http://2008.igem.org/wiki/index.php?title=Team:BCCS-Bristol/Modeling&feed=atom&action=historyTeam:BCCS-Bristol/Modeling - Revision history2024-03-29T10:52:28ZRevision history for this page on the wikiMediaWiki 1.16.5http://2008.igem.org/wiki/index.php?title=Team:BCCS-Bristol/Modeling&diff=60331&oldid=prevIanMiles: /* Bacteria to Particle Adhesion */2008-10-22T15:01:45Z<p><span class="autocomment">Bacteria to Particle Adhesion</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>improve performance even further.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>improve performance even further.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-AdhesionTS_Control.jpg|center|thumb|400px|'''Figure 6a: Average Distance Travelled by Particle Time Series - <del class="diffchange diffchange-inline">With </del>Chemotactic Gradient''']]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-AdhesionTS_Control.jpg|center|thumb|400px|'''Figure 6a: Average Distance Travelled by Particle Time Series - <ins class="diffchange diffchange-inline">Control (Without </ins>Chemotactic Gradient<ins class="diffchange diffchange-inline">)</ins>''']]</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-AdhesionTS_Std.jpg|center|thumb|400px|'''Figure 6b: Average Distance Travelled by Particle Time Series - <del class="diffchange diffchange-inline">Control (Without </del>Chemotactic Gradient<del class="diffchange diffchange-inline">)</del>''']]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-AdhesionTS_Std.jpg|center|thumb|400px|'''Figure 6b: Average Distance Travelled by Particle Time Series - <ins class="diffchange diffchange-inline">With </ins>Chemotactic Gradient''']]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Adhesion.jpg|center|thumb|400px|'''Figure 7: Average Speed Comparison''' - Average particle speeds for varying numbers of adhered bacteria. Lines of best fit, using least squared error, have been used to give the overall trend]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Adhesion.jpg|center|thumb|400px|'''Figure 7: Average Speed Comparison''' - Average particle speeds for varying numbers of adhered bacteria. Lines of best fit, using least squared error, have been used to give the overall trend]]</div></td></tr>
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</table>IanMileshttp://2008.igem.org/wiki/index.php?title=Team:BCCS-Bristol/Modeling&diff=60328&oldid=prevIanMiles: /* Bacteria to Particle Adhesion */2008-10-22T15:00:42Z<p><span class="autocomment">Bacteria to Particle Adhesion</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==== Bacteria to Particle Adhesion ====</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==== Bacteria to Particle Adhesion ====</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">To evaluate the effect particle adhesion would have on overall movement, simulations were generated with varying numbers of bacteria randomly adhered to a single particle. The number of bacteria ranged from 1 to 15 with a static chemotatic gradient increasing in the x direction. Each configuration was run 40 times to calculate average behaviour. A control was included which omitted the chemotatic gradient.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Figures 6a & 6b displays results from these simulations in terms of movement up the chemotatic</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">gradient for differing numbers of adhered bacteria, and for standard and control scenarios.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">With a chemotatic gradient present it is evident that the bacteria are still able to carry out</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">chemotaxis, moving the particle in the correct direction. As the number of bacteria increases</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">so to does the average distance travelled by the particle. The rate of this increase is rapid for 1</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">to 5 bacteria, however, from 6 onwards the rate decreases significantly and ordering becoming</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">mixed.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">When investigating this feature, video output from the simulations was consulted. These</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">illustrated that as the number of bacteria increased, the movement of each bacterium became</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">further restricted. We speculate that this interference leads to a massive decrease in variability</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">of particle movement, with the resultant force becoming an average of the group and additional</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">bacteria having less of an impact on the total resultant force. This would lead to asymptotic type</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">behaviour as the number of bacteria increases and would account for the significant drop off in</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">particle movement. Figure 7 appears to support this showing the difference in average speed</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">reducing as number of bacteria increases. To verify this claim a much larger set of simulations</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">would need to be run to better understand the exact statistics of the systems. This was not</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">possible due to time constraints on the project.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">In both figures the control simulations, as expected, showed random movement about the</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">origin with average speed remaining near 0.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">One of the interesting side effects of adhesion is the increase in efficiency of particle movement</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">speed. With each bacterium exerting a force for a longer period, when compared to</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">collision events alone, the average speed is much greater. For example, the average speed of</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">movement with adhesion remains above 0.2mms<sup>-1</sup> even with only a single bacterium adhered,</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">while our recruitment method only reaches 0.14mms<sup>-1</sup> for a density where 30% of the area</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">is bacteria. By combining adhesion with our existing construction rules it may be possible to</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">improve performance even further.