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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Pharmacol.</journal-id>
<journal-title>Frontiers in Pharmacology</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Pharmacol.</abbrev-journal-title>
<issn pub-type="epub">1663-9812</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">746594</article-id>
<article-id pub-id-type="doi">10.3389/fphar.2021.746594</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Pharmacology</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Effect of CYP3A4 Inhibitors and Inducers on Pharmacokinetics and Pharmacodynamics of Saxagliptin and Active Metabolite M2 in Humans Using Physiological-Based Pharmacokinetic Combined DPP-4 Occupancy</article-title>
<alt-title alt-title-type="left-running-head">Li et&#x20;al.</alt-title>
<alt-title alt-title-type="right-running-head">Saxagliptin PK and PD prediction</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Li</surname>
<given-names>Gang</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="fn" rid="fn1">
<sup>&#x2020;</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1510717/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Yi</surname>
<given-names>Bowen</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="fn" rid="fn1">
<sup>&#x2020;</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1510706/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Liu</surname>
<given-names>Jingtong</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1415870/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Jiang</surname>
<given-names>Xiaoquan</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1458770/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Pan</surname>
<given-names>Fulu</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1510762/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Yang</surname>
<given-names>Wenning</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1443070/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Liu</surname>
<given-names>Haibo</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1431791/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Liu</surname>
<given-names>Yang</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1458800/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Wang</surname>
<given-names>Guopeng</given-names>
</name>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1510690/overview"/>
</contrib>
</contrib-group>
<aff id="aff1">
<label>
<sup>1</sup>
</label>Beijing Adamadle Biotech Co, Ltd., <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<label>
<sup>2</sup>
</label>Xiyuan Hospital, China Academy of Chinese Medical Sciences, <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff3">
<label>
<sup>3</sup>
</label>School of Chinese Materia Medica, Beijing University of Chinese Medicine, <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff4">
<label>
<sup>4</sup>
</label>Chinese Academy of Medical Sciences and Peking Union Medical College, Institute of Medicinal Plant Development, <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff5">
<label>
<sup>5</sup>
</label>Zhongcai Health (Beijing) Biological Technology Development Co, Ltd., <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/106801/overview">Sabina Passamonti</ext-link>, University of Trieste, Italy</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/443258/overview">Zhihao Liu</ext-link>, United&#x20;States Department of Agriculture, United&#x20;States</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/767876/overview">Jinyao Li</ext-link>, Xinjiang University, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Haibo Liu, <email>hbliu@implad.ac.cn</email>; Yang Liu, <email>liuyang@bucm.edu.cn</email>
</corresp>
<fn fn-type="equal" id="fn1">
<label>
<sup>&#x2020;</sup>
</label>
<p>These authors have contributed equally to this&#x20;work</p>
</fn>
<fn fn-type="other">
<p>This article was submitted to Drug Metabolism and Transport, a section of the journal Frontiers in Pharmacology</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>19</day>
<month>10</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="collection">
<year>2021</year>
</pub-date>
<volume>12</volume>
<elocation-id>746594</elocation-id>
<history>
<date date-type="received">
<day>24</day>
<month>07</month>
<year>2021</year>
</date>
<date date-type="accepted">
<day>13</day>
<month>09</month>
<year>2021</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2021 Li, Yi, Liu, Jiang, Pan, Yang, Liu, Liu and Wang.</copyright-statement>
<copyright-year>2021</copyright-year>
<copyright-holder>Li, Yi, Liu, Jiang, Pan, Yang, Liu, Liu and Wang</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these&#x20;terms.</p>
</license>
</permissions>
<abstract>
<p>We aimed to develop a physiological-based pharmacokinetic and dipepidyl peptidase 4 (DPP-4) occupancy model (PBPK-DO) characterized by two simultaneous simulations to predict pharmacokinetic (PK) and pharmacodynamic changes of saxagliptin and metabolite M2 in humans when coadministered with CYP3A4 inhibitors or inducers. Ketoconazole, delavirdine, and rifampicin were selected as a CYP3A4 competitive inhibitor, a time-dependent inhibitor, and an inducer, respectively. Here, we have successfully simulated PK profiles and DPP-4 occupancy profiles of saxagliptin in humans using the PBPK-DO model. Additionally, under the circumstance of actually measured values, predicted results were good and in line with observations, and all fold errors were below 2. The prediction results demonstrated that the oral dose of saxagliptin should be reduced to 2.5&#xa0;mg when coadministrated with ketoconazole. The predictions also showed that although PK profiles of saxagliptin showed significant changes with delavirdine (AUC 1.5-fold increase) or rifampicin (AUC: a decrease to 0.19-fold) compared to those without inhibitors or inducers, occupancies of DPP-4 by saxagliptin were nearly unchanged, that is, the administration dose of saxagliptin need not adjust when there is coadministration with delavirdine or rifampicin.</p>
</abstract>
<kwd-group>
<kwd>saxagliptin</kwd>
<kwd>DDI prediction</kwd>
<kwd>DPP-4 occupancy</kwd>
<kwd>PBPK-DO model</kwd>
<kwd>CYP3A4</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<title>Introduction</title>
