Team:Aberdeen Scotland/Probability
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<p>We wrote a program which takes the equations for our system, calculates the nullclines and records whether or not bistability is achieved. Whether or not bistability is achieved depends strongly on the parameters λ<sub>i</sub>, K<sub>i</sub>, μ<sub>i</sub> and n<sub>i</sub>.</p> | <p>We wrote a program which takes the equations for our system, calculates the nullclines and records whether or not bistability is achieved. Whether or not bistability is achieved depends strongly on the parameters λ<sub>i</sub>, K<sub>i</sub>, μ<sub>i</sub> and n<sub>i</sub>.</p> | ||
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+ | <p>The values for the parameters λ<sub>i</sub>, K<sub>i</sub> and μ<sub>i</sub> were taken from literature<sup>[1]-[13]</sup> but have a large uncertainty attached to them. To take this uncertainty into account we selected each parameter value randomly from a range of two orders of magnitude around the literature value for each parameter. We knew that n<sub>1</sub>=1 and estimated n<sub>2</sub> to be between 1 and 5. Therefore, we ran the program for various combinations of Hill coefficients between 1 and 5. Each time the program was run, the Hill coefficients remained constant but the other parameters varied. </p> | ||
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+ | <p>Choosing the parameters in this way meant that each time the program was run we would sometimes achieve a combination of parameters that allowed bistability, and sometimes not. | ||
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+ | The program was run 100 times and the number of times bistability was achieved was output to the screen as a percentage. This percentage indicated how probable it was that our system would perform under those conditions. | ||
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+ | We then decided to run the program for various different parameter ranges. We cannot change individual parameters specifically, but in the lab it is possible to vary the order of magnitude of a parameter. We wanted to know, if we varied our parameters and Hill coefficients, what is the best percentage we can possibly get? These results are shown in scenarios 2-4.</p> | ||
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Revision as of 20:26, 19 October 2010
University of Aberdeen - ayeSwitch
Parameter Space Analysis
What is the Likelihood of our Switch Working?
Recall that the equations of our system are as follows:
![](https://static.igem.org/mediawiki/2010/4/4f/Equations.jpg)
We wrote a program which takes the equations for our system, calculates the nullclines and records whether or not bistability is achieved. Whether or not bistability is achieved depends strongly on the parameters λi, Ki, μi and ni.
The values for the parameters λi, Ki and μi were taken from literature[1]-[13] but have a large uncertainty attached to them. To take this uncertainty into account we selected each parameter value randomly from a range of two orders of magnitude around the literature value for each parameter. We knew that n1=1 and estimated n2 to be between 1 and 5. Therefore, we ran the program for various combinations of Hill coefficients between 1 and 5. Each time the program was run, the Hill coefficients remained constant but the other parameters varied.
Choosing the parameters in this way meant that each time the program was run we would sometimes achieve a combination of parameters that allowed bistability, and sometimes not.
The program was run 100 times and the number of times bistability was achieved was output to the screen as a percentage. This percentage indicated how probable it was that our system would perform under those conditions.
We then decided to run the program for various different parameter ranges. We cannot change individual parameters specifically, but in the lab it is possible to vary the order of magnitude of a parameter. We wanted to know, if we varied our parameters and Hill coefficients, what is the best percentage we can possibly get? These results are shown in scenarios 2-4.