Team:Oxford/biosensor characterisation
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+ | <div class="white_news_block2"> | ||
+ | <h1>Stochastic Modelling</h1> | ||
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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 GFP from bacteria. | ||
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+ | <br><br> | ||
+ | We started with the Gillespie Algorithm, which considers the expression of GFP to be binary; a molecule of GFP is either produced or degraded. Before we determined which reaction happened, we had to work out when the reaction 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. | ||
+ | <br><br> | ||
+ | <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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+ | <br><br><br><br><br><br> | ||
+ | Where α0 represents the probability that any reaction will happen, given by the following equation: | ||
+ | <br> | ||
+ | <img src="https://static.igem.org/mediawiki/2014/3/37/Oxford_Matt_equations_2.jpg" style="float:left;position:relative; height:4%; width:47%;" /> | ||
+ | <br><br><br><br><br><br> | ||
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+ | We modelled the probability of a molecule of GFP 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 GFP 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 DCM originally, then a large step in DCM at time=0. This is similar to placing the detector in a DCM polluted source, to make the model more realistic the level of DCM would go down as it is degraded but we had no time to obtain data for this rate. | ||
+ | <br><br> | ||
+ | To decide if GFP was produced, we looked at the percentage of “reactions” which were productive, and 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 GFP was created. If it was higher, then GFP was degraded. In this way we make a weighted random choice about whether GFP was created or degraded. We only stored the time and amount of GFP when there was a reaction, to save on computation time. | ||
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+ | <br><br> | ||
+ | <img src="https://static.igem.org/mediawiki/2014/e/e1/Oxford_Matt_equations_3.jpg" style="float:left;position:relative; height:8%; width:30%;" /> | ||
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+ | <br><br><br><br><br><br> | ||
+ | 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 GFP 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 GFP 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. | ||
+ | <br><br> | ||
+ | When running the models, we picked arbitrary constants to view the general response. If we had more time we would have attempted to work out the basal rate, transcription rate and degradation rate of the GFP from DCM. | ||
+ | <br><br> | ||
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+ | </div> | ||
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+ | </div> | ||
+ | </div> | ||
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