<p>Patients undergoing multiple comorbidities are usually treated by complicated polypharmacy schemes and long-term administration, which means that they will be at the risk of drug&#x2013;drug interactions (DDIs). In DDIs, one drug may affect the PK or PD behavior of another drug, thereby resulting in a series of side effects and even a withdrawal of approved pharmaceuticals from the market, for instance, mibefradil and terfenadine (<xref ref-type="bibr" rid="B41">Valicherla et&#x20;al., 2019</xref>; <xref ref-type="bibr" rid="B27">Pelkonen et&#x20;al., 2020</xref>). Therefore, prospective assessment of a potential risk of DDIs is significant within the pharmaceutical industry, such as guaranteeing the safety and reducing unnecessary consumption of new drugs. Cytochrome P450, which is the most comprehensive metabolizing enzyme in the gut and the liver, plays an important role in pharmacokinetic (PK) interaction-related DDIs through the interfering metabolism of most drugs (<xref ref-type="bibr" rid="B11">Dmitriev et&#x20;al., 2019</xref>). Currently, PK-related DDIs mediated by CYP have become a research focus over the past decades (<xref ref-type="bibr" rid="B9">Conner et&#x20;al., 2018</xref>; <xref ref-type="bibr" rid="B28">Peng et&#x20;al., 2021</xref>). However, only focusing on PK-related DDIs is far from enough, and pharmacodynamic (PD)-related DDIs should receive more attention, particularly on dose adjustment for patients. Although PD-related DDIs recorded are roughly 1.9-fold higher than PK-related DDIs (<xref ref-type="bibr" rid="B35">Spanakis et&#x20;al., 2019</xref>), unfortunately, simulation study on PD-related DDIs is far less compared to those on PK-related&#x20;DDIs.</p>
<p>Ketoconazole and delavirdine are strongly competitive and time-dependent inhibitors (TDIs) against the CYP3A4 enzyme, and rifampicin is a strong CYP3A4 inducer. It is well known that ketoconazole and rifampicin are often recommended to assess potential DDIs for other drugs mainly metabolized by the CYP3A4 enzyme (<xref ref-type="bibr" rid="B34">Rytk&#xf6;nen et&#x20;al., 2020</xref>; <xref ref-type="bibr" rid="B42">Xu et&#x20;al., 2021</xref>). To our knowledge, owing to irreversible loss of P450 enzyme functions, TDIs are regarded to have a longer persistent time on the drug metabolic enzyme and consequently to cause clinically more significant DDIs in contrast to competitive inhibitors (<xref ref-type="bibr" rid="B20">Kosaka et&#x20;al., 2017</xref>; <xref ref-type="bibr" rid="B12">Eng et&#x20;al., 2020</xref>; <xref ref-type="bibr" rid="B38">Tanna et&#x20;al., 2021</xref>). Therefore, ketoconazole, delavirdine, and rifampicin were chosen for potential DDI assessments.</p>
<p>Saxagliptin is an orally potent competitive DPP-4 inhibitor and utilized for the treatment of type 2 diabetes at a daily dose of 5&#xa0;mg.<xref ref-type="fn" rid="fn2">
<sup>1</sup>
</xref>. Saxagliptin is metabolized extensively in humans <italic>via</italic> CYP3A4 to be converted into many metabolites, of which 5-hydroxy saxagliptin (M2) is the most major active metabolite. M2&#x20;<italic>in vivo</italic> is roughly in a 2-fold higher amount (44.1 versus 24.0%) and binds to DPP-4 with a &#x223c;2-fold lower affinity than saxagliptin (1.3 versus 2.6&#xa0;nm)<xref ref-type="fn" rid="fn2">
<sup>1</sup>
</xref> (<xref ref-type="bibr" rid="B36">Su et&#x20;al., 2012</xref>). Hence, when coadministered with inhibitors or inducers of CYP3A4, significant effects of them on PK and PD of saxagliptin should be taken into account.</p>
<p>We aimed to develop a mathematical model to assess the dynamic effect of ketoconazole, delavirdine, and rifampicin on the PK and PD of saxagliptin tablets in humans, when coadministered. More precisely, the physiological-based pharmacokinetic (PBPK) model and the DPP-4 occupancy (DO) model were incorporated into a new mathematical model, termed as the PBPK-DO model, which enables the changes of PK and PD of saxagliptin and M2 in humans to be quantified simultaneously with coadministration of CYP3A4 inhibitors or inducers.</p>
</sec>
<sec sec-type="methods" id="s2">
<title>Methods</title>
<sec id="s2-1">
<title>Data Collection</title>
<p>Clinical PK studies of ketoconazole, delavirdine, and rifampicin were taken from the published literature<xref ref-type="fn" rid="fn3 fn4">
<sup>2, 3</sup>
</xref>(<xref ref-type="bibr" rid="B16">Hanke et&#x20;al., 2018</xref>), which could be used in their respective PBPK model establishment and verification. Clinical PK and PD studies of saxagliptin and metabolite M2 were collected from published data (<xref ref-type="bibr" rid="B39">Upreti et&#x20;al., 2011</xref>), which could be used in the PBPK-DO model development and verification for saxagliptin and M2. Physicochemical properties of four drugs, binding kinetics of saxagliptin and M2, and physiological parameters in humans required in developing the PBPK-DO model were obtained from published scientific studies, and the built-in libraries of Gastroplus software were used in this study, including Berkeley Madonna (Version 10.2.8, Berkeley Madonna, Inc Albany, CA, United&#x20;States) and ADMET Predictor (Version 9.0.0.0, Simulation Plus, Inc Lancaster, CA, United&#x20;States).</p>
</sec>
<sec id="s2-2">
<title>Development of the PBPK-DO Model</title>
<p>A PBPK-DO model was developed to simulate PK and DPP-4 occupancy time profiles of saxagliptin and metabolite M2 simultaneously after oral coadministration with ketoconazole, delavirdine, and rifampicin. The PBPK-DO model was composed of three key simulation processes, that is, PK prediction of saxagliptin and M2, simulation of DPP-4 occupancy by saxagliptin and M2, and interaction prediction with inhibitors/inducers of CYP3A4. In this PBPK-DO model, first, the simulation of saxagliptin and M2 concentration changes over time was enabled simultaneously by the PBPK model, which consisted of a stomach&#x2013;gut compartment, a enterocytes compartment, a portal vein compartment, a blood compartment (arterial and venous blood), eliminating tissues (the liver, the kidney), non-eliminating tissues (adipose, the bone, the brain, the heart, muscle, the skin, and the spleen), and the lung. Next, the interactions between inhibitors/inducers and CYP3A4 were calculated through inhibition or inducing parameters (K<sub>i</sub>, K<sub>inact</sub>, E<sub>max</sub>, and EC<sub>50</sub>), CYP3A4 expression amount, and free saxagliptin concentration in the gut and liver. Eventually, time courses of DPP-4 occupancy were characterized by two key rate constants of on-rate (k<sub>on</sub>) and off-rate (k<sub>off</sub>) combined with free drug concentration around the DPP-4. In addition, we assumed that DPP-4 was located in the venous blood compartment in the present model. The overall framework of the PBPK-DO model is represented in <xref ref-type="fig" rid="F1">Figure&#x20;1</xref>.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Schematic representation of the PBPK-DO model for saxagliptin in humans. The PBPK-DO model includes the gut lumen, enterocytes, the portal vein, the liver, blood (arterial supply and venous return), the lung, and other eliminating tissues (kidney) and non-eliminating tissues (11 compartments). The CYP3A metabolism enzyme was set into enterocytes and liver compartments. DPP-4 was assumed to only reside in the venous return compartment.</p>
</caption>
<graphic xlink:href="fphar-12-746594-g001.tif"/>
</fig>
<sec id="s2-2-1">
<title>Stomach&#x2013;Gut Compartment</title>
<p>Assuming that the drug in the stomach was neither absorbed nor metabolized, the drug amount in the stomach (A<sub>0</sub>) is only governed by the gastric emptying rate (K<sub>0</sub>). The change in mass within the stomach is described as follows (<xref ref-type="bibr" rid="B29">Qian et&#x20;al., 2019</xref>):<disp-formula id="e1">
<mml:math id="m1">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>