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-AdhesionTS_Control.jpg|center|thumb|400px|'''Figure 6a: Average Distance Travelled by Particle Time Series - With Chemotactic Gradient''']]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-AdhesionTS_Control.jpg|center|thumb|400px|'''Figure 6a: Average Distance Travelled by Particle Time Series - With Chemotactic Gradient''']]</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-AdhesionTS_Std.jpg|center|thumb|400px|'''Figure <del class="diffchange diffchange-inline">6a</del>: Average Distance Travelled by Particle Time Series - Control (Without Chemotactic Gradient)''']]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-AdhesionTS_Std.jpg|center|thumb|400px|'''Figure <ins class="diffchange diffchange-inline">6b</ins>: Average Distance Travelled by Particle Time Series - Control (Without Chemotactic Gradient)''']]</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Adhesion.jpg|center|thumb|400px|'''Figure <del class="diffchange diffchange-inline">7a</del>: Average Speed Comparison''' - Average particle speeds for varying numbers of adhered bacteria. Lines of best fit, using least squared error, have been used to give the overall trend]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Adhesion.jpg|center|thumb|400px|'''Figure <ins class="diffchange diffchange-inline">7</ins>: Average Speed Comparison''' - Average particle speeds for varying numbers of adhered bacteria. Lines of best fit, using least squared error, have been used to give the overall trend]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Simulation Movies==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Simulation Movies==</div></td></tr>
</table>IanMileshttp://2008.igem.org/wiki/index.php?title=Team:BCCS-Bristol/Modeling&diff=60321&oldid=prevIanMiles: /* Comparing Construction Rules */2008-10-22T14:54:23Z<p><span class="autocomment">Comparing Construction Rules</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>single run making multiple batches difficult. All densities were standardised by using the ratio</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>single run making multiple batches difficult. All densities were standardised by using the ratio</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>of bacteria and simulated environment areas. This allowed simulations with slightly differing</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>of bacteria and simulated environment areas. This allowed simulations with slightly differing</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>configurations to be compared without bias. Control simulations containing no chemotatic <del class="diffchange diffchange-inline">gra-</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>configurations to be compared without bias. Control simulations containing no chemotatic <ins class="diffchange diffchange-inline">gradient </ins>for each rule type were also run and showed average speeds <ins class="diffchange diffchange-inline">of approximately </ins>0, even as bacteria density</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">25</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">dient </del>for each rule type were also run and showed average speeds <del class="diffchange diffchange-inline">� </del>0, even as bacteria density</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>increased. For this reason no further discussion of the control simulations will be made.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>increased. For this reason no further discussion of the control simulations will be made.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Averaged results for different densities and rules are shown in Figure <del class="diffchange diffchange-inline">3.6(a)</del>. Large amounts</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Averaged results for different densities and rules are shown in Figure <ins class="diffchange diffchange-inline">5a</ins>. Large amounts</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>of variation are present for each rule, with co-ordination the only one giving positive speeds</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>of variation are present for each rule, with co-ordination the only one giving positive speeds</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>for all data points. Standard deviations of the results gave values of 0.0226 for directed movement,</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>for all data points. Standard deviations of the results gave values of 0.0226 for directed movement,</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>of interactions between bacteria and particles being much less, allowing the random element of</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>of interactions between bacteria and particles being much less, allowing the random element of</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>bacteria chemotaxis to dominates the small bias in direction.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>bacteria chemotaxis to dominates the small bias in direction.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>To perform a comparison of efficiency between rules, we considered the scaling characteristics,</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>To perform a comparison of efficiency between rules, we considered the scaling characteristics,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>assuming a linear relationship between bacteria density and average particle speed. Taking</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>assuming a linear relationship between bacteria density and average particle speed. Taking</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>and took the gradient of this as the approximate particle speed. Another line of best fit was</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>and took the gradient of this as the approximate particle speed. Another line of best fit was</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>then calculated using these approximations, leading to the overall average scaling law shown</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>then calculated using these approximations, leading to the overall average scaling law shown</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>in Figure <del class="diffchange diffchange-inline">3</del>.