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Hridoy M, Khan I, Ramanjulu M, Anthony P, Childers W, Nagar S, Korzekwa K. Mechanistic studies on pH-permeability relationships: Impact of the membrane polar headgroup region on pKa. Int J Pharm 2025; 673:125383. [PMID: 39993512 PMCID: PMC11949092 DOI: 10.1016/j.ijpharm.2025.125383] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2024] [Revised: 02/18/2025] [Accepted: 02/19/2025] [Indexed: 02/26/2025]
Abstract
Passive permeability through biological membranes requires partitioning of drug molecules into the lipid bilayer and subsequent permeation. Most drugs are weak acids or bases, making their ionization constants (pKa) critical for predicting permeation across biological barriers. The pH-partition hypothesis posits that only the uncharged form contributes to passive permeability, suggesting a proportional relationship between permeability and uncharged fraction. However, experimental pH-permeability profiles are not accurately predicted with neutral fractions calculated using aqueous pKa values. Interactions between charged solutes and phospholipids are expected to alter the pKa of drugs within the membrane. In this study, we use modeling and simulation and experimental partitioning in a biphasic surrogate phospholipid membrane system, diacetyl phosphatidylcholine (DAcPC) and n-hexane, to study pH dependent permeability. Models were constructed in which pKa values were either shifted or distributed around the aqueous pKa and the resulting neutral fractions were compared to pH-dependent permeabilities. For acids, models with shifted or distributed pKa values can explain pH-dependent permeabilities in Caco-2 cells, but these models were not predictive for bases. For partitioning studies, five probe drugs, two acidic (ketoprofen, tolbutamide), two basic (metoprolol, verapamil), and one neutral (diazepam), were partitioned between n-hexane and buffer or buffer-hydrated DAcPC at different pH values. The apparent pKa values in the surrogate phospholipid system (C6/DAcPC) were shifted from their aqueous pKa values. However, the resulting pKa values did not predict observed pH-dependent Caco-2 permeabilities. Models that decrease the pH-pKa difference improve permeability predictions for both bases and acids and use of a pKa shift or distribution can further improve predictions for acids.
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Affiliation(s)
- Md Hridoy
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, Philadelphia, PA 19140, USA; Current address: Merck Research Laboratories, 33 Avenue Louis Pasteur, Boston, MA 02115, USA
| | - Irfan Khan
- Moulder Center for Drug Discovery Research, Temple University School of Pharmacy, Philadelphia, PA 19140, USA
| | - Mercy Ramanjulu
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, Philadelphia, PA 19140, USA; Current address: Recombination Therapeutics, Pennsylvania Biotechnology Center, Doylestown, PA 18902, USA
| | - Paul Anthony
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, Philadelphia, PA 19140, USA
| | - Wayne Childers
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, Philadelphia, PA 19140, USA
| | - Swati Nagar
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, Philadelphia, PA 19140, USA
| | - Ken Korzekwa
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, Philadelphia, PA 19140, USA.
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2
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Krumpholz L, Klimczyk A, Bieniek W, Polak S, Wiśniowska B. Data set of fraction unbound values in the in vitro incubations for metabolic studies for better prediction of human clearance. Database (Oxford) 2024; 2024:baae063. [PMID: 39049520 PMCID: PMC11269425 DOI: 10.1093/database/baae063] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2024] [Revised: 05/20/2024] [Accepted: 07/08/2024] [Indexed: 07/27/2024]
Abstract
In vitro-in vivo extrapolation is a commonly applied technique for liver clearance prediction. Various in vitro models are available such as hepatocytes, human liver microsomes, or recombinant cytochromes P450. According to the free drug theory, only the unbound fraction (fu) of a chemical can undergo metabolic changes. Therefore, to ensure the reliability of predictions, both specific and nonspecific binding in the model should be accounted. However, the fraction unbound in the experiment is often not reported. The study aimed to provide a detailed repository of the literature data on the compound's fu value in various in vitro systems used for drug metabolism evaluation and corresponding human plasma binding levels. Data on the free fraction in plasma and different in vitro models were supplemented with the following information: the experimental method used for the assessment of the degree of drug binding, protein or cell concentration in the incubation, and other experimental conditions, if different from the standard ones, species, reference to the source publication, and the author's name and date of publication. In total, we collected 129 literature studies on 1425 different compounds. The provided data set can be used as a reference for scientists involved in pharmacokinetic/physiologically based pharmacokinetic modelling as well as researchers interested in Quantitative Structure-Activity Relationship models for the prediction of fraction unbound based on compound structure. Database URL: https://data.mendeley.com/datasets/3bs5526htd/1.