</p>
<p>The gut lumen consists of the duodenum, jejunum, and ileum, and the amount of drug in the gut lumen (A<sub>i</sub>) is controlled by the gut transit rate constant (K<sub>t,i</sub>) and absorption rate constant (K<sub>a,i</sub>). The change in mass within each gut lumen was described as follows (<xref ref-type="bibr" rid="B29">Qian et&#x20;al., 2019</xref>):<disp-formula id="e2">
<mml:math id="m2">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>a</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>where <italic>i</italic>&#x20;&#x3d; 1, 2, and 3 corresponds to the duodenum, jejunum, and ileum, respectively. The calculation of the K<sub>a,i</sub> value is given by the following:<xref ref-type="fn" rid="fn5">
<sup>4</sup>
</xref>
<disp-formula id="e3">
<mml:math id="m3">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>a</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>a</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>where K<sub>a,i0</sub> represents the initial absorption rate constant and f<sub>a</sub> represents the absorption adjustment factor. The calculation of the K<sub>a,i0</sub> value is given by the following:<xref ref-type="fn" rid="fn7">
<sup>6</sup>
</xref>
<disp-formula id="e4">
<mml:math id="m4">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>a</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>f</mml:mi>
<mml:mi>f</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>h</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>A</mml:mi>
<mml:mi>S</mml:mi>
<mml:mi>F</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>where P<sub>eff, human</sub> is the effective permeability in humans and r<sub>i</sub> is the average radius of different intestinal segments (the duodenum, jejunum, and ileum). ASF is the absorption scale factor.</p>
</sec>
<sec id="s2-2-2">
<title>Enterocyte Compartment</title>
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</disp-formula>where Q<sub>ent,i</sub> and V<sub>ent,i</sub> represent the blood flow rate and the volume of each enterocyte compartment, respectively. V<sub>pv</sub> is the volume of the portal vein compartment, f<sub>ugut</sub> is the free drug concentration in the enterocyte compartment, and K<sub>p,ent</sub> is the ratio of intestine over blood drug concentration.</p>
<p>CL<sub>int,ent</sub> (t) and Abundance<sub>ent,i</sub> (t) represent the intrinsic metabolic clearance and CYP3A content in the enterocyte compartment with inhibitors/inducers or without inhibitors/inducers, respectively. V<sub>max</sub> and K<sub>m</sub> are metabolic parameters of the drug in each different enterocyte compartment. According to the reported result, saxagliptin is a weak P-glycoprotein substrate (<xref ref-type="bibr" rid="B7">Boulton, 2017</xref>); consequently, the efflux effect of P-glycoprotein on the amount of saxaliptin in the gut lumen was not considered in this&#x20;study.</p>
</sec>
<sec id="s2-2-3">
<title>Portal Vein Compartment</title>
<p>The drug from the enterocyte compartment enters the liver <italic>via</italic> the portal vein, and hence, the change of drug amount over time in the portal vein compartment (A<sub>pv</sub>) is illustrated according to the following equations (<xref ref-type="bibr" rid="B23">Li et&#x20;al., 2012</xref>; <xref ref-type="bibr" rid="B29">Qian et&#x20;al., 2019</xref>):<disp-formula id="e7">
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</disp-formula>where C<sub>ab</sub> is the drug concentration in arterial&#x20;blood.</p>
</sec>
<sec id="s2-2-4">
<title>Liver Compartment</title>
<p>The liver is a main eliminating tissue of saxagliptin, and the amount of drug in the liver is described as follows<xref ref-type="fn" rid="fn7">
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<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>
<disp-formula id="e9">
<mml:math id="m9">
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>t</mml:mi>
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<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
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<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
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</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>A</mml:mi>
<mml:mi>b</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>n</mml:mi>
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<mml:msub>
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</mml:msub>
<mml:mrow>
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</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>I</mml:mi>
<mml:mi>S</mml:mi>
<mml:mi>E</mml:mi>
<mml:mi>F</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mi>m</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mrow>
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<mml:mi>i</mml:mi>
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</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
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<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>M</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>where A<sub>li</sub>, V<sub>li</sub>, Q<sub>li</sub>, and Q<sub>lia</sub> are the drug amount in the liver, the volume and hepatic blood flow, and the hepatic artery blood flow rate of the liver, respectively. Rbp is the blood-to-plasma concentration ratio, f<sub>up</sub> is the fraction of free drug in the plasma, and K<sub>p,li</sub> is liver-to-plasma partition coefficient. M is molecular weight of the&#x20;drug.</p>
<p>CL<sub>int,li</sub>(t) represents the intrinsic metabolic clearance of a drug in the liver. Abundance<sub>li</sub>(t) represents the hepatic CYP3A amount with inhibitors/inducers or without inhibitors/inducers. ISEF is the intersystem extrapolation factor. Owing to the finding that saxagliptin is not almost eliminated through biliary excretion (<xref ref-type="bibr" rid="B14">Fura et&#x20;al., 2009</xref>), biliary clearance of saxagliptin is not incorporated into this PBPK&#x20;model.</p>
<p>The amount of metabolite in the enterocyte compartment (A<sub>met,ent</sub>) is illustrated by the following:<disp-formula id="e10">
<mml:math id="m10">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>e</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:munderover>
<mml:mstyle displaystyle="true">
<mml:mo>&#x2211;</mml:mo>
</mml:mstyle>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mn>3</mml:mn>
</mml:munderover>
<mml:mo>&#xa0;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>e</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>A</mml:mi>
<mml:mi>b</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>c</mml:mi>
<mml:msub>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mi>g</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>e</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mi>m</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mi>g</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>M</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>e</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfrac>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(10)</label>