<del class="diffchange diffchange-inline">6(b). From these calculations the scaling factor of each rule type was found, giving</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>in Figure <ins class="diffchange diffchange-inline">5b</ins>.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">1.3334 for directed movement, 0.3312 for particle sensing, 1.2325 for co-ordination and 4.2948</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">for recruitment.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The ordering of efficiencies seems to match what intuition would lead to. Particle sensing</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The ordering of efficiencies seems to match what intuition would lead to. Particle sensing</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>performs the worse, most likely due to fact that bacteria will initially be performing a random</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>performs the worse, most likely due to fact that bacteria will initially be performing a random</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>particle surface can impart a force in the required direction, the small bias in movement can</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>particle surface can impart a force in the required direction, the small bias in movement can</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>only take effect in half all collision events, reducing overall efficiency.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>only take effect in half all collision events, reducing overall efficiency.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Both short range co-ordination and directed movement produce very similar efficiencies.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Both short range co-ordination and directed movement produce very similar efficiencies.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>This can be accounted for due to directed movement being an extreme case of co-ordination,</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>This can be accounted for due to directed movement being an extreme case of co-ordination,</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Bacteria moving randomly further away therefore, have little effect on the overall movement</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Bacteria moving randomly further away therefore, have little effect on the overall movement</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>speed.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>speed.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Long range recruitment produces what seems to be a huge improvement in efficiency. This</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Long range recruitment produces what seems to be a huge improvement in efficiency. This</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>may be due to the increased density it produces near particles, however, compared to the</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>may be due to the increased density it produces near particles, however, compared to the</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>influencing chemotaxis in a negative way. Further tests would need to be carried out to verify</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>influencing chemotaxis in a negative way. Further tests would need to be carried out to verify</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>this hypothesis.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>this hypothesis.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Due to the large variability in the underlying data, it is difficult to place any confidence on</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Due to the large variability in the underlying data, it is difficult to place any confidence on</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>the predictions of rule efficiency. To improve the accuracy of these results it would be necessary</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>the predictions of rule efficiency. To improve the accuracy of these results it would be necessary</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>space is fully sampled. Even so, these preliminary studies do provide support, showing that</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>space is fully sampled. Even so, these preliminary studies do provide support, showing that</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>co-ordination with recruitment is likely to enable more efficient use of any available resources.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>co-ordination with recruitment is likely to enable more efficient use of any available resources.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-ComparisonRulesRawResults.jpg|center|thumb|400px|'''Figure 5a: Simulation Results''']]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-ComparisonRulesRawResults.jpg|center|thumb|400px|'''Figure 5a: Simulation Results''']]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Comparison_Eff.jpg|center|thumb|400px|'''Figure 5b: Estimated Speeds''' - Lines of best fit using least squared error were generated from data of each individual run. Solid lines represent the range of values over which data was available and dotted lines show the predicted results.]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Comparison_Eff.jpg|center|thumb|400px|'''Figure 5b: Estimated Speeds''' - Lines of best fit using least squared error were generated from data of each individual run. Solid lines represent the range of values over which data was available and dotted lines show the predicted results.]]</div></td></tr>
