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| − | <!-- <div id="model-back"> | + | <h1>Outreach</h1> |
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| − | <article class="col-xs-12 col-sm-12 col-md-8 col-md-offset-2">
| |
| − | <h1>Modeling</h1>
| |
| − | </article>
| |
| | | | |
| | <!-- Contenido principal --> | | <!-- Contenido principal --> |
| − | <article class="col-xs-12 col-sm-12 col-md-8 col-md-offset-2"> | + | <article class="col-xs-12 col-sm-12 col-md-8 col-md-offset-2" id="vision"> |
| − | <h1>Abstract</h1> | + | <h1>Our vision</h1> |
| − | <p>We built a mathematical model for the dynamics in a lytic infection process for the production of a specific protein on the basis of chemical reaction networks. We aim to optimize the protein expression as a function of the multiplicity of infection (MOI).</p> | + | <p>Mexico is one of the top 10 economies in the world; however, its scientific advance grows very slowly, and we are staying behind, especially if we want to compete against other countries. This is why iGEM Team Tec-Monterrey 2015 strives to help synthetic biology grow; not only in our state, but also throughout our country. We believe that by being young people, we have a higher outreach, and can really make a change by letting other people know about synthetic biology and everything you can achieve with it. In this way we make our colleagues, family and citizens more aware of synthetic biology, creating a higher interest.</p> |
| | + | <p>One of the main reasons that made us use the Sf9 cell line was because there isn’t a lot of research about it, and we believe that it has great potential in the future for the making of proteins and other uses. With our project, we hope that other scientists can use our insect cell platform to carry out new research, thus allowing the field to reach new heights. We want to facilitate the use of this cells to other iGEM Teams and hopefully scientists outside of iGEM, by characterizing certain parts and leaving a little more research than there was before. We believe that in the future this cell line will be really helpful and have a greater impact in synthetic biology. </p> |
| | </article> | | </article> |
| | | | |
| − | <article class="col-xs-12 col-sm-12 col-md-8 col-md-offset-2 modeling"> | + | <br> |
| − | <h1>Defining parameters</h1>
| + | |
| − | <p>It was considered a simple chemical reaction network with a quasi-steady state approximation for the interaction between the baculovirus and the sf9. This led to a first approximation in the rate constant in the infection process. More will be discussed below. The parameters that will be used in the development of the model are the following:
| + | |
| − | </p>
| + | |
| − | <table class="table">
| + | |
| − | <tr>
| + | |
| − | <td><strong>C<sub>U</sub></strong></td>
| + | |
| − | <td> Non-infected Cell concentration.</td>
| + | |
| − | </tr>
| + | |
| − | <tr>
| + | |
| − | <td><strong>C<sub>1</sub></strong></td>
| + | |
| − | <td>Infected Cell concentration.</td>
| + | |
| − | </tr>
| + | |
| − | <tr>
| + | |
| − | <td><strong>V</strong></td>
| + | |
| − | <td>Baculovirus concentration.</td>
| + | |
| − | </tr>
| + | |
| − | <tr>
| + | |
| − | <td><strong>C<sub>P</sub></td>
| + | |
| − | <td>Complex concentration (Non-infected Cell+Virus).</td>
| + | |
| − | </tr>
| + | |
| − | <tr>
| + | |
| − | <td><strong>N</strong></td>
| + | |
| − | <td>Effective baculovirus production rate.</td>
| + | |
| − | </tr>
| + | |
| − | <tr>
| + | |
| − | <td><strong>d</strong></td>
| + | |
| − | <td>Dead rate due to infection.</td>
| + | |
| − | </tr>
| + | |
