large interpatient variability. The anticoagulant effect of warfarin is mediated by high-affinity interactions with its pharmacological target, vitamin K 2,3-epoxide reductase (VKOR), located mainly in the liver. The inhibitory potency of warfarin toward its target varied widely (ranging from nanomolar to millimolar concentrations) (Bevans et al., 2013), but the underlying reasons for such discrepancies had remained elusive. Later, the presence of dithiothreitol in vitro was identified to alter the redox state of VKOR, greatly influencing the inhibitory potencies of warfarin toward VKOR (Shen et al., 2017). The target affinity of warfarin is considered to be stereoselective [S-warfarin being more potent by 3–6 times than R-warfarin, based on the relationship between dose or concentration and response (Breckenridge et al., 1974; O’Reilly, 1974; Hignite et al., 1980)]. Yet, lacking is a detailed understanding of the stereoselective warfarin-target interactions and pharmacological and clinical implications in warfarin therapy.
Saturable target binding of warfarin and its nonlinear PK profiles were noted in rats over four decades ago (Takada and Levy, 1980). Nonlinear PK profiles of warfarin in human subjects, in fact, served as the first case analyzed via TMDD-PK modeling (Levy et al., 2003). Later, a clinical study reported that the saturable target binding of warfarin could hamper the PK extrapolation from a microdose (0.1 mg) to a therapeutic dose (5 mg) (Lappin et al., 2006). The hepatic uptake of warfarin was found to be handled by organic anion transporter 2 (OAT2) with stereoselective affinity and capacity (Bi et al., 2018). So far, none of the previous PK modeling of warfarin incorporated all of the reported components for hepatic warfarin disposition (i.e., metabolism, active uptake, and target binding in the liver). In addition, the previous modeling efforts mainly analyzed the data at therapeutic doses of warfarin but not at a microdose (which displayed a large deviation from dose-proportional PKs).
The current study aimed to develop an updated PBPK-TO model of warfarin by incorporating saturable target binding in addition to the metabolism and uptake components in the liver. Our analysis revisited early clinical data that measured the total warfarin levels from a wide dose range of warfarin, including a microdose. Furthermore, the stereoselective differences between R- and S-warfarin were incorporated in analyzing the warfarin blood PK profiles. We believe that our current results may offer important insights into the factors to consider in predicting and exploiting the TMDD occurrence in small-molecule drug candidates, as well as in designing preclinical studies and clinical phase 1 trials that may shed light on the target engagement in vivo.
Materials and Methods
Structure of the Warfarin PBPK Model
Our PBPK model for warfarin was constructed based on in silico, in vitro, and clinical PK data available from the literature. As depicted in Fig. 1, the PBPK model included the central (blood) compartment connected to the liver, subdivided into five extrahepatic and hepatocellular compartments, and incorporated the active uptake and target binding components for warfarin. The structure of our PBPK model was similar to that reported previously, except for having the target binding components in the hepatocellular compartments (Koyama et al., 2021). To accommodate the large volume of distribution observed with warfarin, the central (blood) compartment was connected to three large-volume tissues (adipose, muscle, and skin) with the assumption of rapid equilibrium and using the tissue-to-blood partitioning coefficients (Kp) calculated in silico using the method reported by Rodgers and Rowland (2006). Orally administered warfarin was assumed to be completely absorbed from the intestine to the extrahepatic compartment with a first-order absorption rate constant ka (/h), similar to the previous report (Bi et al., 2018). The hepatic disposition processes of warfarin were described by incorporating the following components: active influx by OAT2, metabolism by cytochrome P450 enzymes, and target binding to VKOR.
Structure of the warfarin PBPK model incorporating saturable components for the hepatic active influx, metabolism, and target binding in the liver. Parameters are defined in the main text and Supplemental Material.
Our PBPK model was fitted to the reported average blood PK profiles of warfarin with no stereoisomeric separation [2, 5, and 10 mg (King et al., 1995); 0.1 mg (Lappin et al., 2006)] (Fig. 2A). The analysis included no interindividual variability, as we had no access to individual-level data. Initially, the modeling was done using ordinary differential equations (ODEs), which did not separate R- and S-warfarin. The model included a total of 24 parameters, including six unknown and 18 fixed parameters (Table 1). Subsequent analyses < RS#1–#3 > used the same reported blood PK dataset, but the ODEs were separated for R- and S-warfarin. Stereoselective parameters were estimated from the information available in the literature. The model included a total of 26 parameters, including six unknown (four stereoselective parameters; total amount of the receptor XTotalR and ka kept the same for R- and S-warfarin) and 20 fixed parameters (Table 2).
