document.getElementById("tab1").innerHTML = '<h2>Introduction</h2><p>We wanted to evaluate the effectiveness of our system in the real intestine of a human. Since it requires a lot of ethical consideration and animal trials to test on real humans we decided to construct a model instead. The model will also give us insight into what parameters are most important when improving our system. Since the thought out medicine is thought of as a pill, see Policy & Practise, this is the premiss we will evaluate our modeling around.<br><br>Our final model is able to produce both a “density map” showing the small intestine as a two dimensional landscape and graphs of the total amount of cells and molecules over time. The first model is more heavy to run and can therefore only run at limited time intervals, while the later model is able to run at much longer intervals. The density map is good for analysing movement of molecules and cells in the domain, while the graphs are nice to show total effect of the system.</p><img src="https://static.igem.org/mediawiki/2014/7/73/Populationsummary1_Uppsala14.PNG"></img><p><i>Figure 1: Mathematical model of our system.</i></p><h2>Design</h2><p>To create our model we created a set of PDE:s to represent our system, see figure 1. The change of state is determined via a set of heaviside step functions(noted as theta) that are controlled by threshold concentrations noted as K_i, where i indicates which density is related to the threshold. Y.enterocolitica have been found to be immobile at 37 degrees celsius and do therefore not have a diffusion term. All parameters are defined in figure 2. You can read more about our design under the design page.</p><br><table id="partsT"><tr><th>Parameter</th><th>Value</th><th>Source</th></tr><tr><td>D_b</td><td>3*10^-4 mm^2/s</td><td>5</td></tr><tr><td>D_c</td><td>4.2*10^-5 mm^2/s</td><td>1</td></tr><tr><td>D_o</td><td>4.9*10^-6 mm^2/s</td><td>2</td></tr><tr><td>K_c</td><td>2.25*10^-7 molecules/mL</td><td>3</td></tr><tr><td>K_a</td><td>10^-8 molecules/mL</td><td>est.</td></tr><tr><td>beta_c</td><td>15.625 s^-1</td><td>1</td></tr><tr><td>beta_o</td><td>1 s^-1</td><td>est.</td></tr><tr><td>etac</td><td>1/1200</td><td>ets.</td></tr><tr><td>eta_o</td><td>1/1200</td><td>4</td></tr></table><p><i>Table 1. Table of parameter values</i></p><h2>Results</h2><p>The model was split into two scenarios depending if the Bactissile could coexist on the Y.enterocolitica or not. Being able to coexist with Y.enterocolitica was 6 times as effective as the case where the Bactissile could only surround the Y.enterocolitica, figure 1 and 2. Both models showed that the production of colicin is the rate limiting step, figure 3 and 4, while OHHL threshold and diffusion coefficients importance differed. In the coexist model it was only needed for the OHHL threshold to be less than the OHHL initial concentration. However in the non coexist model both OHHL and diffusion coefficients changes had a significant impact on the time to kill all Y.enterocolitica.</p<table><tr><td><p><i>Figure 2: Bactissile and Y.enterocolitica coexists. 100s until elimination</i></p></td><td><img class="main_pic_left" src="https://static.igem.org/mediawiki/2014/4/48/Populationtest2_Uppsala14.jpg"></td></tr><tr><td><img class="main_pic_left" src="https://static.igem.org/mediawiki/2014/8/83/Populationtest3_Uppsala14.jpg"></td><td><p><i>Figure 3: Bactissile and Y.enterocolitica does not coexist. 10% remains after 600s.</i></p></td></tr><tr><td><p><i>Figure 4:  Coexist model, Y-axis: Time to eliminate the initial Y.enterocolitica colony. X-axis: Multiplier of the original production rate.</i></p></td><td><img class="main_pic_left" src="https://static.igem.org/mediawiki/2014/a/a0/Populationtest6_Uppsala14.png"></td></tr><tr><td><img class="main_pic_left" src="https://static.igem.org/mediawiki/2014/0/0f/Populationtest9_Uppsala14.png"></td><td><p><i>Figure 5:  Non coexist model, Y-axis: Time to eliminate the initial Y.enterocolitica colony. X-axis: Multiplier of the original production rate.</i></p></td></tr></table>';