Team:Imperial College London/Drylab/Protein production/Simulations

Simulation 1: The state of system prior steady state

We can see that between time units 0 and 7 in the top and bottom plot (where [PlacI] = output amount of LacI and [Pout] = output amount of protein) there is a period of transition towards a fixed concentration. Initially, levels of [PlacI] rise until they reach a constant level, while levels of [Pout] experience a “bump” prior steady state, which settles at a value close to zero when [PlacI] = 2.

Expression of LacI repressor protein is constitutive, therefore, the switching on has already taken place prior IPTG induction. Therefore, we assumed that prior IPTG induction, levels of [PlacI], and consequently, [Pout] were originally at their values of steady state, as shown below:

Simulation 2: How does the amount of LacI protein affect the amount of protein of interest [Pout] produced?

The greater the strength of the promoter, the greater the transcription rate (PoPs, here represented as kml). In these simulations we are showing that by varying the strength of the promoter for different arbitrary PoPs values (from 0-5), we can regulate the initial basal expression of protein of interest [Pout]. From the simulations, when levels of Plac are originally low (for a low PoPs output, kml = 0 or 1), we obtain a high basal expression of [Pout]. This changes when the strength of the promoter is increased (kml=3,4,5), as now levels of [Pout] initially are zero. So initial repression of production of protein of interest is effective when the strength of the PLacI promoter is high.

Simulation 3: How does promoter leakiness affect the basal amount of protein of interest [Pout] produced?

From Equation 4, we remind ourselves that [Pout] at steady state is given by:

Therefore, increasing the leakiness factor k leak (from 0-50%) will increase the basal amounts of [Pout] expressed prior IPTG induction, as can be seen from the figure below. This means that in the absence of IPTG, a residual amount of protein of interest will always be expressed.

Simulation 4: How does the introduction of IPTG into the system affect the amount of protein interest [Pout] produced?

Here, we are interested in varying the initial amount of IPTG introduced into the system. We have used arbitrary concentrations of IPTG, going from 0 to 8.

The more IPTG we introduce, the more LacI is temporarily removed from the system. LacI removal means that production of protein of interest [Pout] is no longer repressed. The more IPTG we add in, the more LacI is removed, and the greater the yield of output protein [Pout].
Note that this model is highly simplified. We have only taken into account the constitutive expression of the LacI repressor, and other features of the dynamics of the Lac operon have been neglected. Therefore, our simulations may not match the observed experimental behavior from the lab. However, they are useful in providing us a better understanding of the mechanism of chemical induction and will provide some of the engineering constraints that the Wetlab must take into account when performing experiments.