**4. Pharmacokinetic modeling and simulations**

#### **4.1 Pharmacokinetic modeling**

686 Non-Viral Gene Therapy

Body weight (kg) 0.267 0.291 0.243 0.26 t1/2 (min) 54.8 42.3 74.8 45.3 C0 (μg/mL) 14.1 22.9 77.1 227.5 AUC (μg min/kg) 259.6 316.8 1528.6 3331.9 Cl (mL/min/kg) 5.6 6.4 5.1 4.6 Vss (mL/kg) 305.8 274.6 411.8 243.7 MRT (min) 68.1 42.6 80.5 54

Body weight (kg) 0.313 0.317 0.317 0.317 t1/2 (min) 139.1 165.8 207.3 359.3 C0 (μg/mL) 1.5 4 3.8 4 AUC (μg min/kg) 108.1 205.2 326.8 508.3 Cl (mL/min/kg) 9.9 8.9 9.2 10.3 Vss (mL/kg) 2170.5 1990.1 2602.2 4567 MRT (min) 194.7 222.5 289.7 492.1

Table 3. Mean non-compartmental pharmacokinetic parameters of PI polyamides after

Determination of the urinary and biliary excretion rates is crucial for the evaluation of the pharmacokinetics of a drug, because drugs are usually eliminated from the body into urine and/or bile (Ullrich, 1997; van Montfoort et al., 2003). The urinary and biliary excretion ratetime profiles are shown in Figs. 7 and 8, respectively. The urinary excretion rates of PI polyamides A and B showed a linear elimination. The biliary excretion rate of PI polyamide A showed saturation at the early period, while PI polyamide B was not detected in the bile. The cumulative urinary excretion rates of PI polyamides A and B at 48 h were 72.4 ± 11.6 and 4.8 ± 0.5% (mean ± SD, n = 3) of the administered dose, respectively. The cumulative biliary excretion rate of PI polyamide A at 24 h was 4.3 ± 0.4% (n = 4) of the administered dose. These observations indicated that unchanged PI polyamides A and B were slowly eliminated from the body. As observed from the plasma concentration-time profile, it is considered that most of the PI polyamide B remained in the lungs. No peaks of metabolites

The differences in the molecular weights of compounds affect their eliminations (Hirom et al., 1976). The molecular weight thresholds for the excretion of organic cations into rat bile were found to be in the ranges of 200 ± 50 for monovalent organic cations and 500-600 for bivalent organic cations. (Hughes et al., 1973a; b) PI polyamide with a molecular weight of

intravenous administration at various doses into rats (n = 3).

1.3 mg/kg 2.0 mg/kg 7.5 mg/kg 15.0 mg/kg

Dose

1.0 mg/kg 2.0 mg/kg 3.0 mg/kg 5.0 mg/kg

Dose

PI polyamide A

Parameter

PI polyamide B

Parameter

**3.2 Urinary and biliary excretions** 

were detected for all the samples.

The plasma concentration-time profiles after the intravenous administration of PI polyamide A was fitted well by a two-compartment model. The estimated pharmacokinetic parameters

Pyrrole-Imidazole Polyamides for Gene Therapy: Bioanalytical Methods and Pharmacokinetics 689

concentration in the lungs immediately after the intravenous administration of PI polyamide B is higher than the calculated value. The early-plasma concentration-time profiles after the intravenous administration of a hairpin polyamide-chlorambucil conjugate, duocarmycin, and nitroglycerin are similar to that of PI polyamide B (Alberts et al., 1998; Chou et al., 2008; Wester et al., 1983) Recently, the biodistribution of a hairpin polyamide-chlorambucil conjugate administered into mice has been reported (Chou et al., 2008). The predominant occupancy of the polyamide-chlorambucil conjugate was observed in the lungs, spleen, small intestine, and pancreas 2 and 24 h after the injection. The concentration of polyamidechlorambucil conjugate in the lungs at 2 h was higher than that of the polyamidechlorambucil conjugate at 24 h. These findings are consistent with our results. PI polyamide B is distributed in the aorta and localizes in the nuclei of aortic midlayer smooth muscle (Matsuda et al., 2006). The lungs consist of pulmonary alveoli, which are surrounded by capillary vessels. It has been reported that weak basic drugs accumulate in the lungs and that such accumulation is attributable to lysosomal trapping (MacIntyre et al., 1988; Rodgers et al., 2005). A high concentration of PI polyamide B in the lungs was thought to be caused by PI polyamide B being distributed in capillary vessels of the lungs and by PI polyamide B being a weak base compared with PI polyamide with a molecular weight of 1422.51. It is also conceivable that PI polyamide B accumulated in the lungs owing to its high molecular weight, as suggested in a previous study (Wiseman et al., 2000). From these considerations, the proposed catenary two-compartment model may be applicable to describing PI

