Modeled Rat Hepatic and Plasma Concentrations of Chemicals after Virtual Administrations Using Two Sets of in Silico Liver-to-Plasma Partition Coefficients

Abstract

The hepatic elimination of chemical substances in pharmacokinetic models requires hepatic intrinsic clearance (CL_h,int) parameters for unbound drug in the liver, and these are regulated by the liver-to-plasma partition coefficients (K_p,h). Both Poulin and Theil and Rodgers and Rowland have proposed in silico expressions for K_p,h for a variety of chemicals. In this study, two sets of in silico K_p,h values for 14 model substances were assessed using experimentally reported in vivo steady-state K_p,h data and time-dependent virtual internal exposures in the liver and plasma modeled by forward dosimetry in rats. The K_p,h values for 14 chemicals independently calculated using the primary Poulin and Theil method in this study were significantly correlated with those obtained using the updated Rodgers and Rowland method and with reported in vivo steady-state K_p,h data in rats. When pharmacokinetic parameters were derived based on individual in vivo time-dependent data for diazepam, phenytoin, and nicotine in rats, the modeled liver and plasma concentrations after intravenous administration of the selected substrates in rats using two sets of in silico K_p,h values were mostly similar to the reported time-dependent in vivo internal exposures. Similar results for modeled liver and plasma concentrations were observed with input parameters estimated by machine-learning systems for hexobarbital, fingolimod, and pentazocine, with no reference to experimental pharmacokinetic data. These results suggest that the output values from rat pharmacokinetic models based on in silico K_p,h values derived from the primary Poulin and Theil model would be applicable for estimating toxicokinetics or internal exposure to substances.

INTRODUCTION

Physiologically based pharmacokinetic (PBPK) models are widely used to predict pharmacokinetics and toxicokinetics in humans and animals.^1–4) The hepatic elimination of chemicals in these PBPK models requires important parameters such as the hepatic intrinsic clearance (CL_h,int) of the unbound fraction (f_u,p) of the substance; CL_h,int values are dependent on liver-to-plasma partition coefficients (K_p,h). Poulin and Theil proposed a mathematical formula for calculating in silico K_p,h values.^5–7) Rodgers and Rowland^8–10) also modified in silico models using more complex equations to account for the ionization states of substances. There have been limited reports^11,12) comparing the applications of K_p,h values derived using these two different methods in PBPK models when assessing in vivo time-course data. The views on the relative accuracies of these two in silico K_p,h models are not consistent.^11–14)

Interactions between human cytochrome P450 (P450) 2C and 3A substrates lead to increased incidences of hepatic toxicity. Among the many relevant factors, polymorphic impaired P450 2C9 or 3A4 variants may underlie these probe drug toxicities. In the course of virtual estimations of plasma and hepatic concentrations of celecoxib¹⁵⁾ and atorvastatin¹⁶⁾ in Asian subjects harboring P450 2C9 or 3A4 variants, we recently used in silico K_p,h values from Poulin and Theil^5,6) to estimate high internal exposure to these medicines. To assess these modeled high virtual plasma or hepatic exposures in special subjects harboring impaired P450 variants by pharmacokinetic modeling, selection of the in silico K_p,h model may be a critical factor.

The aim of this study was to compare the in silico K_p,h values derived using the Poulin and Theil method and those of the Rodgers and Rowland method with in vivo steady-state K_p,h values experimentally determined in recent surveys of 14 substances in rats.¹⁶⁾ The reported values were somewhat different from those obtained in our preliminary calculation using their own in silico physicochemical properties. Furthermore, we compared the reported and predicted hepatic and plasma concentrations after intravenous administration of six selected substrates in rats available in the literature using two sets of in silico K_p,h values as input parameters for simplified rat PBPK models. Herein, we report mostly similar results for the output values from rat pharmacokinetic models based on in silico K_p,h values derived from the simply applicable Poulin and Theil model and the highly selective Rodgers and Rowland models for estimating toxicokinetics or internal exposure to substances with unknown parameter values.

