Team:Alma/Model
Modeling of the pH Safety Switch
In order to control the location in the intestines in which our bacteria will be able to survive and be active, we wanted to use a combination of low and high pH promoters to drive expression of our genes or a toxin (to kill the bacteria when it escapes the intended area).
So, we took the existing design for a low-pH sensor and promoter and created a new version with an inverter, to effectively create a new, high pH promoter. We wanted to model the behavior of each of these. To create this model, we borrowed parameters from the Wageningen 2016 team's excellent modeling work. This included the constants featured below for translation and degradation of both the cI mRNA and the RFP mRNA - the parameters for cI control of the RFP promoter was also used.
Deciding how to model activation of the low-pH promoter, part BBa_K123000 was a challenge - it is not well understood mechanistically how this promoter works. Prevailing theory indicates that the two-component system responsible for phosphate homeostasis interacts with this promoter - in fact, studies have shown that PhoB binds to the asr (low-pH) promoter. How the increase in H+ concentration instigates this binding is not known.
To estimate parameters for the low-pH promoter, we used data from characterization of a higher-order part, BBa_K2762014. When plotting this data as GFP production versus H+ ions, a curve resembling michael menten kinetic data is obtained. This pointed us in the direction of what type of model to use - this was a qualitative insight. We also derived putative Vmax and Km numbers from this data, although this quantitative insight is much less likely to be accurate and will require more experimental validation (for one thing, we collapsed everything from activation of the promoter to fluorescence of mature GFP into a single number). Using these parameters, we sought to model the behavior of both a version of the existing low pH promoter as well as our new high pH promoter.
In the model above, we used the following preliminary numbers:
- Vmax: 5000000
- Km: 0.00001.8
- k1 (Asr Promoter trasncription rate): 1 - captured entirely by the Vmax/Km relationship
- k2 (cI translation rate): 3.8073
- k3 (Transcription rate from R0053, cI promoter): 0.992
- k4 (RFP translation rate): 0.0460
- kd (cI promoter binding factor): 0.1384
- b1 (cI mRNA degradation rate): 1.1579
- b2 (cI protein degradation rate): 0.6563
- b3 (RFP mRNA degradation rate): 2.0224
- b4 (RFP protein degradation rate): 0.2903
From the above model, we ran simulations in which the proton concentration ranged from 1*10^-7 (neutral - pH 7) to 1*10^-4 (acidic - pH 4). The results of these simulations, in which the maximum amount of RFP production over 10 seconds is plotted, can be seen below. Note that the scales are different when comparing the low and high pH sensor - an indication that our model and parameters may need tweaking, as the power and presence of cI seems to be overstated.
These results can be normalized to each other and re-plotted against the more familiar value of pH, along with the experimental values from K2762014 - on which Vmax and Km were based:
There are a few conclusions we can draw from this modelling work. First, the low pH sensor model is a good first approximation of what actually occurs, but more standardized experimental data, as well as a better understanding of how PhoB activates this promoter, is necessary for stronger conclusions and better models. In particular, the PhoB system is responsive to more than just pH conditions, and varying levels of phosphate present in the media (which means comparing M9 and LB media across experiments is problematic) make it hard to model how the system should behave. Our model apparently underestimates the switch-like response demonstrated here with regards to pH.
Our model suggests that a bacteria that had a dual kill-switch, driven by both the low pH expression system and the high pH expression system, would have maximum vitality around pH 5.5. This is a bit low for our system - we would like to have our bacteria maximally active at a pH between 6.15 and 7.35 (proximal area of the small intestine). Therefore, we would need to take one or more of the following steps to ensure bacteria only colonize this area:
- Choose two different toxins as outputs, which have different thresholds of concentration needed before the cell is killed. In other words, the toxin triggered by the high pH sensor could be made to be relatively ineffectual, so that high concentrations of the toxin (and therefore, a relatively higher pH) would be needed before cell growth and activity is stunted. The toxin driven by the low pH sensor could be much more sensitive and a more acute cell toxin. For example, lysozyme could be driven by the high pH system, while a more potent toxin like MazF can be trigged by the low pH system.
- Create a threshold response, in which the direct output of the high pH system is not a coding region for RFP or a toxin, but rather acts as the input into another circuit. Having this be the trigger for a feed forward loop could setup a system in which a threshold of activation is required before the secondary circuit is triggered. This threshold can then be set to be a relatively high amount of expression from the high pH system, which would require a relatively high pH (7 or greater).
- Tweak the P-Asr promoter, part K123000, so that it responds either more or less sensitively to a pH change. Likewise, we can also Modify or replace the use of cI in the inverter - other transcription factors, or cI mutants, may perform differently and give the desired result. In both of these options, we would be essentially changing the underlying BioBrick so as to modify the parameters we used.
We plan to explore all of the above options and have incorporated these insights into our next planned design. Our very next attempt will be a simple change to the above design, based on the final idea - by increasing the amount of cI in the system that is created in response to pH, we should push increase the pH in which RFP is first seen in the high pH sensor. To do this, we will simply have the P-Asr promoter drive multiple copies of cI, and cI which has been made to be more stable thanks to removal of the LVA tag.