Fig. 10. Model fitted PI polyamide B concentration-time profiles in plasma and lungs. A is plasma concentration–time profiles and B is lung concentration-time profiles. The middle bold line indicates the 50th percentiles for 1000 simulations. Symbols depict the observed

(min)

**4.2 Pharmacokinetic modeling with excretion data in addition to plasma concentration**  To predict the plasma concentration-time profile in the elimination phase of PI polyamide A after intravenous administration, two pharmacokinetic models (i.e., one- and twocompartment models with the linear output compartment interpreted as the urine compartment and the non-linear output compartments interpreted as the bile compartment) using the plasma concentration-time profile and cumulative urinary and biliary excretion

data after the intravenous administration of PI polyamide B at 3.0 mg/kg.

polyamide B in detail.

using the model are summarized in Table 4. After the intravenous administration of PI polyamide A at 1.3, 2.0, 7.5, and 15.0 mg/kg, the average CLt and Vss values were in the ranges of 4.9-7.0 mL/min/kg and 245-335 mL/kg, respectively. The CLt and Vss values estimated using a two-compartment model and a non-compartment model are thought to be identical.


Table 4. Estimated pharmacokinetic parameters of PI polyamide A obtained using twocompartment model.

The plasma concentration-time profiles after the intravenous administration of PI polyamide B increased in the early phase and resembled those after the oral administration. The slope of the decline in the lung concentration-time profiles of PI polyamide B was nearly equal to that in the plasma concentration-time profiles of PI polyamide B. To describe the increasing phase of PI polyamide B after the intravenous administration, the lung and plasma concentration-time profiles of PI polyamide B were fitted using a catenary two-compartment model (Fig. 9) (Brown et al., 1981).

Fig. 9. Pharmacokinetic model of PI polyamide B.

C1, X1, and V1 represent the concentration of PI polyamide B in the lungs, the amount of PI polyamide B in the lungs, and the distribution volume of the lung compartment, respectively. C2, X2, and V2 represent the concentration of PI polyamide B in plasma, the amount of PI polyamide B in plasma, and the distribution volume of the plasma compartment, respectively. The pharmacokinetic parameters were calculated using the NONMEM program.

Figure 10 shows the simulation curves for PI polyamide B based on the catenary twocompartment model. The plasma and lung concentrations were fitted well by the model. The estimated pharmacokinetic parameters after the intravenous administration of PI polyamide B are summarized in Table 5. The estimated coefficients of variation (CV%) were small, the catenary two-compartment model better fitted the concentration-time profile after the intravenous administration of PI polyamide B. The model-estimated clearance (6.8 mL/min/kg) calculated as k20 multiplied by V2 was nearly equal to CLt (7.3 mL/min/kg). In this study, lung concentrations of first-point were measured at 10 min. It is thought that the

using the model are summarized in Table 4. After the intravenous administration of PI polyamide A at 1.3, 2.0, 7.5, and 15.0 mg/kg, the average CLt and Vss values were in the ranges of 4.9-7.0 mL/min/kg and 245-335 mL/kg, respectively. The CLt and Vss values estimated using a two-compartment model and a non-compartment model are thought to be

