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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">ijms</journal-id>
<journal-title>International Journal of Molecular Sciences</journal-title>
<abbrev-journal-title>Int. J. Mol. Sci.</abbrev-journal-title>
<issn pub-type="epub">1422-0067</issn>
<publisher>
<publisher-name>Molecular Diversity Preservation International (MDPI)</publisher-name></publisher></journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3390/ijms11082805</article-id>
<article-id pub-id-type="publisher-id">ijms-11-02805</article-id>
<article-categories>
<subj-group>
<subject>Article</subject></subj-group></article-categories>
<title-group>
<article-title>Integral Kinetic Model for Studying Quercetin Degradation and Oxidation as Affected by Cholesterol During Heating</article-title></title-group>
<contrib-group>
<contrib contrib-type="author">
<name><surname>Chien</surname><given-names>John-Tung</given-names></name></contrib>
<contrib contrib-type="author">
<name><surname>Hsu</surname><given-names>Da-Jung</given-names></name></contrib>
<contrib contrib-type="author">
<name><surname>Inbaraj</surname><given-names>Baskaran Stephen</given-names></name></contrib>
<contrib contrib-type="author">
<name><surname>Chen</surname><given-names>Bing-Huei</given-names></name><xref ref-type="corresp" rid="c1-ijms-11-02805">*</xref></contrib>
<aff id="af1-ijms-11-02805">Department of Food Science, Fu Jen University, Taipei 242, Taiwan; E-Mails: <email>002604@mail.fju.edu.tw</email> (J.T.C.); <email>sinbaraj@yahoo.com</email> (B.S.I.)</aff></contrib-group>
<author-notes>
<corresp id="c1-ijms-11-02805">* Author to whom correspondence should be addressed; E-Mail: <email>002622@mail.fju.edu.tw</email>; Tel.: +886-2-2905-3626; Fax: +886-2-2902-1215.</corresp></author-notes>
<pub-date pub-type="collection">
<year>2010</year></pub-date>
<pub-date pub-type="epub">
<day>29</day>
<month>7</month>
<year>2010</year></pub-date>
<volume>11</volume>
<issue>8</issue>
<fpage>2805</fpage>
<lpage>2820</lpage>
<history>
<date date-type="received">
<day>7</day>
<month>7</month>
<year>2010</year></date>
<date date-type="rev-recd">
<day>20</day>
<month>7</month>
<year>2010</year></date>
<date date-type="accepted">
<day>27</day>
<month>7</month>
<year>2010</year></date></history>
<permissions>
<copyright-statement>© 2010 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland.</copyright-statement>
<copyright-year>2010</copyright-year>
<license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/3.0">
<p>This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).</p></license></permissions>
<abstract>
<p>The degradation and oxidation of quercetin, as affected by cholesterol during heating at 150 °C, was kinetically studied using non-linear regression models. Both TLC and HPLC were used to monitor the changes of quercetin, cholesterol and cholesterol oxidation products (COPs) during heating. The formation of COPs, including triol, 7-keto, 7α-OH and 7β-OH, was completely inhibited during the initial 30 minute heating period in the presence of 0.02% quercetin, accompanied by reduction in cholesterol peroxidation and degradation. However, the quercetin degradation or oxidation proceeded fast, with the rate constants (h<sup>−1</sup>) in the presence of nitrogen, oxygen and the combination of oxygen and cholesterol being 0.253, 0.868 and 7.17, respectively. When cholesterol and quercetin were heated together, the rate constants (h<sup>−1</sup>) of cholesterol peroxidation, epoxidation and degradation were 1.8 × 10<sup>−4</sup>, 0.016 and 0.19, respectively. The correlation coefficients (r<sup>2</sup>) for all the oxidative and degradation reactions ranged from 0.82–0.99. The kinetic models developed in this study may be used to predict the degradation and oxidation of quercetin as affected by cholesterol during heating.</p></abstract>
<kwd-group>
<kwd>quercetin</kwd>
<kwd>cholesterol oxidation</kwd>
<kwd>kinetic study</kwd></kwd-group></article-meta></front>
<body>
<sec sec-type="intro">
<title>1. Introduction</title>
<p>Flavonoids are ubiquitously distributed in food plants with approximately 90% occurring as glycosides in nature [<xref ref-type="bibr" rid="b1-ijms-11-02805">1</xref>,<xref ref-type="bibr" rid="b2-ijms-11-02805">2</xref>]. Among flavonoids, quercetin and its glycoside derivatives are the most abundant in plant vegetables [<xref ref-type="bibr" rid="b2-ijms-11-02805">2</xref>,<xref ref-type="bibr" rid="b3-ijms-11-02805">3</xref>], which have been reported to be effective in scavenging free radicals during lipid oxidation [<xref ref-type="bibr" rid="b4-ijms-11-02805">4</xref>–<xref ref-type="bibr" rid="b6-ijms-11-02805">6</xref>]. In addition, several studies have demonstrated that quercetin is more effective than α-tocopherol and BHT in preventing cholesterol oxidation even at a low level [<xref ref-type="bibr" rid="b7-ijms-11-02805">7</xref>–<xref ref-type="bibr" rid="b9-ijms-11-02805">9</xref>].</p>
<p>To date, the kinetic study of the cholesterol oxidation pathway during heating has been well documented, showing the cholesterol oxidation is initiated by the second-order free radical chain reaction to form cholesterol hydroperoxides, followed by degradation to generate various cholesterol oxidation products (COPs), including 5,6α-EP, 5,6β-EP, 7α-OH, 7β-OH, 7-keto and triol [<xref ref-type="bibr" rid="b10-ijms-11-02805">10</xref>–<xref ref-type="bibr" rid="b13-ijms-11-02805">13</xref>]. In a recent study, Xu <italic>et al</italic>. [<xref ref-type="bibr" rid="b14-ijms-11-02805">14</xref>] have shown the presence of four fatty acids, namely, stearic acid, oleic acid, linoleic acid and α-linolenic acid, to promote oxidation of both cholesterol and β-sitosterol. As the consumption of COPs in excess may be detrimental to human health [<xref ref-type="bibr" rid="b15-ijms-11-02805">15</xref>,<xref ref-type="bibr" rid="b16-ijms-11-02805">16</xref>], the inhibition of COPs formed during heating of cholesterol-rich foods is of great importance.</p>
<p>Up until now, there is a lack of data regarding the inhibition mechanism of cholesterol peroxidation as affected by quercetin. In a previous study dealing with development of a kinetic model for studying the effect of quercetin on cholesterol oxidation during heating, the reaction rate constants (h<sup>−1</sup>) for epoxidation, dehydration and dehydrogenation of COPs, as well as free radical chain reaction and thermal degradation of cholesterol were reduced greatly after incorporation of quercetin [<xref ref-type="bibr" rid="b17-ijms-11-02805">17</xref>]. However, the degradation or oxidation of quercetin remained unknown. In this report, our objective was to develop an integral mathematic model for studying the thermal degradation or oxidation of quercetin in the presence and absence of cholesterol. Additionally, the cholesterol peroxidation, epoxidation and degradation as affected by quercetin were determined. The result of this kinetic study may provide a further insight in elucidating the mechanism of quercetin degradation and oxidation as affected by cholesterol during heating.</p></sec>
<sec sec-type="results|discussion">
<title>2. Results and Discussion</title>
<sec>
<title>2.1. Changes of Quercetin during Heating with and without Cholesterol</title>
<p>As an antioxidant, quercetin was reported to be more effective than α-tocopherol in inhibiting lipid hydroperoxide formation even at a low level [<xref ref-type="bibr" rid="b7-ijms-11-02805">7</xref>,<xref ref-type="bibr" rid="b8-ijms-11-02805">8</xref>]. Of the various quercetin levels (0.02, 0.01, 0.005 and 0.002% of 100 mg cholesterol), we found that with the exception of 0.02% quercetin, for all other levels the quercetin were drastically degraded during the initial 10-min heating at 150 °C in the presence of cholesterol. Additionally, a 0.02% level of quercetin was efficient in inhibiting most COPs formation, with a significant residual amount of quercetin over a 30-min heating period (<xref ref-type="fig" rid="f1-ijms-11-02805">Figure 1</xref>). Thus, a level of 0.02% quercetin was selected in our study to elucidate the mechanism involved during heating of quercetin in the presence and absence of cholesterol. A heating temperature of 150 °C was chosen as cholesterol is prone to undergo autoxidation in liquid form when the temperature reaches its melting point of 148.5 °C or higher [<xref ref-type="bibr" rid="b17-ijms-11-02805">17</xref>]. Furthermore, thermal degradation of cholesterol has been reported to dominate over autoxidation at 200–300 °C [<xref ref-type="bibr" rid="b17-ijms-11-02805">17</xref>]. It is also the temperature similar to that used for low-temperature frying of foods [<xref ref-type="bibr" rid="b17-ijms-11-02805">17</xref>]. Thus, the heating temperature of 150 °C was selected in this study to reduce the loss of cholesterol due to thermal degradation and concomitantly accelerate the formation of COPs as well as to mimic the low-temperature frying conditions of foods.</p>