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Affiliation(s)
- Laura Krumpholz
- Pharmacoepidemiology and Pharmacoeconomics Unit, Faculty of Pharmacy, Jagiellonian University Medical College, Medyczna 9, Street, Kraków 30-688, Poland
- Doctoral School in Medical and Health Sciences, Jagiellonian University Medical College, Łazarza Street 16, Kraków 31-530, Poland
| | - Aleksandra Klimczyk
- Pharmacoepidemiology and Pharmacoeconomics Unit, Faculty of Pharmacy, Jagiellonian University Medical College, Medyczna 9, Street, Kraków 30-688, Poland
| | - Wiktoria Bieniek
- Pharmacoepidemiology and Pharmacoeconomics Unit, Faculty of Pharmacy, Jagiellonian University Medical College, Medyczna 9, Street, Kraków 30-688, Poland
| | - Sebastian Polak
- Chair of Pharmaceutical Technology and Biopharmaceutics, Faculty of Pharmacy, Jagiellonian University Medical College, Medyczna 9, Street, Krakow 30-688, Poland
- Certara UK Ltd (Simcyp Division), 1 Concourse Way, Sheffield S1 2BJ, United Kingdom
| | - Barbara Wiśniowska
- Pharmacoepidemiology and Pharmacoeconomics Unit, Faculty of Pharmacy, Jagiellonian University Medical College, Medyczna 9, Street, Kraków 30-688, Poland
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3
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Coutinho AL, Cristofoletti R, Wu F, Al Shoyaib A, Dressman J, Polli JE. Relative Performance of Volume of Distribution Prediction Methods for Lipophilic Drugs with Uncertainty in LogP Value. Pharm Res 2024; 41:1121-1138. [PMID: 38720034 PMCID: PMC11196289 DOI: 10.1007/s11095-024-03703-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2023] [Accepted: 04/16/2024] [Indexed: 06/26/2024]
Abstract
PURPOSE The goal was to assess, for lipophilic drugs, the impact of logP on human volume of distribution at steady-state (VDss) predictions, including intermediate fut and Kp values, from six methods: Oie-Tozer, Rodgers-Rowland (tissue-specific Kp and only muscle Kp), GastroPlus, Korzekwa-Nagar, and TCM-New. METHOD A sensitivity analysis with focus on logP was conducted by keeping pKa and fup constant for each of four drugs, while varying logP. VDss was also calculated for the specific literature logP values. Error prediction analysis was conducted by analyzing prediction errors by source of logP values, drug, and overall values. RESULTS The Rodgers-Rowland methods were highly sensitive to logP values, followed by GastroPlus and Korzekwa-Nagar. The Oie-Tozer and TCM-New methods were only modestly sensitive to logP. Hence, the relative performance of these methods depended upon the source of logP value. As logP values increased, TCM-New and Oie-Tozer were the most accurate methods. TCM-New was the only method that was accurate regardless of logP value source. Oie-Tozer provided accurate predictions for griseofulvin, posaconazole, and isavuconazole; GastroPlus for itraconazole and isavuconazole; Korzekwa-Nagar for posaconazole; and TCM-New for griseofulvin, posaconazole, and isavuconazole. Both Rodgers-Rowland methods provided inaccurate predictions due to the overprediction of VDss. CONCLUSIONS TCM-New was the most accurate prediction of human VDss across four drugs and three logP sources, followed by Oie-Tozer. TCM-New showed to be the best method for VDss prediction of highly lipophilic drugs, suggesting BPR as a favorable surrogate for drug partitioning in the tissues, and which avoids the use of fup.
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Affiliation(s)
- Ana L Coutinho
- Department of Pharmaceutical Sciences, University of Maryland School of Pharmacy, 20 Penn Street, Room 623, HSF2 Building, Baltimore, MD, 21201, USA
| | - Rodrigo Cristofoletti
- Department of Pharmaceutics, Center for Pharmacometrics and Systems Pharmacology, College of Pharmacy, University of Florida, Orlando, FL, USA
| | - Fang Wu
- Office of Generic Drugs, Food and Drug Administration, White Oak, MD, USA
| | | | - Jennifer Dressman
- Fraunhofer Institute of Translational Medicine and Pharmacology, Theodor-Stern-Kai 7, 60596, Frankfurt am Main, Germany
| | - James E Polli
- Department of Pharmaceutical Sciences, University of Maryland School of Pharmacy, 20 Penn Street, Room 623, HSF2 Building, Baltimore, MD, 21201, USA.
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4
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Upton C, Healey J, Rothnie AJ, Goddard AD. Insights into membrane interactions and their therapeutic potential. Arch Biochem Biophys 2024; 755:109939. [PMID: 38387829 DOI: 10.1016/j.abb.2024.109939] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2023] [Revised: 01/31/2024] [Accepted: 02/19/2024] [Indexed: 02/24/2024]
Abstract
Recent research into membrane interactions has uncovered a diverse range of therapeutic opportunities through the bioengineering of human and non-human macromolecules. Although the majority of this research is focussed on fundamental developments, emerging studies are showcasing promising new technologies to combat conditions such as cancer, Alzheimer's and inflammatory and immune-based disease, utilising the alteration of bacteriophage, adenovirus, bacterial toxins, type 6 secretion systems, annexins, mitochondrial antiviral signalling proteins and bacterial nano-syringes. To advance the field further, each of these opportunities need to be better understood, and the therapeutic models need to be further optimised. Here, we summarise the knowledge and insights into several membrane interactions and detail their current and potential uses therapeutically.
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Affiliation(s)
- Calum Upton
- School of Biosciences, Health & Life Science, Aston University, Birmingham, B4 7ET, UK
| | - Joseph Healey
- Nanosyrinx, The Venture Centre, University of Warwick Science Park, Coventry, CV4 7EZ, UK
| | - Alice J Rothnie
- School of Biosciences, Health & Life Science, Aston University, Birmingham, B4 7ET, UK
| | - Alan D Goddard
- School of Biosciences, Health & Life Science, Aston University, Birmingham, B4 7ET, UK.