> (mL/min/kg) 5.8 7 5.8 4.9 Vss (mL/kg) 335 250 323 245 Vc (mL/kg) 90.5 89.6 96.6 69.7

Table 4. Estimated pharmacokinetic parameters of PI polyamide A obtained using two-

The plasma concentration-time profiles after the intravenous administration of PI polyamide B increased in the early phase and resembled those after the oral administration. The slope of the decline in the lung concentration-time profiles of PI polyamide B was nearly equal to that in the plasma concentration-time profiles of PI polyamide B. To describe the increasing phase of PI polyamide B after the intravenous administration, the lung and plasma concentration-time profiles of PI polyamide B were fitted using a catenary two-compartment

C1, X1, and V1 represent the concentration of PI polyamide B in the lungs, the amount of PI polyamide B in the lungs, and the distribution volume of the lung compartment, respectively. C2, X2, and V2 represent the concentration of PI polyamide B in plasma, the amount of PI polyamide B in plasma, and the distribution volume of the plasma compartment, respectively. The pharmacokinetic parameters were calculated using the

Figure 10 shows the simulation curves for PI polyamide B based on the catenary twocompartment model. The plasma and lung concentrations were fitted well by the model. The estimated pharmacokinetic parameters after the intravenous administration of PI polyamide B are summarized in Table 5. The estimated coefficients of variation (CV%) were small, the catenary two-compartment model better fitted the concentration-time profile after the intravenous administration of PI polyamide B. The model-estimated clearance (6.8 mL/min/kg) calculated as k20 multiplied by V2 was nearly equal to CLt (7.3 mL/min/kg). In this study, lung concentrations of first-point were measured at 10 min. It is thought that the

Parameter Dose

1.3 mg/kg 2.0 mg/kg 7.5 mg/kg 15.0 mg/kg

identical.

CLt

compartment model.

NONMEM program.

model (Fig. 9) (Brown et al., 1981).

Fig. 9. Pharmacokinetic model of PI polyamide B.

concentration in the lungs immediately after the intravenous administration of PI polyamide B is higher than the calculated value. The early-plasma concentration-time profiles after the intravenous administration of a hairpin polyamide-chlorambucil conjugate, duocarmycin, and nitroglycerin are similar to that of PI polyamide B (Alberts et al., 1998; Chou et al., 2008; Wester et al., 1983) Recently, the biodistribution of a hairpin polyamide-chlorambucil conjugate administered into mice has been reported (Chou et al., 2008). The predominant occupancy of the polyamide-chlorambucil conjugate was observed in the lungs, spleen, small intestine, and pancreas 2 and 24 h after the injection. The concentration of polyamidechlorambucil conjugate in the lungs at 2 h was higher than that of the polyamidechlorambucil conjugate at 24 h. These findings are consistent with our results. PI polyamide B is distributed in the aorta and localizes in the nuclei of aortic midlayer smooth muscle (Matsuda et al., 2006). The lungs consist of pulmonary alveoli, which are surrounded by capillary vessels. It has been reported that weak basic drugs accumulate in the lungs and that such accumulation is attributable to lysosomal trapping (MacIntyre et al., 1988; Rodgers et al., 2005). A high concentration of PI polyamide B in the lungs was thought to be caused by PI polyamide B being distributed in capillary vessels of the lungs and by PI polyamide B being a weak base compared with PI polyamide with a molecular weight of 1422.51. It is also conceivable that PI polyamide B accumulated in the lungs owing to its high molecular weight, as suggested in a previous study (Wiseman et al., 2000). From these considerations, the proposed catenary two-compartment model may be applicable to describing PI polyamide B in detail.

Fig. 10. Model fitted PI polyamide B concentration-time profiles in plasma and lungs. A is plasma concentration–time profiles and B is lung concentration-time profiles. The middle bold line indicates the 50th percentiles for 1000 simulations. Symbols depict the observed data after the intravenous administration of PI polyamide B at 3.0 mg/kg.

