YU-NIEN SUN, LORRAINE I. MCKAY, 2 DEBRA C. DUBOIS, WILLIAM J. JUSKO and RICHARD R. ALMON

Transcription

1 /99/ $03.00/0 THE JOURNAL OF PHARMACOLOGY AND EXPERIMENTAL THERAPEUTICS Vol. 288, No. 2 Copyright 1999 by The American Society for Pharmacology and Experimental Therapeutics Printed in U.S.A. JPET 288: , 1999 Pharmacokinetic/Pharmacodynamic Models for Corticosteroid Receptor Down-Regulation and Glutamine Synthetase Induction in Rat Skeletal Muscle by a Receptor/Gene-Mediated Mechanism 1 YU-NIEN SUN, LORRAINE I. MCKAY, 2 DEBRA C. DUBOIS, WILLIAM J. JUSKO and RICHARD R. ALMON Department of Pharmaceutics, School of Pharmacy (Y.-N.S., D.C.D., W.J.J., R.R.A.), and Department of Biological Sciences (L.I.M., D.C.D., R.R.A.), State University of New York at Buffalo, Buffalo, New York Accepted for publication August 21, 1998 This paper is available online at After transplantation, patients often are required to undergo long-term treatment with corticosteroids. As a result, hyperglycemia, negative nitrogen balance, muscle weakness, and muscle atrophy often are seen in these steroid-treated patients (Schimmer and Parker, 1996). These problems are related to a process called gluconeogenesis in which corticosteroids stimulate the synthesis of glucose from noncarbohydrate precursors. Protein breakdown and lipolysis are also increased by corticosteroids and serve to provide amino acids and glycerols for gluconeogenesis. Under the influence of corticosteroids, glutamine is synthesized from glutamate in Received for publication May 8, This work was supported by Grants GM24211 and AG10629 from the National Institute of General Medical Sciences and the National Institute on Aging, National Institutes of Health. 2 Present address: National Institute of Environmental Health Science, Research Triangle Park, NC ABSTRACT Muscle wasting and excessive fat deposition are side effects attendant to chronic corticosteroid treatment. Corticosteroid immunosuppression is necessary in circumstances such as transplantation. Pharmacokinetic/pharmacodynamic (PK/PD) modeling was used to help elucidate the relationships between the events in the molecular cascade that result in muscle wasting and fat deposition by corticosteroids. Specifically, the relationships for receptor/gene-mediated effects that result in increased glutamine synthetase (GS) activity in skeletal muscle were quantitatively analyzed after an i.v. bolus dose of 50 mg/kg methylprednisolone in male adrenalectomized Wistar rats. Profiles of methylprednisolone pharmacokinetics, glucocorticoid receptor density, and its mrna, GS mrna, and GS activity in gastrocnemius muscles were determined. The results were used to develop PK/PD models using differential equations in the ADAPT II program. Two indirect response models were tested for the dynamics of glucocorticoid receptor mrna regulation by activated steroid/receptor complex. Both reduction in message synthesis and message destabilization may be involved but with some tissue specificity. The recovery of active receptor after down-regulation is biphasic. The initial recovery may involve receptor recycling from the nucleus, whereas the later phase may involve de novo synthesis of new receptor protein. The nuclear events and GS mrna/gs induction in rat skeletal muscle show sequential relationships for each component for corticosteroid actions. The PK/PD models provide mechanism-based methods of quantifying complex processes in receptor/gene-mediated enzyme induction featuring the characteristics of time delay and possible nonlinearity in intact tissues. the musculature as a vehicle for transferring amino acid carbon and nitrogen to the liver and kidney for gluconeogenesis, urea synthesis, and nitrogen excretion. The conversion from glutamate to glutamine is catalyzed by the enzyme glutamine synthetase (GS) (Stryer, 1995) in skeletal muscle. The induction of GS by corticosteroids in skeletal muscle is mediated by a receptor/gene-mediated mechanism (Max et al., 1988; McKay et al., 1997). Because corticosteroids also cause insulin resistance in skeletal muscle, the result is hyperglycemia and fat deposition, a process often referred to as steroid diabetes (Schimmer and Parker, 1996). Previously, we used pharmacokinetic and pharmacodynamic (PK/PD) modeling to describe the time-dependent relationships between several elements in the receptor-mediated effect cascade in the liver after corticosteroid treatment (Boudinot et al., 1986; Nichols et al., 1989; Haughey and Jusko, 1992; Xu et al., 1995; Sun et al., 1998). Those models ABBREVIATIONS: PK, pharmacokinetic; PD, pharmacodynamic; GS, glutamine synthetase; GR, glucocorticoid receptor; TAT, tyrosine aminotransferase; MPL, methylprednisolone; GRE, glucocorticoid responsive element; AIC, Akaike information criterion; SC, Schwartz criterion; ECV, estimator criterion value; TC, transcription compartment; SDRSS, standardized residual sum-of-squares; AUC, area under the curve; CL, clearance; V c, volume of distribution in the central compartment; V ss, volume of distribution at the steady state. 720