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Gardner I, Xu M, Han C, Wang Y, Jiao X, Jamei M, Khalidi H, Kilford P, Neuhoff S, Southall R, Turner DB, Musther H, Jones B, Taylor S. Non-specific binding of compounds in in vitro metabolism assays: a comparison of microsomal and hepatocyte binding in different species and an assessment of the accuracy of prediction models. Xenobiotica 2022; 52:943-956. [PMID: 36222269 DOI: 10.1080/00498254.2022.2132426] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Non-specific binding in in vitro metabolism systems leads to an underestimation of the true intrinsic metabolic clearance of compounds being studied. Therefore in vitro binding needs to be accounted for when extrapolating in vitro data to predict the in vivo metabolic clearance of a compound. While techniques exist for experimentally determining the fraction of a compound unbound in in vitro metabolism systems, early in drug discovery programmes computational approaches are often used to estimate the binding in the in vitro system.Experimental fraction unbound data (n = 60) were generated in liver microsomes (fumic) from five commonly used pre-clinical species (rat, mouse, dog, minipig, monkey) and humans. Unbound fraction in incubations with mouse, rat or human hepatocytes was determined for the same 60 compounds. These data were analysed to determine the relationship between experimentally determined binding in the different matrices and across different species. In hepatocytes there was a good correlation between fraction unbound in human and rat (r2=0.86) or mouse (r2=0.82) hepatocytes. Similar correlations were observed between binding in human liver microsomes and microsomes from rat, mouse, dog, Göttingen minipig or monkey liver microsomes (r2 of >0.89, n = 51 - 52 measurements in different species). Physicochemical parameters (logP, pKa and logD) were predicted for all evaluated compounds. In addition, logP and/or logD were measured for a subset of compounds.Binding to human hepatocytes predicted using 5 different methods was compared to the measured data for a set of 59 compounds. The best methods evaluated used measured microsomal binding in human liver microsomes to predict hepatocyte binding. The collated physicochemical data were used to predict the human fumic using four different in silico models for a set of 53-60 compounds. The correlation (r2) and root mean square error between predicted and observed microsomal binding was 0.69 & 0.20, 0.47 & 0.23, 0.56 & 0.21 and 0.54 & 0.26 for the Turner-Simcyp, Austin, Hallifax-Houston and Poulin models, respectively. These analyses were extended to include measured literature values for binding in human liver microsomes for a larger set of compounds (n=697). For the larger dataset of compounds, microsomal binding was well predicted for neutral compounds (r2=0.67 - 0.70) using the Poulin, Austin, or Turner-Simcyp methods but not for acidic or basic compounds (r2<0.5) using any of the models. While the lipophilicity-based models can be used, the in vitro binding should be measured for compounds where more certainty is needed, using appropriately calibrated assays and possibly established weak, moderate, and strong binders as reference compounds to allow comparison across databases.
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Affiliation(s)
| | - Mandy Xu
- Pharmaron Beijing Co. Ltd., Beijing, China
| | | | - Yi Wang
- Pharmaron Beijing Co. Ltd., Beijing, China
| | | | | | | | - Peter Kilford
- Certara UK Ltd., Sheffield, United Kingdom.,Labcorp Drug Development, Harrogate, United Kingdom
| | | | | | | | | | - Barry Jones
- Pharmaron UK, Hoddesdon, Hertfordshire, United Kingdom
| | - Simon Taylor
- Pharmaron UK, Hoddesdon, Hertfordshire, United Kingdom
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6
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Radice C, Korzekwa K, Nagar S. Predicting Impact of Food and Feeding Time on Oral Absorption of Drugs with a Novel Rat Continuous Intestinal Absorption Model. Drug Metab Dispos 2022; 50:750-761. [PMID: 35339986 PMCID: PMC9199116 DOI: 10.1124/dmd.122.000831] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2022] [Accepted: 03/17/2022] [Indexed: 11/22/2022] Open
Abstract
Intricacies in intestinal physiology, drug properties, and food effects should be incorporated into models to predict complex oral drug absorption. A previously published human continuous intestinal absorption model based on the convection-diffusion equation was modified specifically for the male Sprague-Dawley rat in this report. Species-specific physiologic conditions along intestinal length - experimental velocity and pH under fasted and fed conditions, were measured and incorporated into the intestinal absorption model. Concentration-time (C-t) profiles were measured upon a single intravenous and peroral (PO) dose for three drugs: amlodipine (AML), digoxin (DIG), and glyburide (GLY). Absorption profiles were predicted and compared with experimentally collected data under three feeding conditions: 12-hour fasted rats were provided food at two specific times after oral drug dose (1 hour and 2 hours for AML and GLY; 0.5 hours and 1 hour for DIG), or they were provided food for the entire study. Intravenous versus PO C-t profiles suggested absorption even at later times and informed design of appropriate mathematical input functions based on experimental feeding times. With this model, AML, DIG, and GLY oral C-t profiles for all feeding groups were generally well predicted, with exposure overlap coefficients in the range of 0.80-0.97. Efflux transport for DIG and uptake and efflux transport for GLY were included, modeling uptake transporter inhibition in the presence of food. Results indicate that the continuous intestinal rat model incorporates complex physiologic processes and feeding times relative to drug dose into a simple framework to provide accurate prediction of oral absorption. SIGNIFICANCE STATEMENT: A novel rat continuous intestinal model predicts drug absorption with respect to time and intestinal length. Feeding time relative to dose was modeled as a key effect. Experimental fasted/fed intestinal pH and velocity, efflux and uptake transporter expression along intestinal length, and uptake transporter inhibition in the presence of food were modeled. The model uses the pharmacokinetic profiles of three model drugs and provides a novel framework to study food effects on absorption.
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Affiliation(s)
- Casey Radice
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, Philadelphia, Pennsylvania
| | - Ken Korzekwa
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, Philadelphia, Pennsylvania
| | - Swati Nagar
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, Philadelphia, Pennsylvania
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7
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Korzekwa K, Radice C, Nagar S. A Permeability- and Perfusion-based PBPK model for Improved Prediction of Concentration-time Profiles. Clin Transl Sci 2022; 15:2035-2052. [PMID: 35588513 PMCID: PMC9372417 DOI: 10.1111/cts.13314] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2021] [Revised: 04/19/2022] [Accepted: 05/08/2022] [Indexed: 12/02/2022] Open
Abstract
To improve predictions of concentration‐time (C‐t) profiles of drugs, a new physiologically based pharmacokinetic modeling framework (termed ‘PermQ’) has been developed. This model includes permeability into and out of capillaries, cell membranes, and intracellular lipids. New modeling components include (i) lumping of tissues into compartments based on both blood flow and capillary permeability, and (ii) parameterizing clearances in and out of membranes with apparent permeability and membrane partitioning values. Novel observations include the need for a shallow distribution compartment particularly for bases. C‐t profiles were modeled for 24 drugs (7 acidic, 5 neutral, and 12 basic) using the same experimental inputs for three different models: Rodgers and Rowland (RR), a perfusion‐limited membrane‐based model (Kp,mem), and PermQ. Kp,mem and PermQ can be directly compared since both models have identical tissue partition coefficient parameters. For the 24 molecules used for model development, errors in Vss and t1/2 were reduced by 37% and 43%, respectively, with the PermQ model. Errors in C‐t profiles were reduced (increased EOC) by 43%. The improvement was generally greater for bases than for acids and neutrals. Predictions were improved for all 3 models with the use of parameters optimized for the PermQ model. For five drugs in a test set, similar results were observed. These results suggest that prediction of C‐t profiles can be improved by including capillary and cellular permeability components for all tissues.
