Template:CLSB-UK Model Stochastic

Stochastic model

The Oxford iGEM team kindly ran stochastic simulations of system for us. They ran both intrinsic and extrinsic simulations and provided us with the final uncertainties.

Intrinsic Simulation

Intrinsic stochastic models find the uncertainty caused by the changes in reaction rate due to the fact reactants collide randomly. This is more accurate than mass action kinetics for low reactant concentrations.

For our stochastic simulation, each time step a reaction rate was determined randomly using the Poisson distribution. As this is random, multiple stochastic simulations have to be run for a large enough sample size. A time step of 0.01 seconds was used.

The intrinsic simulations gave an uncertainty of only 0.0096%. This validated our use of mass action kinetics to model our system. As the intrinsic uncertainty is negligible we could assume rate of reaction was proportional to concentration of the reactants, i.e. the law of mass action.

While we later updated the parameters with our experimental data, the concentration of reactants did not decrease to invalidate this result.

Extrinsic Simulation

Extrinsic stochastic models find the uncertainty cause by the uncertainty of our parameters. The extrinsic uncertainty is by far the more significant of the two uncertainties in our model.

The extrinsic simulation assumes our parameters were normally distributed and runs multiple simulations randomly choosing parameter values.

The specific conclusions of our extrinsic simulations, such as the test being complete in 37 minutes in 90% of cases, are unfortunately no longer useful after our experimental results showed some of our starting parameters were significantly off. However, the extrinsic simulation demonstrated that biggest weakness with our model was our parameter's uncertainties.