2 1999 PK/PD Model for GS Induction by MPL in Rat Skeletal Muscle 721 described the gene-mediated induction of the enzyme tyrosine aminotransferase (TAT) after a single bolus dose of corticosteroid. In the present report, we applied a similar PK/PD modeling approach to the cascade of receptor/genemediated effects occurring in skeletal muscle after a single bolus dose (50 mg/kg) of the synthetic corticosteroid methylprednisolone (MPL). Models were sought to describe and predict the cascade events for glucocorticoid receptor (GR)/GR mrna down-regulation as well as GS/GS mrna induction by a short-term MPL treatment. Based on a review of the literature (Oakley and Cidlowski, 1993), two alternative hypotheses are tested for the GR/GR mrna down-regulation by MPL. Two indirect response models (Dayneka et al., 1993) were applied. The objective was to gain insight into the relationship between the corticosteroid regimen and those molecular events in the musculature. Materials and Methods Animal Care The present animal research adheres to the Guide for the Care and Use of Laboratory Animals (NIH publication No , revised 1985) and was approved by the Institutional Animal Care and Use Committee (IACUC) of the State University of New York at Buffalo. Male adrenalectomized Wistar rats (n 39) weighting 220 to 250 g were purchased from Hilltop Lab Animal Inc. (Scottsdale, PA). Animals were housed in a 12-h light/12-h dark, constant temperature (22 C) environment with free access to rat chow (RMH 1000; Agway) and 0.9% NaCl drinking water. Animals were acclimatized to this environment for at least 1 week. One day before the study, rats were subjected to right external jugular vein cannulation under light ether anesthesia. Cannula patency was maintained with sterile 0.9% NaCl solution. Food was removed 14 h before each experiment. PK Study Methylprednisolone sodium succinate (Solu-Medrol; The Upjohn Company, Kalamazoo, MI) was reconstituted with supplied diluent. Rats received a dose of 50 mg/kg MPL via the cannula over 30 s. Rats in the control group received an equal volume of 0.9% NaCl. About 1 ml of blood was taken from the cannula into a heparinized syringe at various times after MPL administration and centrifuged immediately. Plasma was harvested and frozen at 20 C until analyzed. Rats were sacrificed by exsanguination under ether anesthesia at various time points ( h) while blood was drained from the abdominal aortic artery and handled as indicated previously. Drug Assay Samples were thawed at room temperature. Aliquots of rat plasma ( l) were transferred into Pyrex glass culture tubes (Corning Glass Works, Corning, NY). Plasma samples were extracted with methylene chloride. The organic layer was washed with 0.1 N sodium hydroxide followed by double distilled water. Then, 1 to 2 g of anhydrous sodium sulfate was added to remove water residue in the organic layer. Plasma concentrations of MPL were determined by a high performance liquid chromatography method (Ebling et al., 1985). The limit of quantification was 8 ng/ml, and coefficients of variation were less than 10% (interday and intraday). PK Analysis Plasma MPL concentrations versus time were described by a biexponential equation C MPL C 1 e 1 t C 2 e 2 t (1) where C 1 and C 2 are intercept coefficients, and 1 and 2 are slopes. Parameters were estimated by least-squares fitting using the ADAPT II program by the maximum likelihood method. The area under the MPL concentration-time curve (AUC C 1 / 1 C 2 / 2 ) and the area under the first-moment curve ( C 1 / 1 2 C 2 / 2 2 ) were calculated from the slopes and intercepts. The mean residence time was determined as the ratio of area under the first-moment curve to AUC. The clearance (CL) of MPL was obtained as CL Dose/AUC. The volumes of distribution in the central compartment (V c ) and at steady state (V ss ) were determined as V c Dose/ C i and V ss CL mean residence time (Benet and Galeazzi, 1979). The terminal half-life (T 1/2 ) of MPL was calculated as T 1/ / 2. Eq. 1 served as a forcing function in the PD analysis. PD Study After rats were sacrificed, gastrocnemius muscles were excised and frozen in liquid nitrogen until GR assay, RNA preparation, or enzymatic assay. GR density, GR mrna, glutamine synthetase (GS) mrna, and GS activity in skeletal muscle were determined. GR Density Muscle cytosolic GR density was determined by a [ 3 H]dexamethasone ligand binding method (DuBois and Almon, 1984) with some modifications. Powdered frozen muscle tissue was homogenized in ice-cold molybdate buffer using a Polytron homogenizer (Brinkmann Instruments, Westbury, NY) and centrifuged at 27,000g to form a crude cytosol fraction. Crude cytosol was incubated with dextrancoated charcoal solution (5 mg/ml dextran T-70, 50 mg/ml activated charcoal in molybdate buffer) at a ratio of 0.1 ml/ml cytosol for 2 min to remove residual steroid from dosing. Charcoal was removed via 27,000g centrifugation, and the cytosol was then ultracentrifuged at 105,000g to yield muscle cytosol for the binding assay. Separation of bound from free steroid and subsequent Scatchard analysis of full isothermal association curves to determine numbers of binding sites were performed as previously published (DuBois and Almon, 1984). Such values were then normalized by muscle cytosol protein content (Lowry et al., 1951) to obtain the final estimates for GR densities. Clones for crna and Probe Synthesis GRG-1 external standard was a gift from Dr. Stephen Free (Department of Biological Sciences, State University of New York at Buffalo). It consists of a 580-bp fragment of the glucose repressible gene of Neurospora in a pgem-3 construct. GS 300 is a 310-bp fragment of coding sequence spanning bases 740 to 1050 of the murine GS gene in a pgem-3 construct. It was generated by polymerase chain reaction from an original 3.2-kb clone obtained from Dr. A. P. Young (Ohio State University). The GR