Team:Oxford/biosensor characterisation
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- | Stochastic modelling uses probability theory to predict the behaviour of a system. For our project, we used it to model the expression of | + | Stochastic modelling uses probability theory to predict the behaviour of a system. For our project, we used it to model the expression of the mCherry protein from bacteria. |
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- | We started with the Gillespie Algorithm, which considers the expression of | + | We started with the Gillespie Algorithm, which considers the expression of mCherry to be binary; a molecule of GFP is either expressed or degraded. Before we determined which event happened, we had to work out when the event happened. Using the random number r1 (taken from a uniform distribution between 0 and 1), we produced another random number τ, which determined the time until the next reaction. |
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<img src="https://static.igem.org/mediawiki/2014/8/89/Oxford_Matt_equations_1.jpg" style="float:left;position:relative; height:8%; width:20%;" /> | <img src="https://static.igem.org/mediawiki/2014/8/89/Oxford_Matt_equations_1.jpg" style="float:left;position:relative; height:8%; width:20%;" /> | ||
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- | We modelled the probability of a molecule of | + | We modelled the probability of a molecule of mCherry being created using the Michaelis-Menten model (α1), incorporating a basal transcription rate (b1). For the degradation, we assumed a simple proportional relationship: the more mCherry you have, the more likely it is that a molecule degrades (δ1). The constant of proportionality will be a function of the intrinsic life time of the protein in the cell. We considered there to be no ATC originally, then a large step in ATC at time=50. |
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- | To decide if | + | To decide if mCherry was expressed, we looked at the percentage of events which were expressions. Then we compared this to a second random number r2 (again taken from a uniform distribution from 0 to 1). If the random number was lower, then mCherry was expressed. If it was higher, then a mCherry was degraded. In this way we make a weighted random choice about whether mCherry was expressed or degraded. We only stored the time and amount of mCherry when there was a event, to save on computation time. |
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- | Stochastic modelling is useful because it can show us the stochastic effects which are often observed in individual bacteria. By calculating the variation of the mean of multiple | + | Stochastic modelling is useful because it can show us the stochastic effects which are often observed in individual bacteria. By calculating the variation of the mean of multiple mCherry producing bacteria, we can also work out the standard deviation. Then if we assume that the system varies with respect to the normal distribution, we can produce error bounds for the production of GFP, such that we can say that 90% of the time we can expect the production of mCherry from a single bacterium to be within these two curves. This could be useful for seeing if results are unexpected, or, if there are multiple outliers, that our model is incorrect. If we average an increasing number bacteria, then the mean curve tends towards the deterministic response. This is to be expected, as we are now looking at the system as a whole and fluctuations in the production from individual bacteria are averaged out. In terms of their use, when looking at small amounts of bacterium the stochastic model would be better, because real random fluctuations can be seen. For larger bacterial populations, the deterministic response models the growth very well. The stochastic model can also model large groups but requires large number of realisations which causes simulations to take a lot longer to run. |
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- | When | + | When we originally ran the models, we picked arbitrary constants to view the general response. Later we created a code which was able to produce a line of best fit for fluorescence data from the lab; from this line the constants (a1,b1,d1,k1) could be determined. |
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