| − | <tr>
| + | |
| − | <td><strong>P</strong></td>
| + | |
| − | <td>Natural saturation population.</td>
| + | |
| − | </tr>
| + | |
| − | <tr>
| + | |
| − | <td><strong>r</strong></td>
| + | |
| − | <td>Natural Malthusian parameter for the Sf9.</td>
| + | |
| − | </tr>
| + | |
| − | <tr>
| + | |
| − | <td><strong>k<sub>1</sub></strong></td>
| + | |
| − | <td>Rate constant for the complex formation.</td>
| + | |
| − | </tr>
| + | |
| − | <tr>
| + | |
| − | <td><strong>k<sub>-1</sub></strong></td>
| + | |
| − | <td>Rate constant for the complex degradation.</td>
| + | |
| − | </tr>
| + | |
| − | <tr>
| + | |
| − | <td><strong>k<sub>2</sub></strong></td>
| + | |
| − | <td> Rate constant for the infection process.</td>
| + | |
| − | </tr>
| + | |
| − | <tr>
| + | |
| − | <td><strong>K</strong></td>
| + | |
| − | <td>Quasi-steady-state rate constant in the infection.</td>
| + | |
| − | </tr>
| + | |
| − | <tr>
| + | |
| − | <td><strong>Φ<sub>V</sub></strong></td>
| + | |
| − | <td>Average virus production per infected cell.</td>
| + | |
| − | </tr>
| + | |
| − | <tr>
| + | |
| − | <td><strong>Φ<sub>P</sub></strong></td>
| + | |
| − | <td>Average protein production per infected cell.</td>
| + | |
| − | </tr>
| + | |
| − | <tr>
| + | |
| − | <td><strong>Τ<sub>IV</sub></strong></td>
| + | |
| − | <td>Time lapse between the infection of the cell and the beginning of the virus production. </td>
| + | |
| − | </tr>
| + | |
| − | <tr>
| + | |
| − | <td><strong>Τ<sub>IP</sub></strong></td>
| + | |
| − | <td>Time lapse between the infection of the cell and the beginning of the protein production.</td>
| + | |
| − | </tr>
| + | |
| − | <tr>
| + | |
| − | <td><strong>Τ<sub>D</sub></strong></td>
| + | |
| − | <td>Time lapse between the infection of the cell and cell's death.</td>
| + | |
| − | </tr>
| + | |
| − | </table>
| + | |
| − | </article>
| + | |
| − | | + | |
| − | <article class="col-xs-12 col-sm-12 col-md-8 col-md-offset-2 modeling">
| + | |
| − | <h1>Chemical Reaction Network Modeling</h1>
| + | |
| − | <p>We consider as a first approach that only one virion is required for the infection process of a <span><strong>Sf9</strong></span>cell. An uninfected cell.<strong>C<sub>U</sub></strong> interacts with virions <strong>V</strong> to create a complex <strong>C<sub>P</sub></strong>. Some of them will be infected due to this interaction, i.e. the virion will cross the membrane and begin the infection process, the rest will stay in this complex form or will dissolve:</p>
| + | |
| − | | + | |
| − | <div class="col-md-9 col-md-offset-2 col-sm-9 col-sm-offset-2 col-xs-9 col-xs-offset-2"><img src="rsc/Tec-Monterrey_Formula1.jpg" class="img-responsive"></div>
| + | |
| − | <div class="col-md-1 col-sm-1 col-xs-1"><p>(1)</p></div>
| + | |
| | | | |
| | + | <article class="col-xs-12 col-sm-12 col-md-8 col-md-offset-2"id="geneus"> |
| | + | <h1>Gene Us</h1> |
| | + | <p>We created a strategic alliance with a social entrepreneurship called “GeneUs”. GeneUs needed help to guide middle school students that were doing projects in Biotechnology to in a Science Fair as a conclusion to workshops given during the previous weeks. The role of our team was to guide the students while they were developing their respective projects. At the end, the students were very happy with the results and everything they learned during the process. As a team, we felt really satisfied to be able to teach students more about what we are passionate so they can consider it as an option for their professional careers in the future and to help increase the development of Biotechnology in Mexico.</p> |