clone is a 777-bp fragment of GR in a pgem-3 construct. The original 1-kb clone was obtained from Dr. Gordon Ringold (Syntex Research). Quantitative Northern Hybridization Quantitative Northern hybridization methods allow for the conversion of hybridization signals into values of moles of mrna per gram of tissue (DuBois et al., 1993). GS and GRG-1 probes were generated by random primer labeling. Probe synthesis and hybridization conditions were as described previously (DuBois et al., 1993). The GR riboprobe was generated by in vitro transcription with [ 32 P]GTP as the labeled nucleotide (DuBois et al., 1995). GS Activity GS activity was determined by monitoring the conversion of [ 14 C]glutamate to [ 14 C]glutamine (Rowe, 1985). Frozen muscle powder was homogenized in ice-cold buffer (0.25 M sucrose, 0.2 mm ethylenediaminetetraacetic acid, 2 mm 2-mercaptoethanol) and centrifuged at 30,000g to produce a tissue cytosol. Cytosol was incubated for1hat37 C in a reaction mix containing 10 mm [ 14 C]glutamate, with the reaction stopped by the addition of ice-cold 20 mm imidazole buffer. Unreacted glutamate was removed from the newly formed glutamine by passage over a 1-ml Dowex AG-1X8 anion exchange

3 722 Sun et al. Vol. 288 column. Eluate containing the [ 14 C]glutamine was counted, and DPM values were converted into moles of glutamine formed per micrograms of protein added per hour. PD Analysis The PD model for receptor/gene-mediated effects of corticosteroids in rat skeletal muscle is shown in Fig. 1. A similar model was proposed for TAT induction in rat liver (Sun et al., 1998). This model includes four elements. Down-Regulation of GR mrna. Two indirect PD response models (Dayneka et al., 1993) were tested. Model A assumes that the steroid/receptor complex will decrease the GR mrna transcription rate (Dong et al., 1988) in the nucleus (indirect model I). Model B assumes that the complex will increase the degradation rate of GR mrna (Vedeckis et al., 1989) in the cytoplasm (indirect model IV). For model A: dmrna GR (2A) DR(N) k syn,gr mrna 1 k IC 50,GR mrna DR(N) dgr,gr mrna mrna GR where DR(N) is steroid/receptor complex in the nucleus (defined in eq. 5); IC 50,GR mrna is the level of DR(N) required to reach 50% of maximum inhibition of the transcription rate of GR mrna (k syn,gr mrna ), and k dgr,gr mrna is a first-order degradation rate constant for GR mrna. Assuming that GR mrna baseline level will be restored by a certain time after dosing, k syn,gr mrna k dgr,gr mrna mrna GR,0 was defined in the program, whereas k dgr,gr mrna and mrna GR,0 (GR mrna baseline at its steady state) were estimated. For model B: dmrna GR k syn,gr mrna k dgr,gr mrna 1 S max,gr mrna mrna SC 50,GR mrna DR GR (2B) where DR is the steroid/receptor complex in the cytoplasm (defined in eq. 4); S max,gr mrna is the maximum stimulation for k dgr,gr mrna, SC 50,GR mrna is the DR level that can have 50% maximum stimulation of the degradation rate constant, and k syn,gr mrna k dgr,gr mrna mrna GR,0 was assigned. GR Down-Regulation. Four elements were included: receptor binding, translation of new receptor, degradation of receptor, and receptor recycling. We assumed that the steroid/receptor complex will be activated and then translocated into the nucleus soon after the binding. Free GR quickly disappeared from the cytoplasm, presumably as the result of MPL binding. The recovery of free GR has two phases. It was postulated that the first phase was primarily due to receptor recycling, whereas the second phase was controlled by the translation of GR protein. GR down-regulation by MPL was described as follows: dr k on C p R k syn,gr mrna GR R f k re DR(N) k dgr,gr R (3) ddr k on C p R k T DR (4) ddr N k T DR k re DR N (5) where R is the free GR density; C p is MPL plasma and muscle cytosol concentration; k on is the association rate constant for steroid receptor binding; k syn,gr is a translation factor, assuming that the translation rate of new GR protein is proportional to GR mrna levels; R f is a fraction that reflects the proportion of receptor recycled from the activated steroid/receptor complex in the nucleus [DR(N)]; k re is the overall turnover rate constant of DR(N), including degradation [as a fraction of (1 R f )] and recycling (as a fraction of R f ); k dgr,gr is the degradation rate constant of GR; and k T is a first order rate constant Fig. 1. PD model of corticosteroid actions in rat skeletal muscle. C p, steroid concentration at muscle cytosol receptor site; R, free GR density; DR, steroid/receptor complex in the cytoplasm; DR(N), steroid/receptor complex in the nucleus; mrna GR, GR mrna level; k syn,gr mrna, transcription rate of GR mrna; k dgr,gr mrna, degradation rate of GR mrna; k syn,gr, translation factor for GR synthesis; k dgr,gr, degradation rate of GR; k on, association rate constant for steroid/receptor binding; k T, a first order rate constant for the translocation of steroid/receptor complex into the nucleus; k re, overall turnover rate of DR(N); R f, recycling fraction; TC, TC in which steroid/receptor complex initiates the transcription; k N, distribution rate constant between DR(N) and TC;, a power term; mrna GS, GS mrna level; EF 1, a transcription factor for GS mrna induction; k dgr, GS mrna, degradation rate constant for GS mrna; GS, GS activity level; EF 2, a translation factor for GS induction; k dgr, GS, degradation rate constant for GS. Model A resembles indirect response model I. Model B resembles indirect response model IV.