</disp-formula>
</p>
<p>The amount of metabolite in the liver (A<sub>met,li</sub>) is illustrated by the following:<disp-formula id="e11">
<mml:math id="m11">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>e</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>A</mml:mi>
<mml:mi>b</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>c</mml:mi>
<mml:msub>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mi>m</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>M</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(11)</label>
</disp-formula>where f<sub>scale</sub> is the scale factor of metabolite conversion. The total amount of metabolite (A<sub>met</sub>) enters the venous blood compartment directly without consideration of gut absorption and is calculated by the following:<disp-formula id="e12">
<mml:math id="m12">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>e</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>a</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>m</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(12)</label>
</disp-formula>
<disp-formula id="equ1">
<mml:math id="m13">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>a</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>m</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>a</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>m</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mi>a</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>m</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>where K<sub>a,met0</sub> and K<sub>a,met</sub> are the initial absorption rate constant and absorption rate constant of metabolite M2, respectively. f<sub>a,met</sub> represents the absorption adjustment factor of the metabolite.</p>
</sec>
<sec id="s2-2-5">
<title>Kidney Compartment</title>
<p>The change of drug amount with time within the kidney (A<sub>ki</sub>) is described by the following (<xref ref-type="bibr" rid="B23">Li et&#x20;al., 2012</xref>):<disp-formula id="e14">
<mml:math id="m14">
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<mml:mo>,</mml:mo>
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<label>(14)</label>
</disp-formula>where Q<sub>ki</sub> and V<sub>ki</sub> are the blood flow and the volume of the kidney, respectively. K<sub>p,ki</sub> is the kidney-to-plasma partition coefficient. CLr is the kidney elimination rate of the&#x20;drug.</p>
</sec>
<sec id="s2-2-6">
<title>Lung Compartment</title>
<p>The amount of drug in the lung (A<sub>lu</sub>) is described as follows (<xref ref-type="bibr" rid="B23">Li et&#x20;al., 2012</xref>):<disp-formula id="e13">
<mml:math id="m15">
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<mml:mi>p</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>l</mml:mi>
<mml:mi>u</mml:mi>
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</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
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<label>(13)</label>
</disp-formula>where Q<sub>lu</sub> and V<sub>lu</sub> are the blood flow and the volume of the lung, respectively. K<sub>p,lu</sub> is lung-to-plasma partition coefficient.</p>
</sec>
<sec id="s2-2-7">
<title>Other Non-eliminating Tissue Compartments</title>
<p>Overall, the amount of drug within non-eliminating tissue compartments (A<sub>nt</sub>) (the adipose, the bone, the brain, the heart, the muscle, the skin, the spleen, the red marrow, the yellow marrow, reproductive organs, and the rest of the body), except for the lung, follows the following equation (<xref ref-type="bibr" rid="B23">Li et&#x20;al., 2012</xref>):<disp-formula id="e16">
<mml:math id="m16">
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<mml:mi>d</mml:mi>
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<mml:mrow>
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<mml:mo>,</mml:mo>
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</mml:math>
<label>(16)</label>
</disp-formula>where Q<sub>nt</sub> and V<sub>nt</sub> are the blood flow sum and the mean volume of other non-eliminating tissues, respectively. K<sub>p,nt</sub> is the partition coefficient sum of other non-eliminating over plasma.</p>
</sec>
<sec id="s2-2-8">
<title>Arterial Blood Compartment</title>
<p>The drug concentration within the arterial blood (C<sub>ab</sub>) is described as follows (<xref ref-type="bibr" rid="B23">Li et&#x20;al., 2012</xref>; <xref ref-type="bibr" rid="B13">Fu et&#x20;al., 2019</xref>):<disp-formula id="e19">
<mml:math id="m17">
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</mml:mrow>
<mml:mrow>
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</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
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<mml:mo>,</mml:mo>
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<label>(17)</label>
</disp-formula>where V<sub>ab</sub> is the volume of the arterial blood compartment. <italic>i</italic> represents all eliminating and non-eliminating tissues except for the lung tissue.</p>
</sec>
<sec id="s2-2-9">
<title>Venous Blood Compartment</title>
<p>The drug concentration within the venous blood (C<sub>vb</sub>) is described as follows (<xref ref-type="bibr" rid="B23">Li et&#x20;al., 2012</xref>; <xref ref-type="bibr" rid="B13">Fu et&#x20;al., 2019</xref>):<disp-formula id="e18">
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<label>(18)</label>
</disp-formula>where V<sub>vb</sub> is the volume of the venous blood compartment. <italic>i</italic> represents all eliminating and non-eliminating tissues except for the lung tissue.</p>
</sec>
<sec id="s2-2-10">
<title>CYP3A Dynamics of Inhibition and Induction</title>
<p>Here, the inhibition and induction model of CYP3A were developed assuming that intestinal inhibition and induction dynamic parameters were identical to hepatic dose. The CYP3A reversible competition inhibition dynamics is described as follows (<xref ref-type="bibr" rid="B5">Baneyx et&#x20;al., 2014</xref>):<disp-formula id="equ2">
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</disp-formula>where I<sub>li</sub> is the concentration of the inhibitor/inducer within the targeted tissue (the gut and liver). f<sub>up,in</sub> is the fraction of the free inhibitor/inducer in the plasma. K<sub>p,in</sub> is the partition coefficient of the inhibitor/inducer of the targeted tissue (the gut and liver) to plasma. M<sub>in</sub> is the molecular weight of the inhibitor/inducer. K<sub>i</sub> and k<sub>inact</sub> are inactivation parameters of the inhibitor against CYP3A4. EC<sub>max</sub> and EC50 are inductive parameters of the inducer on CYP3A4. k<sub>deg</sub> is the degradation rate constant of CYP3A4, and in this study, it was assumed that the k<sub>deg</sub> value in the liver is identical to that in the&#x20;gut.</p>
</sec>
<sec id="s2-2-11">
<title>DPP-4 Engagement Dynamics by Saxagliptin and Metabolite M2</title>
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<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>e</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>f</mml:mi>
