Biochemistry...

Biochem stuff...

Stochastic Modelling

Stochastic modelling uses probability to calculate what happens next in a system. For our project we used it to model the expression of genes from bacteria.

We started with the Gillespie Algorithm, which considers the expression of GFP to be binary; either a molecule of GFP was produced or it was degraded. We modelled the chance of a molecule of GFP being created using the Michaelis-Mentin equation and incorporating a basal rate. For the degradation, we assumed a simple proportional relationship, the reasoning being that if we have more GFP then we are more likely that a single GFP molecule will degrade. The constant of proportionality will be a function of the intrinsic life time of the protein in the cell. Now at every increment in time we will not have a GFP reaction occurring, so before we decided what reaction occurs we had to work out if I a reaction occurred. We did this by writing an equation involving the probability of any reaction occurring with a random number generator. To work out which reaction occurred we compared the relative probability of a production to degradation, and used a random number to make a weighted choice.

We later changed this code so that a reaction occurred every time increment, but included a null reaction where no GFP was degraded or created. Although this made the code a lot more data heavy, it allowed for much easier calculation of the mean response of multiple realisations.

Stochastic modelling is useful because it can show us the randomness which is often seen in real bacteria. Calculating the variation of the mean of multiple GFP producing bacteria we can also work out the standard deviation, and if we assume that the system varies with respect to the normal distribution, we can produce error bounds for the error growth. Such that we can say, 90% of the time we can expect the production of GFP from a single bacterium to be within these 2 curves. This could be useful for seeing if results are unexpected, or if there are multiple outliers, that our model is not correct. If we average more and more realisations of reactions then the mean curve tend towards the deterministic response. This is equivalent to looking at the mean of more and more bacteria until we are looking at the system as a whole and fluctuations in individual bacteria are averaged out.

What is stochastic modelling?

How is it useful? Ads/Dis

Tending to deterministic

Modelling activator repressor

Parameter characterisation/Data matching

Matlab graphs

Biochemistry...

Biochem stuff...

Conclusion

The bottom graphs show how each hypothesised system would respond to a step input of both ATC and DCM at the same time. As you can see, there isn’t much difference in the predicted steady state value of the fluorescence. However, providing the basal rate of GFP is low enough, there should be a clear difference in the level of fluorescence before either of these inputs are added. Eventually, we plan to test which gene circuit is present in this system by using this method of differentiating between them.

Calculating the many parameters for this system will be tricky. How are we calculating the parameters?

Having made the models and understanding the assumptions that we’ve made, it is very important to understand where the limits of the predictions are and what range of inputs the model will give reliable information for. After all, no model is perfect. <-- BACK THIS UP?