4 1999 PK/PD Model for GS Induction by MPL in Rat Skeletal Muscle 723 describing the translocation of steroid/receptor complex in the cytoplasm (DR) into nucleus [DR(N)]. Assuming that free GR will eventually return back to the baseline after dosing, k syn,gr k dgr,gr (R 0 /mrna GR,0 ) was defined in the program, whereas k dgr,gr, R 0 (GR baseline), and mrna GR,0 (GR mrna baseline) were estimated. Equations 2 through 5 were fitted simultaneously (where eq. 2A was used for model A, eq. 2B was used for model B) to obtain the estimates of k dgr,gr mrna, IC 50,GR mrna (for model A only), S max,gr mrna, SC 50,GR mrna (for model B only), mrna GR,0, k on, k dgr,gr, k re, k T, R f, and R 0 using the ADAPT II program by the maximum likelihood method. These parameters were subsequently used as constants for the following analysis as piecewise fittings. Induction of GS mrna. Sequential reactions after the translocation of steroid/receptor complex (DR) into the nucleus [DR(N)] initiate the induction of GS mrna. DR(N) in eq. 5 represents the activated steroid/receptor complex in the nucleus. Because the binding sites on DNA are limited and not readily quantified to date, we further assumed that there is a transcription compartment (TC) representing a distribution site for DR(N) in which the complex is a DNA-binding protein that interacts with the glucocorticoid responsive element (GRE). TC is a transit compartment between DR(N) and mrna GS in the receptor-mediated signal transduction process (Sun and Jusko, 1998). Meanwhile, the complex will dissociate from GRE and redistribute back to the form of DR(N). Both processes are assumed to be first order, and the rate constant is denoted as k N.TC and the induction of GS mrna are described as follows: dtc k N DR N k N TC (6) dmrna GS EF 1 TC k dgr,gs mrna mrna GS mrna GS,0 (7) where EF 1 is a transcription factor for GS mrna induction, is a power term representing the amplification effect between cascade step TC and mrna GS (Sun and Jusko, 1998), k dgr, GS mrna is a first order rate constant for the degradation of GS mrna, and mrna GS,0 is the baseline value for GS mrna. Equations 2 through 7 were used simultaneously by fixing parameters in eqs. 2 through 5 (using either eq. 2A or 2B). The least-squares estimates of k N,EF 1,, k dgr, GS mrna, and mrna GS,0 were obtained by the maximum likelihood method using the ADAPT II program. These parameters were fixed as constants in the following analysis as piecewise fittings. Induction of GS Activity. GS mrna induction is followed by the induction of GS. It was described as follows: dgs EF 2 mrna GS mrna GS,0 k dgr,gs GS GS 0 (8) where EF 2 is a translation factor assuming that the translation of GS is proportional to GS mrna level, k dgr, GS is a first-order degradation rate constant for GS mrna, and GS 0 is the baseline value for GS activity. Equations 2 through 8 were used simultaneously by fixing the parameters in eqs. 2 through 7 as constants (using either eq. 2A or 2B). EF 2, k dgr, GS, and GS 0 were estimated using the ADAPT II program by the maximum likelihood method. eqs. 2 through 8. The variance model was defined as (Peck et al., 1984): VAR i V,,t i 1 2 M,t i 2 (9) where VAR i is the variance of the ith data point, is the vector of the parameters for the PK/PD model, 1 and 2 are the vectors of variance, t i is the ith time, and M(, t i )istheith predicted value from the PK/PD model. The variances for each data point generated by the fitting of variance models then served as a weighting factor in the process of minimizing the objective function, the negative of the log likelihood, in the ADAPT II program (D Argenio and Schumitzky, 1997). The maximum likelihood method is more appropriate than other leastsquares methods in this case because of consideration for the interindividual variation. The goodness-of-fit criteria for all fittings include visual inspection, examination of residuals, and the estimator criterion value (ECV) for the maximum likelihood method in the ADAPT program. Akaike information criterion (AIC) and Schwartz criterion (SC) were also applied to compare the two submodels. A likelihood ratio test (Mendenhall et al., 1990) for maximum likelihood ECVs obtained from the fittings of models A and B was performed. A P value was determined by 2 ln (likelihood ratio), which is equal to 2 (maximum likelihood ECV of model A likelihood ECV of model B), from a 2 distribution with df 1 (model B has one more parameter than model A). This P value was used to discriminate models A and B for glucocorticoid-mediated GR mrna/gr down-regulation through a statistical approach. Results PK Study The profile of plasma MPL concentrations versus time are shown in Fig. 2 (Dose 50 mg/kg MPL i.v. bolus). The MPL plasma concentrations declined biexponentially with a terminal half-life (T 1/2 ) of 0.59 h. The intercepts (C 1 and C 2 ) and slopes ( 1 and 2 ) listed in Table 1 were based on the leastsquares fitting using eq. 1. Results for area/moment analysis, CL, V c, and V ss are also listed in Table 1. The PK profile for Data Analysis: Maximum Likelihood Method Our PD data were obtained from a giant rat study. We can only generate one data set (sacrifice time, GR mrna level, free GR density, GS mrna level, and GS activity) from each rat; therefore, a large number of animals are used to determine the PD profiles. Assuming that the errors from the observed data and predicted values for a specific time point were normally distributed, the maximum likelihood method was applied to the least-squares fitting for Fig. 2. Plasma concentrations of MPL after a 50 mg/kg MPL i.v. bolus dose in rats. Data points are observed values, and the solid line is the result of least-squares fitting using eq. 1.

