**2. Bioanalytics**

680 Non-Viral Gene Therapy

AURKB. They also demonstrated a marked antiproliferative synergy in human tumor cell lines as a result of induction of apoptosis-mediated severe catastrophe of cell-cycle progression (Takahashi et al., 2008). PI polyamides specifically inhibited lectin-like oxidized low-density lipoprotein receptor-1 mRNA expression and apoptosis induced by oxidized low-density lipoprotein and angiotensin II in human umbilical vein endothelial cells (Ueno et al., 2009). From these observations, PI polyamides have been identified as novel

Pharmacokinetics is the science that studies the behavior of a circulating drug administered to a body, mainly focusing on absorption, distribution, metabolism, and excretion (ADME) of a drug (Jang et al., 2001). The concentration of a drug in a body can be obtained by a bioanalytical method which includes sample extraction and detection of a drug, and the obtained data are analyzed to evaluate the pharmacokinetics of the drug. Needless to say, a robust bioanalytical procedure is crucial for evaluating the appropriate pharmacokinetic

In this chapter, we show the bioanalytical procedure, pharmacokinetics, and modeling of PI polyamides A and B. PI polyamides A and B are illustrated in Fig. 1. PI polyamide A was composed of Ac-ImPyPy-ImPyPy-β-Dp (β, β-alanine; Dp, *N*, *N*-dimethylaminopropylamide). PI polyamide B was composed of Ac-PyPy-β-PyImPy-PyPyPy-β-ImPy-β-Dp. The molecular weights of PI polyamides A and B were calculated from the sum of the standard atomic weights of all the atoms (Wieser, 2006). The molecular weights of PI polyamides A and B are 1035.12 and 1665.78, respectively. PI polyamide B was designed to bind to the activator protein-1 (AP-1)-binding site of the TGF-β1 promoter, whereas PI polyamide A also, with a hairpin structure, was designed for comparing with other types of PI polyamide with a hairpin

candidates for gene therapy.

structure and a higher molecular weight.

Fig. 1. Chemical structures of PI polyamides A and B.

profile of a drug.

High-performance liquid chromatography (HPLC) has been used for many years as a useful and conventional tool for the analysis of a drug. Bioanalytical methods by HPLC with UV detection were developed for the determination of PI polyamides A and B in the rat matrix. Sample extraction is one of the important steps and key to success in constructing a robust method. A simple protein precipitation method was developed for the extraction of PI polyamides A and B from rat plasma, whereas solid phase extraction was carried out to extract PI polyamides A and B from rat urine and bile, because a large number of urinary and biliary matrices can interfere with the compounds. It is important to determine the rates of urinary and biliary excretions because these excretions play pivotal roles in the elimination pathway of a drug. The developed methods were successively validated for selectivity, sensitivity, linearity, accuracy, and precision, following the guideline for Bioanalytical Method Validation published by Food and Drug Administration in 2001.

Chromatographic separation was conducted using a reversed-phase TSK-GEL ODS-80TM (4.6 mm x 150 mm) column maintained at 40 ºC. The mobile phase of solvent A was 0.1% acetic acid and that of solvent B was acetonitrile (a linear increase from 0 to 80% B over 10 min (plasma and urine) or 35 min (bile) and an isocratic flow at 60% B for 5 min). The flow rate was set at 1.0 mL/min (plasma and urine) or 0.75 mL/min (bile). The detection wavelength was set at 310 nm. PI polyamides A and B were well separated from the coextracted material under the described chromatographic conditions at approximate retention times of 9.7 (25.0 in bile) and 10.5 min, respectively. The peak shapes were satisfactory and completely resolved from one another. No interference from rat matrices was observed (Fukasawa et al., 2007).

Fig. 2. Representative chromatograms of blank rat plasma (A), blank rat urine (B) and blank rat bile (C) spiked with PI polyamide A, and blank rat plasma (D), blank rat urine (E) and blank rat bile (F) spiked with PI polyamide B. The concentrations of PI polyamides were 5 (A), 20 (B), 1 (C), 5 (D), 20 (E) and 5 (F) µg/mL.

Table 1 shows the intra- and inter-assay precision and accuracy of PI polyamides A and B. The intra- and inter-assay accuracies (RE) were within ± 20% for the lower limit of

Pyrrole-Imidazole Polyamides for Gene Therapy: Bioanalytical Methods and Pharmacokinetics 683

Fig. 3. Representative mass spectra of precursor ions (m/z, 1036 [M+H]+, 519 [M+2H]2+, and

Fig. 4**.** Representative product ion mass spectra (*m*/*z*, 519) of PI polyamide A.