<mml:mi>f</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>T</mml:mi>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(23)</label>
</disp-formula>
<disp-formula id="e24">
<mml:math id="m24">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>e</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mtext>TC,</mml:mtext>
</mml:mrow>
</mml:math>
<label>(24)</label>
</disp-formula>
<disp-formula id="e25">
<mml:math id="m25">
<mml:mrow>
<mml:mtext>TO</mml:mtext>
<mml:mo>&#x3d;</mml:mo>
<mml:munderover>
<mml:mstyle displaystyle="true">
<mml:mo>&#x2211;</mml:mo>
</mml:mstyle>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:munderover>
<mml:mfrac>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>100</mml:mn>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(25)</label>
</disp-formula>where <italic>i</italic>&#x20;&#x3d; 1 and 2 corresponds to saxagliptin and active metabolite M2, respectively. TC is the concentration of saxagliptin/M2-DPP-4 complex formed. T<sub>free</sub> is the concentration of free DPP-4. T<sub>total</sub> is the sum of TC plus T<sub>free</sub>. C<sub>vb,i</sub>, k<sub>on,i</sub>, and k<sub>off,i</sub> are the drug concentration within the venous blood and the on-rate and off-rate of saxagliptin and active metabolite M2, respectively.</p>
</sec>
</sec>
<sec id="s2-3">
<title>DDI Prediction Through the PBPK-DO Model</title>
<p>The DDI predictions were conducted to evaluate the parameter changes of PD (TO<sub>AUC</sub>, area under the occupancy&#x2013;time curve; TO<sub>max</sub>, maximum occupancy; and DTO<sub>&#x3e;60%</sub> duration of &#x3e;60% TO) and PK (AUC, area under the concentration&#x2013;time curve; and C<sub>max</sub>, peak concentration) on saxagliptin and M2 with and without inhibitors/inducers.</p>
</sec>
</sec>
<sec sec-type="results" id="s3">
<title>Results</title>
<sec id="s3-1">
<title>Data Collection of the PBPK-DO Model</title>
<p>The input parameters of saxagliptin and metabolite M2 for the PBPK-DO model are given in <xref ref-type="table" rid="T1">Table&#x20;1</xref> (<xref ref-type="bibr" rid="B30">Rodgers et&#x20;al., 2005</xref>; <xref ref-type="bibr" rid="B18">Kim et&#x20;al., 2006</xref>; <xref ref-type="bibr" rid="B31">Rodgers and Rowland, 2006</xref>; <xref ref-type="bibr" rid="B36">Su et&#x20;al., 2012</xref>; <xref ref-type="bibr" rid="B29">Qian et&#x20;al., 2019</xref>). The corresponding parameters of inhibitors/inducers are listed in <xref ref-type="sec" rid="s10">Supplementary Tables S1&#x2013;S3</xref> (<xref ref-type="bibr" rid="B30">Rodgers et&#x20;al., 2005</xref>; <xref ref-type="bibr" rid="B44">Zhou et&#x20;al., 2005</xref>; <xref ref-type="bibr" rid="B31">Rodgers and Rowland, 2006</xref>; <xref ref-type="bibr" rid="B40">Usach et&#x20;al., 2013</xref>; <xref ref-type="bibr" rid="B29">Qian et&#x20;al., 2019</xref>; <xref ref-type="bibr" rid="B26">Motiei et&#x20;al., 2021</xref>; <xref ref-type="bibr" rid="B22">Lanni et&#x20;al., 2021</xref>). The physiological parameters in humans are presented in <xref ref-type="sec" rid="s10">Supplementary Table S4</xref> (<xref ref-type="bibr" rid="B23">Li et&#x20;al., 2012</xref> and <xref ref-type="bibr" rid="B29">Qian et&#x20;al., 2019</xref>)<xref ref-type="fn" rid="fn7">
<sup>6</sup>
</xref>.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Summary of input parameters for saxagliptin and metabolite M2 in the PBPK-DO&#x20;model.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left">Property</th>
<th align="center">Saxagliptin</th>
<th align="center">Metabolite M2</th>
<th rowspan="2" align="center">Source</th>
</tr>
<tr>
<th align="center">Values</th>
<th align="center">Values</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Molecular weight (M)</td>
<td align="char" char=".">315.42&#xa0;g&#xa0;mol<sup>&#x2212;1</sup>
</td>
<td align="char" char=".">331.42&#xa0;g&#xa0;mol<sup>&#x2212;1</sup>
</td>
<td align="left">
<xref ref-type="bibr" rid="B36">Su et&#x20;al. (2012)</xref>
</td>
</tr>
<tr>
<td align="left">PK<sup>a</sup>
</td>
<td align="char" char="( .">7.3 (base)</td>
<td align="char" char="( .">7.6 (base)</td>
<td align="left">Obtained from the literature<xref ref-type="fn" rid="fn10">
<sup>9</sup>
</xref> and Chemspider, respectively</td>
</tr>
<tr>
<td align="left">LogP</td>
<td align="char" char="(">&#x2212;1.82 (@pH1.2)</td>
<td align="center">&#x2212;1.44</td>
<td align="left">Obtained from the literature<xref ref-type="fn" rid="fn10">
<sup>9</sup>
</xref> and Chemspider, respectively</td>
</tr>
<tr>
<td align="left">Effective permeability in humans (P<sub>eff</sub>)</td>
<td align="char" char=".">19 &#xd7; 10<sup>&#x2013;5</sup>&#xa0;cm&#xa0;s<sup>&#x2212;1</sup>
</td>
<td align="char" char=".">19 &#xd7; 10<sup>&#x2013;5</sup>&#xa0;cm&#xa0;s<sup>&#x2212;1</sup>
</td>
<td align="left">Calculated by ADMET Predictor 7.0</td>
</tr>
<tr>
<td align="left">Fraction of free drug (f<sub>up</sub>)</td>
<td align="char" char=".">0.95</td>
<td align="char" char=".">0.95</td>
<td align="left">Plasma protein binding of both compounds was very low<xref ref-type="fn" rid="fn15">
<sup>14</sup>
</xref> and hence assigned at 5%</td>
</tr>
<tr>
<td align="left">Blood-to-plasma concentration ratio (Rbp)</td>
<td align="char" char=".">0.83</td>
<td align="char" char=".">0.83</td>
<td align="left">Calculated by ADMET Predictor 7.0</td>
</tr>
<tr>
<td rowspan="3" align="left">Initial absorption rate constant (K<sub>a,i0</sub>/K<sub>a,met0</sub>)</td>
<td align="char" char="( .">1.51&#xa0;h<sup>&#x2212;1</sup> (duodenum)</td>
<td rowspan="3" align="char" char=".">0.25</td>
<td rowspan="3" align="left">Calculated based on <xref ref-type="disp-formula" rid="e4">Eq. 4</xref> for saxagliptin; optimized by PK curves of M2 for the metabolite</td>
</tr>
<tr>
<td align="char" char="( .">2.25&#xa0;h<sup>&#x2212;1</sup> (jejunum)</td>
</tr>
<tr>
<td align="char" char="( .">2.46&#xa0;h<sup>&#x2212;1</sup> (ileum)</td>
</tr>
<tr>
<td align="left">Absorption adjustment factor (f<sub>a</sub>/f<sub>a,met</sub>)</td>
<td align="char" char=".">0.005&#xa0;&#x3bc;g<sup>&#x2212;1</sup>
</td>
<td align="char" char=".">0.00015&#xa0;&#x3bc;g<sup>&#x2212;1</sup>
</td>
<td align="left">Optimized by matching observed T<sub>max</sub>
</td>
</tr>
<tr>
<td align="left">Scale factor of metabolite conversion (f<sub>scale</sub>)</td>
<td align="center">_</td>
<td align="char" char=".">2</td>
<td align="left">Adjusted based on the PK profile of M2 in humans</td>
</tr>
<tr>
<td align="left">V<sub>max</sub> for 3A4</td>
<td align="char" char="// .">V<sub>max</sub> &#x3d; 31.7&#xa0;pmol M2/pmol CYP/min</td>
<td align="center">_</td>
<td rowspan="2" align="left">
<xref ref-type="bibr" rid="B36">Su et&#x20;al. (2012)</xref>
</td>
</tr>
<tr>
<td align="left">K<sub>m</sub> for 3A4</td>
<td align="center">K<sub>m</sub> &#x3d; 81.7&#xa0;&#x3bc;M</td>
<td align="center">_</td>
</tr>
<tr>
<td align="left">Free drug concentration in the enterocyte compartment (f<sub>ugut</sub>)</td>
<td align="char" char=".">1.0</td>
<td align="char" char=".">1.0</td>
<td align="left">Defaulted according to the literature <xref ref-type="bibr" rid="B29">Qian et&#x20;al. (2019)</xref>