MATERIALS AND METHODS

PBPK Modeling

In the current study, reported values for octanol–water partition coefficient (log P), plasma unbound fraction (f_u,p), acid dissociation constant (pK_a) and K_p,h derived from Poulin and Theil and Rodgers and Rowland models of 14 substances (previously obtained using Gastro Plus software) were taken from the literature.¹²⁾ These literature-derived in silico physicochemical property values were also calculated using different software packages in this study. In silico physicochemical properties, namely, pK_a, f_u,p, and log P, of the test chemicals were obtained by in silico estimation using ACD/Percepta (Advanced Chemistry Development, Toronto, ON, Canada), Simcyp (Certara UK, Sheffield, U.K.), and ChemDraw (PerkinElmer, Inc., Waltham, PA, U.S.A.) software, respectively.^17–19) The hepatic and plasma concentrations over time and the area under the curve (AUC) of the chemical substances were estimated using simplified PBPK models consisting of metabolizing (liver), excreting (kidney), central (main), and distributing (sub) compartments. The details of establishing a simplified PBPK model have been recently reported.¹⁸⁾ The input parameters for the simplified PBPK model of the six substances are listed in Tables 1 and 2. The pharmacokinetic parameters of orally administered diazepam, phenytoin, and nicotine in rats were previously established based on individual in vivo time-dependent concentration data.^20,21) Input parameters for hexobarbital, fingolimod, and pentazocine were estimated using machine learning systems under considerations of a wide variety of chemical space^22–24) without any reference to experimental pharmacokinetic data.

Table 1. Chemical Properties, Reported K_p,h Values, and in Silico K_p,h Values Derived in This Study Using the Poulin and Theil and Rodgers and Rowland Models

Chemical	Substance type		Octanol–water partition coefficient, log P		Plasma unbound fraction, fu,p		Acid dissociation constant, pKa		Liver-to-plasma partition coefficients, Kp,h
	Reported12)	Calculated	Reported12)	Calculated	Reported12)	Calculated	Reported12)	Calculated	In silico Poulin and Theil		In silico Rodgers and Rowland		In vivo stead-state Kp,h from literature
									Reported12)	Calculated	Reported12)	Calculated	Reported12)
Verapamil	Base	Strong base	4.45	4.47	0.172	0.0950	8.46	9.60	7.12	7.16	7.49	82.7	10.1
Nicotine	Base	Strong base	0.72	0.93	0.824	0.721	3.05, 8.56	7.85	0.80	0.81	26.8	2.11	7.00
Tolbutamide	Acid	Acid	2.27	0.52	0.0688	0.201	5.37, 10.9	5.64	2.08	0.50	0.11	1.55	0.30
Diltiazem	Base	Strong base	3.65	3.65	0.270	0.169	8.33	8.37	7.19	6.97	14.8	45.8	3.97
Phenytoin	Acid	Acid	1.71	2.09	0.0944	0.189	−2.83, 1.1 (base) 6.76, 11.4 (acid)	8.28	0.99	1.80	0.14	4.14	0.88
Propranolol	Base	Strong base	2.89	2.75	0.354	0.384	9.48	8.99	5.44	4.88	21.9	20.3	1.24
Diazepam	Base	Ampholyte	2.80	2.96	0.0982	0.124	2.96	13.9, 3.52	4.03	4.80	1.37	20.9	2.03
Fingolimod	Base	Strong base	3.72	5.06	0.207	0.0480	9.21	8.63	7.25	6.95	13.1	29.3	31.4
Chloroquine	Base	Strong base	5.11	5.06	0.0819	0.0540	1.02, 7.25, 9.86	10.7	7.15	6.99	28.5	130	420
Cyclosporine A	Neutral	Acid	3.18	2.90a)	0.241	0.130	–	10.3	5.60	4.59	4.64	18.4	16.6
Ethoxybenzamide	Neutral	Weak base	1.32	1.37	0.362	0.422	11.8	0.09	0.82	0.89	0.48	1.99	1.40
Pentazocine	Base	Weak baseb)	4.20	4.67	0.235	0.550	8.16 (base) 10.3 (acid)	8.04	7.10	10.2	20.2	178	0.47
Hexobarbital	Acid	Acid	1.81	1.63	0.282	0.238	8.17	8.10	1.31	1.02	0.59	2.47	1.30
Quinidine	Base	Strong base	2.65	3.44	0.432	0.325	3.87, 7.95	8.56	4.41	7.42	16.1	23.2	5.50

a) Because ChemDraw software gave 14.4 for log P resulting in a 10⁻⁶ value for f_u,p of cyclosporine A, this property was taken from another report.⁹⁾ b) The pK_a base for pentazocine (8.16) yielded a negative value for K_{p,h_Rodgers and Rowland} using Eq. (4), and a positive in silico K_p,h value was obtained using Eq. (3) for a weak base.