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Affiliation(s)
- Ken Korzekwa
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, Philadelphia, PA, USA
| | - Casey Radice
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, Philadelphia, PA, USA
| | - Swati Nagar
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, Philadelphia, PA, USA
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8
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Hossain SI, Saha SC, Deplazes E. Phenolic compounds alter the ion permeability of phospholipid bilayers via specific lipid interactions. Phys Chem Chem Phys 2021; 23:22352-22366. [PMID: 34604899 DOI: 10.1039/d1cp03250j] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
This study aims to understand the role of specific phenolic-lipid interactions in the membrane-altering properties of phenolic compounds. We combine tethered lipid bilayer (tBLM) electrical impedance spectroscopy (EIS) with all-atom molecular dynamics (MD) simulations to study the membrane interactions of six phenolic compounds: caffeic acid methyl ester, caffeic acid, 3,4 dihydroxybenzoic acid, chlorogenic acid, syringic acid and p-coumaric acid. tBLM/EIS experiments showed that caffeic acid methyl ester, caffeic acid and 3,4 dihydroxybenzoic acid significantly increase the permeability of phospholipid bilayers to Na+ ions. In contrast, chlorogenic acid, syringic acid and p-coumaric acid showed no effect. Experiments with lipids lacking the phosphate group show a significant decrease in the membrane-altering effects indicating that specific phenolic-lipid interactions are critical in altering ion permeability. MD simulations confirm that compounds that alter ion permeability form stable interactions with the phosphate oxygen. In contrast, inactive phenolic compounds are superficially bound to the membrane surface and primarily interact with interfacial water. Our combined results show that compounds with similar structures can have very different effects on ion permeability in membranes. These effects are governed by specific interactions at the water-lipid interface and show no correlation with lipophilicity. Furthermore, none of the compounds alter the overall structure of the phospholipid bilayer as determined by area per lipid and order parameters. Based on data from this study and previous findings, we propose that phenolic compounds can alter membrane ion permeability by causing local changes in lipid packing that subsequently reduce the energy barrier for ion-induced pores.
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Affiliation(s)
- Sheikh I Hossain
- School of Life Sciences, University of Technology Sydney, Ultimo, NSW 2007, Australia.
| | - Suvash C Saha
- School of Mechanical and Mechatronic Engineering, University of Technology Sydney, Ultimo, NSW 2007, Australia
| | - Evelyne Deplazes
- School of Life Sciences, University of Technology Sydney, Ultimo, NSW 2007, Australia. .,School of Chemistry and Molecular Biosciences, University of Queensland, St Lucia, QLD 4072, Australia
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9
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Espiritu MJ, Chen J, Yadav J, Larkin M, Pelletier RD, Chan JM, Gc JB, Natesan S, Harrelson JP. Mechanisms of Herb-Drug Interactions Involving Cinnamon and CYP2A6: Focus on Time-Dependent Inhibition by Cinnamaldehyde and 2-Methoxycinnamaldehyde. Drug Metab Dispos 2020; 48:1028-1043. [PMID: 32788161 PMCID: PMC7543486 DOI: 10.1124/dmd.120.000087] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2020] [Accepted: 07/15/2020] [Indexed: 12/21/2022] Open
Abstract
Information is scarce regarding pharmacokinetic-based herb-drug interactions (HDI) with trans-cinnamaldehyde (CA) and 2-methoxycinnamaldehyde (MCA), components of cinnamon. Given the presence of cinnamon in food and herbal treatments for various diseases, HDIs involving the CYP2A6 substrates nicotine and letrozole with MCA (KS = 1.58 µM; Hill slope = 1.16) and CA were investigated. The time-dependent inhibition (TDI) by MCA and CA of CYP2A6-mediated nicotine metabolism is a complex process involving multiple mechanisms. Molecular dynamic simulations showed that CYP2A6's active site accommodates two dynamic ligands. The preferred binding orientations for MCA and CA were consistent with the observed metabolism: epoxidation, O-demethylation, and aromatic hydroxylation of MCA and cinnamic acid formation from CA. The percent remaining activity plots for TDI by MCA and CA were curved, and they were analyzed with a numerical method using models of varying complexity. The best-fit models support multiple inactivator binding, inhibitor depletion, and partial inactivation. Deconvoluted mass spectra indicated that MCA and CA modified CYP2A6 apoprotein with mass additions of 156.79 (142.54-171.04) and 132.67 (123.37-141.98), respectively, and it was unaffected by glutathione. Heme degradation was observed in the presence of MCA (48.5% ± 13.4% loss; detected by liquid chromatography-tandem mass spectrometry). In the absence of clinical data, HDI predictions were made for nicotine and letrozole using inhibition parameters from the best-fit TDI models and parameters scaled from rats. Predicted area under the concentration-time curve fold changes were 4.29 (CA-nicotine), 4.92 (CA-letrozole), 4.35 (MCA-nicotine), and 5.00 (MCA-letrozole). These findings suggest that extensive exposure to cinnamon (corresponding to ≈ 275 mg CA) would lead to noteworthy interactions. SIGNIFICANCE STATEMENT: Human exposure to cinnamon is common because of its presence in food and cinnamon-based herbal treatments. Little is known about the risk for cinnamaldehyde and methoxycinnamaldehyde, two components of cinnamon, to interact with drugs that are eliminated by CYP2A6-mediated metabolism. The interactions with CYP2A6 are complex, involving multiple-ligand binding, time-dependent inhibition of nicotine metabolism, heme degradation, and apoprotein modification. An herb-drug interaction prediction suggests that extensive exposure to cinnamon would lead to noteworthy interactions with nicotine.