<p><xref ref-type="fig" rid="f1-ijms-11-02805">Figures 1</xref>, <xref ref-type="fig" rid="f2-ijms-11-02805">2</xref> and <xref ref-type="fig" rid="f3-ijms-11-02805">3</xref> show the HPLC chromatograms of quercetin during heating at 150 °C in the presence of both oxygen and cholesterol, oxygen and nitrogen, respectively. With nitrogen, the amount of quercetin decreased gradually and a loss of 7.9, 17.2, 28.6 and 33.9% was generated after 10 min, 0.5, 1 and 2 h of heating, respectively (<xref ref-type="fig" rid="f3-ijms-11-02805">Figures 3</xref> and <xref ref-type="fig" rid="f4-ijms-11-02805">4</xref>). However, a greater loss of 20.4, 28.2, 64.8 and 82.4% of quercetin occurred when heated with oxygen for the same period (<xref ref-type="fig" rid="f2-ijms-11-02805">Figures 2</xref> and <xref ref-type="fig" rid="f4-ijms-11-02805">4</xref>). Apparently the quercetin degradation or oxidation exhibited a similar pattern when heated under nitrogen or oxygen, which is in accordance with a report by Makris and Rossiter [<xref ref-type="bibr" rid="b5-ijms-11-02805">5</xref>,<xref ref-type="bibr" rid="b6-ijms-11-02805">6</xref>]. In contrast, when heated with both cholesterol and oxygen, the level of quercetin drastically decreased to 10.9 and 5.9% after 10 and 30 min of heating, respectively (<xref ref-type="fig" rid="f4-ijms-11-02805">Figure 4</xref>). This is probably because of fast formation of cholesterol hydroperoxide through hydrogen abstraction at C-7 of cholesterol during the initial heating period [<xref ref-type="bibr" rid="b10-ijms-11-02805">10</xref>,<xref ref-type="bibr" rid="b12-ijms-11-02805">12</xref>], which may in turn accelerate quercetin degradation at 150 °C. As a result, the free radical involved in reactions of cholesterol oxidation and the quercetin degradation can be combined into a pathway as depicted in <xref ref-type="fig" rid="f5-ijms-11-02805">Figure 5</xref>. The major reaction pathways and rate constants for cholesterol peroxidation and quercetin degradation are shown in <xref ref-type="table" rid="t3-ijms-11-02805">Tables 3</xref> and <xref ref-type="table" rid="t4-ijms-11-02805">4</xref>. Comparatively, quercetin was degraded faster with cholesterol than without cholesterol, which should be caused by formation of free radicals at C-7 of cholesterol as indicated above. Additionally, quercetin may undergo oxidative degradation (Q→Q<sub>o</sub>) or non-oxidative degradation (Q→Q<sub>d</sub>) during heating at 150 °C, with the rate constant (h<sup>−1</sup>) being higher for the former than for the latter. The reaction pathways for peroxidation and epoxidation of cholesterol were the same as those described in a previous study [<xref ref-type="bibr" rid="b17-ijms-11-02805">17</xref>], with the exception that some other COPs, including 7-OH, 7-keto, triol and cholestan-3β, 5α, 6-one, were excluded for kinetic study as they were not formed in the presence of quercetin over a heating period of 30 min.</p></sec>
<sec>
<title>2.2. Peroxidation and Epoxidation of Cholesterol during Heating</title>
<p>Due to absence of cholesterol hydroperoxide standards, both 7α-OOH and 7β-OOH should be identified and quantified with care. According to Smith and Hill [<xref ref-type="bibr" rid="b18-ijms-11-02805">18</xref>], both 7α-OOH and 7β-OOH could turn red after spraying <italic>N</italic>,<italic>N</italic>-dimethyl-<italic>p</italic>-phenylenediamine dihydrochloride onto a TLC plate. Both 7α-OOH and 7β-OOH were further subjected to HPLC analysis for identification. <xref ref-type="fig" rid="f6-ijms-11-02805">Figure 6</xref> shows the HPLC chromatogram of the acetone extract of the red spots collected from TLC after heating cholesterol with quercetin for 30 min. A total of 5 peaks were present, in which 5,6α-EP, 5,6β-EP, 7α-OOH and 7β-OOH were identified. Both 7α-OOH and 7β-OOH were tentatively identified based on the retention behavior as described by Chien <italic>et al</italic>. [<xref ref-type="bibr" rid="b17-ijms-11-02805">17</xref>].</p>
<p>A total of eight major COPs, namely, 5,6α-EP, 5,6β-EP, 7-keto, 7α-OH, 7β-OH, 7α-OOH, 7β-OOH, and triol, were adequately resolved within 30 min by using the HPLC condition shown in the method section (Figure not shown). Interestingly, with quercetin, 7α-OH, 7β-OH, 7-keto and triol were undetected over a 30-min heating period (<xref ref-type="fig" rid="f6-ijms-11-02805">Figure 6</xref>). Conversely, without quercetin, all the eight COPs (5,6α-EP, 5,6β-EP, 7-keto, 7α-OH, 7β-OH, 7α-OOH, and 7β-OOH and triol) were formed gradually during heating, with the level of 7-OOH (7α-OOH plus 7β-OOH) being 0.82 mg (based on 100 g cholesterol) in the beginning, raised to 3.7 mg in 10 min and 18 mg in 30 min, whereas in the presence of quercetin, the initial level of 7-OOH was 0.13 mg, rose to 0.82 mg in 10 min and 2.6 mg in 30 min (<xref ref-type="fig" rid="f7-ijms-11-02805">Figure 7</xref>). Additionally, a small amount of 5,6-EP (5,6α-EP plus 5,6β-EP) (0.44 mg) was present prior to heating, rose to 3.2 mg in 10 min and 17.7 mg in 30 min. However, with quercetin treatment, a level of 0.46 mg 5,6-EP (based on 100 g cholesterol) was formed initially, followed by an increment to 1.00 mg in 10 min and 2.83 mg in 30 min. This outcome is different from that reported by Chien <italic>et al</italic>. [<xref ref-type="bibr" rid="b17-ijms-11-02805">17</xref>], as the inhibition of 7-OH (7α-OH plus 7β-OH), 7-keto and triol were not possible in the presence of 0.002% quercetin. Obviously a higher level of 0.02% quercetin employed in the present experiment should account for this effect.</p>
<p><xref ref-type="table" rid="t1-ijms-11-02805">Table 1</xref> shows the total COPs formed during heating with or without quercetin at 150 °C. The amount of COPs generated during heating followed a time-dependent response for both treatments, with a lesser content for the treatment with quercetin. For instance, the amount of COPs produced with quercetin was 11.6-fold lower than that without quercetin after 30-min heating, demonstrating the potential of quercetin to be a powerful antioxidant.</p>
<p><xref ref-type="table" rid="t2-ijms-11-02805">Table 2</xref> shows the percentage changes of residual cholesterol during thermal degradation at 150 °C. As it is difficult to estimate the concentration change of thermal degraded data (C<sub>T</sub>), the data in <xref ref-type="table" rid="t2-ijms-11-02805">Table 2</xref> were recalculated by combining the amounts of COPs (C<sub>O</sub>) and residual cholesterol (C<sub>R</sub>) at each interval, <italic>i.e.</italic>, total cholesterol = C<sub>T</sub> + C<sub>O</sub> + C<sub>R</sub> or total cholesterol − C<sub>T</sub> = C<sub>O</sub> + C<sub>R</sub> = actual residual cholesterol due to thermal degradation, so that the overall thermal degradation rate constant could be estimated. The residual concentrations of cholesterol were significantly different between treatments with and without quercetin for the same heating time. Nevertheless, a slight difference in cholesterol loss did occur after extensive heating for 60 and 90 min, as evidenced by a decline of 35.8 and 33.6% without quercetin respectively, in contrast to 19.5 and 22.9% with quercetin. This outcome implied that the thermal degradation of cholesterol proceeded fast in the beginning and a plateau was reached after prolonged heating. By comparing the data in <xref ref-type="table" rid="t1-ijms-11-02805">Tables 1</xref> and <xref ref-type="table" rid="t2-ijms-11-02805">2</xref>, a reversed trend was shown to occur for oxidative degradation, <italic>i.e.</italic>, it proceeded slower in the initial period and faster after extensive heating.</p></sec>
<sec>
<title>2.3. Kinetic Studies of Quercetin Degradation and Oxidation as well as Cholesterol Hydroperoxide Formation</title>
