Difference between revisions of "Team:Warwick/Modelling6"
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| − | < | + | <p><img src="https://static.igem.org/mediawiki/2015/4/42/Warwickbubbles4.png" height="120px" width="800px" border="1px"></p> |
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| + | There was an inherent issue with a previous model in that the structure of the created shape would change as cells grew. We needed to model how they would grow and how the placement of the cells in the start would affect growth. | ||
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| + | <p>________________________________________________________________________________________________________________________________________________</p><h5>Stochastic Modelling for Cell Growth</h5> | ||
| + | We wanted to understand how the placement of cells changes as time progresses. Cells divide, roughly in the same direction in which they were formed. To model cell division we imagined them situated on a Cartesian coordinate system, and division to place on a polar coordinate system with the original cell as the origin. The population count is modelled with the Gompertz function. To decide which direction the division occur we used two criteria: | ||
<br>1. It must not overlap other cells or DNA | <br>1. It must not overlap other cells or DNA | ||
<br>2. The probability is weighted by a normal distribution with the peak in the same direction as the previous generational division | <br>2. The probability is weighted by a normal distribution with the peak in the same direction as the previous generational division | ||
<br>The user inputs the DNA structure, the standard deviation for the normal distribution, and the maximum number of cells it should model. It then outputs an animation of the cell community as it develops. | <br>The user inputs the DNA structure, the standard deviation for the normal distribution, and the maximum number of cells it should model. It then outputs an animation of the cell community as it develops. | ||
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| − | <h5 | + | <p>________________________________________________________________________________________________________________________________________________</p><h5>Simple Exponential Model and Gompertz Function</h5> |
<p> | <p> | ||
<p style="float: right;"><img src="https://static.igem.org/mediawiki/2015/6/63/Warwickgompertz.png" align="right" height="150px" width="270px" border="1px"></p> | <p style="float: right;"><img src="https://static.igem.org/mediawiki/2015/6/63/Warwickgompertz.png" align="right" height="150px" width="270px" border="1px"></p> | ||
<p style="float: left;"><img src="https://static.igem.org/mediawiki/2015/b/b5/Warwickexponential_equation.png" height="300px" width="180px" border="1px"></p> | <p style="float: left;"><img src="https://static.igem.org/mediawiki/2015/b/b5/Warwickexponential_equation.png" height="300px" width="180px" border="1px"></p> | ||
| − | The equation to the left is the simplest model possible to model cell growth and just displays an exponential increase in cells with respect to time. This is a bad model because E.coli has an upper limit to the number of cells that can survive in a given location before they begin to fight for the same resources and some will die. | + | The equation to the left is the simplest model possible to model cell growth and just displays an exponential increase in cells with respect to time. This is a bad model because <i>E.coli</i> has an upper limit to the number of cells that can survive in a given location before they begin to fight for the same resources and some will die. |
<br> | <br> | ||
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</p> | </p> | ||
| − | <h5 | + | <p>________________________________________________________________________________________________________________________________________________</p><h5>Comparing the two</h5> |
<p> | <p> | ||
<img src="https://static.igem.org/mediawiki/2015/f/f1/Warwickgrpahsgompertz.png" class="pics" alt=""> | <img src="https://static.igem.org/mediawiki/2015/f/f1/Warwickgrpahsgompertz.png" class="pics" alt=""> | ||
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</p> | </p> | ||
| − | + | <p>________________________________________________________________________________________________________________________________________________</p> <h5>Cell growth with Interactions</h5> | |
<p> | <p> | ||
Our idea of forcing different cell types to live together in close vicinity will alter this model however. Taking for example forcing 3 cell types together; | Our idea of forcing different cell types to live together in close vicinity will alter this model however. Taking for example forcing 3 cell types together; | ||
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| − | <h5 | + | <p>________________________________________________________________________________________________________________________________________________</p><h5>How Constants affect Growth</h5> |
<p> | <p> | ||
<p style="float: right;"><img src="https://static.igem.org/mediawiki/2015/c/c1/Warwickcellgrowthgraph.png" align="right" height="500px" width="600px" border="1px"></p> | <p style="float: right;"><img src="https://static.igem.org/mediawiki/2015/c/c1/Warwickcellgrowthgraph.png" align="right" height="500px" width="600px" border="1px"></p> | ||
Latest revision as of 20:39, 17 September 2015
