INTRODUCTION PATRICK POULIN. Consultant, Québec city, Québec, Canada

Transcription

1 RESEARCH ARTICLE Pharmacokinetics, Pharmacodynamics and Drug Transport and Metabolism A Paradigm Shift in Pharmacokinetic Pharmacodynamic (PKPD) Modeling: Rule of Thumb for Estimating Free Drug Level in Tissue Compared with Plasma to Guide Drug Design PATRICK POULIN Consultant, Québec city, Québec, Canada Received 9 March 2015; revised 7 April 2015; accepted 7 April 2015 Published online 5 May 2015 in Wiley Online Library (wileyonlinelibrary.com). DOI /jps ABSTRACT: A basic assumption in pharmacokinetics pharmacodynamics research is that the free drug concentration is similar in plasma and tissue, and, hence, in vitro plasma data can be used to estimate the in vivo condition in tissue. However, in a companion manuscript, it has been demonstrated that this assumption is violated for the ionized drugs. Nonetheless, these observations focus on in vitro static environments and do not challenge data with an in vivo dynamic system. Therefore, an extension from an in vitro to an in vivo system becomes the necessary next step. The objective of this study was to perform theoretical simulations of the free drug concentration in tissue and plasma by using a physiologically based pharmacokinetics (PBPK) model reproducing the in vivo conditions in human. Therefore, the effects of drug ionization, lipophilicity, and clearance have been taken into account in a dynamic system. This modeling exercise was performed as a proof of concept to demonstrate that free drug concentration in tissue and plasma may also differ in a dynamic system for passively permeable drugs that are ionized at the physiological ph. The PBPK model simulations indicated that free drug concentrations in tissue cells and plasma significantly differ for the ionized drugs because of the ph gradient effect between cells and interstitial space. Hence, a rule of thumb for potentially performing more accurate PBPK/PD modeling is suggested, which states that the free drug concentration in tissue and plasma will differ for the ionizable drugs in contrast to the neutral drugs. In addition to the ph gradient effect for the ionizable drugs, lipophilicity and clearance effects will increase or decrease the free drug concentration in tissue and plasma for each class of drugs; thus, higher will be the drug lipophilicity and clearance, lower would be the free drug concentration in plasma, and, hence, in tissue, in a dynamic in vivo system. Therefore, only considering the value of free fraction in plasma derived from a static in vitro environment might be biased to guide drug design (the old paradigm), and, hence, it is recommended to use a PBPK model to reproduce more accurately the in vivo condition in tissue (the new paradigm). This newly developed approach can be used to predict free drug concentration in diverse tissue compartments for small molecules in toxicology and pharmacology studies, which can be leveraged to optimize the pharmacokinetics drivers of tissue distribution based upon physicochemical and physiological input parameters in an attempt to optimize free drug level in tissue. Overall, this present study provides guidance on the application of plasma and tissue concentration information in PBPK/PD research in preclinical and clinical studies, which is in accordance with the recent literature. C 2015 Wiley Periodicals, Inc. and the American Pharmacists Association J Pharm Sci 104: , 2015 Keywords: ADME; unbound fraction; pharmacokinetics; pharmacodynamics; disposition; distribution; partition coefficients; PBPK; PKPD INTRODUCTION In preclinical and clinical studies, total drug concentrations in plasma or tissue are often correlated with pharmacodynamics (PD). However, the use of total tissue levels (e.g., tissue concentrations derived from homogenates) or biopsies to draw direct conclusions on drug activity is unwarranted and/or unreliable. 1 4 This is in contrast with the unbound (free) drug concentration at the target site, which should be more pharmacologically relevant. 1 4 Related to this, recent reviews highlighted various examples from the literature where the free Abbreviations used: C max, maximal plasma concentration; fu p, free fraction in plasma; fui p, fraction unionized in plasma; fu t, free fraction in tissue; fui t, fraction unionized in tissue; Kp, tissue plasma partition coefficient; Kpu, unbound tissue water partition coefficient; log P, logn-octanol buffer partition coefficient; i.v., intravenous; PBPK, physiologically based pharmacokinetics; PK, pharmacokinetics; PK/PD, pharmacokinetics pharmacodynamics; pka, ionization constant; RBP, blood plasma ratio. Correspondence to: Dr. Patrick Poulin (Telephone: ; patrick-poulin@videotron.ca) Journal of Pharmaceutical Sciences, Vol. 104, (2015) C 2015 Wiley Periodicals, Inc. and the American Pharmacists Association drug concentration in tissue has demonstrated a superior correlation with the efficacy compared with the free drug concentration in plasma. 1,2 Therefore, the in vivo pharmacokinetics pharmacodynamics (PK/PD) research should rely on the assumption that the free drug level at the site of action in tissue is the relevant measure of drug effect. However, tissue data are rarely available in humans, and, hence, a basic assumption in PK/PD research is that the free drug concentration is similar in plasma and tissue; thus, the free drug concentration in plasma can be used to estimate that concentration in tissues. In other words, the free drug concentration in the aqueous phase should be equal in the different organs under steady-state condition and when passive permeability is the main factor governing the drug transport. Hence, the traditional approach in drug design is to use the unbound free fraction in plasma (fu p ) determined in vitro to estimate the free drug concentration in tissue under in vivo condition (i.e., fu p total plasma concentration = free fraction in tissue (fu t ) total tissue concentration). 1,2,5 These observations focus on in vitro static environments and do not challenge data with an in vivo dynamic system. Therefore, an extension from an in vitro to an in vivo system Poulin, JOURNAL OF PHARMACEUTICAL SCIENCES 104: ,