Blood PK (A) and TO (B) profiles of warfarin (racemic mixture) using the accepted parameter sets from the CGNM-based PBPK modeling of the warfarin blood PK data [2, 5, and 10 mg from King et al. (1995) and 0.1 mg from Lappin et al. (2006)] with the ODEs not separated for R- and S-warfarin. For each dose, open symbols represent the observed data and lines represent the profiles with the accepted parameter sets. The accepted parameter sets (n = 663) were used to draw the profiles, but the results were overlapping and appeared as a nearly single profile for each dose level.
List of optimized and fixed parameters in the warfarin PBPK model with the ordinary differential equations of no stereoisomeric separation
For parameter optimization by the Cluster Gauss-Newton Method (CGNM), the initial estimates were set with the upper and lower ranges as specified from 10−2 and 102-fold to the base values from the literature.
List of optimized and fixed parameters in the stereoselective warfarin PBPK model with the ordinary differential equations of stereoisomeric separation
The parameters were kept the same as Table 1 except for the stereoselective parameters listed below. Out of the six optimized parameters, the two parameters XTotalR and ka were assumed to be same between R- and S-warfarin.
Parameters for the Warfarin PBPK Model
The hepatic permeability clearance of warfarin was considered by incorporating the active influx clearance mediated mainly by OAT2 [permeability surface product (PS)act,inf described using maximum rate in the Michaelis-Menten equation Vmax(act,inf) and Km(act,inf)] along with the permeability clearance via passive influx and efflux (PSdif,inf and PSdif,eff, respectively). The experimentally measured Km(act,inf) values for R- and S-warfarin were reported to be 7.3 and 10.4 μM, respectively (Bi et al., 2018). The same study reported the Vmax(act,inf) and PSdif,inf values (per million hepatocytes), yielding the corresponding values of 3063 μmole/h and 12.0 l/h for an adult of 70 kg body weight (the following scaling factors were used; 118 million hepatocytes/g liver; 24.5 g liver/kg body weight). For the initial model fitting of the warfarin PK profiles, Vmax(act,inf) was set as unknown (the lower and upper ranges set as 10−2 and 102-fold to the base value 3063 μmole/h), and Km(act,inf) was fixed as 8.85 μM (Table 1). Subsequent analyses < RS#1–#3 > considered the stereoselective differences for Km(act,inf) (fixed as 7.3 and 10.4 μM for R- and S-warfarin, respectively) and Vmax(act,inf) [optimized for R-warfarin; the reported fold difference of 0.506 was then used to calculate the corresponding value for S-warfarin (Bi et al., 2018)] (Table 2).
The intrinsic metabolic clearance (CLint(met)) of warfarin in the hepatocellular compartment was described using Vmax(met) and Km(met). For the model fitting of the warfarin PK profiles, Km(met) was fixed as 10 μM, considering the reported Km(met) values ranging from 3.9 to 24.3 μM (Shaik et al., 2016). The previous study reported the CLint(met) values of 0.1175 and 0.365 μmol/min/mg microsomal protein for R- and S-warfarin, respectively (Bi et al., 2018). By applying the scaling factors (40 mg microsomal proteins/g liver; 24.5 g liver/kg body weight) and using the assumed Km(met) value (10 μM), the Vmax(met) values were estimated as 4.145 and 12.88 l/h for R- and S-warfarin, respectively. For the initial model fitting of the warfarin PK profiles, Vmax(met) was set as unknown (the lower and upper ranges set as 10−2 and 102-fold to the base value 8.511 μmole/h) (Table 1). Subsequent analyses < RS#1–#3 > considered the stereoselective differences for Vmax(met) [optimized for R-warfarin; the reported fold difference of 3.10 was used to calculate the corresponding value for S-warfarin (Bi et al., 2018)] (Table 2).
The target binding of warfarin was modeled to be connected to the hepatocellular compartment [reflecting the primary location of VKOR inside hepatocytes (Hazelett and Preusch, 1988)] with the assumption that warfarin binds reversibly to VKOR in the stoichiometric ratio of 1:1 with the dissociation rate constant koff and the equilibrium dissociation constant Kd (the association rate constant kon was defined automatically as koff/Kd). For the initial model fitting of the warfarin PK profiles, the parameters of koff, Kd, and XTotalR were set as unknown parameters [with the base values based on the previous report (Levy et al., 2003); Table 1] using the following eqs. 1 and 2:
(XFreeR(i), XRDcomplex(i), and XTotalR(i) represent the amounts of free target, drug-target complex, and total target in the ith hepatocellular compartment, respectively; fh and CHC(i) represent the fraction of unbound warfarin and the total concentration of warfarin in the ith hepatocellular compartment, respectively).