<p>The free radical chain reaction of cholesterol oxidation can be inhibited in the presence of quercetin, a free radical scavenger [<xref ref-type="bibr" rid="b5-ijms-11-02805">5</xref>,<xref ref-type="bibr" rid="b6-ijms-11-02805">6</xref>,<xref ref-type="bibr" rid="b19-ijms-11-02805">19</xref>,<xref ref-type="bibr" rid="b20-ijms-11-02805">20</xref>]. The initial oxidation and thermal degradation pathways of cholesterol as well as the thermal degradation and oxidation pathways of quercetin are shown in <xref ref-type="fig" rid="f5-ijms-11-02805">Figure 5</xref>. According to the kinetic studies of antioxidants by Pryor <italic>et al</italic>. [<xref ref-type="bibr" rid="b19-ijms-11-02805">19</xref>] and Foti <italic>et al</italic>. [<xref ref-type="bibr" rid="b21-ijms-11-02805">21</xref>], with quercetin the hydroperoxide formation rate can be expressed as follows:</p>
<disp-formula id="FD1">
<label>(1)</label>
<mml:math display="block">
<mml:semantics>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mtext>d</mml:mtext>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>COOH</mml:mtext>
<mml:mo stretchy="false">]</mml:mo></mml:mrow>
<mml:mrow>
<mml:mtext>d</mml:mtext>
<mml:mi>t</mml:mi></mml:mrow></mml:mfrac>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mo stretchy="false">[</mml:mo>
<mml:mi>R</mml:mi>
<mml:mi>H</mml:mi>
<mml:mo stretchy="false">]</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi></mml:mrow>
<mml:mi>i</mml:mi></mml:msub></mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:msup>
<mml:mi>k</mml:mi>
<mml:mo>′</mml:mo></mml:msup>
<mml:mo stretchy="false">[</mml:mo>
<mml:mi>Q</mml:mi>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mfrac></mml:mrow></mml:semantics></mml:math></disp-formula>
<p>where [Q]: percentage concentration of quercetin</p>
<p>[COOH]: the concentration of hydroperoxide</p>
<p>[RH]: the concentration of target compound to be oxidized</p>
<p>R<sub>i</sub>: the initial reaction rate</p>
<p>k, k′: the reaction rate constant</p>
<p>n: number of free radicals scavenged per quercetin molecule</p>
<p>If all the thermal degradation, oxidation and free radical chain reactions for quercetin followed a first-order, the depletion rate of quercetin can be written by setting n. k′= k<sub>f</sub> as follows:</p>
<disp-formula id="FD2">
<label>(2)</label>
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<mml:mtext>k</mml:mtext></mml:mrow>
<mml:mtext>f</mml:mtext></mml:msub>
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<mml:mo stretchy="false">]</mml:mo>
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<mml:msub>
<mml:mrow>
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<mml:mo>+</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mtext>k</mml:mtext></mml:mrow>
<mml:mtext>O</mml:mtext></mml:msub>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mtext>k</mml:mtext></mml:mrow>
<mml:mtext>f</mml:mtext></mml:msub>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>Q</mml:mtext>
<mml:mo stretchy="false">]</mml:mo>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mrow>
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<mml:mi>i</mml:mi></mml:msub>
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<p>where k<sub>d</sub>, k<sub>o</sub>, k<sub>f</sub>, and k<sub>i</sub>: the reaction rate constants (h<sup>−1</sup>) for thermal degradation, oxidation, free radical scavenging and the overall degradation, respectively.</p>
<p>According to the studies by Ozilgen and Ozilgen [<xref ref-type="bibr" rid="b22-ijms-11-02805">22</xref>] and Chien <italic>et al</italic>. [<xref ref-type="bibr" rid="b12-ijms-11-02805">12</xref>], the rate equation for forward formation of 7-OOH from cholesterol through free radical chain reaction (A→A′) is as follows:</p>
<disp-formula id="FD3">
<label>(3)</label>
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<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mrow>
<mml:mrow>
<mml:mtext>max</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow>
<mml:mo>)</mml:mo></mml:mrow>
<mml:mi> </mml:mi>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mtext>A</mml:mtext>
<mml:mo>′</mml:mo></mml:msup></mml:mrow>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:semantics></mml:math></disp-formula>
<p>where [A′]: percentage concentration of 7-OOH</p>
<p>[A′]<sub>max</sub>: the maximum attainable concentration of 7-OOH prior to degradation</p>
<p>k<sub>1</sub>: the reaction rate constant and t: time.</p>
<p>Combining <xref ref-type="disp-formula" rid="FD1">Equations (1)</xref>–<xref ref-type="disp-formula" rid="FD3">(3)</xref>, the <xref ref-type="disp-formula" rid="FD4">Equation (4)</xref> for 7-OOH formation could be obtained by setting [COOH] = [A′] as follows:</p>
<disp-formula id="FD4">
<label>(4)</label>
<mml:math display="block">
<mml:semantics>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mtext>d</mml:mtext>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mtext>A</mml:mtext>
<mml:mo>′</mml:mo></mml:msup></mml:mrow>
<mml:mo stretchy="false">]</mml:mo></mml:mrow>
<mml:mrow>
<mml:mtext>dt</mml:mtext></mml:mrow></mml:mfrac>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>k</mml:mtext></mml:mrow>
<mml:mn>1</mml:mn></mml:msub>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mtext>A</mml:mtext>
<mml:mo>′</mml:mo></mml:msup></mml:mrow>
<mml:mo stretchy="false">]</mml:mo></mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>k</mml:mtext></mml:mrow>
<mml:mtext>f</mml:mtext></mml:msub>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>Q</mml:mtext>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mfrac>
<mml:mrow>
<mml:mo>[</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>-</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mtext>A</mml:mtext>
<mml:mo>′</mml:mo></mml:msup></mml:mrow>
<mml:mo stretchy="false">]</mml:mo></mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mtext>A</mml:mtext>
<mml:mo>′</mml:mo></mml:msup></mml:mrow>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mrow>
<mml:mrow>
<mml:mtext>max</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow>
<mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:semantics></mml:math></disp-formula>
<p>For the second-order formation of 5,6-EP from cholesterol, the concentrations of both cholesterol and 7-OOH should be considered [<xref ref-type="bibr" rid="b12-ijms-11-02805">12</xref>,<xref ref-type="bibr" rid="b23-ijms-11-02805">23</xref>]. Thus, if we also consider the involvement of free radical scavenging effect of quercetin in epoxidation, the rate equations for 5,6-EP formation should be expressed as follows:</p>
<disp-formula id="FD5">
<label>(5)</label>
<mml:math display="block">
<mml:semantics>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mtext>d</mml:mtext>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>E</mml:mtext>
<mml:mo stretchy="false">]</mml:mo></mml:mrow>
<mml:mrow>
<mml:mtext>dt</mml:mtext></mml:mrow></mml:mfrac>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>k</mml:mtext></mml:mrow>
<mml:mn>4</mml:mn></mml:msub>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>A</mml:mtext>
<mml:mo stretchy="false">]</mml:mo>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mtext>A</mml:mtext>
<mml:mo>′</mml:mo></mml:msup></mml:mrow>
<mml:mo stretchy="false">]</mml:mo></mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>k</mml:mtext></mml:mrow>
<mml:mtext>f</mml:mtext></mml:msub>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>Q</mml:mtext>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mfrac></mml:mrow></mml:semantics></mml:math></disp-formula>
<p>Furthermore, it was reported that thermal degradation of cholesterol follows first-order reaction [<xref ref-type="bibr" rid="b12-ijms-11-02805">12</xref>,<xref ref-type="bibr" rid="b13-ijms-11-02805">13</xref>] and the corresponding equation can be given as in <xref ref-type="disp-formula" rid="FD1">Equation (1)</xref> in a previous study [<xref ref-type="bibr" rid="b17-ijms-11-02805">17</xref>]. The integral form is as follows:</p>
<disp-formula id="FD6">
<label>(6)</label>
<mml:math display="block">
<mml:semantics>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mi>A</mml:mi>
<mml:mo stretchy="false">]</mml:mo>
<mml:mo>=</mml:mo>
<mml:mo stretchy="false">[</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>A</mml:mi></mml:mrow>
<mml:mn>0</mml:mn></mml:msub>
<mml:mo stretchy="false">]</mml:mo>