5 724 Sun et al. Vol. 288 MPL is similar to the results from other studies (Haughey and Jusko, 1992; Sun et al., 1998) that used the same strain of adrenalectomized rats given same dose of MPL. PD Study GR mrna. The profile of GR mrna concentrations versus time is shown in Fig. 3. The GR mrna declined from the baseline value (estimated mrna GR,0 : 2.91 fmol/g from model TABLE 1 PK parameters for MPL disposition (dose 50 mg/kg) in rats Parameters (U) Value Biexponential fitting C 1 ( g/ml) 56.3 C 2 ( g/ml) (h 1 ) (h 1 ) 1.22 Area/moment analysis AUC ( g h/ml) 17.6 AUMC ( g h 2 /ml) 10.3 MRT (min) 35.2 PK analysis T ½ (min) 34.1 CL (l/h/kg) 2.85 V C (l/kg) 0.71 V ss (l/kg) 1.67 AUC, area under the curve; AUMC, area under the first-moment curve; MRT, mean residence time. Fig. 3. Plots of GR mrna (top) and free GR density (bottom) in rat skeletal muscle after a 50 mg/kg MPL i.v. bolus dose in rats. Data points are observed values. Error bars are standard deviations at each time point. The solid lines are the least-squares fittings for eqs. 2A through 5 from model A. The dashed lines are the least-squares fittings for eqs. 2B through 5 from model B. A, 3.46 fmol/g from model B) to the trough level (about 35% of the baseline level) in 9.6 h (model A) or 7.4 h (model B). GR mrna then slowly returned to mrna GR,0 in 2 to 3 days after dosing. The estimated parameters for eqs. 2A and 2B are listed in Table 2. Criterion values obtained by fitting eqs. 2 through 5 simultaneously are listed in Table 3. In model A, the estimated IC 50,GR mrna value [0.66 nmol/ liter/mg protein of DR(N)] indicates that the steroid/receptor complex in the nucleus is sufficient to suppress GR transcription for up to 10 h postdosing because DR(N) levels are well above the value required for 50% of maximum inhibition of the transcription rate of GR mrna during that period [simulation for DR(N) is in Fig. 5]. In model B, the estimated S max,gr mrna value (5.25) indicates that GR mrna degradation rate regulated by steroid/receptor complex in cytoplasm can be increased up to 6.25-fold of the k dgr,gr mrna value (0.046 h 1 ). Meanwhile, the estimated SC 50,GR mrna value (1.61 nmol/liter/mg protein of DR) implies that the GR mrna degradation rate should be sufficiently stimulated for up to 6 to 7 h after MPL dosing because during the first 6 h, DR concentrations are much higher than the level needed to have 50% maximum stimulation of the degradation rate constant for GR mrna (simulation for DR is in Fig. 5). The standardized residual sum-of-squares [SDRSS (residual 2 /variance)] for GR mrna in model A (38.70) is slightly better than that in model B (39.82). However, model A seems to overestimate the time to reach the maximum inhibition for GR mrna. As shown in Fig. 3, model A has a longer GR mrna suppression period and returned to the baseline faster than model B. GR Density. The time course of GR density in skeletal muscle after the administration of MPL is shown in Fig. 3. Each data point is the mean value of a single rat with the standard deviation (determined by Scatchard analysis) as indicated (DuBois and Almon, 1984). Free GR disappeared from the cytoplasm quickly after dosing, and recovery was biphasic. The recovery from 0 to 40% of baseline occurred in the first 10 h and was followed by the second phase, which is TABLE 2 PD parameters estimated by the maximum likelihood method Parameter Model A Model B mrna GR,0 (fmol/g) IC 50,GR mrna (nmol/l/mg protein) N.A. S max,gr mrna N.A SC 50,GR mrna (nmol/l/mg protein) N.A k syn,gr mrna (fmol/g/h) k dgr,gr mrna (h 1 ) k on (l/nmol/h) R 0 (fmol/l/mg protein) k syn,gr (fmol GR/l/mg protein/ fmol GR mrna/g/h) k dgr,gr (h 1 ) R f k T (h 1 ) k re (h 1 ) k N (h 1 ) mrna GS,0 (fmol/g) EF 1 (pmol GS mrna/g/fmol GR/ mg protein) k dgr,gs mrna (h 1 ) GS 0 (pmol/ g protein/h) EF 2 (pmol/ g protein/h/pmol of GS mrna/g) k dgr,gs (h 1 ) N.A., not applicable.