</td>
</tr>
<tr>
<td align="left">Intestine/blood concentration ratio (K<sub>p,ent</sub>)</td>
<td align="char" char=".">1.03</td>
<td align="char" char=".">_</td>
<td rowspan="4" align="left">Estimated by Rodgers&#x2019; model <xref ref-type="bibr" rid="B30">Rodgers et&#x20;al. (2005)</xref>; <xref ref-type="bibr" rid="B31">Rodgers and Rowland (2006)</xref>
</td>
</tr>
<tr>
<td align="left">Liver-to-plasma partition coefficient (K<sub>p,li</sub>)</td>
<td align="char" char=".">1.08</td>
<td align="char" char=".">1.21</td>
</tr>
<tr>
<td align="left">Kidney-to-plasma partition coefficient (K<sub>p,ki</sub>)</td>
<td align="char" char=".">0.74</td>
<td align="char" char=".">0.74</td>
</tr>
<tr>
<td align="left">Lung-to-plasma partition coefficient (K<sub>p,lu</sub>)</td>
<td align="char" char=".">0.76</td>
<td align="char" char=".">0.62</td>
</tr>
<tr>
<td align="left">Non-eliminating-to-plasma partition coefficient (K<sub>p,nt</sub>)</td>
<td align="char" char=".">7.8</td>
<td align="char" char=".">7.8</td>
<td align="left">Optimized by the observed PK profile</td>
</tr>
<tr>
<td align="left">Kidney clearance (CLr)</td>
<td align="char" char="/ .">10.8&#xa0;L/h</td>
<td align="char" char="/ .">4.6&#xa0;L/h</td>
<td align="left">
<xref ref-type="bibr" rid="B39">Upreti et&#x20;al. (2011)</xref>
</td>
</tr>
<tr>
<td align="left">On-rate (k<sub>on</sub>) to DPP-4</td>
<td align="char" char=".">565.7&#xa0;&#x3bc;M<sup>&#x2212;1</sup>h<sup>&#x2212;1</sup>
</td>
<td align="char" char=".">2,582.6&#xa0;&#x3bc;M<sup>&#x2212;1</sup>h<sup>&#x2212;1</sup>
</td>
<td align="left">Obtained from the literature <xref ref-type="bibr" rid="B18">Kim et&#x20;al. (2006)</xref> for saxagliptin, calculated with k<sub>off</sub>/K<sub>i</sub> for M2 (K<sub>i</sub> &#x3d; 0.7&#xa0;&#x3bc;M)</td>
</tr>
<tr>
<td align="left">Off-rate (k<sub>off</sub>) from DPP-4</td>
<td align="char" char=".">0.2&#xa0;h<sup>&#x2212;1</sup>
</td>
<td align="char" char=".">1.8&#xa0;h<sup>&#x2212;1</sup>
</td>
<td align="left">Obtained from the literature <xref ref-type="bibr" rid="B18">Kim et&#x20;al. (2006)</xref> for saxagliptin and<xref ref-type="fn" rid="fn10">
<sup>9</sup>
</xref> for M2</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s3-2">
<title>Development of the PBPK-DO Model for Saxagliptin and Metabolite M2</title>
<p>The PBPK-DO model for saxagliptin has been established by a massive number of input parameters from <xref ref-type="table" rid="T1">Table&#x20;1</xref> and <xref ref-type="sec" rid="s10">Supplementary Table S4</xref>. <xref ref-type="fig" rid="F2">Figures 2A,B</xref> show the predictions and observations of the human PK and DPP-4 occupancy for saxagliptin and metabolite M2, respectively, after oral administration of a 5&#xa0;mg saxagliptin. Comparison of observed PK and DPP-4 occupancy parameters with simulated parameters of saxagliptin and M2 is summarized in <xref ref-type="sec" rid="s10">Supplementary Table S5</xref>. It is clearly indicated that human PK simulation corresponds closely to observed values for saxagliptin and M2 (<xref ref-type="bibr" rid="B39">Upreti et&#x20;al., 2011</xref>) and that simulation of time course of DPP-4 occupancy in humans by saxagliptin could also be matched with experimentally determined values very well (<xref ref-type="bibr" rid="B39">Upreti et&#x20;al., 2011</xref>). The simulation results have displayed that the developed PBPK-DO model could accurately predict PK profiles and DPP-4 time profiles in humans for saxagliptin and&#x20;M2.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Simulations of pharmacokinetics and DPP-4 occupancy in humans. <bold>(A)</bold> Predicted and observed human plasma concentration&#x2013;time curves of saxagliptin and M2 after oral administration at a dose of 5&#xa0;mg. Black (&#x2229;) and red (&#x2229;) solid lines represent plasma concentration&#x2013;time curves of saxagliptin and M2, respectively. The blue squares (.) and blue up-triangles (&#x25b3;) refer to experimentally measured pharmacokinetic data of saxagliptin and M2, respectively. <bold>(B)</bold> Predicted and observed time course of DPP-4 occupancy by saxagliptin in humans following oral administration of 5&#xa0;mg. Black (&#x2229;), green (&#x2229;), and red (&#x2229;) solid lines represent human DPP-4 occupancy curves of saxagliptin &#x2b; M2, saxagliptin, and M2, respectively. The blue circles (&#x25ef;) refer to experimentally measured DPP-4 occupancy&#x20;data.</p>
</caption>
<graphic xlink:href="fphar-12-746594-g002.tif"/>
</fig>
</sec>
<sec id="s3-3">
<title>Effect of Inhibitors/Inducers on PK and PD of Saxagliptin in Humans</title>
<p>The PK profile predictions of inhibitors/inducers have been shown in <xref ref-type="sec" rid="s10">Supplementary Figure S1</xref>, and the predicted and observed data are listed in <xref ref-type="sec" rid="s10">Supplementary Table S6</xref>. The accuracies of PK prediction using the developed PBPK model have been verified by comparing predicted and observed PK of the inhibitors/inducers. The comparison displayed that predicted PK profiles matched observed profiles well (<xref ref-type="sec" rid="s10">Supplementary Figure S1</xref>) and that all fold errors were less than 2 between predicted and observed PK data (<xref ref-type="sec" rid="s10">Supplementary Table S6</xref>). The result indicated that the established PBPK model could accurately simulate the PK process in humans of inhibitors and inducers.</p>
<p>The PK profiles and DPP-4 occupancy profiles of saxagliptin in humans at a dose of 5&#xa0;mg were simulated using the developed PBPK-DO model after coadministration of ketoconazole (200&#xb0;mg, twice daily), delavirdine (400&#xb0;mg, twice daily), and rifampicin (600&#xb0;mg, once daily) for 10&#xb0;days, respectively (<xref ref-type="fig" rid="F3">Figures 3</xref>, <xref ref-type="fig" rid="F4">4</xref>). The C<sub>max</sub> and AUC<sub>0-t</sub> of saxagliptin coadministrated with multidose ketoconazole on the sixth day increased by 1.89- and 3.42-fold of those without ketoconazole, respectively, (<xref ref-type="sec" rid="s10">Supplementary Table S7</xref>). Slight underestimation was found in C<sub>max</sub> and AUC of saxagliptin for DDI predictions (C<sub>max</sub> ratio: 1.89; AUC<sub>0-t</sub> ratio: 3.42) versus DDI observations (C<sub>max</sub> ratio: 2.44; AUC<sub>0-t</sub> ratio: 3.67) after coadministration of ketoconazole<xref ref-type="fn" rid="fn8">
<sup>7</sup>