<mml:mi> </mml:mi>
<mml:msup>
<mml:mrow>
<mml:mi>e</mml:mi></mml:mrow>
<mml:mrow>
<mml:mo>-</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>k</mml:mi></mml:mrow>
<mml:mn>5</mml:mn></mml:msub>
<mml:mi>t</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:semantics></mml:math></disp-formula>
<p>The following <xref ref-type="disp-formula" rid="FD7">Equation (7)</xref> can be obtained by integrating of <xref ref-type="disp-formula" rid="FD2">Equation (2)</xref>.</p>
<disp-formula id="FD7">
<label>(7)</label>
<mml:math display="block">
<mml:semantics>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>Q</mml:mtext>
<mml:mo stretchy="false">]</mml:mo>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>Q</mml:mtext>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mrow>
<mml:mn>0</mml:mn></mml:msub>
<mml:msup>
<mml:mrow>
<mml:mtext>e</mml:mtext></mml:mrow>
<mml:mrow>
<mml:mo>-</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mtext>k</mml:mtext></mml:mrow>
<mml:mtext>i</mml:mtext></mml:msub>
<mml:mtext>t</mml:mtext></mml:mrow></mml:msup></mml:mrow></mml:semantics></mml:math></disp-formula>
<p>Likewise, <xref ref-type="disp-formula" rid="FD71">Equations (7-1)</xref> and <xref ref-type="disp-formula" rid="FD72">(7-2)</xref> were used for estimating quercetin degradation under nitrogen and oxygen, respectively. Both equations can be obtained by integration of the first-order rate equation of thermal degradation and oxidative degradation of quercetin as follows:</p>
<disp-formula id="FD71">
<label>(7-1)</label>
<mml:math display="block">
<mml:semantics>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>Q</mml:mtext>
<mml:mo stretchy="false">]</mml:mo>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>Q</mml:mtext>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mrow>
<mml:mn>0</mml:mn></mml:msub>
<mml:msup>
<mml:mrow>
<mml:mtext>e</mml:mtext></mml:mrow>
<mml:mrow>
<mml:mo>-</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mtext>k</mml:mtext></mml:mrow>
<mml:mtext>d</mml:mtext></mml:msub>
<mml:mtext>t</mml:mtext></mml:mrow></mml:msup></mml:mrow></mml:semantics></mml:math></disp-formula>
<disp-formula id="FD72">
<label>(7-2)</label>
<mml:math display="block">
<mml:semantics>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>Q</mml:mtext>
<mml:mo stretchy="false">]</mml:mo>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>Q</mml:mtext>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mrow>
<mml:mn>0</mml:mn></mml:msub>
<mml:msup>
<mml:mrow>
<mml:mtext>e</mml:mtext></mml:mrow>
<mml:mrow>
<mml:mo>-</mml:mo>
<mml:mo stretchy="false">(</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mtext>k</mml:mtext></mml:mrow>
<mml:mtext>d</mml:mtext></mml:msub>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mtext>k</mml:mtext></mml:mrow>
<mml:mtext>O</mml:mtext></mml:msub>
<mml:mo stretchy="false">)</mml:mo>
<mml:mtext>t</mml:mtext></mml:mrow></mml:msup></mml:mrow></mml:semantics></mml:math></disp-formula>
<p>Integration after substituting <xref ref-type="disp-formula" rid="FD7">Equations (7)</xref> into <xref ref-type="disp-formula" rid="FD4">Equation (4)</xref> gave <xref ref-type="disp-formula" rid="FD8">Equation (8)</xref> as follows:</p>
<disp-formula id="FD8">
<label>(8)</label>
<mml:math display="block">
<mml:semantics>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mtext>A</mml:mtext>
<mml:mo>′</mml:mo></mml:msup></mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mtext>A</mml:mtext>
<mml:mo>′</mml:mo></mml:msup></mml:mrow>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mrow>
<mml:mrow>
<mml:mtext>max</mml:mtext></mml:mrow></mml:msub></mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>-</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>-</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mtext>A</mml:mtext>
<mml:mo>′</mml:mo></mml:msup></mml:mrow>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mrow>
<mml:mrow>
<mml:mtext>max</mml:mtext></mml:mrow></mml:msub></mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mtext>A</mml:mtext>
<mml:mo>′</mml:mo></mml:msup></mml:mrow>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mrow>
<mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mrow>
<mml:mo>)</mml:mo></mml:mrow>
<mml:mi>ω</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:semantics></mml:math></disp-formula>
<p>where 
<inline-formula>
<mml:math>
<mml:semantics>
<mml:mrow>
<mml:mi>ω</mml:mi>
<mml:mo>=</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mtext>e</mml:mtext></mml:mrow>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>k</mml:mtext></mml:mrow>
<mml:mn>1</mml:mn></mml:msub></mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>Q</mml:mtext>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mrow>
<mml:mn>0</mml:mn></mml:msub>
<mml:mi> </mml:mi>
<mml:msub>
<mml:mrow>
<mml:mtext>k</mml:mtext></mml:mrow>
<mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:mfrac>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>-</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mtext>e</mml:mtext></mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>k</mml:mtext></mml:mrow>
<mml:mtext>i</mml:mtext></mml:msub>
<mml:mtext>t</mml:mtext></mml:mrow></mml:msup></mml:mrow>
<mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mrow></mml:semantics></mml:math></inline-formula></p>
<p>k<sub>P</sub> = k<sub>i</sub> × k<sub>f</sub></p>
<p>[A]<sub>0</sub>,[A′]<sub>0</sub>,[E]<sub>0</sub>,[Q]<sub>0</sub>: concentration of cholesterol, 7-OOH, 5,6-EP and quercetin at 0-min heating</p>
<p>Integration after substitution of <xref ref-type="disp-formula" rid="FD6">Equations (6)</xref>, <xref ref-type="disp-formula" rid="FD7">(7)</xref> and <xref ref-type="disp-formula" rid="FD8">(8)</xref> into <xref ref-type="disp-formula" rid="FD5">Equation (5)</xref>, the following <xref ref-type="disp-formula" rid="FD9">Equation (9)</xref> can be obtained.</p>
<disp-formula id="FD9">
<label>(9)</label>
<mml:math display="block">
<mml:semantics>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>E</mml:mtext>
<mml:mo stretchy="false">]</mml:mo>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>E</mml:mtext>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mrow>
<mml:mn>0</mml:mn></mml:msub>
<mml:mo>+</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>k</mml:mtext></mml:mrow>
<mml:mn>4</mml:mn></mml:msub>
<mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>A</mml:mtext>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mrow>
<mml:mn>0</mml:mn></mml:msub>
<mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mtext>A</mml:mtext>
<mml:mo>′</mml:mo></mml:msup></mml:mrow>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mrow>
<mml:mrow>
<mml:mtext>max</mml:mtext></mml:mrow></mml:msub></mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>k</mml:mtext></mml:mrow>
<mml:mtext>p</mml:mtext></mml:msub>
<mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>Q</mml:mtext>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mrow>
<mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mfrac>
<mml:mrow>
<mml:msubsup>
<mml:mo>∫</mml:mo>
<mml:mn>0</mml:mn>
<mml:mtext>t</mml:mtext></mml:msubsup>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mtext>e</mml:mtext></mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>k</mml:mi></mml:mrow>
<mml:mi>i</mml:mi></mml:msub>
<mml:mo>-</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>k</mml:mi></mml:mrow>
<mml:mn>5</mml:mn></mml:msub>
<mml:mo stretchy="false">)</mml:mo>
<mml:mtext>t</mml:mtext></mml:mrow></mml:msup></mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>-</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>-</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mtext>A</mml:mtext>
<mml:mo>′</mml:mo></mml:msup></mml:mrow>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mrow>
<mml:mrow>
<mml:mtext>max</mml:mtext></mml:mrow></mml:msub></mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mtext>A</mml:mtext>
<mml:mo>′</mml:mo></mml:msup></mml:mrow>
<mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mrow>
<mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mrow>
<mml:mo>)</mml:mo></mml:mrow>
<mml:mi>ω</mml:mi></mml:mrow></mml:mfrac>
<mml:mtext>dt</mml:mtext></mml:mrow></mml:mrow></mml:mrow></mml:semantics></mml:math></disp-formula>