6 1999 PK/PD Model for GS Induction by MPL in Rat Skeletal Muscle 725 TABLE 3 Criterion values obtained by the maximum likelihood method in the ADAPT II program mrna GR R DR DR(N) TC mrna GS GS Model A Equation No. 2A SDRSS NA NA NA AIC SC ECV 69.06* 69.06* 69.06* 69.06* Model B Equation No. 2B SDRSS NA NA NA AIC SC ECV 62.92* 62.92* 62.92* 62.92* * p.005 for 2 distribution with df 1. NA, not applicable. Fig. 4. Plots of GS mrna (top) and GS induction (bottom) after a 50 mg/kg MPL i.v. bolus dose in rat skeletal muscle. Data points are observed values. The solid lines are the least-square fittings for eq. 2A through 8 from model A. The dashed lines are the least-squares fittings for eqs. 2A through 8 from model B. parallel to the recovery of GR mrna. As shown in Fig. 3, the recovery of GR density in rat skeletal muscle took at least 3 days after 50 mg/kg MPL was given. The estimated parameters for eqs. 3 through 5 are listed in Table 2. We modeled the first phase of GR recovery as coming from the recycling of DR(N). The end of the first phase shown in Fig. 3 was about 40% of the GR baseline value, which is lower than the estimated R f value (0.619 in model A, in model B), suggesting that 60 to 80% of DR(N) will again become a steroid-activatable form of GR in cytoplasm. Because the first phase of GR recovery was within 8 h after dosing, the MPL plasma concentration was sufficient to form DR when free GR was recycled in the first few hours. These results suggest that some of the GRs were involved in the receptor/genemediated action more than once before the receptor protein became inactive or was degraded. The criterion values obtained by fitting eqs. 2 through 5 simultaneously are listed in Table 3. The SDRSS for GR density (R) in model B (17.92) is slightly lower than that in model A (18.79). However, the SDRSS for GR mrna (mrna GR ) in model A (38.70) is lower than that in model B. The AIC, SC, and ECV have the combined effect from GR mrna (eq. 2A or 2B) and GR density (eq. 3). As shown in Table 3, model B has lower AIC, SC, and ECV than model A. From the result of the likelihood ratio test for models A and B, we obtained P.005 (the likelihood ratio is 12.28, whereas P with df 1; therefore, P.005). We thus can conclude that the fitting from model B for GR mrna/gr down-regulation is better than from model A. GS mrna. The induction of GS mrna in skeletal muscle is shown in Fig. 4. It started at about 1.5 h; the peak occurred at about 7.5 h and declined to the baseline by 18 h after MPL dosing. The estimates for the parameters in eqs. 6 and 7 are listed in Table 2. The estimated k N values (0.212 h 1 for model A, h 1 for model B) indicate that the distribution half-life of the activated steroid/receptor complex from the nucleoplasm to the GRE is about 3.3 h (model A) and 4.3 h (model B), where half-life is equal to 0.693/k N. The power term in eq. 7 for GS mrna induction is used to describe the asymmetric peak of the curve. The estimated values are 1.36 (model A) and 1.63 (model B). As shown in Fig. 4, predictions for GS mrna induction from models A and B overlap each other. The estimated values for baseline level mrna GS,0 (99.8 fmol/g for model A, 99.2 fmol/g for model B), transcription factor EF 1 ( pmol GS mrna/g/fmol GR/mg protein for model A, pmol GS mrna/g/ fmol GR/mg protein for model B), and elimination rate constant k dgr, GS mrna (0.306 h 1 for model A, h 1 for model B) are very close for the two models. The AIC and SC values listed in Table 3 indicate that both models can adequately describe GS mrna induction with similar SDRSS values. GS Activity. The induction of GS in skeletal muscle was generally parallel to the GS mrna levels after a short lag time. It started at about 2 h after MPL dosing, reached its maximum activity at about 8.5 h, and declined to the baseline value at about 20 h after dosing. The estimates for the parameters in eq. 8 are listed in Table 2. The estimated values

7 726 Sun et al. Vol. 288 for baseline level GS 0 (1.87 pmol/ g protein/h for model A, 1.83 pmol/ g protein/h for model B), translation factor EF 2 (34.5 pmol/ g protein/h/pmol of GS mrna/g for model A, 34.4 pmol/ g protein/h/pmol of GS mrna/g for model B), and elimination rate constant k dgr, GS (1.94 h 1 for model A, 1.89 h 1 for model B) are very close for the two models. As shown in Fig. 4, predictions for GS induction from the two models overlap. The AIC and SC values listed in Table 3 show that both models can describe GS induction with very close SDRSS values. Simulations for Steroid Receptor/Gene-Mediated Effects Simulations for the major components of the receptor/genemediated effects of MPL in rat skeletal muscle, with comparisons of the two submodels, are shown in Fig. 5. The downregulation of GR mrna by an indirect effect of the steroid/ receptor complex (eq. 2A or 2B), the down-regulation of GR (eq. 3), dynamics of steroid/receptor complex in cytosol (eq. 4) and in the nucleus (eq. 5), the TC (eq. 6), GS mrna (eq. 7), and GS activity (eq. 8) are included. Percentage inductions for DR(N), TC, GS mrna, and GS show a sequential precursor/product relationship for each component. From these simulations, we are able to study some of the inaccessible elements and understand the important characteristics of corticosteroid actions. These actions start from the steroid/receptor binding in the cytoplasm (shown as the abrupt decline in GR density), followed by the transduction phases