Table 2. Calculated Input Parameters for PBPK Modeling for the Six Selected Substances Available in Literature

Chemical	Blood-to-plasma concentration ratio, Rb	Volume of systemic circulation, V1 (L)	Hepatic intrinsic clearance, CLh,int (L/h)	Hepatic clearance, CLh (L/h)	Renal clearance, CLr (L/h)	Reference for time-dependent pharmacokinetics or input parameters by machine-learning systems
Group 1 (Fig. 3)
Diazepam	0.851	0.264	7.21	0.436	0.0465	20)
Phenytoin	0.887	0.365	0.0760	0.0141	0.00145	20)
Nicotine	0.842	1.08	3.98	0.657	0.0994	21)
Group 2 (Fig. 4)
Hexobarbital	0.904	0.840	3.61	0.428	0.0428	22–24)
Fingolimod	0.770	0.595	4.45	0.171	0.0171	22–24)
Pentazocine	0.903	1.56	6.99	0.698	0.0698	22–24)

A set of differential equations was solved for the amounts and concentrations:

  

  

  

  

where V₁, V_h, V_r, C_h, C_r, C_b, X_p, k₁₂, k₂₁, and R_i.v are the volumes of systemic circulation, liver and kidney; hepatic, renal, and blood substrate concentrations; a peripheral-compartment substrate amount; the rate constants for transfer of the drug from/to the central (first) compartment and to/from the peripheral (second) compartment; and the rate of administration, respectively.²³⁾ V_h, V_r, and Q_h/Q_r are the liver (8.5 mL) and kidney (3.7 mL) volumes and the blood flow rates of the systemic circulation to the hepatic/renal compartments (0.853 L/h) in rats (0.25 kg body weight).^25,26) The blood-to-plasma concentration ratio (R_b) was calculated from the f_u,p, and log P values as follows:

  

where

  

The Poulin and Theil model and the Rodgers and Rowland model for K_p,h are shown in Eqs. (1), (3), (4), (7) and (8) below.

Poulin and Theil Model

K_p,h (hereafter K_{p,h_Poulin and Theil}) values can be expressed using Eqs. (1) and (2):

  

(1)

  

(2)

where P is the octanol–water partition coefficient, V_nlt is the fractional tissue volume of neutral lipids (0.0138), V_nlp is the fractional plasma volume of neutral lipids (0.00147), V_pht is the fractional tissue volume of phospholipids (0.0303), V_php is the fractional plasma volume of phospholipids (0.00083), V_wt is the fractional tissue volume of water (0.705), V_wp is the fractional plasma volume of water (0.96), and f_u,t and f_u,p are the plasma and tissue unbound fractions, respectively.^5,6)

Rodgers and Rowland Model

K_p,h (hereafter K_{p,h_Rodgers and Rowland}) values for (1) acid to very weak bases, zwitterionic compounds, and moderate to strong bases; (2) moderate to strong bases; (3) zwitterionic compounds with one pK_a (base) ≥7, and (4) di-basic and di-acidic zwitterionic compounds can be expressed using different equations:

Acid to Very Weak Bases and Zwitterionic Compounds

  

(3)

where X and Y can be expressed as follows:

for very weak monoprotic bases:

  

for monoprotic acids:

  

for neutral substances:

  

for zwitterions:

  

where [PR]_T and [PR]_P are the concentrations of albumin or lipoprotein in tissue and plasma, respectively, and [PR]_T/[PR]_P is obtained from the literature⁹⁾; pH_p is the plasmatic pH (7.4)²⁷⁾; pH_IW is the intracellular water pH (7.0)²⁸⁾; f_NL is the fractional tissue volume of neutral lipid (0.0135)⁹⁾; f_NP is the fractional tissue volume of neutral phospholipid (0.0238)⁹⁾; f_EW is the tissue fraction of extracellular water (0.642)⁹⁾; f_IW is the tissue fraction of intracellular water in liver (0.642)⁹⁾; f_NL,P is the fractional tissue volume of neutral lipid in plasma (0.0023)^5,9,29); and f_NP,P is the fractional tissue volume of neutral phospholipid in plasma (0.0013).^5,9,29)

Moderate to Strong Bases with One pK_a (Base) ≥8

  

(4)

  

