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| + | Click [[here]] for Probabilistic approach. |
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| - | {| style="color:#888888;background-color:##888888;" cellpadding="5" cellspacing="2" border="2" bordercolor=#888888 width="85%" align="center"
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| - | !align="center"|[[Team:University_of_Sheffield |Introduction]]
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| - | !align="center"|[[Team:University_of_Sheffield /Project|Our project]]
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| - | !align="center"|[[Team:University_of_Sheffield /Modelling|Modelling]]
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| - | !align="center"|[[Team:University_of_Sheffield /Wet Lab|Wet Lab]]
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| - | !align="center"|[[Team:University_of_Sheffield /Lab Books| Our team]]
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| - | !align="center"|[[Team:University_of_Sheffield /Timetable| Timetable]]
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| - | !align="center"|[[Team:University_of_Sheffield /Misc| Miscellaneous]]
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| - | =Pathway Modelling=
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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 http://lh4.ggpht.com/coa07mhk/SQZQsubfzCI/AAAAAAAAANw/92s3DnMCXMo/s144/delta_t.PNG The reaction between two diffusing particles can be considered to take place in two steps. First the encounter of CAI-1 with Fusion kinase and second the actual reaction of passing protein to response regulatory receptor. If we let CAI-1 as entity A and fusion kinase as entity B then the rate of reaction can given as:
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| - | http://lh6.ggpht.com/coa07mhk/SQZQslkxAzI/AAAAAAAAAOA/j5Bd0dJ8vtg/s288/eq2.PNG
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| - | Where
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| - | http://lh4.ggpht.com/coa07mhk/SQZQs58C4WI/AAAAAAAAAOI/b5qn3x5R07s/s144/eq3.PNG is the probability of interaction between CAI-1 and Fusion Kinase.
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| - | 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 diffuion and if we let the process under consideration as Poisson process, the probability can be given as:
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| - | http://lh4.ggpht.com/coa07mhk/SQZQx-YyI9I/AAAAAAAAAOY/8wieBfvt0mI/s144/eq5.PNG
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| - | 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:
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| - | http://lh3.ggpht.com/coa07mhk/SQZQypqSCUI/AAAAAAAAAO4/cURij-XIVgc/s288/eq9.PNG
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| - | http://lh5.ggpht.com/coa07mhk/SQZQ0R3tEeI/AAAAAAAAAPA/N_x0O2WupfY/s800/G1.PNG
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