</table>IanMileshttp://2008.igem.org/wiki/index.php?title=Team:BCCS-Bristol/Modeling&diff=60317&oldid=prevIanMiles: /* Comparing Construction Rules */2008-10-22T14:50:45Z<p><span class="autocomment">Comparing Construction Rules</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==== Comparing Construction Rules ====</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==== Comparing Construction Rules ====</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">To compare the efficiency of differing construction rules, we altered the bacteria density to see</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">how the average speed of particle movement was affected. Due to limited available time in running</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">the simulations, only 10 runs, of 10 minutes duration for each density could be performed</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">and the range of densities differed depending on the execution times of the simulations. For</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">example, some of the higher density directed movement simulations took 5 days to complete a</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">single run making multiple batches difficult. All densities were standardised by using the ratio</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">of bacteria and simulated environment areas. This allowed simulations with slightly differing</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">configurations to be compared without bias. Control simulations containing no chemotatic gra-</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">25</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">dient for each rule type were also run and showed average speeds � 0, even as bacteria density</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">increased. For this reason no further discussion of the control simulations will be made.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Averaged results for different densities and rules are shown in Figure 3.6(a). Large amounts</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">of variation are present for each rule, with co-ordination the only one giving positive speeds</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">for all data points. Standard deviations of the results gave values of 0.0226 for directed movement,</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">0.0203 for particle sensing, 0.0511 for co-ordination and 0.0140 for recruitment. Increased</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">variation is also present at lower densities. This is likely to have been caused by the number</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">of interactions between bacteria and particles being much less, allowing the random element of</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">bacteria chemotaxis to dominates the small bias in direction.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">To perform a comparison of efficiency between rules, we considered the scaling characteristics,</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">assuming a linear relationship between bacteria density and average particle speed. Taking</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">the results from each individual simulation run, we fitted a least squared error line of best fit</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">and took the gradient of this as the approximate particle speed. Another line of best fit was</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">then calculated using these approximations, leading to the overall average scaling law shown</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">in Figure 3.6(b). From these calculations the scaling factor of each rule type was found, giving</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">1.3334 for directed movement, 0.3312 for particle sensing, 1.2325 for co-ordination and 4.2948</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">for recruitment.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">The ordering of efficiencies seems to match what intuition would lead to. Particle sensing</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">performs the worse, most likely due to fact that bacteria will initially be performing a random</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">walk, making it equally probable that they will hit any point on a particle. As only half the</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">particle surface can impart a force in the required direction, the small bias in movement can</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">only take effect in half all collision events, reducing overall efficiency.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Both short range co-ordination and directed movement produce very similar efficiencies.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">This can be accounted for due to directed movement being an extreme case of co-ordination,</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">where the range fills the entire simulated environment. The reason for the similarity is likely</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">caused by the range used in the co-ordination simulations being large enough that densities</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">of bacteria moving towards the goal attractant are similar around the particle in both cases.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Bacteria moving randomly further away therefore, have little effect on the overall movement</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">speed.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Long range recruitment produces what seems to be a huge improvement in efficiency. This</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">may be due to the increased density it produces near particles, however, compared to the</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">other rules the results have been generated from a very narrow range of densities. This means</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">predictions have had to be made over much greater density ratios. The major outstanding</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">question of this method is if the increased density only has beneficial effects. For example,</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">there may be a point where bacteria with bacteria interactions start to become a large factor,</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">influencing chemotaxis in a negative way. Further tests would need to be carried out to verify</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">this hypothesis.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Due to the large variability in the underlying data, it is difficult to place any confidence on</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">the predictions of rule efficiency. To improve the accuracy of these results it would be necessary</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">to run much large sets of simulations over a wider range of densities, to ensure that the statistical</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">space is fully sampled. Even so, these preliminary studies do provide support, showing that</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">co-ordination with recruitment is likely to enable more efficient use of any available resources.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-ComparisonRulesRawResults.jpg|center|thumb|400px|'''Figure 5a: Simulation Results''']]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-ComparisonRulesRawResults.jpg|center|thumb|400px|'''Figure 5a: Simulation Results''']]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Comparison_Eff.jpg|center|thumb|400px|'''Figure 5b: Estimated Speeds''' - Lines of best fit using least squared error were generated from data of each individual run. Solid lines represent the range of values over which data was available and dotted lines show the predicted results.]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Comparison_Eff.jpg|center|thumb|400px|'''Figure 5b: Estimated Speeds''' - Lines of best fit using least squared error were generated from data of each individual run. Solid lines represent the range of values over which data was available and dotted lines show the predicted results.]]</div></td></tr>