(5)

  

(6)

where Ka_BC is the ionization constant in blood cells, Kpu_BC is the blood cell to plasma water concentration ratio with R_b instead of B:P,³⁰⁾ [AP⁻]_T is the tissue concentration of acidic phospholipids in the liver (4.56),¹⁰⁾pH_BC is the blood cell pH (7.2),³¹⁾ and H_t is the rat hematocrit (0.45).¹⁹⁾

Zwitterionic Compounds with One pK_a (Base) ≥7

  

(7)

X and Y can be expressed as follows:

  

  

Di-basic and Di-acidic Zwitterionic Compounds with One pK_a (Base) ≥7

  

(8)

  

(9)

X, Y, and Z are defined as follows:

For di-basic group zwitterions:

  

  

  

For di-acidic group:

  

  

  

The necessary input parameters V₁ and CL_h,int for PBPK models for nicotine, phenytoin, and diazepam were conventionally computed to achieve the best fit to reported rat plasma concentrations.^20,21) The in silico derived input parameters for rat PBPK models of hexobarbital, fingolimod, and pentazocine were generated using a previously reported machine learning system.^22–24)

RESULTS AND DISCUSSION

The relationships between the in silico K_p,h values derived from the Poulin and Theil model and the Rodgers and Rowland model based on reported and calculated in silico physicochemical property values were compared for 14 chemicals, as validated in the previous study¹²⁾ (Fig. 1). A significant correlation of K_p,h values by the Poulin and Theil model reported¹²⁾ using ADMET Predictor software and calculated independently in the current study was confirmed (r = 0.93, p < 0.01; Fig. 1A); there were no significant effects when the input physicochemical properties calculated using different software packages were used for the Poulin and Theil model. Despite there being only an apparent relationship (r = 0.51, p = 0.06) between reported and calculated K_p,h values by the Rodgers and Rowland model (Fig. 1B), a significant positive correlation between K_{p,h_Poulin and Theil} and K_{p,h_Rodgers and Rowland} values for the 14 chemicals independently calculated in this study was confirmed (r = 0.80, p < 0.01; Fig. 1C); there were some differences in the output K_{p,h_Rodgers and Rowland} values depending on the input physicochemical property values used for the Rodgers and Rowland models (Table 1). When comparing the in silico K_p,h values calculated based on the in silico physicochemical properties derived using our methods, the Rodgers and Rowland models tended to produce larger K_p,h values than those of the Poulin and Theil model (Fig. 1C, Table 1).

Fig. 1. Comparison of in Silico K_p,h Values for 14 Chemicals Reported in the Literature and Those Calculated in This Study Using Two Different Methods

(A) A significant positive correlation is shown of K_p,h values obtained using the Poulin and Theil model (K_{p,h_Poulin and Theil}) calculated in the current study and those reported using Gastro Plus software.¹²⁾ Solid and dotted lines, respectively, show the linear regression line and 95% confidence intervals. (B) An apparent relationship of reported K_p,h values calculated using the Rodgers and Rowland model (K_{p,h_ Rodgers and Rowland}) and those calculated in the current study is shown with the linear regression line and 95% confidence intervals. (C) A significant positive correlation between K_{p,h_Poulin and Theil} and K_{p,h_Rodgers and Rowland} values for 14 chemicals calculated independently in this study are shown with the linear regression line and 95% confidence intervals (solid and dotted lines, respectively).

Figure 2 shows comparisons between the in vivo experimentally reported K_p,h values and in silico derived K_p,h values. A significant correlation was observed between the experimentally determined K_p,h and in silico K_{p,h_Poulin and Theil} values for 14 chemicals (r = 0.53, p = 0.050), but not between the experimentally determined K_p,h and in silico K_{p,h_Rodgers and Rowland} values (r = 0.46, p = 0.096). The average absolute fold errors of K_{p,h_Poulin and Theil} and K_{p,h_Rodgers and Rowland} values for the 14 chemicals were 3.28 and 5.48, respectively. This finding suggested that the Rodgers and Rowland model exhibits larger errors than the Poulin and Theil model under the present conditions. These results indicate that the Rodgers and Rowland model tended to overestimate K_p,h, whereas the Poulin and Theil model tended to underestimate K_p,h (Figs. 1, 2) for the 14 selected substances under present conditions.

