Biomod/2014/UANL/KineticModel: Difference between revisions
No edit summary |
No edit summary |
||
Line 158: | Line 158: | ||
#content{margin-left:0.7;} | #content{margin-left:0.7;} | ||
.navbar{ | .navbar{ | ||
top: | top:0px; | ||
position:fixed; | position:fixed; | ||
width:96.8%; | width:96.8%; |
Latest revision as of 21:13, 25 October 2014
<html lang="en-US"> <head>
<meta http-equiv="Content-Type" content="text/html;charset=utf-8"> <title>Fixed Top Navigation Toolbar</title> <meta name="author" content="Jake Rocheleau"> <link rel="shortcut icon" href="http://designshack.net/favicon.ico"> <link rel="icon" href="http://designshack.net/favicon.ico"> <link rel="stylesheet" type="text/css" media="all" href="styles.css"> <link rel="stylesheet" type="text/css" media="all" href="http://fonts.googleapis.com/css?family=Capriola"> <script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script> <!-- Latest compiled css and JavaScript --> <script src="http://maxcdn.bootstrapcdn.com/bootstrap/3.2.0/js/bootstrap.min.js"></script> <!--j--query--> <!--Nav Bar Theme--> <link href="http://maxcdn.bootstrapcdn.com/bootswatch/3.2.0/yeti/bootstrap.min.css" rel="stylesheet">
<style> html, body, div, span, applet, object, iframe, h1, h2, h3, h4, h5, h6, p, blockquote, pre, a, abbr, acronym, address, big, cite, code, del, dfn, em, img, ins, kbd, q, s, samp, small, strike, strong, sub, sup, tt, var, b, u, i, center, dl, dt, dd, ol, ul, li, fieldset, form, label, legend, table, caption, tbody, tfoot, thead, tr, th, td, article, aside, canvas, details, embed, figure, figcaption, footer, header, hgroup, menu, nav, output, ruby, section, summary, time, mark, audio, video {
margin: 0; padding: 0; border: 0; font-size: 100%; font: inherit; vertical-align: baseline; outline: none; -webkit-text-size-adjust: 100%; -webkit-box-sizing: border-box; -moz-box-sizing: border-box; box-sizing: border-box;
} html { height: 101%; } body { font-family: Tahoma, Verdana, Arial, sans-serif; font-size: 62.5%; line-height: 1; padding-bottom: 65px; background: #444 url('images/bg.png'); }
article, aside, details, figcaption, figure, footer, header, hgroup, menu, nav, section { display: block; } ol, ul { list-style: none; }
blockquote, q { quotes: none; } blockquote:before, blockquote:after, q:before, q:after { content: ''; content: none; } strong { font-weight: bold; }
table { border-collapse: collapse; border-spacing: 0; } img { border: 0; max-width: 100%; }
h1 {
font-family: 'Capriola', Tahoma, Arial, sans-serif; font-weight: normal; font-size: 2.95em; line-height: 1.2em; letter-spacing: -.0.03em; color: #383838; margin-bottom: 16px;
}
p { font-size: 1.2em; line-height: 1.45em; margin-bottom: 15px; color: #434343; text-align: justify; }
a { color: #5b77a4; text-decoration: underline; } a:hover { color: #7d94bb; }
- w {
display: block; width: 710px; padding: 14px 15px; margin: 0 auto; margin-top: 45px;
}
- content {
display: block; background: #fff; padding: 80px 50px;
}
- logo { display: block; border: 1px solid #232323; border-bottom-width: 0; }
- logobg {
display: block; width: 100%; height: 130px; background: url('images/logo.png') top left no-repeat; text-indent: 100%; white-space: nowrap; overflow: hidden;
}
/* top navigation */
- navigation {
display: block; height: 35px; background-color: #131313; background-image: -webkit-gradient(linear, left top, left bottom, from(#202020), to(#131313)); background-image: -webkit-linear-gradient(top, #202020, #131313); background-image: -moz-linear-gradient(top, #202020, #131313); background-image: -ms-linear-gradient(top, #202020, #131313); background-image: -o-linear-gradient(top, #202020, #131313); background-image: linear-gradient(top, #202020, #131313);
}
- navigation ul { list-style: none; padding: 0px 7px; }
- navigation ul li { display: inline; float: left; }
- navigation ul li a {
display: block; padding: 0 8px; color: #fff; font-size: 1.1em; text-decoration: none; line-height: 35px; font-weight: bold; margin-right: 6px; text-shadow: 1px 1px 1px #000; -webkit-transition: all 0.2s linear; -moz-transition: all 0.2s linear; transition: all 0.2s linear;
}
- navigation ul li a:hover { color: #a8d6e7; }
/* hidden fixed navigation */
- fixedbar {
display: none; position: fixed; top: 0; width: 100%; height: 80px; background: rgba(0,0,0,0.75);
}
- fixednav {
display: block; width: 710px; margin: 0 auto; padding: 0px 25px;
}
- fixednav li { }
- fixednav li a {
display: block; float: left; font-size: 1.75em; font-weight: bold; color: #96aed8; line-height: 80px; text-decoration: none; padding: 0px 8px; margin-right: 6px; -webkit-transition: all 0.2s linear; -moz-transition: all 0.2s linear; transition: all 0.2s linear;
}
- fixednav li a:hover {
color: #fff; background: rgba(0,0,0,0.3);
}
- content{margin-left:0.7;}
.navbar{ top:0px; position:fixed; width:96.8%; z-index: 9999 !important;
background-color: #A68F6A;
left: 152px }
div img {
position: absolute; top: 0px; left: 0px;
}
div imglogo {
position: absolute; top: 20px; left: 20px;
}
footer { position: relative; /* Altura total del footer en px con valor negativo */ margin-top: -50px; /* Altura del footer en px. Se han restado los 5px del margen superior mas los 5px del margen inferior */ height: 40px; padding:5px 0px; clear: both; background: #286af0; text-align: center; color: #fff;
z-index: 9999 !important;
}
</style> </head>
<body>
<!--Nav-->
<div class="navbar navbar-default">
<div class="navbar-header"> <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse"> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button> <a class="navbar-brand" href="#"></a> </div> <div class="navbar-collapse collapse navbar-responsive-collapse"> <ul class="nav navbar-nav">
<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>
</ul> </div>
</div> <!--Nav Bar Done-->>
<div> <img src="http://openwetware.org/images/7/76/Cell_cluster-4052b.png" />
</div>
<div id="content">
<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>
</div> </div>
</div>
<script type="text/javascript"> $(document).ready(function(){
$('#navigation a, #fixedbar a').on('click', function(e) { e.preventDefault(); }); $(window).on('scroll',function() { var scrolltop = $(this).scrollTop();
if(scrolltop >= 215) { $('#fixedbar').fadeIn(250); } else if(scrolltop <= 210) { $('#fixedbar').fadeOut(250); } });
}); </script>
</body> </html>