</table>IanMileshttp://2008.igem.org/wiki/index.php?title=Team:BCCS-Bristol/Modeling&diff=60314&oldid=prevIanMiles: /* Basic Chemotaxis Model */2008-10-22T14:48:38Z<p><span class="autocomment">Basic Chemotaxis Model</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==== Basic Chemotaxis Model ====</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==== Basic Chemotaxis Model ====</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">To assess that the chemotaxis model was producing bacteria movement in the correct direction,</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">a simulation was created where 1000 bacteria were placed uniformly at random in an area of</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">size (100, 300) centred at the origin. A static chemotatic gradient was generated increasing in</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">the x direction and all distances were analysed using the average x component from x = 0. Each</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">simulation lasted 5 minutes and was run 300 times to allow for the distribution of movement</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">speeds to be approximated. For comparison, a control was also produced using the same</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">configuration, however, without a chemotactic gradient.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">A time series plot of the distance travelled up the chemotatic gradient can be seen in Figure</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">4a. This perfectly illustrates that even though chemotaxis contains stochastic elements, the</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">bias in run length permits directed movement. Also, as we would expect the control shows an</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">average distance of 0 for the entire simulation.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">To generate the probability distribution of movement speeds, each simulation run had a line</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">of best fit calculated using least squared error. This was taken to be approximately the speed of</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">movement up the gradient. These speeds were then plotted as a histogram to give the overall</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">distribution, shown in Figure 4b. Both histograms roughly show a normal distribution with</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">mean values of 1.2mms<sup>-1</sup> and 0mms<sup>-1</sup>, for with and without chemotatic gradient respectively.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">The standard deviation of both is also similar, approximately 0.2mms<sup>-1</sup>.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">These results confirm that our model is producing movement in the correct direction. To</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">further verify the accuracy of the movement speeds, it would have been useful to compare our</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">values to experimental results. The difficulty in measuring the individual locations of large</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">groups of bacteria made this task prohibitive, however, may be something that could be carried</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">out in the future.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Chemo_TS.jpg|center|thumb|400px|'''Figure 4a: Average Distance Travelled''']]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Chemo_TS.jpg|center|thumb|400px|'''Figure 4a: Average Distance Travelled''']]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Chemo_Dist.jpg|center|thumb|400px|'''Figure 4b: Average Speed Distribution''']]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Chemo_Dist.jpg|center|thumb|400px|'''Figure 4b: Average Speed Distribution''']]</div></td></tr>
</table>IanMileshttp://2008.igem.org/wiki/index.php?title=Team:BCCS-Bristol/Modeling&diff=60302&oldid=prevIanMiles: /* Transport */2008-10-22T14:19:38Z<p><span class="autocomment">Transport</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>over time. A delta input of size 50 was used and the concentration distribution calculated over</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>over time. A delta input of size 50 was used and the concentration distribution calculated over</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>a 30 minute period. Figure 2 shows the distribution at 5 minute intervals. A value of 0.23 s<sup>-1</sup></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>a 30 minute period. Figure 2 shows the distribution at 5 minute intervals. A value of 0.23 s<sup>-1</sup></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>was selected for the diffusion co-efficient<del class="diffchange diffchange-inline">, taken from [10]</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>was selected for the diffusion co-efficient.