</xref>. It was observed that C<sub>max</sub> and AUC of saxagliptin increased by 1.33- and 1.50-fold with delavirdine compared to those without the inhibitor, respectively (<xref ref-type="sec" rid="s10">Supplementary Table S8</xref>). The PK profiles and parameters of saxagliptin were strongly influenced following coadministration of rifampicin, while PK profiles and parameters of metabolite M2 were nearly unchanged (<xref ref-type="fig" rid="F3">Figure&#x20;3D</xref> and <xref ref-type="sec" rid="s10">Supplementary Table S9</xref>). Slight overestimation was observed in C<sub>max</sub> and AUC of saxagliptin compared to actually experimentally determined values, with DDI predictions of a C<sub>max</sub> ratio of 0.31 and an AUC<sub>0-t</sub> ratio of 0.19 versus DDI observations of a C<sub>max</sub> ratio of 0.42 and an AUC<sub>0-t</sub> ratio of 0.24 (<xref ref-type="bibr" rid="B39">Upreti et&#x20;al., 2011</xref>). The predicted AUC<sub>0-t</sub> ratio of M2 was slightly below clinical experiment data (0.78 versus 0.91) (<xref ref-type="bibr" rid="B39">Upreti et&#x20;al., 2011</xref>), while the C<sub>max</sub> ratio of M2 had medium differences between predicted and experimentally determined values (0.88 versus 1.38) (<xref ref-type="bibr" rid="B39">Upreti et&#x20;al., 2011</xref>).</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Human plasma level of saxagliptin and M2 following coadministration of inhibitors or inducers. Human plasma profiles of saxagliptin with ketoconazole (<bold>A</bold>, 200&#xb0;mg, twice daily), with delavirdine (<bold>B</bold>, 400&#xb0;mg, twice daily) and rifampicin (<bold>C</bold>, 600&#xb0;mg, once daily) and of M2 with rifampicin <bold>(D)</bold>. The blue squares, blue up-triangles, and red up-triangles refer to observed PK data of saxagliptin without inhibitors/inducers (&#x25a1;) and observed PK data of saxagliptin (&#x25b3;) and M2 (&#x25b3;) with rifampicin on the sixth day, respectively.</p>
</caption>
<graphic xlink:href="fphar-12-746594-g003.tif"/>
</fig>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Human DPP-4 occupancy by saxagliptin and M2 following coadministration of inhibitors or inducers. <bold>(A)</bold> Human DPP-4 by saxagliptin of 5&#xa0;mg (&#x2229;) and 2.5&#xa0;mg (&#x2229;) with ketoconazole (200&#xa0;mg, twice daily). <bold>(B)</bold> Human DPP-4 by saxagliptin of 5&#xa0;mg (&#x2229;) with delavirdine (400&#xb0;mg, twice daily). <bold>(C)</bold> Human DPP-4 by saxagliptin of 5&#xa0;mg (&#x2229;) with rifampicin (600&#xb0;mg, once daily). The black lines (&#x2229;) represent human DPP-4 by saxagliptin of 5&#xa0;mg without inhibitors/inducers. The blue squares (&#x25a1;) and blue up-triangles (&#x25b3;) refer to observed DPP-4 occupancy data of saxagliptin and M2 without inhibitors/inducers and observed DPP-4 occupancy data of saxagliptin and M2 with rifampicin on the sixth day, respectively.</p>
</caption>
<graphic xlink:href="fphar-12-746594-g004.tif"/>
</fig>
<p>The levels of DPP-4 occupancy by saxagliptin (5&#xa0;mg) and M2 coadministrated with multidose ketoconazole have been significantly enhanced compared to that without ketoconazole, with the lowest DPP-4 occupancy being &#x3e;80% (<xref ref-type="fig" rid="F4">Figure&#x20;4A</xref>, red line). Owing to significant improvement of DPP-4 occupancy, next, the time course of DPP-4 occupancy was simulated at a lower dose of 2.5&#xa0;mg (<xref ref-type="fig" rid="F4">Figure&#x20;4A</xref>, green line). The comparison between the DPP-4 occupancy profile at 5&#xa0;mg of saxagliptin without ketoconazole (black line in <xref ref-type="fig" rid="F4">Figure&#x20;4A</xref>) and that at 2.5&#xa0;mg of saxagliptin with ketoconazole (green line in <xref ref-type="fig" rid="F4">Figure&#x20;4A</xref>) demonstrated that oral saxagliptin should be decreased to 2.5&#xa0;mg when there is coadministration with ketoconazole. The result was in good agreement with reported data in the literature<xref ref-type="fn" rid="fn8">
<sup>7</sup>
</xref>. Although AUC of saxagliptin increased 1.5-fold with delavirdine, however, the DPP-4 occupancy time profile by saxagliptin and M2 coadministrated with multidose delavirdine almost coincided with that without delavirdine (<xref ref-type="fig" rid="F4">Figure&#x20;4B</xref>). In contrast, while C<sub>max</sub> and AUC of saxagliptin with coadministration of rifampicin had a considerable decrease, the percent occupancy of DPP-4 by saxagliptin and M2 with coadministration of rifampicin closely resembled that without rifampicin (<xref ref-type="fig" rid="F4">Figure&#x20;4C</xref>). This prediction was in line with the published result in the study (<xref ref-type="bibr" rid="B39">Upreti et&#x20;al., 2011</xref>). The similar occupancy of DPP-4 indicated that M2 was likely the main contributor to human DPP-4 occupancy under the circumstance of coadministration with rifampicin.</p>
</sec>
</sec>
<sec sec-type="discussion" id="s4">
<title>Discussion</title>
<p>In this study, we have developed a PBPK-DO mathematical model characterized by two simultaneous simulations (parent/metabolite and PK/PD), which was first utilized to quantify the impacts of CYP3A4 inhibitors and inducers on the PK and PD of saxagliptin and M2 in humans simultaneously. Ketoconazole and rifampicin are recommended as the standard CYP3A4 competitive inhibitor and inducer for the potential clinical DDI study, respectively. In addition, we also assessed the effect of a TDI (delavirdine) on the PK and PD of saxagliptin and M2, which is a distinct inhibition type from ketoconazole.</p>
<p>Although some studies have showed that P450 metabolic activity of a drug could be frequently different in the gut and the liver (<xref ref-type="bibr" rid="B8">Choe et&#x20;al., 2017</xref>; <xref ref-type="bibr" rid="B17">Kapetas et&#x20;al., 1208</xref>; <xref ref-type="bibr" rid="B21">Kurucz et&#x20;al., 2019</xref>; <xref ref-type="bibr" rid="B19">Klomp et&#x20;al., 2020</xref>), the metabolic parameter of saxagliptin by intestinal CYP3A4 was considered comparable to hepatic CYP3A4 in this PBPK-DO model. f<sub>a</sub> and ASF were incorporated into this model to optimize PK peak time of saxagliptin and scale the effective permeability<xref ref-type="fn" rid="fn5">
<sup>4, </sup>
</xref>
<xref ref-type="fn" rid="fn7">
<sup>6</sup>
</xref>, which greatly improved prediction performance. According to the literature (<xref ref-type="bibr" rid="B39">Upreti et&#x20;al., 2011</xref>; <xref ref-type="bibr" rid="B7">Boulton, 2017</xref>), here, we assumed that all DPP-4 enzymes were located in the blood compartment in the present model. Across published studies (<xref ref-type="bibr" rid="B33">Rowland Yeo et&#x20;al., 2011</xref>; <xref ref-type="bibr" rid="B6">Bolleddula et&#x20;al., 2021</xref>), k<sub>deg</sub> values of CYP3A4 ranged from 0.0077<sup>&#x2013;1</sup> to 0.03&#xa0;h<sup>&#x2212;1</sup>. However, a recent study has confirmed that it was a more reasonable value at 0.03&#xa0;h<sup>&#x2212;1</sup> for the most accurate prediction (<xref ref-type="bibr" rid="B33">Rowland Yeo et&#x20;al., 2011</xref>); hence, the k<sub>deg</sub> value was set at 0.03&#xa0;h<sup>&#x2212;1</sup> in this PBPK-DO model. The induction activity (E<sub>max</sub> and EC<sub>50</sub>) of rifampicin suggested major individual variability between different literature studies (<xref ref-type="bibr" rid="B43">Yamazaki et&#x20;al., 2015</xref>; <xref ref-type="bibr" rid="B1">Almond et&#x20;al., 2016</xref>; <xref ref-type="bibr" rid="B3">Asaumi et&#x20;al., 2018</xref>; <xref ref-type="bibr" rid="B16">Hanke et&#x20;al., 2018</xref>). To minimize the variation, we used mean values of E<sub>max</sub> (6.2&#xa0;&#x3bc;m) and EC<sub>50</sub> (0.6&#xa0;&#x3bc;m) in the current model (<xref ref-type="bibr" rid="B29">Qian et&#x20;al., 2019</xref>). Use of rifampicin induction parameters could have been rationalized indirectly that the predicted expression amount of mean intestinal CYP3A4 after induction by rifampicin was close to the experimentally determined value in humans<xref ref-type="fn" rid="fn9">
