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<center><img src="http://lh3.ggpht.com/coa07mhk/SPPlRq6tCVI/AAAAAAAAAKQ/9n4ghMQfa_E/s800/UniShefBanner.jpg"></center> | <center><img src="http://lh3.ggpht.com/coa07mhk/SPPlRq6tCVI/AAAAAAAAAKQ/9n4ghMQfa_E/s800/UniShefBanner.jpg"></center> | ||
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<td width="20%" align="center"><a href="https://2008.igem.org/Team:University_of_Sheffield"> | <td width="20%" align="center"><a href="https://2008.igem.org/Team:University_of_Sheffield"> | ||
<img src="http://lh3.ggpht.com/coa07mhk/SPPkus8pGzI/AAAAAAAAAHI/ffc8-4zpnvM/s144/HOME_shef.jpg" /> | <img src="http://lh3.ggpht.com/coa07mhk/SPPkus8pGzI/AAAAAAAAAHI/ffc8-4zpnvM/s144/HOME_shef.jpg" /> | ||
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<td width="20%" align="center"><a href="https://2008.igem.org/Team:University_of_Sheffield_/Modelling"> | <td width="20%" align="center"><a href="https://2008.igem.org/Team:University_of_Sheffield_/Modelling"> | ||
<img src="http://lh4.ggpht.com/coa07mhk/SPPk2T9PvfI/AAAAAAAAAHg/gJqoTZNnCQk/s144/MODELL_2_shef.jpg" /> | <img src="http://lh4.ggpht.com/coa07mhk/SPPk2T9PvfI/AAAAAAAAAHg/gJqoTZNnCQk/s144/MODELL_2_shef.jpg" /> | ||
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- | Let us consider the probability of CAI-1 interacting with our fusion kinase with a reaction rate k, diffusion rates D1 and D2 and they start at a distance d apart at the beginning of the time interval<img src="http://lh4.ggpht.com/coa07mhk/SQZQsubfzCI/AAAAAAAAANw/92s3DnMCXMo/s144/delta_t.PNG" /> | + | <br> |
+ | Let us consider the probability of CAI-1 interacting with our <a href="https://2008.igem.org/Team:University_of_Sheffield_/Project#Downstream_the_Fusion_Kinase">fusion kinase</a> with a reaction rate k, diffusion rates D1 and D2 and they start at a distance d apart at the beginning of the time interval<img src="http://lh4.ggpht.com/coa07mhk/SQZQsubfzCI/AAAAAAAAANw/92s3DnMCXMo/s144/delta_t.PNG" /> | ||
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<img src="http://lh6.ggpht.com/coa07mhk/SQZQslkxAzI/AAAAAAAAAOA/j5Bd0dJ8vtg/s288/eq2.PNG" /> | <img src="http://lh6.ggpht.com/coa07mhk/SQZQslkxAzI/AAAAAAAAAOA/j5Bd0dJ8vtg/s288/eq2.PNG" /> | ||
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<H>Where</H> | <H>Where</H> | ||
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- | <img src="http://lh4.ggpht.com/coa07mhk/SQZQs58C4WI/AAAAAAAAAOI/b5qn3x5R07s/s144/eq3.PNG" /> | + | <img src="http://lh4.ggpht.com/coa07mhk/SQZQs58C4WI/AAAAAAAAAOI/b5qn3x5R07s/s144/eq3.PNG" /> |
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<img src="http://lh4.ggpht.com/coa07mhk/SQZQs9D-DyI/AAAAAAAAAOQ/FdveIv00mZU/s144/eq4.PNG" /> is the reaction once CAI-1 has interacted with Fusion Kinase. | <img src="http://lh4.ggpht.com/coa07mhk/SQZQs9D-DyI/AAAAAAAAAOQ/FdveIv00mZU/s144/eq4.PNG" /> is the reaction once CAI-1 has interacted with Fusion Kinase. | ||
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- | This interaction will follow the law of | + | This interaction will follow the law of diffusion and if we let the process under consideration as <a href="http://en.wikipedia.org/wiki/Poisson_process">Poisson process</a>, the probability can be given as: |
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<img src="http://lh4.ggpht.com/coa07mhk/SQZQx-YyI9I/AAAAAAAAAOY/8wieBfvt0mI/s144/eq5.PNG" /> | <img src="http://lh4.ggpht.com/coa07mhk/SQZQx-YyI9I/AAAAAAAAAOY/8wieBfvt0mI/s144/eq5.PNG" /> | ||
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<img src="http://lh3.ggpht.com/coa07mhk/SQZQyavXd-I/AAAAAAAAAOg/qsc_qvPTep8/s144/eq6.PNG" /> | <img src="http://lh3.ggpht.com/coa07mhk/SQZQyavXd-I/AAAAAAAAAOg/qsc_qvPTep8/s144/eq6.PNG" /> | ||
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To find the probability of rest of reaction i.e. from activation of UvrY till the shining of our protein we can use the Gaussian Distribution, which can be given as: | To find the probability of rest of reaction i.e. from activation of UvrY till the shining of our protein we can use the Gaussian Distribution, which can be given as: | ||
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<img src="http://lh3.ggpht.com/coa07mhk/SQZQypqSCUI/AAAAAAAAAO4/cURij-XIVgc/s288/eq9.PNG" /> | <img src="http://lh3.ggpht.com/coa07mhk/SQZQypqSCUI/AAAAAAAAAO4/cURij-XIVgc/s288/eq9.PNG" /> | ||
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+ | The two probabilities were then plotted using MatLab. It is to be noted here that a 'random number generator' was used for plotting. The reason is, as the trigering of process will vary each time therefore 'random number generator' is a good choice. | ||
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+ | <img src="http://lh3.ggpht.com/coa07mhk/SQeGUJunwsI/AAAAAAAAAPo/Viyi5w7QBfA/s400/Pathway.PNG" /> | ||
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<img src="http://lh5.ggpht.com/coa07mhk/SQZQ0R3tEeI/AAAAAAAAAPA/N_x0O2WupfY/s800/G1.PNG" /> | <img src="http://lh5.ggpht.com/coa07mhk/SQZQ0R3tEeI/AAAAAAAAAPA/N_x0O2WupfY/s800/G1.PNG" /> | ||
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Latest revision as of 01:10, 29 October 2008
Let us consider the probability of CAI-1 interacting with our fusion kinase with a reaction rate k, diffusion rates D1 and D2 and they start at a distance d apart at the beginning of the time interval is the reaction once CAI-1 has interacted with Fusion Kinase. This interaction will follow the law of diffusion and if we let the process under consideration as Poisson process, the probability can be given as: To find the probability of rest of reaction i.e. from activation of UvrY till the shining of our protein we can use the Gaussian Distribution, which can be given as: The two probabilities were then plotted using MatLab. It is to be noted here that a 'random number generator' was used for plotting. The reason is, as the trigering of process will vary each time therefore 'random number generator' is a good choice. |
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