Subsequent analysis < RS#1–#3 > used the ODEs separated for R- and S-warfarin except for eq. 3, which was revised from eq. 1 to consider the competitive interactions of S- and R-warfarin for the free target:
(XRDcomplex(i),R-warfarin and XRDcomplex(i),S-warfarin represent the amounts of drug-target complex by the respective R- and S-isomers in the ith hepatocellular compartment; CHC(i),R-warfarin and CHC(i),S-warfarin represent the total concentration of R- and S-warfarin in the ith hepatocellular compartment, respectively).
The analyses of < RS#2 > and < RS#3 > incorporated S-warfarin having the Kd value 3-fold lower than R-warfarin but assumed the stereoselective differences at the association and dissociation steps, respectively (Table 2).
Parameter Optimization by the Cluster Gauss-Newton Method
Being computationally efficient and robust in obtaining multiple possible solutions to nonlinear least-square problems, the Cluster Gauss-Newton method (CGNM) has been recently applied to the PBPK modeling of bosentan (Koyama et al., 2021) and CP-1 (Mochizuki et al., 2022; Yoshikado et al., 2022). A key assumption of the CGNM is that for some model parameters not identifiable from the data, multiple parameter combinations may provide equally as good model fits as the best model fit. Briefly, the CGNM finds multiple best-fit parameter combinations by repeating the parameter estimations from a wide range of initial iterates. Our initial analysis with the ODEs of no stereoisomeric separation uniformly and randomly generated 1000 initial combinations of six unknown parameters (Kd, koff, XTotalR, ka, Vmax(met), and Vmax(act,inf)) with user-specified upper and lower ranges (typically 10−2 to 102-fold to the base values; Table 1). Then using each of these parameter combinations as the initial iterate, the parameter combination was iteratively moved until it reached the minimum sum of squared residuals (SSR) as defined below:
(yobs,i, the ith observed value; ymodel-predicted,i, the ith model-predicted value)
As the above-mentioned approach using a conventional nonlinear least-squares algorithm (e.g., Gauss-Newton method) is computationally intensive, the CGNM was made to remedy the computational bottleneck [see Aoki et al. (2020) for detailed comparison with conventional algorithms].
The PBPK modeling was done by numerically integrating a set of ODEs by RxODE version 1.1.2 with default setting (Fidler et al., 2022), and the CGNM was implemented in R version 4.0.3, CGNM package version 0.3.1 (Aoki, 2022) with default setting except having a set number of initial parameter combinations (num_minimizersToFind) to 1000 and the number of iteration (num_iteration) to 100 as suggested in the user manual. To select parameter combinations from final iterates with similarly small SSR values, the SSR values from parameter combinations were plotted in ascending order. In theory, we wish to find parameter combinations with identical minimum SSR values. However, in reality, it is often not possible with numerical artifacts. Thus, we used a heuristic called the “elbow method” to detect a sudden increase in SSR. Before we applied the elbow method, we rejected parameter combinations that were statistically significantly worse than the minimum SSR by assuming chi square distribution of SSR (with cutoff alpha 0.05). If there were multiple sudden increases in SSR, the elbow method may not find the first sudden increase. In that case, the elbow method was repeated until similarly small SSRs were selected. The analysis was conducted using acceptedApproximateMinimizers command in the CGNM package, and the resulting selections of parameter combinations were referred to as “accepted.”
Parameter Estimation Uncertainty Quantification by the Bootstrap Analysis
To quantify the parameter estimation uncertainty, residual resampling bootstrap analyses were conducted by creating 200 bootstrap datasets and re-estimating the parameters. Each re-estimation was conducted from an initial iterate randomly selected from the accepted parameter combinations. This analysis was conducted using Cluster_Gauss_Newton_Bootstrap_method command in CGNM package, and the parameter distributions obtained from the bootstrap analysis were plotted as histograms.