Table 2 shows the intra- and inter-assay precision and accuracy of PI polyamide A. The intra- and inter-assay accuracies (RE) were within ± 20% for the LLOQ and ± 15% for the other QC samples. The intra- and inter-assay precisions (CV) were also within the acceptable ranges of 20% for the LLOQ and 15% for the other QC samples. The LLOQ was

346 [M+3H]3+) of PI polyamide A.

quantitation (LLOQ) and ± 15% for the other QC samples. The intra- and inter-assay precisions (CV) were also within the acceptable ranges of 20% for the LLOQ and 15% for the other QC samples. The LLOQ was determined as 1 µg/mL for both PI polyamides A and B. All of the methods were successfully applied to evaluate the pharmacokinetics of the PI polyamides (Fukasawa et al., 2009; Fukasawa et al., 2007; Nagashima et al., 2009b).


Table 1. Intra- and inter-assay accuracy and precision for the determination of PI polyamides A and B in rat plasma and urine.

Although HPLC with UV detection is a useful tool for the determination of a drug, the sensitivity is a limitation factor for evaluating pharmacokinetic characteristic for many hours. Recently, liquid chromatography-tandem mass spectrometry (LC-MS/MS) has been used for the determination of a drug, especially when a sensitivity higher than that of HPLC is required. A bioanalytical method for the determination of PI polyamide A in rat plasma was successfully developed and validated by ultra-performance liquid chromatography (UPLC)-MS/MS with electrospray ionization (Nagashima et al., 2009a).

An MS scan was conducted in the positive ion mode to obtain the precursor ion of PI polyamide A. The mass spectra of PI polyamide A showed significant ions at the *m/z* of 1036, 519, and 346, which corresponds to [M+H]+, [M+2H]2+, and [M+3H]3+, respectively (Fig. 3). The doubly charged polyamide showed the highest sensitivity during ionization. The product ion spectra of the doubly charged PI polyamide A are shown in Fig. 4. The multiple reaction monitoring (MRM) transition was selected at the *m/z* of 519 and 288.

Chromatographic separation was performed using an ACQUITY UPLC HSS T3 (1.8 µm, 2.1×50 mm) column with an in-line filter and maintained at 40 ºC. The liquid flow rate was set at 0.3 mL/min. The mobile phase of solvent A was acetonitrile/water/acetic acid (5/95/0.1, v/v/v) and that of solvent B was acetonitrile/water/acetic acid (95/5/0.1, v/v/v). The gradient started at the mobile phase A-B (95:5%), changed linearly to A-B (45:55%) until 2 min, washed with A-B (0:100%) until 3.5 min, and equilibrated under the initial condition until 5.5 min. PI polyamide A was well separated from the coextracted material under the described conditions at an approximate retention time of 1.5 min. No interference from rat matrices was observed (Fig. 5).

quantitation (LLOQ) and ± 15% for the other QC samples. The intra- and inter-assay precisions (CV) were also within the acceptable ranges of 20% for the LLOQ and 15% for the other QC samples. The LLOQ was determined as 1 µg/mL for both PI polyamides A and B. All of the methods were successfully applied to evaluate the pharmacokinetics of the PI

RE (%) CV (%) RE (%) CV (%)

Intra-assay Inter-assay

20 1.4 1.4 -8.7 9.7 100 7.7 3.7 3.6 3.5

20 -2.5 0.6 -9.2 7.9 100 3.7 2.6 3.2 3.2

20 -0.9 0.7 -4.7 3.6 200 0.4 0.3 -2.6 4.5

10 1.9 1.2 0.1 2.3 20 0.4 0.5 0.1 0.8

polyamides (Fukasawa et al., 2009; Fukasawa et al., 2007; Nagashima et al., 2009b).

Nominal concentration (μg/mL)

Matrix

Plasma PI polyamide A 1 2.2 5.3 6.7 14.4

Urine PI polyamide A 1 13.4 1.2 4.6 7.9

Table 1. Intra- and inter-assay accuracy and precision for the determination of PI

(UPLC)-MS/MS with electrospray ionization (Nagashima et al., 2009a).

polyamides A and B in rat plasma and urine.

interference from rat matrices was observed (Fig. 5).