2 2360 RESEARCH ARTICLE Pharmacokinetics, Pharmacodynamics and Drug Transport and Metabolism becomes the necessary next step. This is because living systems are dynamic, with many simultaneous physiological actions on the free drug molecules, for example, ph gradient, binding to the target, binding to lipids and proteins, metabolism, movement between cellular and tissue compartment. 2 Accordingly, it is has already been suggested in the literature that the free drug concentration would depend, throughout the time course, on the intrinsic clearance, lipophilicity, and ionization potential of drugs For example, the free drug concentration in plasma and tissue should decrease when the intrinsic clearance value of a drug increases. Similarly, the free drug concentration in plasma and tissue should also decrease as the amount of drug bound to proteins and lipids increases because of the effect of drug lipophilicity. And the free drug concentration in plasma and tissue would also be influenced by drug ionization due to the ph gradient effect between the intracellular and interstitial spaces. Intracellular unbound (free) drug concentrations determine affinity to targets in the cell interior; however, there is a ph gradient effect compared to the interstitial space and plasma. Similalry, extracellular unbound drug concentrations determine affinity to targets in the interstitial space, but there is no ph gradient effect compared to plasma under normal conditions in healthy tissues. Therefore, in cultured cells under in vitro conditions, intracellular accumulation of unbound drug was consistent with ph-dependent subcellular sequestration and compound lipophilicity. 13 Hence, these observations should be further tested with a dynamic in vivo system. In this context, for the ionizable drugs, the ionization state of both the drug and the binding site potentially change as a function of ph. It is indeed important to realize that for bases and acids there are ionized and nonionized fractions that are usually lumped into a single unbound concentration. However, considering that only the unbound unionized drug is able to permeate cell membranes in vivo, the free drug concentration in plasma and tissue, at equilibrium, would differ by the fraction of unionized drug (fui) on both sides of the membrane [i.e., fu p fui p (fraction unionized in plasma) total plasma concentration = fu t fui t (fraction unionized in tissue) total tissue concentration, and, hence, the free drug concentration in plasma and tissue would differ by the ratio of fui p /fui t ] Accordingly, in a companion manuscript, it has been demonstrated that the values of plasma fu p and muscle fu t determined in vitro in humans depended on the physiological ph. 5 In other words, the correlation between the fu p and fu t values was more robust when these two parameters are determined at the same ph value (i.e., 7.4) compared with when fu p and fu t are determined at a different ph value (i.e., ph 7.4 for fu p vs. 7.0 for fu t ). These observations suggest a drug ionization effect in the aqueous phase; therefore, under in vivo condition, the free drug concentration in plasma at ph 7.4 would not equal the free drug concentration in tissue cells at ph 7.0 particularly for the ionizable drugs, which follows the ph partition hypothesis. The lower intracellular ph caused basic drugs to be trapped inside the cell, as they are not able to permeate the cell membrane in the ionized form, and, inversely, for the ionized acids. For interstitial concentrations, the role of microdialysis should also be acknowledged. Microdialysis has become one of the major tools to sample endogenous and exogenous substances in interstitial spaces. 12 As a matter of fact, there are a number of papers using microdialysis, where the unbound drug concentrations in plasma and interstitial space were similar, which was expected as the ph of plasma and interstitial space is similar under normal conditions in healthy tissues, and, hence, the ph gradient effect would be minimal (i.e., fui p /fui t 1). This is true particularly true when passive permeability is the predominant distribution process. For example, the unbound drug concentrations in plasma and the interstitial space of skeletal muscle determined by microdialysis were similar for acetaminophen and gemcitabine as well as for some ionizable drugs. 12 Conversely, the unbound drug concentrations in plasma and the interstitial space significantly differed for other drugs and tissues (e.g., brain); however, this is expected to be governed by efflux transport effects at the membrane level and/or permeation limitation effects at the capillary level. 12 Therefore, the free drug level in human tissue is the relevant metric to optimize on particularly under real dynamic in vivo condition. 1 5 Alternatively, the published tissue compositionbased models, which were successfully validated in the past, can be used to replace the microdialysis as the free and bound drug concentrations can be predicted in both the cellular fraction and interstitial space in human tissues only on the basis of in vitro and physiological input data Hence, the tissueto-plasma concentration ratios observed in humans for several drugs were accurately predicted by considering the dissimilarities in the binding and ionization on both sides of the membrane (i.e., by predicting fu p /fu t fui p /fui t ) To date, the ph gradient and transport effects as well as the binding to lipids and proteins have been incorporated in these models; therefore, they could also be used to explore the differences in the free and bound drug concentrations that can potentially be observed between tissue compartments and plasma under real dynamic in vivo condition. Moreover, the tissue composition-based models can be associated with a physiologically-based (PBPK) model to predict drug distribution in tissues by considering separately the cells and interstial space under dynamic in vivo conditions. Overall, this implies that a drug with a high value of fu p for plasma will indicate important free drug concentration in plasma, and, hence, in tissues, but this is true only in an in vitro static environment; conversely, in a dynamic in vivo system, the free drug concentration in tissue can be much lower than expected based on the in vitro fu p value when the drug in tissue is rapidly cleared, highly bound, and/or ionized, for example. 