Post Hoc Study Design Evaluation To Assess the Importance of Dose Selection for the Estimation of Target Binding-Related Parameters
To assess how the study design, in terms of dose selection, can impact the estimation of target binding-related parameters (Kd, koff, and XTotalR), we investigated their estimation uncertainties with varying three-dose-level designs. The following designs were created by removing one dose arm from the full dataset: < design A> contains 2, 5, and 10 mg arms; < design B> contains 0.1, 5, and 10 mg arms; <design C> contains 0.1, 2, and 5 mg arms; < design D> contains 0.1, 2, and 10 mg arms. CGNM was used to obtain accepted parameter combinations for each dataset, and then the bootstrap analyses were conducted for Kd, koff, and XTotalR for each dataset.
Results
CGNM-Based Parameter Optimization for Warfarin PBPK Modeling and Prediction of TO Profiles
Our PBPK-TO modeling analyzed the reported nonlinear PK profiles of warfarin over 120 hours at four warfarin dose levels (0.1, 2, 5, and 10 mg) (Fig. 2A). The “accepted” parameter sets (determined by the elbow method described in the Materials and Methods section) showed nearly identical SSR values of around 0.115 (Table 3). When the CGNM runs were repeated two additional times with different initial iterates, the results were nearly identical (Supplemental Table 1). Five out of six optimized parameters were distributed in a very tight range, with the “rank 1” parameter values (with the smallest SSR) and median values nearly identical. The exception was for Vmax(act,inf), which varied widely among the accepted parameter sets. Similar to our previous study of bosentan (Koyama et al., 2021), the CGNM-based PBPK modeling of the blood warfarin PK profiles alone appeared to achieve practical identifiability for three parameters related to the target binding in vivo (Kd, koff, and XTotalR).
Summary of the accepted parameters (n = 663 sets, SSR ranging from 0.11526 to 0.11532, rank 1 values in bold) for the CGNM run analyzing the blood PK data from all four warfarin dose levels with no stereoisomeric consideration (results shown in Fig. 2) and additional secondary parameters calculated for metabolic clearance (CLmet,inf), permeability clearance (PSact,inf), and overall intrinsic clearance (CLint,all).
For all four dose levels, the accepted parameter sets well captured the observed blood PK profiles and predicted the TO profiles in a narrow range for each dose level (Fig. 2). Despite a wide variation in the Vmax(act,inf) values among the 663 sets of the accepted parameters, the accepted parameter sets yielded overlapping blood PK profiles, which appeared as nearly a single profile for each dose level (Fig. 2A). Such good agreements could be explained by the calculation results showing nearly identical values of 11.93 l/h for the overall intrinsic clearance (CLint,all based on the extended clearance concept model) despite a wide variation in the Vmax(act,inf) values (Table 3). These results support that the active uptake is unlikely to be rate determining in the overall hepatic elimination of warfarin. The 663 sets of the accepted parameter combinations also led to the simulated TO profiles, which appeared as nearly a single profile for each dose level (Fig. 2B). The ranges of the accepted parameters were very narrow, with the rank 1 and median values nearly identical. As an example, the rank 1 parameter combinations were used to simulate the TO profiles. The maximum TO values were 0.064, 0.818, 0.952, and 0.980 for 0.1, 2, 5, and 10 mg, respectively. The predicted TO values at 120 hours postdosing were 0.050, 0.574, 0.757, and 0.859 for 0.1, 2, 5, and 10 mg, respectively.
Impact of Dose Selection on Prediction of Warfarin TO Profiles via PBPK-TO Modeling
To examine whether and how much dose selection impacts parameter estimation and TO prediction from the blood PK data, the CGNM results were compared using four study designs of three-dose-level combinations. Similar to < ALL dataset (0.1, 2, 5, and 10 mg)>, all four study designs < designs A to D> well captured the observed blood PK profiles (Fig. 3A) and predicted the TO profiles in a tight range (Fig. 3B). < Design A> omitting the dose of 0.1 mg yielded the rank 1 parameter values comparable to those from < ALL dataset>, except for koff (0.0903 vs. 0.0432/h; 2.1-fold differences) and Vmax(act,inf) (Fig. 4A; Table 4). The ranges of the final parameters were very narrow, yielding nearly identical values for the rank 1 and median values. The rank 1 parameter koff value (0.0432/h) from < design A> was comparable to the reported koff value (0.0405/h) from the previous TMDD-PK modeling, which had analyzed the 2-, 5-, and 10-mg doses (Levy et al., 2003). For < designs B, C, and D>, which included 0.1 mg data, the accepted parameters also well captured the observed blood PK profiles of warfarin and predicted the TO profiles in a tight range (Fig. 3). Unlike < design A>, the rank 1 parameter values for koff were comparable between < designs B, C, and D> and < ALL dataset>: 0.0961, 0.932, 0.0901 versus 0.0903/h (Table 4). The bootstrap analysis informed that < design A> was associated with greater uncertainty in parameter estimation, noticeably, for the two parameters related to the target binding (Kd and koff) (Fig. 4B). Compared with < design A>, the uncertainty in parameter estimation was reduced to some extent in < design B> and to a greater extent in < designs C and D>, which included both 0.1 and 2 mg, noticeable for XTotalR (Fig. 4B).