<p>Among the above equations, <xref ref-type="disp-formula" rid="FD6">Equations (6)</xref>, <xref ref-type="disp-formula" rid="FD7">(7)</xref> and <xref ref-type="disp-formula" rid="FD8">(8)</xref> are in the forms of exact integration. As the exact integrations for <xref ref-type="disp-formula" rid="FD9">Equation (9)</xref> are not possible, we can only get a better approximation to the integral term in equation by using a quadratic polynomial of Taylor’s series as follows:</p>
<disp-formula id="FD10">
<label>(10)</label>
<mml:math display="block">
<mml:semantics>
<mml:mtable columnalign="left">
<mml:mtr>
<mml:mtd>
<mml:mo stretchy="false">[</mml:mo>
<mml:mtext>E</mml:mtext>
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<p>where m<sub>2</sub> = [A′]<sub>0</sub>/A′]<sub>max</sub>;</p>
<p>m<sub>3</sub> = k<sub>1</sub>/k<sub>f</sub>[Q]<sub>0</sub>;</p>
<p>m<sub>4</sub> = m<sub>3</sub>(2m<sub>3</sub>m<sub>2</sub><sup>2</sup> - m<sub>2</sub>k<sub>i</sub> - 3m<sub>2</sub>m<sub>3</sub> + k<sub>i</sub> + m<sub>3</sub>).</p>
<p>The experimental data were thus analyzed in sequence and fitted best to the corresponding non-linear regression model. The residual percentage of quercetin in <xref ref-type="fig" rid="f4-ijms-11-02805">Figure 4</xref> was used for computing the reaction rate constants (h<sup>−1</sup>) for thermal degradation (k<sub>d</sub>), oxidation (k<sub>o</sub>) and the overall degradation (k<sub>i</sub>). The <xref ref-type="disp-formula" rid="FD71">Equations (7-1)</xref>, <xref ref-type="disp-formula" rid="FD72">(7-2)</xref> and <xref ref-type="disp-formula" rid="FD7">(7)</xref> implied that for a first-order reaction, the natural logarithm of the residual quercetin percentage is a linear function of time and thus, k<sub>d</sub>, k<sub>o</sub>, and k<sub>i</sub> in <xref ref-type="disp-formula" rid="FD71">Equations (7-1)</xref>, <xref ref-type="disp-formula" rid="FD72">(7-2)</xref> and <xref ref-type="disp-formula" rid="FD7">(7)</xref> can be estimated using a linear regression model [<xref ref-type="bibr" rid="b24-ijms-11-02805">24</xref>]. The results are shown in <xref ref-type="table" rid="t3-ijms-11-02805">Table 3</xref>, with K<sub>d</sub> being 0.253 h<sup>−1</sup> and correlation coefficients (r<sup>2</sup>) 0.94, which was lower than that for oxidative degradation of quercetin (k<sub>O</sub> (h<sup>−1</sup>) = 0.615 = 0.868 - 0.253). Although the correct value of k<sub>f</sub> for quercetin degradation in the free radical chain reaction should be evaluated from <xref ref-type="disp-formula" rid="FD8">Equation (8)</xref>, the k<sub>f</sub> (h<sup>−1</sup>) values from <xref ref-type="disp-formula" rid="FD72">Equations (7-2)</xref> and <xref ref-type="disp-formula" rid="FD7">(7)</xref> (6.302 h<sup>−1</sup> or 7.17 - 0.868 h<sup>−1</sup>) can still be used for subsequent comparison, and was approximately 24.9 and 10.2-folds higher than k<sub>d</sub> or k<sub>O</sub>, respectively.</p>
<p>The data in <xref ref-type="table" rid="t2-ijms-11-02805">Table 2</xref> were used for computing k<sub>5</sub> in <xref ref-type="disp-formula" rid="FD6">Equation (6)</xref> by using a linear regression model [<xref ref-type="bibr" rid="b24-ijms-11-02805">24</xref>], with K<sub>5</sub> (h<sup>−1</sup>) being 0.19 ± 0.01 (r<sup>2</sup> = 0.99), which was lower than the treatment without quercetin (0.94 ± 0.03) by 4.9-fold (<xref ref-type="table" rid="t4-ijms-11-02805">Table 4</xref>). The rate constants in <xref ref-type="disp-formula" rid="FD8">Equations (8)</xref> and <xref ref-type="disp-formula" rid="FD10">(10)</xref> were estimated by using the least squares method with a nonlinear Marquardt iterative method until the convergences of best-fitted parameters were met. <xref ref-type="table" rid="t4-ijms-11-02805">Table 4</xref> shows the rate constants of the reaction pathways of cholesterol peroxidation and epoxidation as well as free radical chain reaction and degradation of quercetin over a 30-min heating period. With quercetin, the r<sup>2</sup> of all the reactions were higher than 0.82, especially for the free radical chain reaction of quercetin, as a high r<sup>2</sup> (0.94) was found after a non-linear estimation from <xref ref-type="disp-formula" rid="FD8">Equation (8)</xref> with a k<sub>f</sub> (h<sup>−1</sup>) of 3.28. This value was close to that estimated from <xref ref-type="disp-formula" rid="FD7">Equation (7)</xref>, <italic>i.e.</italic>, 6.302 = 7.17 - 0.868 in <xref ref-type="table" rid="t3-ijms-11-02805">Table 3</xref> by a difference of 1.9-fold. Though we do not have a plausible explanation for the difference in k<sub>f</sub> value, it may be possibly due to the low amount of COPs formed over a 30-min heating period (<xref ref-type="table" rid="t1-ijms-11-02805">Table 1</xref>), which made it more difficult to estimate the k<sub>f</sub> value from <xref ref-type="disp-formula" rid="FD8">Equation (8)</xref>. By combining all the results shown above, it is apparent that all the reactions involved for quercetin during heating, including thermal degradation, oxidative degradation and free radical chain reaction, fit well the first-order model. In addition, the formation of 7-OOH, the initial oxidation product generated from peroxidation of cholesterol, was further plotted based on the corresponding rate equation, <italic>i.e.</italic>, <xref ref-type="disp-formula" rid="FD8">Equation (8)</xref> (<xref ref-type="fig" rid="f7-ijms-11-02805">Figure 7</xref>) and the rate constants are listed in <xref ref-type="table" rid="t4-ijms-11-02805">Table 4</xref>. Both curves fitted well with the data points with or without quercetin. All these findings suggested that the <xref ref-type="disp-formula" rid="FD8">Equation (8)</xref> could successfully estimate the degradation of cholesterol and quercetin over a 30-min heating period.</p>
<p>For cholesterol oxidation in the presence of quercetin, the r<sup>2</sup> of peroxidation and epoxidation were 0.94 and 0.82, respectively, whereas the free radical chain reaction of quercetin was 0.94 (<xref ref-type="table" rid="t4-ijms-11-02805">Table 4</xref>). It may be postulated that both formation of 7-OOH and 5,6-epoxide during heating of cholesterol with quercetin fit the second-order, but the free radical chain reaction of quercetin fits the first-order.</p>
<p>It was also observed that the k<sub>1</sub> (h<sup>−1</sup>) dropped sharply from 488.2 for the treatment without quercetin to 1.8 × 10<sup>−4</sup> for the treatment with quercetin, implying the incorporation of 0.02% quercetin to be effective in inhibiting free radical formation. Similarly, a substantial decline in k<sub>4</sub> by 2.7 × 10<sup>5</sup>-fold after quercetin treatment was shown for epoxidation, which may be accounted for by a pronounced inhibition of 7-OOH formation during heating with quercetin. By comparison, the rate constants (h<sup>−1</sup>) of the major reaction pathways of cholesterol oxidation in <xref ref-type="table" rid="t4-ijms-11-02805">Table 4</xref> followed the order: k<sub>5</sub> &gt;&gt; k<sub>4</sub> &gt; k<sub>1</sub> for the quercetin treatment, and k<sub>4</sub> &gt; k<sub>1</sub> &gt;&gt; k<sub>5</sub> for the treatment without quercetin.</p></sec></sec>
<sec>
<title>3. Experimental Section</title>
<sec sec-type="materials">
<title>3.1. Materials</title>
<p>Several COPs standards, including 7β-hydroxycholesterol (7β-OH), 7α-hydroxycholesterol (7α-OH), 5,6α-epoxycholesterol, (5,6α-EP), 5,6β-epoxycholesterol, (5,6β-EP), 7-ketocholesterol (7-keto) and 5α-cholestane-3β,5,6β-triol (triol) were purchased from Sigma (St. Louis, MO, USA) and Steraloids Inc. (Wilton, NH, USA). Standards of cholesterol, quercetin and lauryl alcohol were also from Sigma and were used without further purification. The HPLC-grade solvents such as n-hexane, ethanol, methanol and isopropanol were from Mallinckrodt Co. (Paris, KY, USA). The analytical grade solvent 1,2-dichloroethane was from Riedel-de Haën Co. (Barcelona, Spain). Paraffin oil, acetonitrile, phosphoric acid and potassium dihydrogen phosphate were from Merck (Darmstadt, Germany). The NH<sub>2</sub> cartridges were from Unichrom Scientific (Taipei, Taiwan). The Strata C18-E solid phase extraction cartridges (500 mg/3 mL, 55 μm, 70 Å) were from Phenomenex Co. (Torrance, CA, USA).</p></sec>
<sec>
<title>3.2. Instrumentation</title>