2,5 At present, this theory needs to be further challenged to guide drug design. The objective of this study was to perform theoretical simulations of the free drug concentration in tissue and plasma by using a PBPK model reproducing the in vivo condition in humans. For the purpose of this study, the dissimilarities in the binding and ionization on both sides of the membrane were investigated for passively permeable compounds (i.e., the dissimilarities in the interstitial and intracellular free drug concentrations were investigated first). Therefore, the effect of drug lipophilicity, ionization, and clearance has been taken into account in a dynamic system. This modeling exercise was performed as a proof of concept to demonstrate that free drug concentration in tissue and plasma may also differ in a dynamic in vivo system, particularly for the ionizable drugs. Accordingly, a rule of thumb for potentially performing more accurate PK/PD modeling research and to guide drug design is suggested in this study. Poulin, JOURNAL OF PHARMACEUTICAL SCIENCES 104: , 2015 DOI /jps.24468

3 RESEARCH ARTICLE Pharmacokinetics, Pharmacodynamics and Drug Transport and Metabolism 2361 hypothesis), and, hence, the dissimilarity in the free drug concentration on both sides of the membrane can be quantified by the dissimilarity in the fraction of drug unionized in plasma and tissue (i.e., fui p /fui t ). 5,8 11 To prove this above assumption under dynamic condition, the current PBPK model was arranged in a way that the free drug concentration in tissue and plasma can be compared separately for the diverse simulation scenarios considered in this study (i.e., fu p total concentration simulated in plasma was compared with fu t total concentration simulated in tissue, and, hence, free drug concentrations in tissue cells and plasma would differ by fui p /fui t ). An arbitrary intravenous (i.v.) bolus administration of 1 mg/kg and an infusion until steady-state condition is reach in tissue were investigated in this study. The secondary pharmacokinetic parameters (i.e., maximal plasma concentration, C max, and area under the curve, AUC last ) for the unbound drug, which we relate to pharmacology and toxicology effects, were simulated in this study for tissue and plasma. Hence, to test the bolus administration condition, the AUC last was simulated, whereas for the infusion study, the C max at steady state was simulated. As a proof of concept, the theoretical simulation exercise was made for plasma and heart in humans, which the later organ represents a relevant target tissue in cardiology study. Nonetheless, this exercise may apply to any other organ because the outcome will be similar. Simulation Scenarios Figure 1. Physiologically-based pharmacokinetics (PBPK) model framework introduced in ADME Workbench R ( based on the literature. 7 The symbol Q is defined as the blood-flow rate. Each organ is described with more details in Figure 2 as well as in Tables 3 and 4. METHOD Theoretical PBPK modeling simulations in humans were made for diverse scenarios to compare the resulting free drug concentration in plasma and tissue. As said, the dissimilarities in the binding and ionization on both sides of the membrane were investigated first. Hence, for passively permeable compounds either ionized or not at the physiological ph, the maximal dissimilarity between the interstitial and intracellular (free) drug concentrations were quantified. PBPK Simulations to Human The simulations were performed in ADME Workbench Software R (version 1.4.2; Aegis Technologies Inc., Orlando, Florida; where a published human PBPK model has been reproduced. 7 The PBPK model is illustrated in Figure 1. The most recent version of a published tissue composition-based model has also been incorporated in that PBPK model to estimate the free and bound drug concentrations in tissue and plasma 5,8 10 (Fig. 2). Nonetheless, if only the unbound unionized drug is able to permeate cell membranes in vivo, then the concentrations of unbound unionized drug in tissue and plasma will equilibrate at steady state (ph partition The plasma and tissue PK was simulated with a PBPK model for 14 simulation scenarios as presented in Tables 1 and 2. These scenarios covered different drug examples (1) hydrophilic and lipophilic drugs, (2) mono and diprotic acids and bases as well as neutral drugs, (3) poorly and highly bound drugs, and (4) slowly and rapidly cleared compounds. Therefore, these simulation scenarios cover a large range of physicochemical and tissue distribution properties that can be observed in a dynamic in vivo system. Modeling Assumptions The theoretical PBPK model simulations were performed by considering the dissimilarities in the binding and ionization on both sides of the membrane in each organ of the PBPK model. Therefore, it was assumed that tissue distribution is determined by a (1) nonspecific binding to lipid components in cells, (2) specific binding to plasma proteins or lipoproteins in tissue interstitial space, (3) ph gradient effect between the intra- and extracellular water, (4) rapid equilibrium between plasma and tissue (i.e., passive permeability), (5) homogeneous tissue distribution, (6) active transport does not contribute significantly to distribution, and (7) distributive processes are nonsaturating. The liver is considered to be the only eliminating organ. No other elimination routes were considered for the purpose of this study. Drug-Specific Input Parameters Estimation of fu p,fu t,fui p and fui t The published tissue composition-based model used in this study is illustrated in Figure 2 as well as in Tables 3 and 4 based on literature. 5,8 10 The corresponding equations and the human tissue composition data are further detailed in two previous studies and in the ADME Workbench Software R. 8,10 Note DOI /jps Poulin, JOURNAL OF PHARMACEUTICAL SCIENCES 104: , 2015