Blood PK (A) and TO (B) profiles of warfarin using varying three-dose-level combinations: designs A to D. For each dose (shown in different colors), open symbols represent the observed data and lines represent the profiles with the accepted parameter sets. The accepted parameter sets were used to draw the profiles, but the results were overlapping and appeared as a nearly single profile for each dose level.
(A) Distribution of the accepted parameter sets from the CGNM runs using varying three-dose-level combinations: designs A to D. The closed circles represent median values and the dashed lines are drawn from the minimum to maximum values, whereas the solid lines mark quartile values. The bandwidth represents kernel density estimated by Silverman’s method. (B) Histograms for the bootstrap distribution of the accepted parameter sets from the CGNM runs using designs A to D.
Summary of the accepted parameters (rank 1 values in bold; minimum, maximum, and median values in parentheses) for the CGNM runs using the blood PK data from all four warfarin dose levels (ALL) or varying three-dose level designs (Designs A–D) and additional secondary parameters calculated for metabolic clearance (CLmet,inf), permeability clearance (PSact,inf), and overall intrinsic clearance (CLint,all)
Warfarin PBPK-TO Modeling Incorporating Stereoselective Differences and Prediction of TO Profiles by Individual Stereoisomers
For the scenario of < RS#1 > (with stereoselective consideration in the hepatic metabolism and uptake processes but not in target interactions), the accepted parameter sets well captured the reported blood PK profiles of warfarin (measured with no stereoisomeric separation) at all four dose levels (sold black lines, Fig. 5A). The predicted blood PK profiles for S-warfarin declined more rapidly than those for R-warfarin, in line with the calculated CLint,all values of 20.7 and 7.29 l/h for S- and R-warfarin, respectively (Table 5). At the dose levels of 0.1 and 2 mg, the simulated TO profiles for S- and R-warfarin decreased over 120 hours, with a more rapid decline for S-warfarin than R-warfarin (Fig. 5A). At the dose levels of 5 and 10 mg, the TO profiles by S-warfarin declined steadily, but those by R-warfarin increased over time, attributable to the increasing engagement of R-warfarin to the target that became available from the dissociation of the target complexed with S-warfarin (Fig. 5A).
Summary of the stereoselective PBPK-TO modeling (< RS #1, RS#2, and RS#3 >) of R- and S-warfarin based on the warfarin blood PK data (0.1, 2, 5, and 10 mg racemic warfarin doses). (A) The < RS #1 > incorporated the R- vs. S-warfarin differences in the hepatic metabolism and uptake processes but no differences in target interactions (Kd values kept the same for R- and S-warfarin). (B and C) Whereas < RS#2 > assumed that Kd differences arise from the association process (i.e., kon,S-warfarin being three times to kon,R-warfarin), < RS#3 > assumed that Kd differences arise from the dissociation process (i.e., koff,S-warfarin being one-third to koff,R-warfarin). Blood PK and TO profiles of warfarin (separate profiles for S- and R-warfarin shown in purple and orange, respectively; combined profiles for both R- and S-warfarin shown in gray). For each dose, symbols represent the observed data and lines represent the profiles with the accepted parameter sets, which appear to overlap.
