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From 2008.igem.org
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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 can given as:
 is the probability of interaction between CAI-1 and Fusion Kinase.
 is the reaction once CAI-1 has interacted with Fusion Kinase.
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: 
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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