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Affiliation(s)
- Michael J Espiritu
- School of Pharmacy, Pacific University Oregon, Hillsboro, Oregon (M.J.E., M.L., J.P.H.); College of Pharmacy and Pharmaceutical Sciences, Washington State University, Spokane, Washington (J.C., J.B.G., S.N.); Amgen, Cambridge, Massachusetts (J.Y.); Department of Medicinal Chemistry, University of Washington, Seattle, Washington (R.D.P.); and Chemistry Department, Pacific University Oregon, Forest Grove, Oregon (J.M.C.)
| | - Justin Chen
- School of Pharmacy, Pacific University Oregon, Hillsboro, Oregon (M.J.E., M.L., J.P.H.); College of Pharmacy and Pharmaceutical Sciences, Washington State University, Spokane, Washington (J.C., J.B.G., S.N.); Amgen, Cambridge, Massachusetts (J.Y.); Department of Medicinal Chemistry, University of Washington, Seattle, Washington (R.D.P.); and Chemistry Department, Pacific University Oregon, Forest Grove, Oregon (J.M.C.)
| | - Jaydeep Yadav
- School of Pharmacy, Pacific University Oregon, Hillsboro, Oregon (M.J.E., M.L., J.P.H.); College of Pharmacy and Pharmaceutical Sciences, Washington State University, Spokane, Washington (J.C., J.B.G., S.N.); Amgen, Cambridge, Massachusetts (J.Y.); Department of Medicinal Chemistry, University of Washington, Seattle, Washington (R.D.P.); and Chemistry Department, Pacific University Oregon, Forest Grove, Oregon (J.M.C.)
| | - Michael Larkin
- School of Pharmacy, Pacific University Oregon, Hillsboro, Oregon (M.J.E., M.L., J.P.H.); College of Pharmacy and Pharmaceutical Sciences, Washington State University, Spokane, Washington (J.C., J.B.G., S.N.); Amgen, Cambridge, Massachusetts (J.Y.); Department of Medicinal Chemistry, University of Washington, Seattle, Washington (R.D.P.); and Chemistry Department, Pacific University Oregon, Forest Grove, Oregon (J.M.C.)
| | - Robert D Pelletier
- School of Pharmacy, Pacific University Oregon, Hillsboro, Oregon (M.J.E., M.L., J.P.H.); College of Pharmacy and Pharmaceutical Sciences, Washington State University, Spokane, Washington (J.C., J.B.G., S.N.); Amgen, Cambridge, Massachusetts (J.Y.); Department of Medicinal Chemistry, University of Washington, Seattle, Washington (R.D.P.); and Chemistry Department, Pacific University Oregon, Forest Grove, Oregon (J.M.C.)
| | - Jeannine M Chan
- School of Pharmacy, Pacific University Oregon, Hillsboro, Oregon (M.J.E., M.L., J.P.H.); College of Pharmacy and Pharmaceutical Sciences, Washington State University, Spokane, Washington (J.C., J.B.G., S.N.); Amgen, Cambridge, Massachusetts (J.Y.); Department of Medicinal Chemistry, University of Washington, Seattle, Washington (R.D.P.); and Chemistry Department, Pacific University Oregon, Forest Grove, Oregon (J.M.C.)
| | - Jeevan B Gc
- School of Pharmacy, Pacific University Oregon, Hillsboro, Oregon (M.J.E., M.L., J.P.H.); College of Pharmacy and Pharmaceutical Sciences, Washington State University, Spokane, Washington (J.C., J.B.G., S.N.); Amgen, Cambridge, Massachusetts (J.Y.); Department of Medicinal Chemistry, University of Washington, Seattle, Washington (R.D.P.); and Chemistry Department, Pacific University Oregon, Forest Grove, Oregon (J.M.C.)
| | - Senthil Natesan
- School of Pharmacy, Pacific University Oregon, Hillsboro, Oregon (M.J.E., M.L., J.P.H.); College of Pharmacy and Pharmaceutical Sciences, Washington State University, Spokane, Washington (J.C., J.B.G., S.N.); Amgen, Cambridge, Massachusetts (J.Y.); Department of Medicinal Chemistry, University of Washington, Seattle, Washington (R.D.P.); and Chemistry Department, Pacific University Oregon, Forest Grove, Oregon (J.M.C.)
| | - John P Harrelson
- School of Pharmacy, Pacific University Oregon, Hillsboro, Oregon (M.J.E., M.L., J.P.H.); College of Pharmacy and Pharmaceutical Sciences, Washington State University, Spokane, Washington (J.C., J.B.G., S.N.); Amgen, Cambridge, Massachusetts (J.Y.); Department of Medicinal Chemistry, University of Washington, Seattle, Washington (R.D.P.); and Chemistry Department, Pacific University Oregon, Forest Grove, Oregon (J.M.C.)