Summary of the CGNM runs < RS#1–#3 > analyzing all four warfarin dose levels with stereoselective considerations applied (as described in Table 2): the accepted parameters (rank 1 values in bold; minimum, maximum, and median values in parentheses) and additional secondary parameters calculated for metabolic clearance (CLmet,inf), permeability clearance (PSact,inf), and overall intrinsic clearance (CLint,all)
The scenarios of < RS#2 > and < RS#3 > assumed 3-fold differences in the target affinity (Kd) between R- and S-warfarin (S-warfarin having a 3-fold lower Kd value than R-warfarin), arising from the differences at the association and dissociation steps, respectively. In either scenario, the PBPK models captured the reported blood PK profiles of warfarin with the accepted SSR comparable to those of < RS#1 > (Fig. 5, B and C; Table 5). For < RS#2 > (S-warfarin with 3-fold greater kon than R-warfarin), the simulation results showed that at early time points, the target engagement was dominated by S-warfarin over R-warfarin: at 2 hours postdosing, the target engagement by S-warfarin was greater by 1.56-, 1.93-, 2.29- and 2.46-fold than by R-warfarin at the 0.1-, 2-, 5-, and 10-mg dose levels, respectively (Fig. 5B). However, the target engagement by R-warfarin was predicted to be dominant from approximately 60 hours postdosing on (Fig. 5B, appearing as crossover points in the simulated TO profiles). Different from < RS#2 >, the results from < RS#3 > (S-warfarin assumed to have one-third koff to R-warfarin) predicted the target engagement comparable between R- and S-warfarin at early time points, especially within 1 hour postdosing (Fig. 5C). The target engagement by S-warfarin stayed dominant over R-warfarin until the crossover points at approximately 60 hours postdosing (Fig. 5C).
Discussion
The current study developed a PBPK-TO model that can analyze the systemic warfarin PK profiles and predict TO profiles in vivo. Like the case of bosentan (Koyama et al., 2021), the CGNM-based analysis of the systemic warfarin PK profiles alone yielded practically identifiable target binding parameters and predicted TO profiles in a very tight range (Fig. 2; Table 3). Further analyses indicated that dose selection (the inclusion of 0.1-mg dose, which leads to systemic drug exposure well below target saturation) is important in reducing the uncertainty in estimating target binding-related parameters (Fig. 4; Table 4). By incorporating the stereoselective differences between R- and S-warfarin, the current PBPK-TO model predicted the target engagement of each stereoisomer under differing scenarios (Fig. 5). Overall, these findings extend the validity of the approach by which the mechanistic PBPK-TO modeling captures the impact of saturable target binding on the systemic PK data and, in turn, allows for the identification of target binding parameters (thereby, TO profiles in vivo) based on the systemic PK data alone.
In developing the current PBPK-TO model, the two previous reports on warfarin PK modeling provided a key foundation (Levy et al., 2003; Bi et al., 2018). Bi et al. (2018) provided the estimates for various parameters of the PBPK model, including the handling of warfarin by OAT2. The authors reported that the active uptake of warfarin mediated by OAT2 contributes to the interpatient variability (Bi et al., 2018). Those results are not contradictory to those from our current study in that the interpatient variability of CLint,all may be impacted by both PSact,inf and CLmet,int (shown in eq. 2 and Table 3 footnote). If one compares, regarding their relative contribution to interpatient variability associated with CLint,all, CLmet,int is likely to have a greater contribution than PSact,inf, which has additional terms of γ and PSdif,inf in eq. 2. Different from the previous TMDD modeling of warfarin based on the compartmental model with the target binding component connected to the central component (Levy et al., 2003), our current PBPK-TO model incorporated target binding connected to the hepatocellular compartment (reflecting the primary location of VKOR in hepatocytes) (Fig. 1). During CGNM-based parameter optimization in our current study, the initial parameter sets were randomly selected from the ranges covering 10−2- to 102-fold to the base values from the previous reports (Tables 1 and 2). Despite having four orders of magnitude ranges in which initial iterates could be selected, our analysis with the ODEs of no stereoisomeric separation yielded the final optimized parameters for target binding in vivo in a tight range, indicating that these parameters are identifiable from the plasma concentration data: the rank 1 and median parameter values were nearly identical, being 6.30 nM, 0.0903/h, and 4.26 μmole for Kd, koff, and XTotalR, respectively (Table 3). In the literature, the Kd values for the binding of warfarin to VKOR vary widely, attributable in part to the differences in in vitro binding assay conditions (in particular, the presence of reducing agents altering the redox state of VKOR) (Bevans et al., 2013; Shen et al., 2017). Our current study supports the predictive utility of the PBPK-TO modeling for in vivo target binding parameters when the blood PK profiles are available with appropriate dose selection.