including the activated complex (DR), translocation to the nucleus [DR(N)], and distribution into the TC. These cascade steps lead to the transcription of GS mrna followed by the induction of the GS enzyme. As shown in Fig. 5, each step in the process has substantial time delays between steps. The delayed PD response of GS induction by MPL is actually a multistep signal transduction function that is controlled by the MPL concentration as well as GR occupancy. This leads us to believe that the corticosteroid receptor/genemediated effects should be dose dependent but not dose proportional because the quantity of free GR is limited and Fig. 5. Simulations for the full PD model of receptor/gene-mediated GS induction by a 50 mg/kg MPL i.v. bolus dose in rat skeletal muscle. Results from model A (left) and model B (right) are displayed. Full courses for GR density and GR mrna levels (top); cascades of R, DR, DR(N), and TC (middle); and percent induction for DR(N), TC, GS mrna, and GS activity (bottom) show the sequential events for corticosteroid action in rat skeletal muscle after MPL treatment.

8 1999 PK/PD Model for GS Induction by MPL in Rat Skeletal Muscle 727 indirectly regulated by corticosteroids. We have seen such phenomenon from TAT induction in rat liver by MPL (Haughey and Jusko, 1992). Therefore, our extended PK/PD models are able to describe time delay as well as nonlinearity as the two important characteristics of corticosteroid receptor/gene-mediated effects. Discussion This report presents the first application of PK/PD modeling to corticosteroid effects in skeletal muscle. We are able to quantify multiple factors determining important processes in intact muscle and estimate real life dynamic parameters from experimentally inaccessible sites under certain assumptions. In this case, a sequence of molecular events that cause steroid-induced wasting of the musculature were studied. Our PK/PD models adequately describe the receptor/genemediated induction of GS mrna and GS activity in rat skeletal muscle at the present MPL dose level. GR mrna and GR down-regulations by MPL were investigated and included in the model. Understanding receptor regulation at both the mrna and protein levels may be important in designing dosing regimens that minimize wasting of the musculature. We believe that the PK properties of corticosteroids are key factors for their receptor/gene-mediated effects. Free steroid from plasma enters the target cells and initiates the process. The disposition profile controls the duration of time that MPL can serve to occupy receptors before all processes begin to return to baseline conditions. The protein binding of some steroids is of concern. Fortunately, MPL has linear binding to albumin and no binding to transcortin, which causes most of the nonlinear binding of corticosteroids (Jusko and Ludwig, 1992). It has been shown that MPL has a constant free fraction of at plasma concentrations up to 80,000 ng/ml (Haughey, 1990). The total plasma concentration of MPL thus can be used as a forcing function in the PK/PD system (eq. 1) with the assumption of rapid diffusion into tissue cytosol. Reversible metabolism between MPL and methylprednisone has been observed in rats (Haughey, 1990). The latter 11-keto metabolite of MPL is inactive for receptor-mediated effects. Haughey showed that nonlinear interconversion and elimination processes occur between MPL doses of 5 to 50 mg/kg in rats, although the cycled fraction between MPL and methylprednisone is only about 10%. The nonlinear MPL disposition requires caution in using the PK function (eq. 1) when this PK/PD modeling system is applied for different steroid regimens. The availability of free binding active GR in target cells is another important factor for steroid dynamics. Our direct measurement of GR mrna makes it possible to describe the DR dynamic profile as a combined effect of translation of the receptor protein, receptor binding, recycling, and the turnover of the protein. In the first 10 h after MPL dosing, GR mrna declined to about 35% of the baseline level. The pattern of the data suggests that receptor recycling may play a key role in the recovery of GR density from 0 to 40% in the first phase. Under this assumption, the models propose that GR density actually increases during that initial period of time (see simulations in Fig. 5). The results also suggest that the second phase of recovery of binding active GR is controlled by the translation of new receptor. Therefore, we assumed in our model that binding-active receptor is proportional to recovering GR mrna levels. As a result, the time profile for receptor occupancy (steroid/receptor complex, DR), which leads to the gene-mediated effects on steroid induced protein and receptor down-regulation, is controlled by the steroid kinetics and the complexity of receptor dynamics itself. The values of IC 50,GR mrna (for model A) and SC 50,GR mrna (for model B) are the potency factors for the indirect response of GR mrna down-regulation by corticosteroids in the respective biophases (nucleoplasm for model A, cytoplasm for model B). It should be emphasized that it is the activated steroid/receptor complex, DR, not the steroid alone, that mediates the GR mrna down-regulation. This is the first report on the full PK/PD modeling for the corticosteroid receptor/gene-mediated effects (down-regulation of GR mrna/gr, induction of the enzyme and its mrna) as well as