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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   . 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 is given as:
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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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<H>Where</H>
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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.
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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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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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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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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

Where

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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