PI polyamide B 1 2.8 10.0 2.2 15.0

PI polyamide B 1 7.3 1.9 11.9 4.4

Although HPLC with UV detection is a useful tool for the determination of a drug, the sensitivity is a limitation factor for evaluating pharmacokinetic characteristic for many hours. Recently, liquid chromatography-tandem mass spectrometry (LC-MS/MS) has been used for the determination of a drug, especially when a sensitivity higher than that of HPLC is required. A bioanalytical method for the determination of PI polyamide A in rat plasma was successfully developed and validated by ultra-performance liquid chromatography

An MS scan was conducted in the positive ion mode to obtain the precursor ion of PI polyamide A. The mass spectra of PI polyamide A showed significant ions at the *m/z* of 1036, 519, and 346, which corresponds to [M+H]+, [M+2H]2+, and [M+3H]3+, respectively (Fig. 3). The doubly charged polyamide showed the highest sensitivity during ionization. The product ion spectra of the doubly charged PI polyamide A are shown in Fig. 4. The multiple reaction monitoring (MRM) transition was selected at the *m/z* of 519 and 288. Chromatographic separation was performed using an ACQUITY UPLC HSS T3 (1.8 µm, 2.1×50 mm) column with an in-line filter and maintained at 40 ºC. The liquid flow rate was set at 0.3 mL/min. The mobile phase of solvent A was acetonitrile/water/acetic acid (5/95/0.1, v/v/v) and that of solvent B was acetonitrile/water/acetic acid (95/5/0.1, v/v/v). The gradient started at the mobile phase A-B (95:5%), changed linearly to A-B (45:55%) until 2 min, washed with A-B (0:100%) until 3.5 min, and equilibrated under the initial condition until 5.5 min. PI polyamide A was well separated from the coextracted material under the described conditions at an approximate retention time of 1.5 min. No

Fig. 3. Representative mass spectra of precursor ions (m/z, 1036 [M+H]+, 519 [M+2H]2+, and 346 [M+3H]3+) of PI polyamide A.

Fig. 4**.** Representative product ion mass spectra (*m*/*z*, 519) of PI polyamide A.

Table 2 shows the intra- and inter-assay precision and accuracy of PI polyamide A. The intra- and inter-assay accuracies (RE) were within ± 20% for the LLOQ and ± 15% for the other QC samples. The intra- and inter-assay precisions (CV) were also within the acceptable ranges of 20% for the LLOQ and 15% for the other QC samples. The LLOQ was

Pyrrole-Imidazole Polyamides for Gene Therapy: Bioanalytical Methods and Pharmacokinetics 685

under the first moment curve (AUMC(0-Tlast)) were obtained using the linear trapezoidal rule. AUC(Tlast-∞) and AUMC(Tlast-∞) were respectively calculated using Cn/λz and tnCn/λ<sup>z</sup> + Cn/λz 2, where Cn is the last quantifiable concentration. Terminal-phase rate constant (λz) was calculated by the regression of the terminal log-linear portion of the plasma concentration curve. Terminal elimination half-life (t1/2) was calculated to be 0.693/λz. Systemic clearance (CLt), mean residence time (MRT), and the volume of distribution in the steady state (Vss) were calculated as dose/AUC, AUMC/AUC, and CLt•MRT, respectively. The plasma concentrations of PI polyamides A and B were extrapolated to time zero (C0). The maximum plasma concentration (Cmax) of PI polyamide B was directly

Fig. 6. Mean plasma concentration–time profiles of PI polyamides in rats after intravenous

The pharmacokinetic parameters of PI polyamides A and B obtained in rats using noncompartmental analysis are summarized in Table 3. After the intravenous administration of PI polyamide A at 1.3, 2.0, 7.5, and 15.0 mg/kg, the average t1/2, CLt, and Vss values were in the ranges of 42.3-74.8 min, 4.6-6.4 mL/min/kg, and 244-412 mL/kg, respectively. After the intravenous administration of PI polyamide B at 1.0, 2.0, 3.0, and 5.0 mg/kg, the average t1/2, CLt, and Vss values were in the ranges of 27.5-58.7 min, 7.3-11.9 mL/min/kg, and 407- 667 mL/kg, respectively. The CLt and Vss of PI polyamides A and B showed no significant differences as functions of administration dose. The pharmacokinetics of PI polyamides A and B are linear in the intravenous dose ranges of 1.3-15.0 mg/kg and 1.0-5.0 mg/kg, respectively as revealed by the fact that AUC increased linearly as a function of dose, and