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>As we do not know the maximal expression level C<sub>pMax</sub> of the response regulator CpxR it</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>As we do not know the maximal expression level C<sub>pMax</sub> of the response regulator CpxR it</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>was difficult to estimate the rate that an individual cell would produce AHL. For this reason</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>was difficult to estimate the rate that an individual cell would produce AHL. For this reason</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>we attempted to concentrate on understanding the distance over which a threshold value was</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>we attempted to concentrate on understanding the distance over which a threshold value was</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>exceeded. The receiver GRN has been shown to be sensitive to low levels of AHL, see <del class="diffchange diffchange-inline">Section</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>exceeded. The receiver GRN has been shown to be sensitive to low levels of AHL, see <ins class="diffchange diffchange-inline">previous section</ins>, and so we assumed a large response would occur at concentrations of 3 and greater.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">3.1.3</del>, and so we assumed a large response would occur at concentrations of 3 and greater.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Transport.jpg|center|thumb|400px|'''Figure 2: Transport Results''' - Concentration distribution over a 30 min period for an initial delta function input at 0 of 50]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Transport.jpg|center|thumb|400px|'''Figure 2: Transport Results''' - Concentration distribution over a 30 min period for an initial delta function input at 0 of 50]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
</table>IanMileshttp://2008.igem.org/wiki/index.php?title=Team:BCCS-Bristol/Modeling&diff=60239&oldid=prevIanMiles: /* Transport */2008-10-22T12:19:22Z<p><span class="autocomment">Transport</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>For the transport aspect of the system we investigated how the concentration distribution varied</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>For the transport aspect of the system we investigated how the concentration distribution varied</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>over time. A delta input of size 50 was used and the concentration distribution calculated over</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>over time. A delta input of size 50 was used and the concentration distribution calculated over</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>a 30 minute period. Figure 2 shows the distribution at 5 minute intervals. A value of 0.23 s<<del class="diffchange diffchange-inline">super</del>>-1</<del class="diffchange diffchange-inline">super</del>></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>a 30 minute period. Figure 2 shows the distribution at 5 minute intervals. A value of 0.23 s<<ins class="diffchange diffchange-inline">sup</ins>>-1</<ins class="diffchange diffchange-inline">sup</ins>></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>was selected for the diffusion co-efficient, taken from [10].</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>was selected for the diffusion co-efficient, taken from [10].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>As we do not know the maximal expression level C<sub>pMax</sub> of the response regulator CpxR it</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>As we do not know the maximal expression level C<sub>pMax</sub> of the response regulator CpxR it</div></td></tr>
</table>IanMileshttp://2008.igem.org/wiki/index.php?title=Team:BCCS-Bristol/Modeling&diff=60238&oldid=prevIanMiles: /* Transport */2008-10-22T12:18:31Z<p><span class="autocomment">Transport</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==== Transport ====</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==== Transport ====</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">For the transport aspect of the system we investigated how the concentration distribution varied</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">over time. A delta input of size 50 was used and the concentration distribution calculated over</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">a 30 minute period. Figure 2 shows the distribution at 5 minute intervals. A value of 0.23 s<super>-1</super></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">was selected for the diffusion co-efficient, taken from [10].</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">As we do not know the maximal expression level C<sub>pMax</sub> of the response regulator CpxR it</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">was difficult to estimate the rate that an individual cell would produce AHL. For this reason</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">we attempted to concentrate on understanding the distance over which a threshold value was</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">exceeded. The receiver GRN has been shown to be sensitive to low levels of AHL, see Section</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">3.1.3, and so we assumed a large response would occur at concentrations of 3 and greater.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Transport.jpg|center|thumb|400px|'''Figure 2: Transport Results''' - Concentration distribution over a 30 min period for an initial delta function input at 0 of 50]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Transport.jpg|center|thumb|400px|'''Figure 2: Transport Results''' - Concentration distribution over a 30 min period for an initial delta function input at 0 of 50]]</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==== Reciever ====</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==== Reciever ====</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>For the receiver we wanted to understand how varying AHL concentration altered output of our</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>For the receiver we wanted to understand how varying AHL concentration altered output of our</div></td></tr>