4 2362 RESEARCH ARTICLE Pharmacokinetics, Pharmacodynamics and Drug Transport and Metabolism Figure 2. Distribution mechanisms considered in the published tissue composition-based model associated with a PBPK model. 6,8 11 that the tissue composition-based model has been extensively validated in the last decade, and, hence, this model is suitable for the purpose of this present study. Briefly, the input fu p value for plasma was simply fixed equal to 0.01 and 0.9 for the lipophilic and hydrophilic drugs, respectively, whereas the fu t value for tissue was estimated from the unbound tissue plasma partition coefficient (Kpu), which refers to the tissue aqueous phase partition coefficient [i.e., bound to free ratio, and, hence, fu t = 1/1+Kpu (unbound tissue water partition coefficient)]. The fraction of drug unionized on both sides of the membrane (i.e., fui p and fui t ) was estimated from the ionization constant (pka) value of each drug and the Henderson Hasselbalch equations as well as the corresponding physiological ph values. The estimation of these parameters is further detailed just below. The value of Kpu of each tissue was calculated by considering the dissimilarities in the binding and ionization on both sides of the membrane. The value of log P (n-octanol buffer partition coefficient) was used to estimate the lipids water ratio in a tissue for all classes of drugs, whereas the value of fu p was used to estimate the plasma proteins water or lipoproteins water ratio in the interstitial space for the acids and neutral drugs. The blood plasma ratio (RBP) was used to predict the acidic phospholipids water ratio in the cell membrane for the basic drugs according to the model principles (the value of RBP has been fixed to unity by default). Overall, the model calculated the bound to free ratio (i.e., the tissue water partition coefficient; Kpu), which refers to the ratio between the bound drug concentration in a tissue (i.e., bound to lipids and plasma proteins) and the free drug concentration in plasma water, at equilibrium. As said, the value of fu t in tissue due to drug binding was approximated by 1/(1+Kpu). However, the water content in tissue compared with plasma was also considered; accordingly, the additional effect of drug ionization in water was estimated by the fraction of unionized drug on both sides of the membrane. Hence, the value of fu t fui t /fui p was obtained, and the corresponding values of fui t and fui p were estimated from the pka value of each drug and the Henderson Hasselbalch equations according to the class of drug as presented in Table 3. The physiological ph values were considered (i.e., 7.0 for cells and 7.4 for the extracellular water). The cells and interstitial space fractions observed in each tissue were considered in the calculations of fu t for the global tissue, and, hence, the maximal ph gradient effect can be estimated (i.e., between the intracellular and interstitial spaces). Note that the whole tissue plasma ratio (Kp) of each tissue compartment used in the PBPK model was estimated by the product of fu p /fu t and fui p /fui t,whichis mathematically equivalent to the previously published equations derived from the tissue composition-based model (i.e., Poulin, JOURNAL OF PHARMACEUTICAL SCIENCES 104: , 2015 DOI /jps.24468

5 RESEARCH ARTICLE Pharmacokinetics, Pharmacodynamics and Drug Transport and Metabolism 2363 Table 1. Theoretical Simulation Scenarios Investigated with the Human PBPK Model After 1 mg/kg Given i.v. as a Bolus Dose or an Infusion Under Steady-State Condition for a Monoprotic Acid and Monoprotic Base As Well As a Neutral Drug Example PBPK Model Simulations in Humans Input Parameters Bolus i.v. Unbound AUC last (ng h/ml) Steady-State i.v. Unbound C max (ng/ml) Drugs log P pka fu p a fu t a Ratio fui p /fui t b Hepatic Clearance (ml/min kg) Ratio Heart Cells/Plasma c,d Ratio Heart Cells/Plasma c,d Monoprotic acid (50/125) 0.4(1.1/2.8) (2.8/6.6) 0.4(0.055/0.14) (2870/7134) 0.4(124/312) (250/602) 0.4(6/16) Monoprotic base (29/11.5) 2.5(3.7/1.5) (14.9/4.5) 2.5(0.35/0.14) (5280/2112) 2.5(540/214) (1632/536) 2.5(78/31) Neutral (60/60) 1(6.4/6.4) 20 1(7.5/7.6) 1(0.35/0.35) e 1 1 1(5000/5000) 1(567/567) 20 1(658/660) 1(32.5/32.5) a For the purpose of this study, the value of fu p for plasma was simply fixed equal to 0.01 and 0.9 for the lipophilic and hydrophilic drug, respectively, whereas the value of fu t because of drug binding was estimated with a tissue composition-based model, as explained in the Method. Rounded values. b Ratio of fraction unionized of drug between tissue cells and plasma that was calculated from the Henderson Hasselbalch equations (Table 3). c Derived from the total concentration simulated in plasma fu p as explained in the Method. d Derived from the total concentration simulated in tissue fu t as explained in the Method. e As for a neutral drug the Kp value is equal to the ratio of fu p /fu t, the derived fu t becomes equal to 1.22 but this is an hypothetical situation as the value of fu p has been arbitrarily fixed in this study. Table 2. Theoretical Simulation Scenarios Investigated with the Human PBPK Model After 1 mg/kg Given i.v. as a Bolus Dose or an Infusion Under Steady-State Condition for a Diprotic Acid and Diprotic Base Example PBPK Model Simulations in Humans Bolus i.v. Steady-State i.v. Input Parameters Unbound AUC last (ng h/ml) Unbound C max (ng/ml) Drugs log P pka1 pka2 fu p a fu t a Ratio fui p /fui t b Hepatic Clearance (ml/min kg) Ratio Heart Cells/Plasma c,d Ratio Heart Cells/Plasma c,d Diprotic acid (19.9/125) 0.16(1.2/7.5) Diprotic base (53/8.4) 6.3(8.2/1.3) a For the purpose of this study, the value of fu p for plasma was simply fixed equal to 0.01 and 0.9 for the lipophilic and hydrophilic drug, respectively, whereas the value of fu t because of drug binding was estimated with a tissue composition-based model, as explained in the Method. Rounded values. b Ratio of fraction unionized of drug between tissue cells and plasma that was calculated from the Henderson Hasselbalch equations (Table 3). c Derived from the total concentration simulated in plasma fu p as explained in the Method. d Derived from the total concentration simulated in tissue fu t as explained in the Method. Kp = fu p /fu t fui p /fui t = total concentration in tissue/total concentration in plasma 1+ionization factor for tissue/1+ionization factor for plasma) 5,8 (Tables 3 and 4). Estimation of Clearance To verify the impact of clearance, the hepatic metabolism in the PBPK model was set low or high (i.e., 5% and 90% of the liver blood flow rate in human, respectively), and was described by including the corresponding intrinsic clearance value in the well-stirred model for liver. 