**4.2 Pharmacokinetic modeling with excretion data in addition to plasma concentration**  To predict the plasma concentration-time profile in the elimination phase of PI polyamide A after intravenous administration, two pharmacokinetic models (i.e., one- and twocompartment models with the linear output compartment interpreted as the urine compartment and the non-linear output compartments interpreted as the bile compartment) using the plasma concentration-time profile and cumulative urinary and biliary excretion

Pyrrole-Imidazole Polyamides for Gene Therapy: Bioanalytical Methods and Pharmacokinetics 691

because the percentage of the administered dose was calculated from the urine and bile concentrations, urine and bile volumes, and administered dose. The choice of model was based on model fitting criteria such as visual inspection of the fitted curves, objective function value of NONMEM (OFV), and CV% of the parameter estimates (Hazra et al., 2007;

The plasma concentration and cumulative urinary and biliary excretion-time profiles after intravenous administration of PI polyamide A were fitted well by the two-compartment model with the linear output compartment interpreted as the urine compartment and the non-linear output compartment interpreted as the bile compartment (Fig. 12). The 50th percentiles of the model-based prediction for plasma concentrations and cumulative urinary and biliary excretions are presented together with the observed value. To obtain 50th percentiles of the model estimations, 10000 simulations were performed using the estimated model parameters, variability in the estimated parameters, and residual variability of the data. Compared with a one-compartment model using only plasma data, more accurate data can be obtained from the two-compartment model including urine and bile data because PI polyamide A was excreted into urine and bile until at least 36 and 18 h, respectively, after administration. The plasma concentration-time profile in the elimination phase could also be described better using both the linear and non-linear

Fig. 12. Plasma concentration–time profile (A), cumulative urinary excretion rate (B), and cumulative biliary excretion rate (C) of PI polyamide A after intravenous administration at 2.0 mg/kg to rats. Each data point represents observed data from three (for plasma and urine) and four rats (for bile). The solid line indicates 50th percentiles from model

To predict the plasma concentration-time profile in the elimination phase of PI polyamide B after intravenous administration, two pharmacokinetic models (i.e., one- and twocompartment models with the linear output compartment interpreted as the urine compartment) using the plasma concentration-time profile and cumulative urinary excretions of PI polyamide B were tested. A scheme of the two-compartment model with the linear output compartment interpreted as the urine compartment is shown in Fig. 11B. The residual error models of the plasma concentration of PI polyamide B were the same as

The plasma concentration and cumulative urinary excretion-time profiles after intravenous administration of PI polyamide B were fitted well by the two-compartment model with the

Matsumoto et al., 2005).

compartments than using plasma data only.

estimations of 10000 simulations.

described in the part of PI polyamide A.


Table 5. Pharmacokinetic parameters of PI polyamide B from model fitting.

Fig. 11. Scheme of pharmacokinetic model describing the disposition and elimination of PI polyamides A (A) and B (B)

rates of PI polyamide A were tested. A scheme of the two-compartment model, with the linear output compartment interpreted as the urine compartment and the non-linear output compartment interpreted as the bile compartment, is shown in Fig. 11A.

X and V are the amount and volume of distribution in the corresponding compartments designated by the subscripts C, P, U, and B representing central, peripheral, urine, and bile compartments, respectively. CLD is the distribution clearance, CLR is the renal clearance, CLext is the clearance excluding renal and biliary clearances, VMAX is the maximum velocity for excretion into bile, and Km is the Michaelis constant for excretion into bile. Cc represents the plasma concentration of PI polyamide A. CU% and CB% represent the cumulative urinary and biliary excretion rates (percentage of administered dose), respectively.