<p>The HPLC instrument was composed of a Jasco PU980 pump (Jasco Co., Tokyo, Japan), an UV-VIS detector, a Jasco 830 refractive index detector and an Agilent 1100 series G1316A column temperature controller (Palo Alto, CA). A Borwin software system was used to process data. A Vydac 201TP54 C18 column (250 × 4.6 mm i.d., 5-μm particle size; Vydac Inc., Hesperia, CA, USA) was used to separate and quantify quercetin in heated samples. Two Merck Lichrospher 100 CN columns (244 × 2.4 mm i.d.) with both containing 5-μm packing material were used to separate and quantify cholesterol as well as COPs in heated samples. The Sorvall RC5C high-speed centrifuge was from Du Pont (Wilmington, DL).</p></sec>
<sec>
<title>3.3. Heating of Quercetin with or without Cholesterol</title>
<p>A mixture containing 0.6-mL of lauryl alcohol and 2.4-mL of paraffin oil was poured into a 100-mL round-bottom flask, followed by adding 600 mg of cholesterol standard and 0.12 mg (0.02% of cholesterol) of quercetin dissolved in 2-mL of ethanol. Lauryl alcohol was used as a solvent to dissolve the mixture of cholesterol and quercetin, as well as induce triol formation in an aqueous system through alcoholysis of the epoxy-containing COPs [<xref ref-type="bibr" rid="b17-ijms-11-02805">17</xref>]. The flask was soaked in a paraffin-oil bath, which was preheated for 5 min with nitrogen gas flushing into the flask at the same time until the internal temperature reached 150 ± 1 °C. Then, oxygen was pumped into the flask during heating for 0, 5, 10, 20 and 30 min. After heating, the flask was inserted into dry ice to terminate the reaction and then each sample was analyzed by HPLC. For the other two treatments, the same procedure as described for heating of quercetin with cholesterol was used with the exception that 1.0 mg of quercetin was heated alone and the heating times were changed to 0, 5, 10, 30, 60, 90 and 120 min, with nitrogen or oxygen being pumped-in separately. For each heating treatment, triplicate experiments were carried out and the data were analyzed by a non-linear regression method [<xref ref-type="bibr" rid="b24-ijms-11-02805">24</xref>].</p></sec>
<sec>
<title>3.4. Extraction and Purification of Cholesterol and COPs</title>
<p>A method based on Nourooz-Zadeh [<xref ref-type="bibr" rid="b25-ijms-11-02805">25</xref>] was modified for extraction and purification of COPs from the samples containing quercetin and cholesterol. Each heated sample was mixed with 20-mL of hexane-isopropanol (3:2, v/v), and the solution was flushed with nitrogen gas and shaken vigorously for 3 min in a sealed flask. Then the mixture was centrifuged at 26,000 × g for 5 min at 25 °C. The upper layer was collected, transferred to a centrifuge tube and 12-mL of distilled water was added, after which the mixture was centrifuged again for another 5 min, followed by collecting the upper phase and evaporating to dryness at 35 °C under vacuum. The residue was dissolved in 1-mL of hexane-1,2-dichloroethane (1:1, v/v) and the solution was poured into a NH<sub>2</sub> cartridge for purification. Initially, 5-mL of hexane was added to the cartridge to remove impurities such as paraffin oil, followed by adding 25-mL of hexane-1,2-dichloroethane-isopropanol (50:30:15, v/v/v) to elute cholesterol and COPs. The eluate was evaporated to dryness at 35 °C under vacuum, with the residue dissolved in hexane-isopropanol (95:5, v/v) and filtered through a 0.2-μm membrane filter for HPLC analysis.</p></sec>
<sec>
<title>3.5. Extraction and Purification of Quercetin</title>
<p>Each heated quercetin sample containing cholesterol was mixed with 7.5-mL of hexane-isopropanol (3:2, v/v) in a flask, the mixture was then flushed with nitrogen gas and shaken vigorously for 3 min, after which 3-mL of distilled water was added and the mixture was shaken vigorously for another 3 min. Then the solution was centrifuged at 26,000 × g for 5 min at 25°C, followed by collecting the lower layer containing quercetin, pouring into a centrifuge tube, adding 3-mL of absolute ethanol, centrifuging again for 5 min and collecting the lower phase. Next, a 500-μL of the lower phase was poured into a C18-E solid phase extraction cartridge, which was previously activated with 3-mL of methanol. Five mL of water-acetonitrile (1:1, v/v) was added to elute quercetin, and the elute was filtered through a 0.2-μm membrane filter for HPLC analysis.</p></sec>
<sec sec-type="methods">
<title>3.6. HPLC Analysis of Quercetin</title>
<p>The heated sample containing quercetin was dissolved in 20-mL of acetonitrile/phosphate buffer (pH 4) (55:45, v/v). Six concentrations of 1, 5, 10, 15, 20 and 25 mg/L of quercetin were each prepared in the same buffer solution. All the quercetin standard solutions were filtered through a 0.2-μm membrane filter and a 20-μL sample was injected into HPLC. A mobile phase of acetonitrile-phosphoric acid buffer (pH 4) (55:45, v/v) and a Vydac 201TP54 C18 column with flow rate at 1.5 mL/min was used to separate and quantify quercetin at 460 nm. The standard curve of quercetin was obtained by plotting concentration against peak area, and the regression equation and correlation coefficient (r<sup>2</sup>) were calculated. A high recovery of 98% was obtained when quercetin standard was added and subjected to the same extraction and purification procedure. Triplicate analyses were conducted and the mean values were determined.</p></sec>
<sec sec-type="methods">
<title>3.7. TLC Analysis of COPs</title>
<p>The Wurster dye was prepared as described by Smith and Hill [<xref ref-type="bibr" rid="b18-ijms-11-02805">18</xref>]. One g of <italic>N</italic>,<italic>N</italic>-dimethyl-<italic>p-</italic>phenylenediamine dihydrochloride was dissolved in 100 mL of 50% methanol solution, followed by shaking the mixture thoroughly, adding 1-mL of glacial acetic acid, pouring the solution into a glass vial and storing at −20 °C until use. For TLC analysis, the plate (20 × 20 cm) precoated with silica gel with a thickness of 250 μm was lined with a filter paper in a developing glass tank. A mobile phase of 200 mL of benzene-ethyl acetate (60:40, v/v) was poured into the tank and allowed to equilibrate for 30 min for vapor saturation prior to development [<xref ref-type="bibr" rid="b26-ijms-11-02805">26</xref>]. A micropipette was used to spot a 10-μL volume of extract onto the glass plate, and the chromatogram was developed for a distance of 18 cm at 25 °C, after which the plate was dried in an oven at 110 °C for 10 min, followed by spraying with 50% H<sub>2</sub>SO<sub>4</sub>. The color development of COPs under UV radiation at 254 nm was observed and recorded. In addition, the red spot was further subjected to HPLC analysis.</p></sec>
<sec sec-type="methods">
<title>3.8. HPLC Analysis of COPs</title>
<p>Two LiChrospher 100 CN columns connected in series and an isocratic solvent system of hexaneisopropanol (95:5, v/v) with flow rate at 1.0 mL/min were used to separate cholesterol and various COPs with RI detection. Identification was accomplished by comparing retention times of unknown peaks with authentic standards and cochromatography with added standards. An external calibration method was employed for quantification of various COPs. Seven concentrations of cholesterol (0.5, 1.0, 2.5, 5, 10, 25 and 50 mg/mL) and COPs (50, 100, 200, 500, 1000, 2500 and 5000 μg/mL) were each prepared and the standard curve was obtained by plotting concentration against area after injecting into HPLC. The regression equations and correlation coefficients (r<sup>2</sup>) were obtained by using a Borwin software system. Recovery was carried out by adding a fixed concentration of cholesterol and various COPs standards to samples for extraction and HPLC analysis, and a high recovery ranging from 97–100% was attained.</p></sec>
<sec sec-type="methods">
<title>3.9. Kinetic Analysis of COPs and Quercetin</title>
<p>The concentration changes of quercetin during heating in the presence of nitrogen, oxygen or cholesterol were statistically analyzed using a non-linear regression procedure of SAS [<xref ref-type="bibr" rid="b24-ijms-11-02805">24</xref>]. Also, the formation of COPs and degradation of cholesterol were analyzed statistically. The rate constant of each reaction was determined based on the least square method, <italic>i.e.</italic>, the Marquardt iterative procedure, until the convergence of all the parameters was best fitted. The precision of the parameters for each kinetic equation was also assessed. Analysis of variance and comparison of the residual amounts of cholesterol at various heating time intervals were carried out by using the SAS system [<xref ref-type="bibr" rid="b24-ijms-11-02805">24</xref>]. After a preliminary F test, the differences among the residual cholesterol were analyzed by Duncan’s multiple range test (p &lt; 0.05).</p></sec></sec>