<sup>8</sup>
</xref> (6.4-fold change versus 4.4-fold change). The content of human microsomal protein was set at 38&#xa0;mg/g in the liver<xref ref-type="fn" rid="fn7">
<sup>6</sup>
</xref> rather than 45&#xa0;mg/g liver in some studies (<xref ref-type="bibr" rid="B15">Guo et&#x20;al., 2013</xref>; <xref ref-type="bibr" rid="B29">Qian et&#x20;al., 2019</xref>) because the former parameter had been proved to be a more reasonable value in more studies and built-in business software<sup>6</sup>.</p>
<p>All predictions were within 2-fold of observations among them, and the highest fold error was 1.5-fold, which occurred between the predicted and observed C<sub>max</sub> ratios of M2 with rifampicin. In accordance with FDA clinical DDI guidance (<xref ref-type="bibr" rid="B37">Sudsakorn et&#x20;al., 2020</xref>), if the AUC ratio of a drug with and without the inhibitor is &#x2265;1.25 or &#x2264;0.8 with and without the inducer, clinically relevant DDI should be considered. In our simulations, the AUC ratio of saxagliptin was found to be 1.50 with delavirdine and to be 0.19 with rifampicin, which could occur in significant clinical DDIs based predominantly on PK comparisons. Nevertheless, DPP-4 occupancy by saxagliptin with delavirdine or rifampicin was almost unchanged, and PD simulations displayed that delavirdine or rifampicin would not cause human DDIs for saxagliptin, which was in good agreement in clinical experiments (<xref ref-type="bibr" rid="B39">Upreti et&#x20;al., 2011</xref>). The simulation results also have further demonstrated the importance of two simultaneous simulations in the present&#x20;model.</p>
<p>It was reported that the C<sub>max</sub> and AUC<sub>0-t</sub> of saxagliptin increased by less than 2-fold in patients with severe hepatic impairment but by more than 2-fold in patients with severe renal impairment, respectively (<xref ref-type="bibr" rid="B7">Boulton, 2017</xref>). PK simulation in humans with hepatic or renal impairment is performed by modulating many physiological parameters based on healthy humans (<xref ref-type="bibr" rid="B25">Malik et&#x20;al., 2020</xref>). However, currently, this simulation model cannot simulate PK of patients with hepatic or renal impairment yet. Recent literature reported that catalytic activities of 27 CYP3A4 variants on the <italic>in&#x20;vitro</italic> metabolism of saxagliptin were evaluated (<xref ref-type="bibr" rid="B24">Liu et&#x20;al., 2021</xref>). CYP3A4 variants showed decreased activities ranging from 1.9 to 77.1% as compared to the wild type. Hence, we also preliminarily evaluated the effect of genetic variations in metabolizing enzymes on PK and PD of saxagliptin using this model. Here, we only simulated the PK and PD of saxagliptin in humans with variant CYP3A4&#x2a;22. In the simulation, expression and activity of CYP3A4 were replaced with 59 and 40% of the wild type (<xref ref-type="bibr" rid="B2">Alqahtani and Kaddoumi, 2016</xref>). The results displayed that C<sub>max</sub> and AUC<sub>0-t</sub> of saxagliptin increased by about 2-fold, and DPP-4 occupancies by saxagliptin between three oral doses (5, 2.5, and 1&#xa0;mg) have a slight difference (<xref ref-type="sec" rid="s10">Supplementary Table S10</xref> and <xref ref-type="sec" rid="s10">Supplementary Figure S2</xref>). Of note, due to clinical data unavailability, prediction accuracy need be proven with further <italic>in vivo</italic> studies.</p>
</sec>
<sec sec-type="conclusion" id="s5">
<title>Conclusion</title>
<p>Taken together, this mathematic model is characterized by two simultaneous simulations (parent/metabolite and PK/PD), describing two interaction processes between inhibitors/inducer-CYP3A4 and saxagliptin/M2-DPP-4. We conceive that compared to most current single PK-DDI predictions, the wide application of the PBPK-DO model has the power to improve the predictions of potential clinical DDIs for victim drugs metabolized by CYP3A4.</p>
</sec>
</body>
<back>
<sec id="s6">
<title>Data Availability Statement</title>
<p>The original contributions presented in the study are included in the article/<xref ref-type="sec" rid="s10">Supplementary Material</xref> further inquiries can be directed to the corresponding authors.</p>
</sec>
<sec id="s7">
<title>Author Contributions</title>
<p>Conceptualization, HL, YL, and GW; methodology, GL, BY, and GW; software, GL and FP; validation, BY and JL; formal analysis, GW, GL, and BY; investigation, JL; resources, XJ; data curation, WY; writing&#x2014;original draft preparation, GW, GL, and BY; writing&#x2014;review and editing, GW, GL, and BY; visualization, GL and BY; supervision, GL and BY; project administration, HL, YL, and GW. All authors have read and agreed to the published version of the article.</p>
</sec>
<sec sec-type="COI-statement" id="s8">
<title>Conflict of Interest</title>
<p>The authors GL and GW were employed by the companies Beijing Adamadle Biotech Co., Ltd. and Zhongcai Health (Beijing) Biological Technology Development Co.,&#x20;Ltd., respectively.</p>
<p>The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s9">
<title>Publisher&#x2019;s Note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.</p>
</sec>
<sec id="s10">
<title>Supplementary Material</title>
<p>The Supplementary Material for this article can be found online at <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/fphar.2021.746594/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/fphar.2021.746594/full&#x23;supplementary-material</ext-link>
</p>
<supplementary-material xlink:href="DataSheet1.docx" id="SM1" mimetype="application/docx" xmlns:xlink="http://www.w3.org/1999/xlink"/>
</sec>
<fn-group>
<fn id="fn2">
<label>1</label>
<p>Saxagliptin.pdf</p>
</fn>
<fn id="fn3">
<label>2</label>
<p>Clinical Pharmacokinetics of Ketoconazole.pdf</p>
</fn>
<fn id="fn4">
<label>3</label>
<p>Delavirdine mesylate and didanosine</p>
</fn>
<fn id="fn5">
<label>4</label>
<p>PBPK book.pdf</p>
</fn>
<fn id="fn6">
<label>5</label>
<p>Drug&#x2013;drug interaction of.pdf</p>
</fn>
<fn id="fn7">
<label>6</label>
<p>GastroPlusManual-9.7.pdf</p>
</fn>
<fn id="fn8">
<label>7</label>
<p>Saxagliptin instruction.pdf</p>
</fn>
<fn id="fn9">
<label>8</label>
<p>ClinPharmR_P1.pdf</p>
</fn>
<fn id="fn10">
<label>9</label>
<p>The role of intestinal P-glycoprotein.pdf</p>
</fn>
<fn id="fn11">
<label>10</label>
<p>Clinical Pharmacokinetics of Systemically.pdf</p>
</fn>
<fn id="fn12">
<label>11</label>
<p>Disposition of Azole Antifungal Agents.&#x20;I.pdf</p>
</fn>
<fn id="fn13">
<label>12</label>
<p>metabolism of dalavirdine.pdf</p>
</fn>
<fn id="fn14">
<label>13</label>
<p>An Examination of IC50 and IC50-Shift Experiments in Assessing.pdf</p>
</fn>
<fn id="fn15">
<label>14</label>
<p>IF.pdf</p>
</fn>
</fn-group>
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