7 RESULTS A total of 14 simulation scenarios were evaluated in the present study for the comparison of the simulated C max and AUC last for the unbound drug (used as a measured of free drug concentrations in plasma and heart cells in humans). The comparative assessment is presented in Tables 1 and 2. As expected, the results indicate that free drug concentrations in plasma and tissue cells are not equal as observed by the dissimilarities in the simulated values of C max and AUC last for the unbound drug. This is true only for the ionizable drugs, as for the neutral drugs DOI /jps Poulin, JOURNAL OF PHARMACEUTICAL SCIENCES 104: , 2015

6 2364 RESEARCH ARTICLE Pharmacokinetics, Pharmacodynamics and Drug Transport and Metabolism Table 3. Calculation of the Ionization Effect in the Tissue Composition-Based Model Depicted in Figure 2 and Table 4 Class Standard Approach a Tissue Composition-Based Model a Fraction Unionized (fui) Ionization Factor (I) Monoprotic: fui = X 1+X Diprotic: fui = X 1+X Y 1+Y Monoprotic: 1+I Diprotic: 1+I Acids X = 10 pka-ph X = 10 pka1-ph I = 10 ph-pka I = 10 ph-pka pH-pKa1-pka2 Y = 10 pka2-ph Bases X = 10 ph-pka X = 10 ph-pka1 I = 10 pka-ph I = 10 pka2 ph + 10 pka1+pka2 2pH Y = 10 ph-pka2 Neutrals fui = 1 fui = 1 I = 0 I = 0 a These two approaches are mathematically equivalent as explained in the Method (i.e., fui p /fui t = 1+I tissue /1+I plasma ). The physiological ph values were considered (i.e., 7.0 for cells, 7.4 for the extracellular water, and 7.2 for the erythrocytes water). Table 4. Equations Derived from the Published Unified Tissue Composition-Based Model Tissue Composition-Based Model Original equations Kp = Kp u fu p Kpu tissue = F cells Kpu cells + F inters Kpu inters = 1 fu fuip t fui t Kpu cells = ( 1 + I cells) F w,cells + P nl,cells F nl,cells + I cells P apl,cells F apl,cells + (1 + I cells) P pr,cells F pr,cells (1 + I cells) Kpu inters = (1 + I inters) F w,inters + P nl,inters F nl,inters + I inters P apl,inters F apl,inters + (1 + I inters) P pr,inters F pr,inters (1 + I inters) Equivalent equations used in this study Kp = fup fu fuip t fui t fut = 1/(1+ Kpu without the ionization effect) Input parameters All drugs fu p is fixed equal to 0.01 and 0.9 fui p fui t is calculated in Table 3 I is calculated in Table 3 P nl = P ow Neutrals, acids, [ and weak bases P pr,inters = 1 fu p 1 P ] nl,plasma F nl,plasma I plasma F pr,plasma P pr,cells = 0 P apl,cells = 0 P apl,inters = 0 Predominantly [ ionized bases (at least one pka 7.0): ( ) ] 1 + Ierythrocytes Fw,erythrocytes + P P apl,cells = P erythrocytes:buffer nl,erytrocytes F nl,erythrocytes 1 + I plasma P erythrocytes:buffer = {[ RBP (1 0.45) ] /0.45 } /fu p P apl,inters = 0 P pr,inters = 0 P pr,cells = I p,plasma I eryrhrocytes F apl,erytrocytes F apl, fractional content of acidic phospholipids equivalent; F cells, fractional content of cells in tissues; F inters, fractional content of interstitial space in tissues; F nl, fractional content of neutral lipids equivalent; F pr, fractional content of binding proteins (albumin for acids and weak bases and lipoproteins for neutrals); fu p, unbound fraction in plasma; fui p, fraction unionized in plasma; fu t, unbound fraction in tissue, fui t, fraction unionized in tissue; F w, fractional content of water equivalent; I, ionization factor; inters, interstitial space; Kp, tissue plasma partition coefficient; Kpu, tissue aqueous phase partition coefficient; P apl, acidic phospholipids aqueous phase partition coefficient; pka, ionization constant; P ow, n-octanol buffer partition coefficient for the unionized species; P nl, neutral lipids aqueous phase partition coefficient; P pr, proteins aqueous phase partition coefficient; RBP, blood plasma ratio in vitro. the values of these parameters are similar. The dissimilarities observed in unbound C max and AUC last values follow the ph partition hypothesis for the acids and bases (i.e., are equal to the ratios fui p /fui t ). Furthermore, increasing the drug lipophilicity significantly decreased the unbound C max and AUC last values in plasma and heart cells. Similarly, increasing the intrinsic clearance in liver, and/or increasing the plasma protein binding, also significantly decreased the unbound C max and AUC last values in plasma and heart cells. Overall, the free drug concentrations in plasma and tissue were influenced by several effects occuring under dynamic in vivo conditions (i.e. ionization, plasma protein binding, lipophilicity, and intrinsic clearance). Therefore, these observations provide much more relevant information compared with the traditional approach based only upon the in vitro fu p value. In other words, the current PBPK model simulations indicate that drug design should be based on free drug concentration derived in tissues from a dynamic in vivo system by contrast of using the free drug concentration Poulin, JOURNAL OF PHARMACEUTICAL SCIENCES 104: , 2015 DOI /jps.24468