the transduction phases [DR, DR(N), and TC] in skeletal muscle. Because precedents are available for considering regulating the amount of available message by translational control (Dong et al., 1988) or by changes in message stabilization (Vedeckis et al., 1989), we modeled both possibilities for the down-regulation of GR mrna. Based on the result of the likelihood ratio test for the analysis of GR mrna downregulation, the nonlinear least-squares fitting for model B (steroid/receptor complex in the cytosol increases the degradation rate of GR mrna) is better than model A (steroid/ receptor complex in the nucleus decreases the transcription rate of GR mrna). The AIC and SC values also favor model B, even though it has one more parameter than model A (number of parameters is a penalty term in AIC and SC). Therefore, model B seems to best describe GR mrna/gr down-regulation in this case. However, it is important to examine the physiological significance of the estimated parameters from both models. By converting k dgr,gr mrna to half-life of GR mrna, the prediction for half-life of GR mrna from model B (15.2 h) is much longer than that from model A (5.1 h). Literature (Oakley and Cidlowski, 1993) suggests that the half-life of steroid-untreated GR mrna from in vitro studies is 4 to 5 h, which is consistent with model A. Perhaps it is too simplistic to assume that only one of the two mechanisms for these two submodels is valid. It is possible that different target tissues will have different sensitivities for the GR mrna/gr down-regulation by blocking the GR mrna transcription by the steroid/receptor complex in the nucleus or stimulating the degradation of GR mrna by the complex in the cytosol. This possiblility is suggested by our work on liver, in which decreased synthesis is favored as the mechanism of GR mrna down-regulation (Sun et al., 1998). Together, the two analyses suggest that GR mrna down-regulation by MPL in rat skeletal muscle may be dominated by increased turnover rate, whereas in rat liver, it may be controlled by decreased transcription rate. The two mechanisms may be operating at the same time but with different influences in different target cells. In other words, a hybrid PD model of model A and model B may be most suitable for the analysis. However, it will be difficult to test this hypothesis because the parameters for such hybrid model may not be accurately estimated with the information and data available to date. One solution is to study GR mrna down-regulation in both tissues at varying doses of

9 728 Sun et al. Vol. 288 steroid or on repeated dosing with the hope that the nonlinear regression methods can recognize and discriminate the input (transcription) and output (degradation) rates of GR mrna in the indirect response model from different response curves and accurately estimate those parameters involved in both processes. We are presently conducting such studies. The GS mrna/gs induction profile in rat skeletal muscle by corticosteroids demonstrates waves of signal transduction starting from receptor occupancy, followed by induction of message, and ending with the increase of enzymatic activity. We use a TC with a distribution rate constant k N, which is analogous to the effect site compartment with k eo (Sheiner et al., 1979), to describe the time lag for steroid/receptor complex in the nucleus to be distributed to the transcription sites and interact with GRE. Meanwhile, the distribution half-life between DR(N) and TC (0.693/k N ) can be accounted for by the delay between receptor occupancy and GS mrna induction as shown in the simulation (Fig. 5). The time to reach the maximum level of GS mrna and GS induction ( h) in skeletal muscle is longer than that found for TAT mrna and TAT induction (5.5 7 h) in liver. Such differences may result from PK factors such as differential distribution of MPL in various target organs mediated by capillary bed properties and PD factors such as different GR dynamics (including GR baseline values, sensitivities to down-regulation, and so on), steroid/receptor binding properties, and transcription/translation efficiency for GR itself. This report is the first attempt to apply a PK/PD modeling approach to analyze the effect of corticosteroids on skeletal muscle. The results of this study may help us to understand the relationships between molecular events leading to muscle wasting and negative nitrogen balance caused by longterm glucocorticoid exposure. In addition, results such as those demonstrating the prolonged down-regulation of both GR mrna and GR may allow us to use this PK/PD modeling approach to investigate and optimize corticosteroid dosing regimens. Acknowledgments The excellent technical assistance of Ms. Nancy Pyszczynski is appreciated. We also thank Dr. Stephen Free (State University at New York at Buffalo) for the GRG-1 clone, Dr. Gordon Ringold (Syntex Research) for the original 1-kb GR clone, and Dr. A. P. Young (Ohio State University) for the 3.2-kb GS clone. References Benet LZ and Galeazzi RL (1979) Noncompartmental determination of the steadystate volume of distribution. J Pharm Sci 68: Boudinot FD, D Ambrosio R and Jusko WJ (1986) Receptor-mediated pharmacodynamics of prednisolone in the rat. 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Almon, Ph.D., 107 Hochstetter Hall, Department of Biological Sciences, State University of New York at Buffalo, Buffalo, New York almon@acsu.buffalo.edu