Goals
When designing our system for E. coli we found that a high ratio between the regulatory output (i.e. STAR and consequently amilGFP) and the simulated endogenous gene (i.e. RFP) was paramount. But the easily interchangeable parameters (i.e. promoter and RBS) for controlling the prevalence of the regulatory output and the endogenous gene could not be used to control this ratio as they were synchronised in our system. The next best tunable parameter was the number of ribozyme-STAR-ribozyme (RSR) constructs. Adding multiples of these constructs downstream of the simulated endogenous gene will have a linear relationship to an increase in the ratio between the regulatory output and the simulated endogenous gene, but an increase in the transcription level of the regulatory output does not guarantee an increase in the activated expression of the reporter protein. To determine whether increasing the number of RSR constructs would also increase the expression level of the reporter protein plasmids with one RSR construct and two RSR constructs were modelled mathematically and compared.
Design
To build our model we developed two reaction networks one for the construct with a single RSR unit (Fig. 1) and one for the construct with two RSR units (Fig. 2). We also made the following assumptions to simplify the model:
A steady-state approximation was used to model the binding/unbinding of STAR to the t500-terminator in the STAR regulatory unit upstream of the amilGFP. Since RNA/RNA interactions happen on a significantly faster timescale than transcription and translation this approximation should not introduce significant errors.
STAR is inactive until both ribozymes of the RSR unit have been cleaved.
Both ribozymes cleave completely, i.e. there are no defective ribozymes.
Parameters
| Part | Value | References |
|---|---|---|
| Transcription rate DH5alpha | 55 nt/s | 1 |
| Translationrate DH5alpha | 15 res/s | 2 |
| Maturationrate RFP | 60 min | 3 |
| Maturationrate amilGFP | 45 min | 4 |
| Rate constant HHRz | 1.0 min^-1 | 5 |
| Rate constant HDVRz | 1.7 min^-1 | 6 |
| Degradationrate RNA | halflife: 3 min | 7 |
| Degradationrate | ~3.49 days | 8 |
| Time until medium activity (STAR-500) | 3.4 h | 9 |
Results
The trajectory of the number of amilGFP molecules per cell is shown in figure 3. Figure A shows the trajectory when only a single RSR unit is used. Figure B shows the trajectory when two RSR units are used. The trajectories show that the two constructs should behave similarly approaching equilibrium states that only differ by 0.2 %. Though the trajectories slope for small t is steeper when using two RSR units. The results show that an increase in the number of RSR units only impacts the response time, not the response strength.
As our constructs are intended to fight infections this long-term equilibrium is the key metric for their effectiveness. While quicker response times are preferable they do not provide significant advantages that would justify the significant increase in complexity.
Based on these results we decided to design the constructs for our proof of concept with only a single RSR unit though we would suggest two or even more RSR units for applications requiring fast response times. Multiple RSR units could also be used to optimize our constructs for real world applications.
References
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