The plasma concentration-time profiles after the intravenous administration of PI polyamide B resembled those after the oral administration. After the intravenous administration of PI polyamide B at 1.0, 2.0, 3.0, and 5.0 mg/kg, Cmax gradually increased. The concentrations of PI polyamide B in the lungs, liver, heart, kidney and spleen were measured. The mean concentrations of PI polyamide B in the lungs were the highest among those in other tissues, and the mean concentrations 10, 30, and 60 min after injection were 134.7, 97.0, and 73.9 μg/g, respectively. Among various tissues, the concentration of PI polyamide B was observed to be highest in the lungs. The mean lung concentration of PI polyamide B

administration. (A) and (B) show PI polyamides A and B.

obtained from the observed data.

CLt and Vss remained unaltered.

decreased with time.

10 ng/mL, which means it has a sufficient sensitivity to evaluate the pharmacokinetics of PI polyamides.

Fig. 5. Representative MRM chromatograms (*m/z*, 519>288) of (A) blank rat plasma, (B) blank rat plasma spiked with PI polyamide A (10 ng/mL).


Table 2. Intra- and inter-assay accuracy and precision for the determination of PI polyamide A in rat plasma.

#### **3. Pharmacokinetics of PI polyamides A and B**

#### **3.1 Plasma and lung concentrations of PI polyamides A and B**

PI polyamide B significantly inhibited the expressions of TGF-β1 mRNA and protein in the renal cortex of the Dahl-S rats and reduced the rates of increases in the amounts of urinary protein and albumin in the Dahl-S rats independent of blood pressure at a dose of 1.0 mg (Matsuda et al., 2006). From these observations, the doses of PI polyamides were selected on the basis of 1.0 mg dose of PI polyamide B per rat (about 3.0 mg/kg). PI polyamide B had a lower water solubility than PI polyamide A. The doses of PI polyamides A and B were determined to be in the ranges of 1.3-15.0 mg/kg and 1.0-5.0 mg/kg, respectively.

The mean plasma concentration-time profiles after the intravenous administration of PI polyamide A at 1.3, 2.0, 7.5, and 15.0 mg/kg and after that of PI polyamide B at 1.0, 2.0, 3.0, and 5.0 mg/kg are shown in Fig. 6. The plasma concentrations of PI polyamides A and B declined in a polyexponential manner for the four doses studied. The plasma concentration-time profiles of PI polyamides were analyzed by a non-compartmental method. The area under the plasma concentration-time curve (AUC(0-Tlast)) and the area

10 ng/mL, which means it has a sufficient sensitivity to evaluate the pharmacokinetics of PI

Fig. 5. Representative MRM chromatograms (*m/z*, 519>288) of (A) blank rat plasma, (B)

Table 2. Intra- and inter-assay accuracy and precision for the determination of PI polyamide

PI polyamide B significantly inhibited the expressions of TGF-β1 mRNA and protein in the renal cortex of the Dahl-S rats and reduced the rates of increases in the amounts of urinary protein and albumin in the Dahl-S rats independent of blood pressure at a dose of 1.0 mg (Matsuda et al., 2006). From these observations, the doses of PI polyamides were selected on the basis of 1.0 mg dose of PI polyamide B per rat (about 3.0 mg/kg). PI polyamide B had a lower water solubility than PI polyamide A. The doses of PI polyamides A and B were determined to be in the ranges of 1.3-15.0 mg/kg and 1.0-5.0

The mean plasma concentration-time profiles after the intravenous administration of PI polyamide A at 1.3, 2.0, 7.5, and 15.0 mg/kg and after that of PI polyamide B at 1.0, 2.0, 3.0, and 5.0 mg/kg are shown in Fig. 6. The plasma concentrations of PI polyamides A and B declined in a polyexponential manner for the four doses studied. The plasma concentration-time profiles of PI polyamides were analyzed by a non-compartmental method. The area under the plasma concentration-time curve (AUC(0-Tlast)) and the area

RE (%) CV (%) RE (%) CV (%)

Intra-assay Inter-assay

10 -10.6 3.3 3.7 11.2 1000 -11.7 1.5 -2.1 9.2 10000 -0.6 4.6 -5.0 8.9

blank rat plasma spiked with PI polyamide A (10 ng/mL).

**3. Pharmacokinetics of PI polyamides A and B** 

**3.1 Plasma and lung concentrations of PI polyamides A and B** 

Nominal concentration (ng/mL)

polyamides.

