The Input-dependent model

For this model, we no longer assume a trivial process of repression of lacI being liften and QS being turned on. The LacI repression is now a repression / induction hill function with a K_d of 1200 molecules per cell for IPGT forming IPGT lacI complexes. We assume IPGT leaks into the cell from outside. We only set the outside concentration of IPGT. For quorum sensing all we set is an elevated HSL concentration outside which is free to defuse in. We now include a feedback loop into the QS mechanism. To do this we attach a lux box onto the plasmid for producing luxR and luxI, like so:

However, we are taking the production strengths of this lux box to be reduced in comparison to our lux box for producing X, Y and cI. The strengths are

Production max for X, Y and cI = 0.44 pops

taken from the iGEM page of ***** and personal communication with **** on ****

Production min for X Y and cI = 0.013 pops

taken from *****

Production max for QS feedback = 0.002 pops

Production min for QS feedback = 0.00015 pops

These values are taken from the paper “ FIOADAOIDFJAOFJASDIOJASOIJADOAJSDAFOJAFOAJSD”

An important new parameter is K_P. This is the dissociation constant for “P” activating the lux boxes. P is the luxR/HSL complex . To take a break from the wordy descriptions we will now show some small sections of results for this model, which should be easily interpretable after following the section about the Monte Carlo analysis

Exterior levels of IPTG and HSL required for success

The outside levels of IPGT and HSL are the only two assumptions we make in this model, let’s see what these assumptions need to be in order to achieve success

So we need about 6000 molecules of both HSL and IPGT for success... although this will depend on our 3 old K_d values of K_LacI K_TetR K_cI and our new one of K_P. (P is the luxR HSL complex activating the lux boxes)

For this experiment the K_d values are

K_LacI = 700 molecules per cell

K_cI = 5000 molecules per cell

K_tetR = 3000 molecules per cell

K_P = 200 molecules per cell

For now we will take our outside levels of IPGT and HSL to be 10,000 molecules. Although we have not yet calculated physically appropriate values yet.

K_TetR, K_cI and K_LacI relation

We studied this relationship in the simplified input model. Let’s now look at it again for the new input dependant one

Knowing that the relationship between success with K_LacI is quite uninteresting, our next plot will let us find another way of viewing the relationship between success, K _TetR and K_CI, and use our 4th dimension more cleverly

It seems that this model is a lot more intricate in nature, and also success is much harder to find. Also we note that X concentration never really gets above 80 percent of its maximum, and is usually a great deal lower.

K_TetR, K_cI and K_P relation

K_P plays a very important role in the success of the system. In essence K_P has to be low, and the lower the better, as we see in the following Montecarlo simulations

The reason K_P has to be so low is because in this system there is equal production of LuxR and LuxI. This production level is governed by a feedback loop but the minimal production must be low in order to stop the system triggering itself. As they are both expressed quite weakly it is hard to accululate a large quantity of the LuxR /HSL complex, P. As it is P that leads to the expression of the glue molecule X and CI and then K_P must be low in order to express them to a large degree.

It is here that we find our first major flaw with the new model. The problem is that our assumption that K_P can has to be as low as 200 molecules per cell is unrealistic. This means that while our first input, which is the lifting of LacI repression from IPGT induction works perfectly, our second input, the quorum sensing, fails at expressing the glue molecule X to a large degree. This means that we have to rethink, for a second time, our Quorum sensing system. This will be done in the next section “A rethink of Quorum sensing” but for now we will show some graphs of protein concentrations demonstrating the problem.

Correct functionality

Here are a few graphs demonstrating how the new input dependant model should work

Failure due to high K_P value

Here are the graphs showing how we expect the system to function with different values of K_P. We also demonstrate that it is K_P which is the governing problem in this model, and that the model is quite robust to changes in K_TetR and K_CI within our expected values.

The relationship between HSL outside, IPGT outside, K_P, and system failure

Let us now try an experiment to check that it is not our input levels of HSL and IPGT that are creating the problem. Let us elevate our outside levels from 10,000 molecules to 50,000 molecules

So the system runs much more successfully under these conditions. Let us use our parameter analysis approach to explore this relationship.

So essentially we see that having input levels of 30,000 molecules outside of the cell would be perfect. We will calculate in later sections whether this is achievable, but in any case it would be advisable to change our Quorum sensing mechanism at this stage regardless because we cannot guarantee that K_P will be of the order of ~50 to 500 molecules; in fact we can make an educated guess that it will in fact be much larger than this.

Conclusion

While the last few sections have been dealing with system failures it is important to note that this system works on many levels. Firstly, the value of K_LacI is ideal and should pose no problem at all. Secondly, our estimates of K _CI and K_TetR should also pose no serious problem as long as they are within the range of a few thousand to around 7000. So in summary, the processing and output of our system works as intended, and as for our “AND gate” input we can say that half is fully functional while the other half needs work.

In the next section we will describe this Quorum sensing input in detail and outline the next model we shall explore.

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