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10
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Martinotti C, Ruiz-Perez L, Deplazes E, Mancera RL. Molecular Dynamics Simulation of Small Molecules Interacting with Biological Membranes. Chemphyschem 2020; 21:1486-1514. [PMID: 32452115 DOI: 10.1002/cphc.202000219] [Citation(s) in RCA: 38] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2020] [Revised: 05/22/2020] [Indexed: 12/12/2022]
Abstract
Cell membranes protect and compartmentalise cells and their organelles. The semi-permeable nature of these membranes controls the exchange of solutes across their structure. Characterising the interaction of small molecules with biological membranes is critical to understanding of physiological processes, drug action and permeation, and many biotechnological applications. This review provides an overview of how molecular simulations are used to study the interaction of small molecules with biological membranes, with a particular focus on the interactions of water, organic compounds, drugs and short peptides with models of plasma cell membrane and stratum corneum lipid bilayers. This review will not delve on other types of membranes which might have different composition and arrangement, such as thylakoid or mitochondrial membranes. The application of unbiased molecular dynamics simulations and enhanced sampling methods such as umbrella sampling, metadynamics and replica exchange are described using key examples. This review demonstrates how state-of-the-art molecular simulations have been used successfully to describe the mechanism of binding and permeation of small molecules with biological membranes, as well as associated changes to the structure and dynamics of these membranes. The review concludes with an outlook on future directions in this field.
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Affiliation(s)
- Carlo Martinotti
- School of Pharmacy and Biomedical Sciences, Curtin Health Innovation Research Institute and, Curtin Institute for Computation, Curtin University, Perth, WA 6845, Australia
| | - Lanie Ruiz-Perez
- School of Pharmacy and Biomedical Sciences, Curtin Health Innovation Research Institute and, Curtin Institute for Computation, Curtin University, Perth, WA 6845, Australia
| | - Evelyne Deplazes
- School of Life Sciences, University of Technology Sydney, Sydney, NSW 2007, Australia
| | - Ricardo L Mancera
- School of Pharmacy and Biomedical Sciences, Curtin Health Innovation Research Institute and, Curtin Institute for Computation, Curtin University, Perth, WA 6845, Australia
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11
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Holt K, Ye M, Nagar S, Korzekwa K. Prediction of Tissue-Plasma Partition Coefficients Using Microsomal Partitioning: Incorporation into Physiologically based Pharmacokinetic Models and Steady-State Volume of Distribution Predictions. Drug Metab Dispos 2019; 47:1050-1060. [PMID: 31324699 PMCID: PMC6750188 DOI: 10.1124/dmd.119.087973] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2019] [Accepted: 07/09/2019] [Indexed: 11/22/2022] Open
Abstract
Drug distribution is a necessary component of models to predict human pharmacokinetics. A new membrane-based tissue-plasma partition coefficient (K p) method (K p,mem) to predict unbound tissue to plasma partition coefficients (K pu) was developed using in vitro membrane partitioning [fraction unbound in microsomes (f um)], plasma protein binding, and log P The resulting K p values were used in a physiologically based pharmacokinetic (PBPK) model to predict the steady-state volume of distribution (V ss) and concentration-time (C-t) profiles for 19 drugs. These results were compared with K p predictions using a standard method [the differential phospholipid K p prediction method (K p,dPL)], which differentiates between acidic and neutral phospholipids. The K p,mem method was parameterized using published rat K pu data and tissue lipid composition. The K pu values were well predicted with R 2 = 0.8. When used in a PBPK model, the V ss predictions were within 2-fold error for 12 of 19 drugs for K p,mem versus 11 of 19 for Kp,dPL With one outlier removed for K p,mem and two for K p,dPL, the V ss predictions for R 2 were 0.80 and 0.79 for the K p,mem and K p,dPL methods, respectively. The C-t profiles were also predicted and compared. Overall, the K p,mem method predicted the V ss and C-t profiles equally or better than the K p,dPL method. An advantage of using f um to parameterize membrane partitioning is that f um data are used for clearance prediction and are, therefore, generated early in the discovery/development process. Also, the method provides a mechanistically sound basis for membrane partitioning and permeability for further improving PBPK models. SIGNIFICANCE STATEMENT: A new method to predict tissue-plasma partition coefficients was developed. The method provides a more mechanistic basis to model membrane partitioning.
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Affiliation(s)
- Kimberly Holt
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, Philadelphia, Pennsylvania
| | - Min Ye
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, Philadelphia, Pennsylvania
| | - Swati Nagar
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, Philadelphia, Pennsylvania
| | - Ken Korzekwa
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, Philadelphia, Pennsylvania
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12
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Heterogeneous drug tissue binding in brain regions of rats, Alzheimer's patients and controls: impact on translational drug development. Sci Rep 2019; 9:5308. [PMID: 30926941 PMCID: PMC6440985 DOI: 10.1038/s41598-019-41828-4] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2018] [Accepted: 03/18/2019] [Indexed: 01/08/2023] Open
Abstract
For preclinical and clinical assessment of therapeutically relevant unbound, free, brain concentrations, the pharmacokinetic parameter fraction of unbound drug in brain (fu,brain) is commonly used to compensate total drug concentrations for nonspecific brain tissue binding (BTB). As, homogenous BTB is assumed between species and in health and disease, rat BTB is routinely used. The impact of Alzheimer’s disease (AD) on drug BTB in brain regions of interest (ROI), i.e., fu,brain,ROI, is yet unclear. This study for the first time provides insight into regional drug BTB and the validity of employing rat fu,brain,ROI as a surrogate of human BTB, by investigating five marketed drugs in post-mortem tissue from AD patients (n = 6) and age-matched controls (n = 6). Heterogeneous drug BTB was observed in all within group comparisons independent of disease and species. The findings oppose the assumption of uniform BTB, highlighting the need of case-by-case evaluation of fu,brain,ROI in translational CNS research.