<sec sec-type="conclusions">
<title>4. Conclusions</title>
<p>In conclusion, the major reaction pathways during heating of quercetin with and without cholesterol at 150 °C included cholesterol peroxidation and epoxidation, as well as thermal degradation, oxidative degradation and free radical chain reaction of quercetin. The correlation coefficients (r<sup>2</sup>) for all the reactions ranged from 0.82–0.99 based on non-linear regression analysis for cholesterol when heated with quercetin. The reactions for 7-OOH and 5,6-epoxide formation fitted the second-order, while all the reaction for quercetin degradation and free radical reaction fitted the first-order. The kinetic model developed in this study may be applied to predict the concentration changes of quercetin degradation in the presence and absence of cholesterol during heating at 150 °C.</p></sec></body>
<back>
<ref-list>
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<sec sec-type="display-objects">
<title>Figures and Tables</title>
<fig id="f1-ijms-11-02805" position="float">
<label>Figure 1</label>
<caption>
<p>HPLC chromatograms of quercetin during heating at 150 °C under combination of oxygen and cholesterol.</p></caption><graphic xlink:href="ijms-11-02805f1.gif"/></fig>
<fig id="f2-ijms-11-02805" position="float">
<label>Figure 2</label>
<caption>
<p>HPLC chromatograms of quercetin during heating at 150 °C under oxygen.</p></caption><graphic xlink:href="ijms-11-02805f2.gif"/></fig>
<fig id="f3-ijms-11-02805" position="float">
<label>Figure 3</label>
<caption>
<p>HPLC chromatograms of quercetin during heating at 150 °C under nitrogen.</p></caption><graphic xlink:href="ijms-11-02805f3.gif"/></fig>
<fig id="f4-ijms-11-02805" position="float">
<label>Figure 4</label>
<caption>
<p>Changes of quercetin during heating at 150 °C. Quercetin was heated under nitrogen (◆), oxygen (●) or combination of oxygen and cholesterol (▴); the best fitting line (—). A concentration of 200 μg/g quercetin was used. Heating time (min)</p></caption><graphic xlink:href="ijms-11-02805f4.gif"/></fig>
<fig id="f5-ijms-11-02805" position="float">
<label>Figure 5</label>
<caption>
<p>The possible pathways for quercetin degradation and oxidation as well as cholesterol peroxidation during heating at 150 °C. Cholesterol (A); 7-hydroperoxycholesterol (A′); 5,6-epoxycholesterol (E); degraded products (D); quercetin (Q); degraded plus oxidized product of quercetin (Q<sub>d</sub>, Q<sub>o</sub>); quercetin free radical (Q<sup>•</sup>). k<sub>1</sub>, k<sub>4</sub>, k<sub>5</sub>, k<sub>o</sub>, k<sub>d</sub>, and k<sub>f</sub> are the corresponding rate constants.</p></caption><graphic xlink:href="ijms-11-02805f5.gif"/></fig>
<fig id="f6-ijms-11-02805" position="float">
<label>Figure 6</label>
<caption>
<p>HPLC chromatogram of the acetone extract obtained from TLC after heating cholesterol with quercetin for 30 min.</p></caption><graphic xlink:href="ijms-11-02805f6.gif"/></fig>
<fig id="f7-ijms-11-02805" position="float">
<label>Figure 7</label>
<caption>
<p>The amounts of 7-OOH (7α-OOH plus 7β-OOH) formed during heating of cholesterol with and without quercetin at 150 °C. Means of experimental data of cholesterol in the absence of quercetin (■), and cholesterol in the presence of quercetin (●); the best fitting line (—).</p></caption><graphic xlink:href="ijms-11-02805f7.gif"/></fig>
<table-wrap id="t1-ijms-11-02805" position="float">
<label>Table 1</label>
<caption>
<p>Inhibitory effect of quercetin on total COPs formed during heating at 150 °C.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="center" valign="top" rowspan="2">Heating time (min)</th>
<th colspan="2" align="center" valign="bottom">COPs (%)<xref ref-type="table-fn" rid="tfn1-ijms-11-02805">a</xref><hr/></th></tr>
<tr>
<th align="center" valign="bottom">Control<xref ref-type="table-fn" rid="tfn2-ijms-11-02805">b</xref></th>
<th align="center" valign="bottom">Quercetin<xref ref-type="table-fn" rid="tfn2-ijms-11-02805">b</xref></th></tr></thead>
<tbody>
<tr>
<td align="center" valign="top">0</td>
<td align="center" valign="top">0.08 ± 0.00 <sup>A</sup>,<xref ref-type="table-fn" rid="tfn1-ijms-11-02805">a</xref></td>
<td align="center" valign="top">0.07 ± 0.00 <sup>A</sup>,<xref ref-type="table-fn" rid="tfn2-ijms-11-02805">b</xref></td></tr>
<tr>
<td align="center" valign="top">5</td>
<td align="center" valign="top">0.18 ± 0.01 <sup>A</sup>,<xref ref-type="table-fn" rid="tfn1-ijms-11-02805">a</xref></td>
<td align="center" valign="top">0.09 ± 0.00 <sup>A</sup>,<xref ref-type="table-fn" rid="tfn2-ijms-11-02805">b</xref></td></tr>
<tr>
<td align="center" valign="top">10</td>
<td align="center" valign="top">0.94 ± 0.01 <sup>B</sup>,<xref ref-type="table-fn" rid="tfn1-ijms-11-02805">a</xref></td>
<td align="center" valign="top">0.16 ± 0.01 <sup>A</sup>,<xref ref-type="table-fn" rid="tfn2-ijms-11-02805">b</xref></td></tr>
<tr>
<td align="center" valign="top">30</td>
<td align="center" valign="top">5.94 ± 0.05 <sup>C</sup>,<xref ref-type="table-fn" rid="tfn1-ijms-11-02805">a</xref></td>
<td align="center" valign="top">0.51 ± 0.00 <sup>B</sup>,<xref ref-type="table-fn" rid="tfn2-ijms-11-02805">b</xref></td></tr>
<tr>
<td align="center" valign="top">60</td>
<td align="center" valign="top">15.4 ± 0.3<sup>D</sup>,<xref ref-type="table-fn" rid="tfn1-ijms-11-02805">a</xref></td>
<td align="center" valign="top">2.05 ± 0.03 <sup>C</sup>,<xref ref-type="table-fn" rid="tfn2-ijms-11-02805">b</xref></td></tr>
<tr>
<td align="center" valign="top">90</td>
<td align="center" valign="top">30.9 ± 0.5<sup>E</sup>,<xref ref-type="table-fn" rid="tfn1-ijms-11-02805">a</xref></td>
<td align="center" valign="top">7.77 ± 0.06 <sup>D</sup>,<xref ref-type="table-fn" rid="tfn2-ijms-11-02805">b</xref></td></tr>
<tr>
<td align="center" valign="top">120</td>
<td align="center" valign="top">—<xref ref-type="table-fn" rid="tfn3-ijms-11-02805">c</xref></td>
<td align="center" valign="top">24.4 ± 0.4 <sup>E</sup></td></tr></tbody></table>
<table-wrap-foot><fn id="tfn1-ijms-11-02805">
<label>a</label>
<p>Values are expressed as percentage relative to cholesterol content at 0 min heating time; mean ± standard deviation of triplicate determinations.</p></fn><fn id="tfn2-ijms-11-02805">
<label>b</label>
<p>Symbols bearing the letters A-E in the same column or a-b in the same row are significantly different (p &lt; 0.05);</p></fn><fn id="tfn3-ijms-11-02805">
<label>c</label>
<p>Not detected.</p></fn></table-wrap-foot></table-wrap>
<table-wrap id="t2-ijms-11-02805" position="float">
<label>Table 2</label>
<caption>
<p>Percentage changes of residual cholesterol due to thermal degradation at 150 °C.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="center" valign="top" rowspan="2">Heating time (min)</th>
<th colspan="2" align="center" valign="bottom">Cholesterol (%) <xref ref-type="table-fn" rid="tfn4-ijms-11-02805">a</xref><hr/></th></tr>
<tr>
<th align="center" valign="bottom">Control <xref ref-type="table-fn" rid="tfn5-ijms-11-02805">b</xref></th>
<th align="center" valign="bottom">Quercetin <xref ref-type="table-fn" rid="tfn5-ijms-11-02805">b</xref></th></tr></thead>
<tbody>
<tr>
<td align="center" valign="top">0</td>
<td align="center" valign="top">97.9 ± 0.6 <sup>A</sup>,<xref ref-type="table-fn" rid="tfn4-ijms-11-02805">a</xref></td>
<td align="center" valign="top">96.9 ± 0.3 <sup>A</sup>,<xref ref-type="table-fn" rid="tfn4-ijms-11-02805">a</xref></td></tr>
<tr>
<td align="center" valign="top">5</td>
<td align="center" valign="top">93.2 ± 1.05 <sup>B</sup>,<xref ref-type="table-fn" rid="tfn4-ijms-11-02805">a</xref></td>
<td align="center" valign="top">95.7 ± 0.2 <sup>A</sup>,<xref ref-type="table-fn" rid="tfn5-ijms-11-02805">b</xref></td></tr>
<tr>
<td align="center" valign="top">10</td>
<td align="center" valign="top">87.5 ± 0.4 <sup>C</sup>,<xref ref-type="table-fn" rid="tfn4-ijms-11-02805">a</xref></td>
<td align="center" valign="top">94.1 ± 0.1 <sup>A</sup>,<xref ref-type="table-fn" rid="tfn5-ijms-11-02805">b</xref></td></tr>
<tr>
<td align="center" valign="top">30</td>
<td align="center" valign="top">69.0 ± 1.0 <sup>D</sup>,<xref ref-type="table-fn" rid="tfn4-ijms-11-02805">a</xref></td>