Fig. 2. Significant and Apparent Correlations of Reported Experimentally Determined K_p,h Values for 14 Chemicals¹²⁾ and in Silico K_{p,h_Poulin and Theil} (Open Circles) and K_{p,h_Rodgers and Rowland} (Gray Circles) Values Independently Calculated in This Study

A significant linear regression line and 95% confidence intervals are shown for in silico K_{p,h_Poulin and Theil} values (solid and dotted lines).

After pharmacokinetic parameters were established based on individual in vivo time-dependent concentration data for diazepam, phenytoin, and nicotine in rats, the modeled liver and plasma concentrations after intravenous administration in rats were determined using two sets of in silico derived K_p,h values. Figure 3 shows the reported measured plasma and liver concentrations for substances and the predicted plasma and liver concentrations over time generated using the above-described PBPK models based on two sets of calculated K_p,h values, i.e., those derived using the Poulin and Theil model and the Rodgers and Rowland model.

Fig. 3. Liver and Plasma Concentrations of Diazepam (Single Intravenous Administration of 1.2 mg/kg), Phenytoin (Single Intravenous Administration of 10 mg/kg), and Nicotine (Single Intra-Arterial Administration of 0.1 mg/kg) in Rats Were Estimated Using PBPK Models after Virtual Intravenous Administrations Using Two Sets of in Silico K_p,h Values

The input pharmacokinetic parameters for the PBPK model were derived based on in vivo time-dependent data for diazepam, phenytoin, and nicotine in rats. Liver (solid lines) and plasma (dashed lines) concentrations of diazepam (A), phenytoin (B), and nicotine (C) in rats after virtual intravenous administrations were modeled using in silico K_{p,h_Poulin and Theil} (in black) or K_{p,h_Rodgers and Rowland} (in gray) values calculated in this study. The reported in vivo plasma (open circles) and liver (gray circles) concentrations for diazepam,²⁰⁾ phenytoin,²⁰⁾ and nicotine²¹⁾ are also shown.

The measured and predicted AUC values in plasma and liver were calculated and are presented in Table 3 for the selected substances. Ratios of measured to predicted AUC in plasma were confirmed to be within a 2- or 3-fold range, providing evidence for valid PBPK model predictions. The ratios of the measured to predicted hepatic AUCs for diazepam (Fig. 3A) and phenytoin (Fig. 3B) were 1.9-fold and 2.1-fold, respectively, for the Poulin and Theil model, and 8.5-fold and 4.6-fold, respectively, for the Rodgers and Rowland models (Table 3). The Poulin and Theil model performed better than the Rodgers and Rowland models for the measured hepatic concentrations of diazepam and phenytoin (Figs. 3A, B). In contrast, the predicted liver concentrations of nicotine using the two sets of K_p,h values were not consistent with the reported measured liver concentrations (Fig. 3C).

Table 3. The Estimated or Reported Plasma and Hepatic AUC Values Obtained Using Rat PBPK Models after Virtual Administration

	AUC, ng h/mL
	In vivo reported, Reference		In silico Poulin and Theil	In silico Rodgers and Rowland
Plasma
Diazepam	AUC0–8  h	222 (1.0)6)	683 (3.1)	684 (3.1)
Phenytoin	AUC0–3  h	11700 (1.0)32)	6080 (0.52)	5970 (0.51)
Nicotine	AUC0–5  h	38.4 (1.0)33)	36.6 (0.95)	36.6 (0.95)
Hexobarbital	AUC0–1.5  h	28100 (1.0)34)	18300 (0.65)	18200 (0.65)
Fingolimod	AUC0–12 h	2090 (1.0)35)	2960 (1.4)	2830 (1.4)
Pentazocine	AUC0–1.5  h	462 (1.0)36)	338 (0.73)	283 (0.61)
Liver
Diazepam	AUC0–8 h	806 (1.0)6)	1530 (1.9)	6840 (8.5)
Phenytoin	AUC0–3 h	5210 (1.0)32)	10700 (2.1)	24100 (4.6)
Nicotine	AUC0–5 h	200 (1.0)33)	5.97 (0.030)	15.5 (0.078)
Hexobarbital	AUC0–1.5  h	29500 (1.0)34)	8840 (0.30)	21300 (0.72)
Fingolimod	AUC0–24 h	63200 (1.0)35)	16100 (0.25)	68300 (1.1)
Pentazocine	AUC0–5 h	543 (1.0)36)	1110 (2.0)	16900 (31)

The numbers in parentheses indicate fold changes relative to the reported in vivo values.