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13
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Yadav J, Korzekwa K, Nagar S. Improved Predictions of Drug-Drug Interactions Mediated by Time-Dependent Inhibition of CYP3A. Mol Pharm 2018; 15:1979-1995. [PMID: 29608318 PMCID: PMC5938745 DOI: 10.1021/acs.molpharmaceut.8b00129] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Time-dependent inactivation (TDI) of cytochrome P450s (CYPs) is a leading cause of clinical drug-drug interactions (DDIs). Current methods tend to overpredict DDIs. In this study, a numerical approach was used to model complex CYP3A TDI in human-liver microsomes. The inhibitors evaluated included troleandomycin (TAO), erythromycin (ERY), verapamil (VER), and diltiazem (DTZ) along with the primary metabolites N-demethyl erythromycin (NDE), norverapamil (NV), and N-desmethyl diltiazem (NDD). The complexities incorporated into the models included multiple-binding kinetics, quasi-irreversible inactivation, sequential metabolism, inhibitor depletion, and membrane partitioning. The resulting inactivation parameters were incorporated into static in vitro-in vivo correlation (IVIVC) models to predict clinical DDIs. For 77 clinically observed DDIs, with a hepatic-CYP3A-synthesis-rate constant of 0.000 146 min-1, the average fold difference between the observed and predicted DDIs was 3.17 for the standard replot method and 1.45 for the numerical method. Similar results were obtained using a synthesis-rate constant of 0.000 32 min-1. These results suggest that numerical methods can successfully model complex in vitro TDI kinetics and that the resulting DDI predictions are more accurate than those obtained with the standard replot approach.
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Affiliation(s)
- Jaydeep Yadav
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, 3307 North Broad Street, Philadelphia, Pennsylvania 19140, United States
| | - Ken Korzekwa
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, 3307 North Broad Street, Philadelphia, Pennsylvania 19140, United States
| | - Swati Nagar
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy, 3307 North Broad Street, Philadelphia, Pennsylvania 19140, United States
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14
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Pearce RG, Setzer RW, Davis JL, Wambaugh JF. Evaluation and calibration of high-throughput predictions of chemical distribution to tissues. J Pharmacokinet Pharmacodyn 2017; 44:549-565. [PMID: 29032447 DOI: 10.1007/s10928-017-9548-7.evaluation] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2017] [Accepted: 09/30/2017] [Indexed: 05/27/2023]
Abstract
Toxicokinetics (TK) provides critical information for integrating chemical toxicity and exposure assessments in order to determine potential chemical risk (i.e., the margin between toxic doses and plausible exposures). For thousands of chemicals that are present in our environment, in vivo TK data are lacking. The publicly available R package "httk" (version 1.8, named for "high throughput TK") draws from a database of in vitro data and physico-chemical properties in order to run physiologically-based TK (PBTK) models for 553 compounds. The PBTK model parameters include tissue:plasma partition coefficients (Kp) which the httk software predicts using the model of Schmitt (Toxicol In Vitro 22 (2):457-467, 2008). In this paper we evaluated and modified httk predictions, and quantified confidence using in vivo literature data. We used 964 rat Kp measured by in vivo experiments for 143 compounds. Initially, predicted Kp were significantly larger than measured Kp for many lipophilic compounds (log10 octanol:water partition coefficient > 3). Hence the approach for predicting Kp was revised to account for possible deficiencies in the in vitro protein binding assay, and the method for predicting membrane affinity was revised. These changes yielded improvements ranging from a factor of 10 to nearly a factor of 10,000 for 83 Kp across 23 compounds with only 3 Kp worsening by more than a factor of 10. The vast majority (92%) of Kp were predicted within a factor of 10 of the measured value (overall root mean squared error of 0.59 on log10-transformed scale). After applying the adjustments, regressions were performed to calibrate and evaluate the predictions for 12 tissues. Predictions for some tissues (e.g., spleen, bone, gut, lung) were observed to be better than predictions for other tissues (e.g., skin, brain, fat), indicating that confidence in the application of in silico tools to predict chemical partitioning varies depending upon the tissues involved. Our calibrated model was then evaluated using a second data set of human in vivo measurements of volume of distribution (Vss) for 498 compounds reviewed by Obach et al. (Drug Metab Dispos 36(7):1385-1405, 2008). We found that calibration of the model improved performance: a regression of the measured values as a function of the predictions has a slope of 1.03, intercept of - 0.04, and R2 of 0.43. Through careful evaluation of predictive methods for chemical partitioning into tissues, we have improved and calibrated these methods and quantified confidence for TK predictions in humans and rats.
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Affiliation(s)
- Robert G Pearce
- National Center for Computational Toxicology, Office of Research and Development, United States Environmental Protection Agency, Research Triangle Park, 109 T.W. Alexander Dr, Durham, NC, 27711, USA
- Oak Ridge Institute for Science and Education, Oak Ridge, TN, 37831, USA
| | - R Woodrow Setzer
- National Center for Computational Toxicology, Office of Research and Development, United States Environmental Protection Agency, Research Triangle Park, 109 T.W. Alexander Dr, Durham, NC, 27711, USA
| | - Jimena L Davis
- National Center for Computational Toxicology, Office of Research and Development, United States Environmental Protection Agency, Research Triangle Park, 109 T.W. Alexander Dr, Durham, NC, 27711, USA
- Syngenta, Research Triangle Park, NC, 27709, USA
| | - John F Wambaugh
- National Center for Computational Toxicology, Office of Research and Development, United States Environmental Protection Agency, Research Triangle Park, 109 T.W. Alexander Dr, Durham, NC, 27711, USA.