The model-predicted target abundance (XTotalR) for warfarin was 4.26 μmole for 70-kg human body (Table 3). For warfarin doses of 0.1 and 2 mg (corresponding to 0.325 and 6.49 μmole, respectively), the high-affinity interaction of the drug with the target (XTotalR of 4.26 μmole) may represent a significant fraction of the doses. The binding mode of warfarin to VKOR is not fully understood, and some controversies still exist as to whether the binding is reversible (Wu et al., 2018). When the formation of the warfarin-target complex is assumed to be reversible (thus not serving as a clearance mechanism), the high-affinity interactions between warfarin and its target may still impact the volume of distribution (Vd) by providing additional drug distribution space to which the drug initially and preferentially distributes. The Vd values calculated using noncompartmental analysis confirm such a nonlinear relationship for the blood PK dataset analyzed in the current study (Fig. 6A). In theory, at a very low dose, the apparent Vd would approximate the summation of XTotalR/Kd and Vd via nonspecific (non–target-mediated) tissue binding, Vd(nontarget), as illustrated in Fig. 6B. With escalating doses, the high-affinity target binding becomes saturated and no longer contributes to apparent drug distribution space (thus approximating Vd(nontarget)). In the case of warfarin and other drugs with targets of high affinity and abundance (i.e., small Kd and large XTotalR) and limited distribution via nonspecific tissue binding (i.e., small Vd(nontarget)), the substantial contribution of XTotalR/Kd to the Vd can be expected, noticeable especially at low doses. For highly lipophilic drugs with less confined tissue distribution (i.e., large Vd(nontarget)), the impact of target binding would be minimal or not readily discernible (Fig. 6B). For small-molecule drugs that feature large XTotalR/Kd and small Vd(nontarget) values, it can be postulated that the PK data at low doses, including a microdose, can provide valuable information in ascertaining the ratio of XTotalR/Kd. When the dose ranges cover from low (well below target saturation; informative on XTotalR/Kd) and high doses (at target saturation; informative on Vd(nontarget)), the analysis of the systemic PK data alone may allow for the prediction of TO with reasonable certainty.
(A) Parameters (CL/F and Vd/F) calculated via noncompartmental analysis of the observed blood PK profiles of warfarin [2, 5, and 10 mg from King et al. (1995) and 0.1 mg from Lappin et al. (2006)]. (B) A theoretical basis for the impact of dose selection on the apparent Vd for drugs that interact with targets of high affinity and abundance. Modeling-based analysis of the systemic PK data from low and intermediate doses (with varying levels of target saturation) can provide valuable information ascertaining the ratio of XTotalR/Kd, thereby reducing uncertainty in the estimation of target binding parameters.
Our current results using warfarin imply a potentially important yet underappreciated advantage that the PBPK modeling and microdosing approach may offer for the development of small-molecule drug candidates with potential for TMDD (Burt et al., 2020). If a drug candidate is predicted to have a significant contribution to the target binding-related component (i.e., large XTotalR/Kd and relatively small Vd(nontarget)), our proposal is to verify the in vivo occurrence of the TMDD in preclinical animals by obtaining the blood PK data with ascending doses, including a microdose and intermediate and high doses (covering varying degrees of target binding). In the case of warfarin, the blood PK data in rats clearly indicated much larger Vd values in those receiving 0.1 mg/kg than in those receiving 1 mg/kg (Takada and Levy, 1980). With appropriate consideration of the species differences in the target binding-related parameters (e.g., XTotalR, Kd, unbound fraction), it may be possible to identify drug candidates with a high likelihood of TMDD in humans. In such cases, the blood PK data from a microdosing study and PBPK-TO modeling can provide invaluable insights into TO profiles in vivo, potentially guiding the interpretation and optimization of pharmacodynamic responses in humans. The prospect of obtaining the TO profiles in vivo from the blood PK data alone may aid in overcoming the difficulties in translating in vitro potency to in vivo efficacy.
