Biomod/2014/UANL/KineticModel

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<li><a href="http://openwetware.org/wiki/Biomod/2014/UANL">Home</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2014/UANL/Background">Background</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2014/UANL/Method">Method</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2014/UANL/MedicalApplication">Medical Application</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2014/UANL/IndustrialApplication">Industrial Application</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2014/UANL/Discussion">Discussion</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2014/UANL/DiffusionModel">Diffusion Model</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2014/UANL/KineticModel">Kinetic Model</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2014/UANL/Team/">Team</a></li>

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<h1>Kinetic model</h1> <p>A mathematical model will help describe the behavior of the reactions that develop inside the reactor </p>

<br></br> The following reactions are proposed to describe the system: </p> <IMG STYLE="position:absolute; TOP:280px; LEFT:300px;" SRC="http://openwetware.org/images/1/18/Ki0.png"> <br></br> <br></br> <br></br>


<p>The Michaelis-Menten equation is prefered as it describes better the selected reactions. It is represented by the following symbols:</p> <IMG STYLE="position:absolute; TOP:390px; LEFT:170px;" SRC="http://openwetware.org/images/5/52/Ki1.png"> <br></br> <br></br> <br></br> <br></br> <br></br> <br></br> <p> Where: <br></br> Sustrates: S1 is uric acid y S2 is peroxyde.<br></br> Enzymes: E1 is uricase and E2 is catalase. <br></br> W: water<br></br> O: diatomic oxygen<br></br> P1 : products (allantoin and carbon dioxide)<br></br> ES1 and ES2  : enzyme - substrate complex <br></br> These are the substrate's reaction rates: </p> <br></br> <br></br> <br></br> <br></br> <br></br> <br></br> <IMG STYLE="position:absolute; TOP:1000px; LEFT:230px;" SRC="http://openwetware.org/images/d/de/Ki2.png">

<p>These are the enzyme-substrate’s net reaction rates:</p> <br></br> <br></br> <br></br> <br></br> <br></br> <IMG STYLE="position:absolute; TOP:1310px; LEFT:345px;" SRC="http://openwetware.org/images/f/fe/Ki3.png">

<p>Enzymes does not get consumed so the concentrations (Et) remain constant and equal to the sum of the free enzyme E plus the substrate-enzyme complex ES*.</p> <br></br> <br></br> <br></br> <br></br> <IMG STYLE="position:absolute; TOP:1500px; LEFT:350px;" SRC="http://openwetware.org/images/9/98/Ki4.png"> <p>The equations above can be rearranged to show the rates of reaction using measurable variables:</p> <br></br> <br></br> <br></br> <br></br> <IMG STYLE="position:absolute; TOP:1700px; LEFT:320px;" SRC="http://openwetware.org/images/d/d0/Ki5.png"> <p>Assuming excess water and oxygen, equations (7) and (8) can be rewritten as:</p> <br></br> <br></br> <br></br> <br></br> <IMG STYLE="position:absolute; TOP:1870px; LEFT:335px;" SRC="http://openwetware.org/images/8/88/Ki6.png"> <p>Where :</p> <br></br> <br></br> <br></br> <br></br> <IMG STYLE="position:absolute; TOP:2100px; LEFT:345px;" SRC="http://openwetware.org/images/d/da/Ki7.png"> <br></br> <br></br> <br></br> <IMG STYLE="position:absolute; TOP:2210px; LEFT:345px;" SRC="http://openwetware.org/images/8/80/Ki8.png"> <p>Maximun rates of reaction for each enzyme are represented as Vmax and the following equations are obtained:</p> <br></br> <br></br> <br></br> <IMG STYLE="position:absolute; TOP:2380px; LEFT:345px;" SRC="http://openwetware.org/images/e/ee/Ki9.png"> <p>Where:</p> <br></br> <br></br> <br></br> <IMG STYLE="position:absolute; TOP:2550px; LEFT:345px;" SRC="http://openwetware.org/images/d/dd/Ki10.png"> <p>Reverting the equation (11):</p> <br></br> <br></br> <br></br> <IMG STYLE="position:absolute; TOP:2700px; LEFT:345px;" SRC="http://openwetware.org/images/f/fe/Ki11.png"> <p>The graphic shows that equation (13) has the shape of a straight line. Its intersection with the Y axis is the maximum velocity’s inverse and the slope is Michaelis constant divided over the maximum velocity. This graphic is known as Lineweaver-Burk. The diagram allow to find some parameters of the Michaelis -Menten equation like Vmax y Km</p> <br></br> <br></br> <br></br> <br></br> <br></br> <br></br> <br></br> <br></br> <br></br> <IMG STYLE="position:absolute; TOP:2865px; LEFT:150px;" SRC="http://openwetware.org/images/c/c9/Graficacinetica_opt_%282%29.png"> <br></br> <p>It can be found on available literature that the relation between uric acid and uricase has a Km = 16.2mmol/min and a Vmax = 0.025mmol/min. at pH=7.0 and 350C. <br></br> Considering the nanoreactor as a batch reactor, isothermal and with a constant pH, mol balances can be defined as: </p> <br></br> <br></br> <br></br> <IMG STYLE="position:absolute; TOP:3400px; LEFT:345px;" SRC="http://openwetware.org/images/1/13/Ki13.png"> <br></br> <br></br> <p>Combining equations (11) and (12) with (14) and (15) respectively, the next result is obtained:</p> <br></br> <br></br> <br></br> <IMG STYLE="position:absolute; TOP:3600px; LEFT:345px;" SRC="http://openwetware.org/images/f/fb/Ki14.png"> <p>Where:</p> <br></br> <br></br> <br></br> <IMG STYLE="position:absolute; TOP:3800px; LEFT:350px;" SRC="http://openwetware.org/images/f/f1/Ki15.png"> <p>Equations (16) and (17) have the shape of a straight line, so intersection with the Y axis and slope should be easily found taking into account conversion and time of reaction. The Vmax and Km can be mathematically obtained. </p>

<hr size="10px" width=100% align="center"/> <h2>References:</h2> <p>PRASHANT PRADHAN1*, J. G. (2008). A Facile Microfluidic Method for Production of Liposomes. ANTICANCER RESEARCH. <br></br>

 Bo Yu*, †. R. (2009). Microfluidic Methods for Production of Liposomes. Methods Enzymol , 5-6.
M.E. Lanioa†, M. L.-L. (2009). Las vesículas liposomales: obtención, propiedades y aplicaciones potencialesen la biomedicina. Rev. Cub. Física , 23-30.<br></br>
   Hairul Hisham Hamzah1, 3. Z. (2013). Spectrophotometric Determination of Uric Acid in Urine Based-Enzymatic . J Anal Bioanal Tech , 4.<br></br>
 Fogler, H. S. (1999). Elements of Quemical Reaction Engineering (Third Edition ed.). New Jersey, E.U.A.: Prentice-Hall.</p>

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