| | </article> | | </article> |
| | | | |
| − | <article class="col-xs-12 col-sm-12 col-md-8 col-md-offset-2 modeling"> | + | <br> |
| − | <p>The <span><strong>Sf9</strong></span> cells will continue to replicate naturally as long as it doesn't get infected. After the infection, the corresponding malthusian parameter will decrease dramatically and, in fact, can be neglected after the infection: Combining both processes, we obtain the following rates for the <strong>C<sub>U</sub></strong> and the complex <strong>C<sub>P</sub></strong>:</p>
| + | |
| | | | |
| − | <div class="col-md-9 col-md-offset-2 col-sm-9 col-sm-offset-2 col-xs-9 col-xs-offset-2"><img src="rsc/Tec-Monterrey_Formula2.jpg" class="img-responsive"></div>
| + | <article class="col-xs-12 col-sm-12 col-md-8 col-md-offset-2" id="media"> |
| − | <div class="col-md-1 col-sm-1 col-xs-1"><br><p>(2)</p><br><br><p>(3)</p></div>
| + | <h1>Social media</h1> |
| − | | + | <p>To let the world know about our project, achievements, events and progress, we made a great use of social media. By having 1729 likes on our Facebook page and 546 followers on Twitter we are sure that people believe in our project and are interested in knowing about it. This is why we did our best job in demonstrating our moments of excitement when parts arrived, bonding time with other iGEM Teams and interesting articles that involve biotechnology, so people can be more informed about the great impact it has. We also submitted a video at www.idea.me to help us raise funds for our project and took advantage of our outreach for promotion. Social media is a really important tool nowadays to reach people with different interests and all around the world, such as other iGEM Teams.</p> |
| − | </article>
| + | <p>You can find us in the following websites:</p> |
| − | | + | <ul> |
| − | <article class="col-xs-12 col-sm-12 col-md-8 col-md-offset-2 modeling"> | + | < li><a href="https:// www. facebook.com/ IgemTecMonterrey?fref= ts"> iGEM ITESM in Facebook</ a></ li> |
| − | <p>After infection, the cells will die because of it with an specific death rate <strong>d</strong>. After it's death, virions will be released, but only a certain fraction of them will continue to cause infection, because of this we consider an effective rate of virions production <strong>N</strong>. This is represented in the following reaction:</p>
| + | < li><<a href="https:// twitter.com/ iGEMTecMty"> iGEM ITESM in Twitter</ a></ li> |
| − | | + | </ul> |
| − | <div class="col-md-7 col-md-offset-4 col-sm-9 col-sm-offset-2 col-xs-9 col-xs-offset-2"><img src="rsc/Tec-Monterrey_Formula3.jpg" class="img-responsive f3"></div>
| + | |
| − | <div class="col-md-1 col-sm-1 col-xs-1"><p>(4)</p></div>
| + | |
| − | | + | |
| − | </article>
| + | |
| − | | + | |
| − | <article class="col-xs-12 col-sm-12 col-md-8 col-md-offset-2 modeling">
| + | |
| − | <p>From the reactions in (1) and the rates described in the previous paragraph, we get the following equations:</p>
| + | |
| − | <div class="col-md-9 col-md-offset-2 col-sm-9 col-sm-offset-2 col-xs-9 col-xs-offset-2"><img src="rsc/Tec-Monterrey_Formula4.jpg" class="img-responsive"></div>
| + | |
| − | <div class="col-md-1 col-sm-1 col-xs-1"><p>(5)</p><br><br><br><p>(6)</p></div>
| + | |
| − | </article>
| + | |
| − | | + | |
| − | <article class="col-xs-12 col-sm-12 col-md-8 col-md-offset-2 modeling">
| + | |
| − | <h1>Quasi-steady state assumption</h1> | + | |
| − | <p>Since the complex is a temporary interaction, in the order of seconds, due to regular movement, the changes in <strong>C<sub>P</sub></strong> are in a much faster time-scale than the rest of the system, which develops during a couple of days, therefore it may be treated with a quasi-steady state approximation:</p> | + | |