7 RESEARCH ARTICLE Pharmacokinetics, Pharmacodynamics and Drug Transport and Metabolism 2365 derived in plasma from an in vitro static environment. The reason is that the free drug concentration in tissue and plasma significantly differed for ionized drugs because of the ph gradient effect and additional effects related to the extent of drug lipophilicity and clearance, for example. Overall, the free drug concentration in tissue (heart) cells and plasma differed by the ratio of fui p /fui t for the ionizable drugs, but the free drug concentration in tissue cells compared with plasma was decreased or increased by the lipophilicity and/or clearance effect. For the neutral drugs, the free drug level in tissue (heart) cells and plasma was similar, but again the free drug concentration in tissue cells compared with plasma was decreased or increased by the lipophilicity and/or clearance effect. DISCUSSION Data from in vitro plasma protein-binding experiments that determine the fraction of protein-bound drug are frequently used in drug discovery to guide structure design and to prioritize compounds for in vivo studies. 2 Therefore, this old paradigm (using only fu p derived from an in vitro static environment) is usually misleading, because this practice yields no enhancement of the in vivo free drug concentration in a dynamic system. Hence, in vivo efficacy should be determined by the free drug concentration surrounding the therapeutic target in tissue, not by the free drug fraction in plasma. So, it has been suggested that decisions based on free drug fraction determined in in vitro static systems could result in the wrong compounds being advanced through drug discovery programmes. 2 It should be realized that unbound drug concentration at the target site is what should drive activity. 1 4 This is in contrast to using biopsies and total tissue levels. Accordingly, it has been demonstrated in this study that in a dynamic in vivo system the interstitial and intracellular concentrations may significantly differ because of diverse dynamic processes; therefore, this new paradigm is in accordance with the recent literature. 1 5 In this case, the current PBPK model simulations demonstrated that free drug concentration in tissue under in vivo condition would be influenced, for example, by the additional effect related to drug ionization and clearance. Furthermore, it has been demonstrated that free drug concentrations in tissue and plasma decreased when drug lipophilicity increased (and inversely). However, the free drug concentrations in tissue cells and plasma were not equal particularly for the ionizable drugs, and, hence, the free drug concentrations in plasma and tissue differed by the ratio of fui p /fui t for the ionizable drugs, as demonstrated in this study (i.e., by assuming that fu p fui p total plasma concentration = fu t fui t total tissue concentration) (Tables 1 and 2). This violated the basic assumption in PKPD research (i.e., fu p total plasma concentration = fu t total tissue concentration). For a large number of compounds that are substrates for uptake and/or efflux transporters expressed at the tissue level, significant discrepancies are expected between the free drug concentrations in plasma and tissues. However, the present study supports the notion that free drug concentrations in plasma and tissues would also differ for passively permeable compounds. As mentioned, in a companion manuscript, the correlation of plasma fu p with muscle fu t values depended on the ph value. Accordingly, the total drug concentrations observed in diverse human tissues were accurately predicted by combining the free and bound drug concentrations with the tissue composition-based model, which considered the dissimilarities in the binding and ionization on both sides of the membrane. Therefore, this present study and a companion manuscript indicate that the main reason for the discrepancies between the free drug concentrations in tissue and plasma water is the ph gradient effect for passively permeable acidic and basic drugs. Accordingly, the dissimilarities observed in the free drug concentrations simulated in tissue and plasma (or in the unbound C max and AUC last used as a measure of the free drug concentration) followed the ph partition hypothesis for these two classes of drugs (Table 1). For the ionized acid, the dissimilarity in the fu p and tissue is 2.5-fold. The main reason is that the acidic drug is trapped in the interstitial (ph 7.4) compared with the cellular (ph 7.0) water because of the ionic driving force, and, hence, the ph gradient effect between tissue and plasma is maximal at the lowest pka value. This pattern is similar for the ionized base; therefore, the dissimilarity in the fu p and tissue is 2.5-fold. Again, the main reason is that the basic drug is trapped in cells compared with the interstitial space, and, hence, the ph gradient effect between tissue and plasma is maximal at highest pka value. The ph gradient effect becomes much more relevant for a diprotic acid and a diprotic base compared with a monoprotic compound (Table 1 vs. Table 2). The ph partition theory is well described in the literature, 5 11 but in this present study this theory has been challenged with a PBPK model based on in vivo condition as explained in the method section. Therefore, drug ionization may influence free drug concentration in tissue cells compared with plasma also in a dynamic system. Accordingly, the intracellular unbound drug accumulation was consistent with passive ph-dependent subcellular partitioning in cultured cells under in vitro conditions. 13 Furthermore, considering a drug ionization effect on both sides of the hepatocyte membrane is one of the explanations that improved the in vitro-to-in vivo extrapolation of drug clearance in rats and humans. 14,15 Overall, these observations indicate that it becomes essential to cover drug ionization effect in PK/PD research. Conversely, for the neutral drug, there is no ph gradient effect; therefore, this explains why the free drug concentrations simulated in heart cells and plasma are similar (Table 1). At this step, it can be argued that there is no need to estimate the free drug concentration in tissues, as the readily available value of fu p for plasma could simply be adjusted for the ph gradient effect between plasma and tissue in order to estimate the free drug concentration in that tissue. As seen in this study, this is not a valuable approach under dynamic in vivo condition. Furthermore, the values of fu t for the individual tissues are key input parameters in PBPK model, as they are used to estimate the overall distribution kinetics (i.e., the volume of distribution), the main clinical application of which is to compute a loading dose in order to reach the target therapeutic concentration. 