The residual error model of the plasma concentration was assumed to be the proportional error model because the plasma concentration was measured by HPLC. The model of the cumulative urinary and biliary excretions was assumed to be the additive error model

k12 (L/min) 0.0109 k20 (L/min) 0.1476 V1 (mL/kg) 20.88 V2 (mL/kg) 45.86

Fig. 11. Scheme of pharmacokinetic model describing the disposition and elimination of PI

rates of PI polyamide A were tested. A scheme of the two-compartment model, with the linear output compartment interpreted as the urine compartment and the non-linear output

X and V are the amount and volume of distribution in the corresponding compartments designated by the subscripts C, P, U, and B representing central, peripheral, urine, and bile compartments, respectively. CLD is the distribution clearance, CLR is the renal clearance, CLext is the clearance excluding renal and biliary clearances, VMAX is the maximum velocity for excretion into bile, and Km is the Michaelis constant for excretion into bile. Cc represents the plasma concentration of PI polyamide A. CU% and CB% represent the cumulative

The residual error model of the plasma concentration was assumed to be the proportional error model because the plasma concentration was measured by HPLC. The model of the cumulative urinary and biliary excretions was assumed to be the additive error model

urinary and biliary excretion rates (percentage of administered dose), respectively.

compartment interpreted as the bile compartment, is shown in Fig. 11A.

polyamides A (A) and B (B)

Table 5. Pharmacokinetic parameters of PI polyamide B from model fitting.

Parameter Estimates

because the percentage of the administered dose was calculated from the urine and bile concentrations, urine and bile volumes, and administered dose. The choice of model was based on model fitting criteria such as visual inspection of the fitted curves, objective function value of NONMEM (OFV), and CV% of the parameter estimates (Hazra et al., 2007; Matsumoto et al., 2005).

The plasma concentration and cumulative urinary and biliary excretion-time profiles after intravenous administration of PI polyamide A were fitted well by the two-compartment model with the linear output compartment interpreted as the urine compartment and the non-linear output compartment interpreted as the bile compartment (Fig. 12). The 50th percentiles of the model-based prediction for plasma concentrations and cumulative urinary and biliary excretions are presented together with the observed value. To obtain 50th percentiles of the model estimations, 10000 simulations were performed using the estimated model parameters, variability in the estimated parameters, and residual variability of the data. Compared with a one-compartment model using only plasma data, more accurate data can be obtained from the two-compartment model including urine and bile data because PI polyamide A was excreted into urine and bile until at least 36 and 18 h, respectively, after administration. The plasma concentration-time profile in the elimination phase could also be described better using both the linear and non-linear compartments than using plasma data only.

Fig. 12. Plasma concentration–time profile (A), cumulative urinary excretion rate (B), and cumulative biliary excretion rate (C) of PI polyamide A after intravenous administration at 2.0 mg/kg to rats. Each data point represents observed data from three (for plasma and urine) and four rats (for bile). The solid line indicates 50th percentiles from model estimations of 10000 simulations.

To predict the plasma concentration-time profile in the elimination phase of PI polyamide B after intravenous administration, two pharmacokinetic models (i.e., one- and twocompartment models with the linear output compartment interpreted as the urine compartment) using the plasma concentration-time profile and cumulative urinary excretions of PI polyamide B were tested. A scheme of the two-compartment model with the linear output compartment interpreted as the urine compartment is shown in Fig. 11B. The residual error models of the plasma concentration of PI polyamide B were the same as described in the part of PI polyamide A.

The plasma concentration and cumulative urinary excretion-time profiles after intravenous administration of PI polyamide B were fitted well by the two-compartment model with the

Pyrrole-Imidazole Polyamides for Gene Therapy: Bioanalytical Methods and Pharmacokinetics 693

1981). It was suggested that the features of various compositions of Py and Im were related to their unique pharmacokinetic profiles. Further examination will be conducted using other

This work was supported in part by a Grand-in-Aid from the High-Tech Research Center Project for 2007-2011 and the Academic Frontier Project for 2006-2010 for Private Universities: matching fund subsidy from the Ministry of Education, Culture, Sports, Science and Technology. We thank Takashi Nagashima, Ph.D. and Akiko Fukawasa, Ph.D.

Alberts, S. R.; Erlichman, C.; Reid, J. M.; Sloan, J. A.; Ames, M. M.; Richardson, R. L. &

Brown, P. H.; Krishnamurthy, G. T.; Bobba, V. V. & Kingston, E. (1981). Radiation dose

Chou, C. J.; Farkas, M. E.; Tsai, S. M.; Alvarez, D.; Dervan, P. B. & Gottesfeld, J. M. (2008).