</table>IanMileshttp://2008.igem.org/wiki/index.php?title=Team:BCCS-Bristol/Modeling&diff=60236&oldid=prevIanMiles: /* Sender */2008-10-22T12:16:23Z<p><span class="autocomment">Sender</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=== Gene Regulatory Network ===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=== Gene Regulatory Network ===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==== Sender ====</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==== Sender ====</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">To assess the sender GRN we were interested in how the strength of the response regulator C<sub>pMax</sub> affects the overall dynamics and the final output of AHL. For a C<sub>pMax</sub> range of [0.1, 100] the qualitative behaviour of the GRN was the same, shown in Figure 1a for a C<sub>pMax</sub> value of 5 molecules per cell. Both GFP and LuxI proteins rise rapidly in the first hour, while CpxR and LuxI mRNA reaches a maximum after 60 minutes. The final LuxI mRNA concentration is low, causing the rate of increase in LuxI protein to slow towards the end of the simulation. In</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">contrast, both mRNA and protein concentrations of GFP continue to increase rapidly for the duration.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Figure 1b shows how the initial C<sub>pMax</sub> value effects AHL output over time. The behaviour is seen to be asymptotic, tending to a final concentration after approximately 400 minutes. The relationship between C<sub>pMax</sub> and AHL appears to be non-linear, with a rapid increase seen between 0.1 and 1. After this point the rate seems to slows, reaching a maximum near 4300. The huge variability in output AHL, even when the initial C<sub>pMax</sub> value is only varied by a small amount, makes it difficult to estimate a realistic output for a single cell. Experimental</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">techniques would need to be used to refine the accuracy of these results and allow for an appropriate CpMax value to be chosen. Overall, the GRN exhibits the correct dynamics, giving a sizeable AHL production in the presence of a CpxR response.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-SenderGRNGraph.jpg|center|thumb|400px|'''Figure 1a: Sender GRN Dynamics''' - Plots showing the mRNA and protein variation when C<sub>pMax</sub> = 5. All states were given initial values of 0]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-SenderGRNGraph.jpg|center|thumb|400px|'''Figure 1a: Sender GRN Dynamics''' - Plots showing the mRNA and protein variation when C<sub>pMax</sub> = 5. All states were given initial values of 0]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-AHL_Variation.jpg|center|thumb|400px|'''Figure 1b: AHL Output''' - Each line represents a different C<sub>pMax</sub> value.]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-AHL_Variation.jpg|center|thumb|400px|'''Figure 1b: AHL Output''' - Each line represents a different C<sub>pMax</sub> value.]]</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==== Transport ====</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==== Transport ====</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Transport.jpg|center|thumb|400px|'''Figure 2: Transport Results''' - Concentration distribution over a 30 min period for an initial delta function input at 0 of 50]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Transport.jpg|center|thumb|400px|'''Figure 2: Transport Results''' - Concentration distribution over a 30 min period for an initial delta function input at 0 of 50]]</div></td></tr>
</table>IanMileshttp://2008.igem.org/wiki/index.php?title=Team:BCCS-Bristol/Modeling&diff=60234&oldid=prevIanMiles: /* Reciever */2008-10-22T12:12:33Z<p><span class="autocomment">Reciever</span></p>
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<td colspan='2' style="background-color: white; color:black;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black;">Revision as of 12:12, 22 October 2008</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Transport.jpg|center|thumb|400px|'''Figure 2: Transport Results''' - Concentration distribution over a 30 min period for an initial delta function input at 0 of 50]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-Transport.jpg|center|thumb|400px|'''Figure 2: Transport Results''' - Concentration distribution over a 30 min period for an initial delta function input at 0 of 50]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==== Reciever ====</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==== Reciever ====</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">For the receiver we wanted to understand how varying AHL concentration altered output of our</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">signalling protein mCherry. This relationship is shown in Figure 3b. Availability of any AHL</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">causes a large increase in mCherry output, however, the rate of increase decays exponentially.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Output increases very little once a concentration of 3 molecules per cell has been reached.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">The internal dynamics of the receiver GRN is shown in Figure 3a for an input AHL</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">concentration of 3. From an initial starting condition with all other states at 0, the LuxR protein</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">can be seen to rise to a stable maximum concentration of 9 molecules per cell after 100 minutes.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">The LuxR–AHL complex also appears to have asymptotic behaviour tending to a concentration</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">of approximately 40 molecules per cell. Production of mCherry protein occurs rapidly once</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">LuxR concentration reaches a suitable level after 30 minutes. As LuxR in a living cell would</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">be maintained at a high level due to the constitutive promoter, the response would normally</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">be much quicker. With microscopes able to register individual mCherry proteins, the large</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">response to small AHL increases means the GRN behaves as we require, producing a visible</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">signal quickly.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-ReceiverGRN.jpg|center|thumb|400px|'''Figure 3a: Reciever GRN Dynamics''' - All states were given initial values of 0, apart from AHL concentration which was set to 3 molecules per cell]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-ReceiverGRN.jpg|center|thumb|400px|'''Figure 3a: Reciever GRN Dynamics''' - All states were given initial values of 0, apart from AHL concentration which was set to 3 molecules per cell]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-mCherryOutput.jpg|center|thumb|400px|'''Figure 3b: mCherry Output''' - Each line represents a different AHL concentration in molecules per cell]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:BCCS-Modelling-mCherryOutput.jpg|center|thumb|400px|'''Figure 3b: mCherry Output''' - Each line represents a different AHL concentration in molecules per cell]]</div></td></tr>
</table>IanMiles