| − | <div class="col-md-9 col-md-offset-2 col-sm-9 col-sm-offset-2 col-xs-9 col-xs-offset-2"><img src="rsc/Tec-Monterrey_Formula5.jpg" class="img-responsive f5"></div>
| + | |
| − | <div class="col-md-1 col-sm-1 col-xs-1"><p>(7)</p></div>
| + | |
| − | </article>
| + | |
| − | | + | |
| − | <article class="col-xs-12 col-sm-12 col-md-8 col-md-offset-2 modeling">
| + | |
| − | <p>If we substitute (7) back into (2), (5) and (6), we get:</p>
| + | |
| − | <div class="col-md-9 col-md-offset-2 col-sm-9 col-sm-offset-2 col-xs-9 col-xs-offset-2"><img src="rsc/Tec-Monterrey_Formula6.jpg" class="img-responsive"></div>
| + | |
| − | <div class="col-md-1 col-sm-1 col-xs-1">
| + | |
| − | <br><p>(8)</p><br><br><br><p>(9)</p><br><br><br><p>(10)</p><br>
| + | |
| − | </div>
| + | |
| − | </article>
| + | |
| − | | + | |
| − | <article class="col-xs-12 col-sm-12 col-md-8 col-md-offset-2 modeling">
| + | |
| − | <p>where we have defined <strong>K≡(k<sub>1</sub>k<sub>2</sub>)/(k<sub>-1</sub>+k<sub>2</sub>)</strong>.It should be noticed that this is equivalent to the following system:</p>
| + | |
| − | <div class="col-md-9 col-md-offset-2 col-sm-9 col-sm-offset-2 col-xs-9 col-xs-offset-2"><img src="rsc/Tec-Monterrey_Formula7.jpg" class="img-responsive"></div>
| + | |
| − | <div class="col-md-1 col-sm-1 col-xs-1">
| + | |
| − | <div class="col-md-1 col-sm-1 col-xs-1"><br><p>(11)</p></div>
| + | |
| − | </article>
| + | |
| − | | + | |
| − | <article class="col-xs-12 col-sm-12 col-md-8 col-md-offset-2 modeling">
| + | |
| − | <p>Where <strong>k</strong> serves as a parameter that describes the affinity between the baculovirus and the <strong><span>Sf9</span></strong>, mainly because of the interactions in the membrane of the cell. On the other side, <strong>N</strong> tells how effective is the production of new virions due to the lytic infection. It contains the information of the internal process in the cell, as well as the externalization.</p>
| + | |
| − | </article>
| + | |
| − | | + | |
| − | <article class="col-xs-12 col-sm-12 col-md-8 col-md-offset-2 modeling">
| + | |
| − | <h1>A second approach: Delay differential equations</h1>
| + | |
| − | <p>We also consider a second approach in the term of the virions production. The virions are not produced instantaneously after the infection of a cell. We consider a period <strong>Τ<sub>IV</sub></strong> after infection before starting the production. Also, the cell only produces virions while they are alive, from this we have to consider an average period <strong>Τ<sub>D</sub></strong> from the moment the cell is infected until the moment that it finally dies.</p><br> | + | |
| − | <p>Consider an instant <strong>t<sub>I</sub></strong>, at this moment we consider that a certain amount of <strong>dC<sub>I</sub></strong> new healthy cells are infected. By definition this differential is given by <strong>dC<sub>I</sub>=C'<sub>I</sub>(t<sub>I</sub>)dt<sub>I</sub></strong>. We will work under the assumption that every cell has the same behavior after infection. They should produce only while they are alive, from this the production rate should have a positive value only in [<strong>t<sub>I</sub></strong>+<strong>Τ<sub>IV</sub></strong>,<strong>t<sub>I</sub></strong>+<strong>Τ<sub>D</sub></strong>] and be zero everywhere else, from this we know we are looking for a production rate of the form:</p> | + | |
| | </article> | | </article> |
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