16 Thus, only considering the in vitro value of fu p in drug design might be biased. In other words, if a drug has a high in vitro fu p value, one will expect that the free drug concentration in tissue is high under in vivo condition; however, the drug ionization, lipophilicity, and clearance effects may drastically reduce the free drug concentration in tissue in a dynamic in vivo system as demonstrated in this study. Similarly, if drug design is only based on a low in vitro fu p value, one will expect that the free drug concentration in tissue is low, but it could be unexpectedly much lower in a dynamic in vivo system because of these additional effects. Therefore, it has also been demonstrated that free drug concentration in plasma and DOI /jps Poulin, JOURNAL OF PHARMACEUTICAL SCIENCES 104: , 2015

8 2366 RESEARCH ARTICLE Pharmacokinetics, Pharmacodynamics and Drug Transport and Metabolism tissue will decrease as drug lipophilicity increases; therefore, the bound drug concentration will increase with drug lipophilicity because of the binding effect to lipids and plasma proteins. 5 11,13 Furthermore, the rapidly cleared compounds will show much lower free drug concentration in plasma and tissue compared with the slowly cleared compounds (Table 1). Thus, these observations demonstrated that, in a dynamic system, the impact of lipophilicity and clearance can also be of significance. Overall, the free drug concentration in a tissue under dynamic in vivo conditions may vary, for example, with the pka, log P, fu p, and clearance values as expected, and, hence, considering all of these effects should improve the PK/PD modeling strategy under real in vivo condition. These observations are in accordance with the literature on the PBPK modeling of drugs In this context, how all of these observations would influence the PK/PD modeling of efficacy and/or toxicity still needs further exploration, but the literature at least demonstrated better correlations with drug efficacy from the free drug concentration in tissue compared with plasma for several ionizable drugs. 1,2 Furthermore, although the drug concentration in cardiac tissue seems better predictor for physiological and electrophysiological changes than its level in plasma, the knowledge of its value is very limited; 17 however, this present study demonstrated that plasma and heart cells showed different free drug concentrations for the ionizable drugs, which might be an explanation for these observations. Such analyses depict potential problems in defining the active concentration location; however, the present study at least demonstrated the feasibility of predicting the maximal free drug concentration gradient between cells and plasma. However, tissues are made of distinct compartments (interstitial fluid, cells, and subcellular organelles) and a given drug is not likely to distribute homogeneously throughout. Nonetheless, this present study has separated each organ in two compartments (e.g., cells and interstitial space), and the estimation of the corresponding fu t and fui t values was made by considering a passive tissue distribution. Hence, whether the exact site of action is present in the interstitial or intracellular space, the current tissue composition-based model can at least be used to estimate the corresponding free drug concentrations, which could have the benefit to improve the current PBPK/PD relationships observed in cardiology and infectiology studies, for example. 3,4,12,17,18 In this context, the PBPK/PD model can be used to predict the in vivo exposure conditions that would produce free drug concentrations in the target site equivalent to the concentrations at which effects were observed with in vitro assays of tissue/organ toxicity. However, the concentration of a drug in cells and interstitial space is probably not always informative with respect to drug concentration at the exact site of action in tissue. For example, in organelles such as the lysosomes (ph ), the ph gradient effect on the free drug concentration would become much more relevant as compared with cells and the interstitial space for highly ionized diprotic bases (at least by a factor of 1000 compared with plasma) (not shown). Nevertheless, the tissue composition-based model is built in such a way that the values of fu t and fui t were also predicted in diverse subcompartments separately (e.g., hepatocytes, microsomes, and tumor cell lines), as the corresponding physiological and ph input data are available in the literature. 5 10,19,20 Therefore, the tissue compositionbased model can be developed for any subcompartment as the corresponding composition and ph data become available. As Poulin, JOURNAL OF PHARMACEUTICAL SCIENCES 104: , 2015 the ionization state of both the drug and the target binding site potentially change as a function of ph, this would necessitate knowing the necessary ph value that is used in the Henderson Hasselbach equations to estimate the value of fui t. Similarly, as the ph of tissue can also be influenced by the disease state, for example, knowing the related ph relationship would help simulating the free drug concentration in such populations. And the target binding site can change for the same reasons so that there is also a potential ph effect on the PD (e.g., a change in the tridimensional structure of the binding site as a function of ph); therefore, adequate PD model of the target sites could potentially be associated with PBPK model simulations of the free drug concentration at these sites. This would help the conduct of PK/PD analyses in pharmacology and toxicology studies. At present, the published PBPK/PD modeling approaches are solely based on the simulation of total tissue concentration. Hence, recently published approaches using PBPK models coupled with PD models would gain in value by considering the free drug concentration at the target binding site. The role of microdialysis should also be acknowledged; however, the microdialysis can only be used to estimate free drug concentration in the interstitial space based on in vivo data in contrast to a PBPK model associated with a tissue composition-based model where the free drug concentrations could virtually be predicted in any compartment of each organ on the basis of in vitro or in silico data, 5 8,12 which would be helpful in the early drug discovery. This is because the intracellular and interstitial free drug concentrations differed by the ph gradient effect as observed in this present study and the literature. 