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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" />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: | 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" />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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<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" /> is the probability of interaction between CAI-1 and Fusion Kinase. | <img src="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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<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 diffuion and if we let the process under consideration as Poisson process, the probability can be given as: | 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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<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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Revision as of 21:31, 28 October 2008
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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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