By incorporating the stereoselective differences in hepatic disposition and target binding between R- and S-warfarin, the current PBPK-TO model analyzed the blood PK profiles of warfarin (measured with no stereoisomeric separation) and predicted the TO profiles by individual stereoisomers under differing scenarios. Both < RS#2 > and < RS#3 > shared the assumption that S-warfarin has a 3-fold higher affinity than R-warfarin (i.e., Kd,S-warfarin being one-third to Kd,R-warfarin) based on the information available in the literature (Breckenridge et al., 1974; O’Reilly, 1974; Hignite et al., 1980). Whereas < RS#2 > assumed that Kd differences arise from the association process (i.e., kon,S-warfarin being three times to kon,R-warfarin), < RS#3 > assumed that Kd differences arise from the dissociation process (i.e., koff,S-warfarin being one-third to koff,R-warfarin). Currently, there is no data that experimentally verified the stereoselective differences in the binding affinity of R- and S-warfarin. Of note, Cheng et al. (2023) applied the PK modeling with the TMDD components to the observed plasma PK profiles of S- and R-warfarin independently. The results showed 3.61-fold differences in the Kd values of S- and R-warfarin (in line with the assumption of 3-fold Kd differences in our current study). Molecular docking simulation predicted more energetically favorable interactions for S-warfarin than for R-warfarin in binding with human VKOR (Lewis et al., 2016). Yet, it remains to be verified whether the stereoselective differences between S- and R-warfarin in interacting with VKOR involve association, dissociation, or both. In our analysis, the TO profiles by individual stereoisomers showed some differences between < RS#2 > and < RS#3 > (Fig. 5). However, between < RS#2 > and < RS#3 >, little differences were observed in the summed TO profiles by R- and S-warfarin. These results may be explained by the compensatory, competitive formation of the drug-target complex between R- and S-warfarin. For instance, S-warfarin is more rapidly cleared than R-warfarin and the equilibrium gets shifted toward the dissociation of the S-warfarin–target complex, and the dissociated target would become available to complex with R-warfarin. When the TO profiles were simulated for a typical repeated warfarin dosing regimen (10 mg for 2 days and 3 mg afterward), the results also showed a similar profile of the compensatory formation of R-warfarin–target complex (Supplemental Fig. 1). As such, the dosing of racemic warfarin may prolong the target engagement and produce the target engagement and pharmacodynamic effect with a lesser degree of inter- and intraindividual variability than the dosing of single stereoisomeric warfarin.
In conclusion, we successfully developed and applied an updated PBPK-TO model to analyze the blood PK profiles of warfarin over a wide dose range, including a microdose. Our results using warfarin support the approach by which target engagement in vivo may be predicted with reasonable certainty from the analysis of the systemic PK data impacted by target binding. Opportunity for prediction of target engagement in vivo may be attainable with the model-informed selection of a dose range covering a varying extent of target saturation, in particular by including low doses below target saturation during dose escalation of clinical phase 1 trials. Information obtained on target engagement in vivo can serve as a valuable guide and tool in interpreting and optimizing pharmacodynamic responses.
Acknowledgments
The authors would like to thank Satoshi Koyama and Kota Toshimoto (Astellas Pharma Inc.) for the support in conducting the initial PBPK modeling. Byung Woo Han, Jin Mo Kang (Seoul National University), and Sangwook Wu (Pukyong National University) are acknowledged for their helpful discussion regarding the interpretation and prediction of the target binding kinetics of warfarin.
Data Availability
The authors declare that all the data supporting the findings of this study are contained within the paper.
Authorship Contributions
Participated in research design: Lee, Aoki, Sugiyama.
Performed data analysis: Lee, M-S. Kim, J. Kim, Aoki, Sugiyama.
Wrote or contributed to the writing of the manuscript: Lee, M-S. Kim, J. Kim, Aoki, Sugiyama.
Footnotes
- Received May 30, 2022.
- Accepted March 9, 2023.
Financial support for this research was provided by the international cooperation program managed by the National Research Foundation of Korea [Grant NRF-2020K2A9A2A08000172] (to W.L.), Creative-Pioneering Researchers Program through Seoul National University (to W.L.), Grant-in-Aid for Scientific Research (B) [Grant JP19H03392] (to Y.S.), and JSPS Bilateral Program [Grant JPJSBP 120208820] (to Y.S.).
No author has any potential conflict of interest to disclose.
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This article has supplemental material available at dmd.aspetjournals.org.
Abbreviations
- CGNM
- Cluster Gauss-Newton method
- CLint, all
- overall intrinsic clearance
- CLint(met)
- intrinsic metabolic clearance
- ka
- absorption rate constant
- Kd
- equilibrium dissociation constant
- koff
- dissociation rate constant
- kon
- association rate constant
- Kp
- tissue-to-blood partitioning coefficients
- OAT2
- organic anion transporter 2
- ODE
- ordinary differential equation
- PBPK
- physiologically based pharmacokinetic
- PK
- pharmacokinetic
- PS
- permeability surface product
- SSR
- sum of squared residuals
- TMDD
- target-mediated drug disposition
- Vd
- volume of distribution
- VKOR
- vitamin K 2, 3-epoxide reductase
- Vmax
- maximum rate in the Michaelis-Menten equation
- XTotalR
- total amount of the receptor
- Copyright © 2023 by The American Society for Pharmacology and Experimental Therapeutics