Dickinson, L. A.; Gulizia, R. J.; Trauger, J. W.; Baird, E. E.; Mosier, D. E.; Gottesfeld, J. M. &

Fukasawa, A.; Aoyama, T.; Nagashima, T.; Fukuda, N.; Ueno, T.; Sugiyama, H.; Nagase, H.

Fukasawa, A.; Nagashima, T.; Aoyama, T.; Fukuda, N.; Matsuda, H.; Ueno, T.; Sugiyama,

Hazra, A.; Pyszczynski, N.; DuBois, D. C.; Almon, R. R. & Jusko, W. J. (2007).

Goldberg, R. M. (1998). Phase I study of the duocarmycin semisyntheticderivative KW-2189 given daily for five days every six weeks. *Clin Cancer Res*, Vol. 4, No. 9,

calculation for Tc-99m HIDA in health and disease. *J Nucl Med*, Vol. 22, No. 2, pp.

Small molecules targeting histone H4 as potential therapeutics for chronic myelogenous leukemia. *Mol Cancer Ther*, Vol. 7, No. 4, pp. 769-778, ISSN 1535-7163

Dervan, P. B. (1998). Inhibition of RNA polymerase II transcription in human cells by synthetic DNA-binding ligands. *Proc Natl Acad Sci U S A*, Vol. 95, No. 22, pp.

& Matsumoto, Y. (2009). Pharmacokinetics of pyrrole-imidazole polyamides after intravenous administration in rat. *Biopharm Drug Dispos*, Vol. 30, No. 2, pp. 81-89,

H.; Nagase, H. & Matsumoto, Y. (2007). Optimization and validation of a highperformance liquid chromatographic method with UV detection for the determination of pyrrole-imidazole polyamides in rat plasma. *J Chromatogr B Analyt Technol Biomed Life Sci*, Vol. 859, No. 2, pp. 272-275, ISSN 1570-0232 (Print)

Pharmacokinetics of methylprednisolone after intravenous and intramuscular administration in rats. *Biopharm Drug Dispos*, Vol. 28, No. 6, pp. 263-273, ISSN 0142-

PI polyamides that have unique Py and Im combinations for gene therapy.

pp. 2111-2117, ISSN 1078-0432 (Print) 1078-0432 (Linking).

177-183, ISSN 0161-5505 (Print) 0161-5505 (Linking).

12890-12895, ISSN 0027-8424 (Print) 0027-8424 (Linking).

ISSN 1099-081X (Electronic) 0142-2782 (Linking).

(Print) 1535-7163 (Linking).

1570-0232 (Linking).

2782 (Print) 0142-2782 (Linking).

**6. Acknowledgements** 

for their help.

**7. References** 

linear output compartment interpreted as the urine compartment (Fig. 13). The 50th percentiles of the model-based prediction for plasma concentrations and cumulative urinary excretions are presented together with the observed value. To obtain 50th percentiles of the model estimations, 10000 simulations were performed using the estimated model parameters, variability in the estimated parameters, and residual variability of the data.

Fig. 13. Plasma concentration–time profile (A) and cumulative urinary excretion (B) of PI polyamide B after intravenous administration at 2.0 mg/kg to rats. Each data point represents observed data from three rats (for plasma and urine). The solid line indicates 50th percentiles from model estimations of 10000 simulations.

To predict the effective dose of PI polyamide B in Dahl-S rats administered at 1 mg every 2 or 3 days for 4 weeks, pharmacokinetic simulations of PI polyamide B were performed using a slightly modified pharmacokinetic model (Nagashima et al., 2009b) by NONMEM program. The average plasma concentrations of PI polyamide B after the administration at 1 mg every 3 and 2 days were 0.18 and 0.28 µg/mL, respectively, which were calculated by the area under the concentration-time curves between 0 and 27 days, divided by 27 days. PI polyamide B did not accumulate following multiple-dose administration.