A in rat plasma.

mg/kg, respectively.

under the first moment curve (AUMC(0-Tlast)) were obtained using the linear trapezoidal rule. AUC(Tlast-∞) and AUMC(Tlast-∞) were respectively calculated using Cn/λz and tnCn/λ<sup>z</sup> + Cn/λz 2, where Cn is the last quantifiable concentration. Terminal-phase rate constant (λz) was calculated by the regression of the terminal log-linear portion of the plasma concentration curve. Terminal elimination half-life (t1/2) was calculated to be 0.693/λz. Systemic clearance (CLt), mean residence time (MRT), and the volume of distribution in the steady state (Vss) were calculated as dose/AUC, AUMC/AUC, and CLt•MRT, respectively. The plasma concentrations of PI polyamides A and B were extrapolated to time zero (C0). The maximum plasma concentration (Cmax) of PI polyamide B was directly obtained from the observed data.

Fig. 6. Mean plasma concentration–time profiles of PI polyamides in rats after intravenous administration. (A) and (B) show PI polyamides A and B.

The pharmacokinetic parameters of PI polyamides A and B obtained in rats using noncompartmental analysis are summarized in Table 3. After the intravenous administration of PI polyamide A at 1.3, 2.0, 7.5, and 15.0 mg/kg, the average t1/2, CLt, and Vss values were in the ranges of 42.3-74.8 min, 4.6-6.4 mL/min/kg, and 244-412 mL/kg, respectively. After the intravenous administration of PI polyamide B at 1.0, 2.0, 3.0, and 5.0 mg/kg, the average t1/2, CLt, and Vss values were in the ranges of 27.5-58.7 min, 7.3-11.9 mL/min/kg, and 407- 667 mL/kg, respectively. The CLt and Vss of PI polyamides A and B showed no significant differences as functions of administration dose. The pharmacokinetics of PI polyamides A and B are linear in the intravenous dose ranges of 1.3-15.0 mg/kg and 1.0-5.0 mg/kg, respectively as revealed by the fact that AUC increased linearly as a function of dose, and CLt and Vss remained unaltered.

The plasma concentration-time profiles after the intravenous administration of PI polyamide B resembled those after the oral administration. After the intravenous administration of PI polyamide B at 1.0, 2.0, 3.0, and 5.0 mg/kg, Cmax gradually increased. The concentrations of PI polyamide B in the lungs, liver, heart, kidney and spleen were measured. The mean concentrations of PI polyamide B in the lungs were the highest among those in other tissues, and the mean concentrations 10, 30, and 60 min after injection were 134.7, 97.0, and 73.9 μg/g, respectively. Among various tissues, the concentration of PI polyamide B was observed to be highest in the lungs. The mean lung concentration of PI polyamide B decreased with time.

Pyrrole-Imidazole Polyamides for Gene Therapy: Bioanalytical Methods and Pharmacokinetics 687

1422.51 was excreted at 2% into rat urine 24 h after administration and was not detected in rat bile (data not shown). These findings suggested that PI polyamides with high molecular weights tend to be poorly excreted in both rat urine and bile, whereas those with molecular weights less than that of PI polyamide A can be readily eliminated. As described above, the differences in the elimination pathway between PI polyamides A and B may be attributed to

Fig. 7. Urinary excretion rate versus time profile of PI polyamides A (A) and B (B) in rats.

Fig. 8. Biliary excretion rate versus time profile of PI polyamide A in rats.

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

**4. Pharmacokinetic modeling and simulations** 

**4.1 Pharmacokinetic modeling** 

the differences in their molecular weights.


#### PI polyamide B


Table 3. Mean non-compartmental pharmacokinetic parameters of PI polyamides after intravenous administration at various doses into rats (n = 3).

#### **3.2 Urinary and biliary excretions**

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 were detected for all the samples.

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 1422.51 was excreted at 2% into rat urine 24 h after administration and was not detected in rat bile (data not shown). These findings suggested that PI polyamides with high molecular weights tend to be poorly excreted in both rat urine and bile, whereas those with molecular weights less than that of PI polyamide A can be readily eliminated. As described above, the differences in the elimination pathway between PI polyamides A and B may be attributed to the differences in their molecular weights.

Fig. 7. Urinary excretion rate versus time profile of PI polyamides A (A) and B (B) in rats.

Fig. 8. Biliary excretion rate versus time profile of PI polyamide A in rats.