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15
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Pearce RG, Setzer RW, Davis JL, Wambaugh JF. Evaluation and calibration of high-throughput predictions of chemical distribution to tissues. J Pharmacokinet Pharmacodyn 2017; 44:549-565. [PMID: 29032447 PMCID: PMC6186149 DOI: 10.1007/s10928-017-9548-7] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2017] [Accepted: 09/30/2017] [Indexed: 12/25/2022]
Abstract
Toxicokinetics (TK) provides critical information for integrating chemical toxicity and exposure assessments in order to determine potential chemical risk (i.e., the margin between toxic doses and plausible exposures). For thousands of chemicals that are present in our environment, in vivo TK data are lacking. The publicly available R package "httk" (version 1.8, named for "high throughput TK") draws from a database of in vitro data and physico-chemical properties in order to run physiologically-based TK (PBTK) models for 553 compounds. The PBTK model parameters include tissue:plasma partition coefficients (Kp) which the httk software predicts using the model of Schmitt (Toxicol In Vitro 22 (2):457-467, 2008). In this paper we evaluated and modified httk predictions, and quantified confidence using in vivo literature data. We used 964 rat Kp measured by in vivo experiments for 143 compounds. Initially, predicted Kp were significantly larger than measured Kp for many lipophilic compounds (log10 octanol:water partition coefficient > 3). Hence the approach for predicting Kp was revised to account for possible deficiencies in the in vitro protein binding assay, and the method for predicting membrane affinity was revised. These changes yielded improvements ranging from a factor of 10 to nearly a factor of 10,000 for 83 Kp across 23 compounds with only 3 Kp worsening by more than a factor of 10. The vast majority (92%) of Kp were predicted within a factor of 10 of the measured value (overall root mean squared error of 0.59 on log10-transformed scale). After applying the adjustments, regressions were performed to calibrate and evaluate the predictions for 12 tissues. Predictions for some tissues (e.g., spleen, bone, gut, lung) were observed to be better than predictions for other tissues (e.g., skin, brain, fat), indicating that confidence in the application of in silico tools to predict chemical partitioning varies depending upon the tissues involved. Our calibrated model was then evaluated using a second data set of human in vivo measurements of volume of distribution (Vss) for 498 compounds reviewed by Obach et al. (Drug Metab Dispos 36(7):1385-1405, 2008). We found that calibration of the model improved performance: a regression of the measured values as a function of the predictions has a slope of 1.03, intercept of - 0.04, and R2 of 0.43. Through careful evaluation of predictive methods for chemical partitioning into tissues, we have improved and calibrated these methods and quantified confidence for TK predictions in humans and rats.
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Affiliation(s)
- Robert G Pearce
- National Center for Computational Toxicology, Office of Research and Development, United States Environmental Protection Agency, Research Triangle Park, 109 T.W. Alexander Dr, Durham, NC, 27711, USA
- Oak Ridge Institute for Science and Education, Oak Ridge, TN, 37831, USA
| | - R Woodrow Setzer
- National Center for Computational Toxicology, Office of Research and Development, United States Environmental Protection Agency, Research Triangle Park, 109 T.W. Alexander Dr, Durham, NC, 27711, USA
| | - Jimena L Davis
- National Center for Computational Toxicology, Office of Research and Development, United States Environmental Protection Agency, Research Triangle Park, 109 T.W. Alexander Dr, Durham, NC, 27711, USA
- Syngenta, Research Triangle Park, NC, 27709, USA
| | - John F Wambaugh
- National Center for Computational Toxicology, Office of Research and Development, United States Environmental Protection Agency, Research Triangle Park, 109 T.W. Alexander Dr, Durham, NC, 27711, USA.
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16
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Nagar S, Korzekwa RC, Korzekwa K. Continuous Intestinal Absorption Model Based on the Convection-Diffusion Equation. Mol Pharm 2017; 14:3069-3086. [PMID: 28712300 DOI: 10.1021/acs.molpharmaceut.7b00286] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Prediction of the rate and extent of drug absorption upon oral dosing needs models that capture the complexities of both the drug molecule and intestinal physiology. We report here the development of a continuous intestinal absorption model based on the convection-diffusion equation. The model includes explicit enterocyte apical membrane and intracellular lipid radial compartments along the length of the intestine. Physiologic functions along length x are built into the model and include velocity, diffusion, surface areas, and pH of the intestine. Also included are expression levels of the intestinal active uptake transporter OATP2B1 and efflux transporter P-gp. Oral dosing of solution as well as solid (with a dissolution function) was modeled for several drugs. The fraction absorbed (FA) and concentration-time (C-t) profiles were predicted and compared with clinical data. Overall, FA was well predicted upon oral (n = 21) or colonic dosing (n = 11), with four outliers. The overall accuracy (prediction of the correct bin) was 81% with outliers and 90% without outliers. Of the nine solution dosing data sets, six drugs were very well predicted with an exposure overlap coefficient (EOC) > 0.9 and predicted Cmax and Tmax values similar to those observed. Of the six solid dose formulations evaluated, the EOC values were > 0.9 for all drugs except budesonide. The observed precipitation of nifedipine at high doses was predicted by the model. Most of the poor predictions were for drugs that are known to be transporter substrates. As proof of concept, incorporating OATP2B1 and P-gp markedly improved the EOC and predicted Cmax and Tmax for fexofenadine. Finally, the continuous intestinal model accurately recapitulated the known relationships between drug absorption and permeability, solubility, and particle size. Together, these results indicate that this preliminary intestinal absorption model offers a simple and straightforward framework to build in complexities such as drug permeability, lipid partitioning, solubility, metabolism, and transport for improved prediction of the rate and extent of drug absorption.
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Affiliation(s)
- Swati Nagar
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy , Philadelphia, Pennsylvania 19140, United States
| | - Richard C Korzekwa
- Department of Physics, University of Texas , Austin, Texas 78712, United States
| | - Ken Korzekwa
- Department of Pharmaceutical Sciences, Temple University School of Pharmacy , Philadelphia, Pennsylvania 19140, United States
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