Difference between revisions of "Team:Warwick/BindingAffinity"
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<h4>Binding Affinity Modelling</h4> | <h4>Binding Affinity Modelling</h4> | ||
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| − | + | <p><img src="https://static.igem.org/mediawiki/2015/6/64/Warwickbubbles1.png" height="120px" width="800px" border="1px"></p> | |
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| + | So you have a bunch of cells and binding sites that you want to join together. But it’s not that simple. There’s also a chance that they’ll unbind, and so this means that the binding and unbinding will form an equilibrium. This is exactly what we have tried to model. Ka represents the chance that they bind, and kd is the chance that they unbind. Here A represents the amount of cells, and B the amount of DNA binding sites. | ||
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| + | Once we find ka and kd, we use this information to tell biologists about expense, times for reactions, and what values for A and B they should use. | ||
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<p> | <p> | ||
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We will call the amount (concentration multiplied by volume) of the bacteria A, and the amount of binding site on the DNA (concentration multiplied by volume multiplied by binding sites per DNA sequence) as B. | We will call the amount (concentration multiplied by volume) of the bacteria A, and the amount of binding site on the DNA (concentration multiplied by volume multiplied by binding sites per DNA sequence) as B. | ||
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<br><i>The rate of change of A= the rate of unbinding-the rate of binding. </i> | <br><i>The rate of change of A= the rate of unbinding-the rate of binding. </i> | ||
<br>These rates are proportional to the amount of unbinded or binded molecules there are. | <br>These rates are proportional to the amount of unbinded or binded molecules there are. | ||
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<br>By letting | <br>By letting | ||
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<p><img src="https://static.igem.org/mediawiki/2015/2/25/Warwickmodeling2.png" align="left" height="300px" width="400px" border="1px"></p> | <p><img src="https://static.igem.org/mediawiki/2015/2/25/Warwickmodeling2.png" align="left" height="300px" width="400px" border="1px"></p> | ||
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<br>We can solve this differential equation using separation of variables. | <br>We can solve this differential equation using separation of variables. | ||
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<p><img src="https://static.igem.org/mediawiki/2015/4/4f/Warwickmodeling3.png" align="left" height="300px" width="400px" border="1px"></p><br><br><br><br> | <p><img src="https://static.igem.org/mediawiki/2015/4/4f/Warwickmodeling3.png" align="left" height="300px" width="400px" border="1px"></p><br><br><br><br> | ||
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<br>Where χ is an unknown constant. To find χ we set A=A_0 at t=0. | <br>Where χ is an unknown constant. To find χ we set A=A_0 at t=0. | ||
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<p><img src="https://static.igem.org/mediawiki/2015/d/d4/Warwickmodeling4.png" align="left" height="300px" width="400px" border="1px"></p><br><br><br><br><br><br><br> | <p><img src="https://static.igem.org/mediawiki/2015/d/d4/Warwickmodeling4.png" align="left" height="300px" width="400px" border="1px"></p><br><br><br><br><br><br><br> | ||
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<br>Note that 4ac-b^2 is negative, so the square root cannot be calculated. We now rearrange to cancel out imaginary parts. | <br>Note that 4ac-b^2 is negative, so the square root cannot be calculated. We now rearrange to cancel out imaginary parts. | ||
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<p><img src="https://static.igem.org/mediawiki/2015/6/66/Warwickmodeling5.png" align="left" height="320px" width="450px" border="1px"></p><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br> | <p><img src="https://static.igem.org/mediawiki/2015/6/66/Warwickmodeling5.png" align="left" height="320px" width="450px" border="1px"></p><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br> | ||
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<br>Therefore | <br>Therefore | ||
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<br><br><br><br><br><br><br><br><br><br> | <br><br><br><br><br><br><br><br><br><br> | ||
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<br>Substituting the values for a, b, and c. | <br>Substituting the values for a, b, and c. | ||
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<p><img src="https://static.igem.org/mediawiki/2015/1/1f/Warwickmodeling7.png" align="left" height="500px" width="700px" border="1px"></p><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br> | <p><img src="https://static.igem.org/mediawiki/2015/1/1f/Warwickmodeling7.png" align="left" height="500px" width="700px" border="1px"></p><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br> | ||
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<br>Let | <br>Let | ||
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<br>Then | <br>Then | ||
Latest revision as of 12:52, 17 September 2015