13 Conversely, as mentioned in the Introduction section, there are a number of researches on the microdialysis technique that have observed similar unbound drug concentrations in plasma and interstitial space (e.g., in muscle). 12 However, this was expected because there is no ph gradient effect between plasma and interstitial space compared with cells under normal in vivo conditions in healthy tissues when passive permeability is the predominating distribution process, which is in accordance with the current PBPK model associated with a tissue composition-based model. Nonetheless, the microdialysis technique will still be useful to estimate free drug concentration in complex organs (e.g., brain) while the efflux transport effect at the membrane level and/or permeation limitation effect at the capillary level predominate compared to passive permeability to explain dissimilarities in the unbound drug concentrations that were observed between plasma and interstitial space for several other drugs. 12 In this context, the addition in PBPK model of a relevant efflux transport effect in an organ is expected to further increase the free drug concentration in the interstitial space compared with cells, and inversely, for the influx effect. 6,25 28 Similarly, the addition of a permeation limitation effect at the cell membrane (and/or capillary level) in an organ would further reduce free drug concentration in the cells (and/or interstitial space) but only under nonsteady-state conditions. 25 Finally, the addition of a low bioavailability effect after oral administration is also expected to further reduce drug exposure, and, hence, free drug concentration in plasma and tissue compared with higher bioavailability effect. 2 These later scenarios deserve further exploration with a PBPK model; however, the current literature on the PBPK modeling of drugs indicates that adding these processes in a PBPK model would significantly affect the simulation of drug PK in tissue, and, hence, in the intracellular and interstitial space. 2,6,25 28 DOI /jps.24468

9 RESEARCH ARTICLE Pharmacokinetics, Pharmacodynamics and Drug Transport and Metabolism 2367 CONCLUSION This present study is a first step toward the comparison of free drug concentration in tissue and plasma under dynamic in vivo condition either after nonsteady-state and steady-state intravenous administrations in humans for passively permeable drugs that can be ionized at the physiological ph. Therefore, these observations provide much more relevant information compared with the traditional approach based only upon in vitro fu p value. In other words, the current PBPK model simulations indicate that drug design should be based on free drug concentration derived in tissue from a dynamic in vivo system in contrast of using the free drug concentration in plasma derived from an in vitro static environment. The reason is that the free drug concentration in tissue and plasma significantly differed for ionized drugs in a dynamic in vivo system because of the ph gradient effect and additional effects related to the extent of drug lipophilicity and clearance, for example. A rule of thumb for potentially performing more accurate PBPK/PD modeling is suggested, which states that the free drug concentration in tissue cells and plasma will differ for the ionizable drugs in contrast to the neutral drugs (i.e., the free drug concentration in plasma and tissue cells will differ by the ratio of fui p /fui t for the ionizable drugs since the corrected assumption should be equal to fu p fui p total plasma concentration = fu t fui t total tissue concentration). This violated the basic assumption in PKPD research (i.e., fu p total plasma concentration = fu t total tissue concentration). In addition to the ph gradient effect for the ionizable drugs, lipophilicity and clearance effects will increase or decrease the free drug concentration in tissue and plasma for each classe of drugs; thus, higher will be the drug lipophilicity and clearance, lower would be the free drug concentration in plasma, and, hence, in tissue, in a dynamic in vivo system (and inversely). Accordingly, other PK processes (e.g., bioavailability, transport, and permeation limitation effects) that may also affect free drug exposure level under in vivo condition still need to be challenged. Therefore, only considering the value of free fraction in plasma derived from a static in vitro environment might be biased to guide drug design (the old paradigm), and, hence, it is recommended to use a PBPK model to reproduce more accurately the in vivo condition in tissue (the new paradigm). This newly developed approach can be used to predict free drug concentration in diverse tissue compartments for small molecules in toxicology and pharmacology studies, which can be leveraged to optimize the PK drivers of tissue distribution based upon physicochemical and physiological input parameters in an attempt to decrease (increase) free drug level in tissue, and improve safety margins (or efficacy). Overall, this present study provides guidance on the application of plasma and tissue concentration information in PBPK/PD research in preclinical and clinical studies, which is in accordance with the recent literature. 1 5 ACKNOWLEGMENTS This work represents an initiative undertaken as a part of Dr Poulin s research program. The author wishes to thank Conrad Housand at Aegies Technologies Inc. in Orlando, Florida, for the simulation software ADME Workbench R ( that has facilitated the conduct of this study. REFERENCES 1. 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