<td align="center" valign="top">86.4 ± 0.1 <sup>B</sup>,<xref ref-type="table-fn" rid="tfn5-ijms-11-02805">b</xref></td></tr>
<tr>
<td align="center" valign="top">60</td>
<td align="center" valign="top">64.2 ± 0.9 <sup>E</sup>,<xref ref-type="table-fn" rid="tfn4-ijms-11-02805">a</xref></td>
<td align="center" valign="top">80.5 ± 0.3 <sup>C</sup>,<xref ref-type="table-fn" rid="tfn5-ijms-11-02805">b</xref></td></tr>
<tr>
<td align="center" valign="top">90</td>
<td align="center" valign="top">66.4 ± 0.7 <sup>E</sup>,<xref ref-type="table-fn" rid="tfn4-ijms-11-02805">a</xref></td>
<td align="center" valign="top">77.1 ± 0.5 <sup>D</sup>,<xref ref-type="table-fn" rid="tfn5-ijms-11-02805">b</xref></td></tr>
<tr>
<td align="center" valign="top">120</td>
<td align="center" valign="top">—<xref ref-type="table-fn" rid="tfn6-ijms-11-02805">c</xref></td>
<td align="center" valign="top">77.4 ± 2.4 <sup>D</sup></td></tr></tbody></table>
<table-wrap-foot><fn id="tfn4-ijms-11-02805">
<label>a</label>
<p>Values are expressed as percentage relative to cholesterol content at 0 min heating time; mean ± standard deviation of triplicate determinations.</p></fn><fn id="tfn5-ijms-11-02805">
<label>b</label>
<p>Symbols bearing different letters of A-E in the same column or a-b in the same row are significantly different (p &lt; 0.05);</p></fn><fn id="tfn6-ijms-11-02805">
<label>c</label>
<p>Not detected.</p></fn></table-wrap-foot></table-wrap>
<table-wrap id="t3-ijms-11-02805" position="float">
<label>Table 3</label>
<caption>
<p>Oxidation and degradation rate constants of quercetin during heating at 150 °C.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="center" valign="bottom">Treatment</th>
<th align="center" valign="bottom">Rate equations <xref ref-type="table-fn" rid="tfn7-ijms-11-02805">a</xref></th>
<th align="center" valign="bottom">k (h<sup>−1</sup>)</th>
<th align="center" valign="bottom">r<sup>2</sup></th></tr></thead>
<tbody>
<tr>
<td align="center" valign="top">Nitrogen</td>
<td align="left" valign="top">
<inline-formula>
<mml:math>
<mml:semantics>
<mml:mrow>
<mml:mtext>Q</mml:mtext>
<mml:mover>
<mml:mo>→</mml:mo>
<mml:mrow>
<mml:mtext>kd</mml:mtext></mml:mrow></mml:mover>
<mml:msub>
<mml:mrow>
<mml:mtext>Q</mml:mtext></mml:mrow>
<mml:mtext>d</mml:mtext></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula></td>
<td align="center" valign="top">0.253 ± 0.027</td>
<td align="center" valign="top">0.94</td></tr>
<tr>
<td align="center" valign="top">Oxygen</td>
<td align="left" valign="top">
<inline-formula>
<mml:math>
<mml:semantics>
<mml:mrow>
<mml:mtext>Q</mml:mtext>
<mml:mover>
<mml:mo>→</mml:mo>
<mml:mrow>
<mml:mtext>kd</mml:mtext>
<mml:mo>+</mml:mo>
<mml:mtext>ko</mml:mtext></mml:mrow></mml:mover>
<mml:msub>
<mml:mrow>
<mml:mtext>Q</mml:mtext></mml:mrow>
<mml:mtext>d</mml:mtext></mml:msub>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mtext>Q</mml:mtext></mml:mrow>
<mml:mtext>o</mml:mtext></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula></td>
<td align="center" valign="top">0.868 ± 0.019</td>
<td align="center" valign="top">0.99</td></tr>
<tr>
<td align="center" valign="top">Oxygen and Cholesterol</td>
<td align="left" valign="top">
<inline-formula>
<mml:math>
<mml:semantics>
<mml:mrow>
<mml:mtext>Q</mml:mtext>
<mml:mover>
<mml:mo>→</mml:mo>
<mml:mrow>
<mml:mtext>kd</mml:mtext>
<mml:mo>+</mml:mo>
<mml:mtext>ko</mml:mtext>
<mml:mo>+</mml:mo>
<mml:mtext>kf</mml:mtext></mml:mrow></mml:mover>
<mml:msub>
<mml:mrow>
<mml:mtext>Q</mml:mtext></mml:mrow>
<mml:mtext>d</mml:mtext></mml:msub>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mtext>Q</mml:mtext></mml:mrow>
<mml:mtext>o</mml:mtext></mml:msub>
<mml:mo>+</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mtext>Q</mml:mtext></mml:mrow>
<mml:mo>•</mml:mo></mml:msup></mml:mrow></mml:semantics></mml:math></inline-formula></td>
<td align="center" valign="top">7.17 ± 0.67</td>
<td align="center" valign="top">0.91</td></tr></tbody></table>
<table-wrap-foot><fn id="tfn7-ijms-11-02805">
<label>a</label>
<p>Q (quercetin), Q<sub>d</sub> (degraded products of quercetin), Q<sub>o</sub> (oxidized products of quercetin), Q<sup>•</sup> (quercetin free radical) and k<sub>d</sub>, k<sub>o</sub> and k<sub>f</sub> are the rate constants.</p></fn></table-wrap-foot></table-wrap>
<table-wrap id="t4-ijms-11-02805" position="float">
<label>Table 4</label>
<caption>
<p>Oxidation and degradation rate constants of cholesterol during heating at 150 °C.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="center" valign="top" rowspan="2">Rate equations <xref ref-type="table-fn" rid="tfn8-ijms-11-02805">a</xref></th>
<th align="center" valign="top" rowspan="2">Reactions</th>
<th colspan="2" align="center" valign="bottom">C <xref ref-type="table-fn" rid="tfn9-ijms-11-02805">b</xref><hr/></th>
<th colspan="2" align="center" valign="bottom">Qu <xref ref-type="table-fn" rid="tfn9-ijms-11-02805">b</xref><hr/></th></tr>
<tr>
<th align="center" valign="bottom">k (h<sup>−1</sup>)</th>
<th align="center" valign="bottom">r<sup>2</sup></th>
<th align="center" valign="bottom">k (h<sup>−1</sup>)</th>
<th align="center" valign="bottom">r<sup>2</sup></th></tr></thead>
<tbody>
<tr>
<td align="left" valign="top">
<inline-formula>
<mml:math>
<mml:semantics>
<mml:mrow>
<mml:mtext>Chol</mml:mtext>
<mml:mover>
<mml:mo>→</mml:mo>
<mml:mrow>
<mml:mtext>k</mml:mtext>
<mml:mn>1</mml:mn></mml:mrow></mml:mover>
<mml:mn>7</mml:mn>
<mml:mrow>
<mml:mo>-</mml:mo>
<mml:mtext>OOH</mml:mtext></mml:mrow></mml:mrow></mml:semantics></mml:math></inline-formula></td>
<td align="center" valign="top">Free radical chain</td>
<td align="center" valign="top">488.2 ± 0.2</td>
<td align="center" valign="top">1.00</td>
<td align="center" valign="top">1.8×10<sup>−4</sup> ± 0.1×10<sup>−4</sup></td>
<td align="center" valign="top">0.94</td></tr>
<tr>
<td align="left" valign="top">
<inline-formula>
<mml:math>
<mml:semantics>
<mml:mrow>
<mml:mtext>Chol</mml:mtext>
<mml:mover>
<mml:mo>→</mml:mo>
<mml:mrow>
<mml:mtext>k</mml:mtext>
<mml:mn>4</mml:mn></mml:mrow></mml:mover>
<mml:mn>5</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>6</mml:mn>
<mml:mrow>
<mml:mo>-</mml:mo>
<mml:mtext>EP</mml:mtext></mml:mrow></mml:mrow></mml:semantics></mml:math></inline-formula></td>
<td align="center" valign="top">Epoxidation</td>
<td align="center" valign="top">4240.8 ± 344.7</td>
<td align="center" valign="top">0.89</td>
<td align="center" valign="top">0.016 ± 0.001</td>
<td align="center" valign="top">0.82</td></tr>
<tr>
<td align="left" valign="top">
<inline-formula>
<mml:math>
<mml:semantics>
<mml:mrow>
<mml:mtext>Chol</mml:mtext>
<mml:mover>
<mml:mo>→</mml:mo>
<mml:mrow>
<mml:mtext>k</mml:mtext>
<mml:mn>5</mml:mn></mml:mrow></mml:mover>
<mml:mtext>D</mml:mtext></mml:mrow></mml:semantics></mml:math></inline-formula></td>
<td align="center" valign="top">Degradation</td>
<td align="center" valign="top">0.94 ± 0.03</td>
<td align="center" valign="top">0.99</td>
<td align="center" valign="top">0.19 ± 0.01</td>
<td align="center" valign="top">0.99</td></tr>
<tr>
<td align="left" valign="top">
<inline-formula>
<mml:math>
<mml:semantics>
<mml:mrow>
<mml:mtext>Q</mml:mtext>
<mml:mover>
<mml:mo>→</mml:mo>
<mml:mrow>
<mml:mtext>kf</mml:mtext></mml:mrow></mml:mover>
<mml:msup>
<mml:mrow>
<mml:mtext>Q</mml:mtext></mml:mrow>
<mml:mo>•</mml:mo></mml:msup></mml:mrow></mml:semantics></mml:math></inline-formula></td>
<td align="center" valign="top">Free radical chain</td>
<td align="center" valign="top">—<xref ref-type="table-fn" rid="tfn10-ijms-11-02805">c</xref></td>
<td align="center" valign="top">—</td>
<td align="center" valign="top">3.28 ± 0.00</td>
<td align="center" valign="top">0.94</td></tr></tbody></table>
<table-wrap-foot><fn id="tfn8-ijms-11-02805">
<label>a</label>
<p>Chol (cholesterol), 7-OOH (7-hydroperoxycholesterol), 5,6-EP (5,6-epoxycholesterol), D (degraded product of cholesterol), Q (quercetin), Q<sup>•</sup> (quercetin free radical) and k<sub>1</sub>, k<sub>4</sub>, k<sub>5</sub> and k<sub>f</sub> are the rate constants.</p></fn><fn id="tfn9-ijms-11-02805">
<label>b</label>
<p>C: autoxidation of cholesterol without quercetin. Qu: the initial stage during heating of cholesterol with quercetin (t ≤ 30 min).</p></fn><fn id="tfn10-ijms-11-02805">
<label>c</label>
<p>No detected reaction product.</p></fn></table-wrap-foot></table-wrap></sec></back></article>
