Thermodynamic Modeling
First of all we made a series of 3 assumptions in the process of screening our final structures [1]. The first assumption is that the minimum free energy (MFE) of the toehold switch correlates with the expression leakage meaning that the minimum energy that the toehold has in all the possible structures is related with the likelihood of the reporter gene to be expressed besides the lack of its trigger sequence, these phenomena can be expressed as follows:
To activate the toehold switch, an amount of energy is needed to open the toehold switch hairpin. The Switch MFE represents the difficulty for the toehold switch unwinding process. We assume that the more negative the Switch MFE, the harder for the unwinding to take place, and hence we will have a lower leakage.
The second assumption is that the ΔG RBS-Linker correlates with the duplex expression , this ΔG RBS-Linker is the Gibbs free energy of the RNA sequence starting from the RBS to the linker in the switch-trigger duplex meaning the reporter expression of the switch-trigger system. We also looked for negative values because in order to make easy the process of unwinding the structure we should have minimal base pairs in the RBS-Linker section, allowing ribosomes to bind to the RBS and move along the RNA for translation of the RFP or AmilCP reporter genes. Since ΔG RBS-Linker reflects the difficulty for the unwinding process of the RBS-linker region It is assumed that more negative values of the ΔG RBS-Linker will make the unwinding process more difficult, leading to lower translation rates. Thus, the duplex expression would be reduced.
Finally our third assumption is that the ΔMFE correlates with the reporter expression of the Switch-Trigger duplex, this change in the MFE is defined as the MFE of the switch-trigger complex minus the summatory of the MFE of the switch and the MFE of the trigger, we can expressed this as follows:
Where R represents the gas constant, T the temperature and K the equilibrium constant, we can assume that the more negative the MFE difference is the higher the switch-trigger complex concentration will be compared to that of the switch in equilibrium [2].
Consequently, increased equilibrium concentrations of the switch-trigger duplex RNA would provide an increased number of active mRNAs for the translation of the reporter gene.
Once we have made this assumption and after the toeholds are generated we need to prioritize the sequences that have the best properties in terms or several factors ensuring that we will obtain structures that are optimal to be implemented in a time-sensitive detection device. For this we analyse the optimality of the structure of the generated sequences by evaluating the target's availability for binding to the toehold, the toehold's availability for binding with the target and lastly the sensor's complex defect, together these parameters will allow us to filter our best options and can be expressed mathematically as reported by Green et al (2014), where the toeholds with the lowest score are the more optimal switches:
Where lmRNA represents the local single-strandedness from the mRNA in the binding site of the sensor, ltoehold represents the single-strandedness of the toehold section on the sensor (first 30 nt) and lsensor that represents the ensemble defect of the sensor which means an approximation of the average number of nucleotides mismatched in equilibrium according to a given secondary structure [1].
The need to know the single-strandedness of the target sequence is that if the target dimerizes during the reaction the toehold would not be able to form the complex and allow the expression of the reporter protein, on the other hand we need to know the single-strandedness of the toehold section so the trigger will bind effortlessly to the switch, and finally with need to know the ensemble defect because it gives us an insight of the overall stability of the toehold, we calculate these and more parameters partly by using the tools given by a python package called ViennaRNA [3].
Finally, an important consideration is that different conformations of RNAs with the same sequence coexist in solution, and the concentrations of those populations are determined by their structures and free energy. Therefore, we calculated the suboptimal structures of each toehold in an energy range (usually 1 kcal/mol). This last step allows us to evaluate the stability of the toehold in this energy range, meaning that if the toehold structure and MFE does not vary within that energy range it will maintain its functionality.
Results
Taking all of these assumptions and both thermodynamic and structural parameters into account for the development of our software, we were able to design toehold switches for Fusarium Oxysporum and Agave tequilana which will be implemented on our detection system. In the following tables we listed the resulting sequences that are more optimal according to our software (secondary structure images were generated using the NUPACK package).
Table I. Toehold Switches for Agave tequilana
| Part Name | Score | MFE | ΔG | Secondary Structure |
|---|---|---|---|---|
| BBa_K4092000 | 9.78 | -31.80 | -34.22 |
|
| BBa_K4092001 | 9.84 | -35.90 | -32.54 |
|
| BBa_K4092002 | 9.82 | -31.70 | -34.74 |
|
| BBa_K4092003 | 9.79 | -31.20 | -33.83 |
|
| BBa_K4092004 | 9.82 | -33.20 | -34.65 |
|
Table II. Toehold Switches for Fusarium Oxysporum
| Part Name | Score | MFE | ΔG | Secondary Structure |
|---|---|---|---|---|
| BBa_K4092006 | 9.69 | -26.70 | -33.09 |
|
| BBa_K4092007 | 9.85 | -28.90 | -32.61 |
|
| BBa_K4092008 | 9.84 | -30.80 | -31.72 |
|
| BBa_K4092009 | 9.83 | -36.40 | -33.33 |
|
| BBa_K4092010 | 9.67 | -28.80 | -32.34 |
|
References
- Green, A. A., Silver, P. A., Collins, J. J., & Yin, P. (2014). Toehold Switches: De-Novo-Designed Regulators of Gene Expression. Cell, 159(4), 925–939. https://doi.org/10.1016/j.cell.2014.10.002
- The Chinese Hong Kong University. (2017). Modeling: Designing Toehold Switch. Available at: https://2017.igem.org/Team:Hong_Kong-CUHK/Model
- Lorenz, R., Bernhart, S. H., Höner, C., & Hofacker, I. L. (2011, November 24). ViennaRNA package 2.0. ResearchGate; BioMed Central. https://www.researchgate.net/publication/51828551_ViennaRNA_package_20