The ratios of the predicted to reported hepatic AUC values for hexobarbital, fingolimod, and pentazocine were 0.30-, 0.25-, and 2.0-fold, respectively, using the Poulin and Theil model, and 0.72-, 1.1-, and 31-fold, respectively, using the Rodgers and Rowland models (Table 3, Fig. 4). For hexobarbital (Fig. 4A) and fingolimod (Fig. 4B), the predicted liver concentrations derived from the Rodgers and Rowland model were more accurate than those derived from the Poulin and Theil model. However, for pentazocine, the opposite result was observed: the predicted liver concentrations derived using the Rodgers and Rowland model were overestimated (Fig. 4C). The actual reasons for some discrepancies between the modeled and reported time profiles of the liver and plasma concentrations are not clear. It should be noted that most reported experimental values have been obtained in intravenous administration experiments, whereas our input parameters for the simulations were originally derived from oral administrations based on the actual reported pharmacokinetics or their machine-learning systems.

Fig. 4. Liver and Plasma Concentrations of Hexobarbital (Single Intravenous Administration of 60 mg/kg), Fingolimod (Single Intravenous Administration of 2.0 mg/kg), and Pentazocine (Single Intravenous Administration of 2.0 mg/kg) in Rats Were Estimated Using PBPK Models after Virtual Intravenous Administrations with Two Sets of in Silico K_p,h Values

The input parameters for the PBPK models were estimated by machine-learning systems with no reference to experimental pharmacokinetic data. Liver (solid lines) and plasma (dotted lines) concentrations of hexobarbital (A), fingolimod (B), and pentazocine (C) were modeled in rats after virtual intravenous administrations using in silico K_{p,h_Poulin and Theil} (in black) or K_{p,h_Rodgers and Rowland} (in gray) values calculated in this study. The reported in vivo plasma (open circles) and liver (gray circles) concentrations for hexobarbital,³⁴⁾ fingolimod,³⁵⁾ and pentazocine³⁶⁾ are also shown.

Previously, it was reported that the Rodgers and Rowland model outperformed the Poulin and Theil model in reproducing measured liver concentrations.¹²⁾ However, when using our in silico physicochemical property prediction methods, the results showed approx. 50% accuracy and no clear superiority or inferiority could be determined. In contrast, in silico K_p,h values obtained using the Poulin and Theil model were closer to the experimentally determined K_p,h values (slope coefficient of 1.0, Fig. 2) than those obtained using the Rodgers and Rowland models (slope coefficient of 0.54, Fig. 2). Unlike the Poulin and Theil model, the Rodgers and Rowland models, including Eqs. (3), (4), (7), and (8), exhibit a significant dependence on the input physicochemical properties, resulting in substantial variations in the calculated outcomes. In the case of basic substances categorized near the boundary between weak bases and strong bases, different outputs can be generated depending on the selection of Eqs. (3) and (4) for weak bases or strong bases, particularly when different prediction software automatically provide different pK_a values.

The choice between these two in silico K_p,h model equations depends on the availability of accurate physicochemical data for the test substances. If test substances such as medicines can be investigated in detail to obtain reliable physicochemical properties, these chemical descriptors could work well to obtain accurate in silico K_p,h values using the Rodgers and Rowland model. This study focused on the in silico K_p,h values derived using the Poulin and Theil method and those of the Rodgers and Rowland method with in vivo steady-state K_p,h values experimentally determined in recent limited surveys of 14 medicinal substances in rats¹⁶⁾ It should be expected to accumulate cases of liver concentrations measured in in vivo experiments for various chemical substances to generalize the current findings. In conclusion, these results suggest that the output values from rat pharmacokinetic models based on in silico K_p,h values derived from the primary Poulin and Theil model are applicable for estimating toxicokinetics or internal exposure to medicines, and are possibly expandable in the future to industry or food substances consisting of a wide variety of chemical spaces for which physicochemical values are unknown.

Acknowledgments

This study was supported in part by the Japan Chemical Industry Association Long-Range Research Initiative Program. The authors thank Norie Murayama, Haruka Nishimura, Fumiaki Shono, and Kimito Funatsu for their assistance. We are also grateful to David Smallbones for copyediting a draft of this article.

Conflict of Interest

The authors declare no conflict of interest.

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