Team:Hong Kong HKUST/Modelling Prediction Model
Prediction Model
The last step is to predict the behaviour of the system. For a global prediction, all species and processes that are related to the system should be covered. Therefore, we also consider the dynamic of mRNA and fluorescent proteins in the prediction model. Nevertheless, another problem is brought about because this setting is contradictory to our model as the dynamic of mRNA is ignored before. In fact, the equilibrium of mRNA is a fast process when compared to proteins so we argue that the inclusion of mRNA dynamic will not give a picture differs a lot from the case in which mRNA dynamic is neglected. In addition, the dynamic of inducers is introduced, the cooperativity and the binding affinity of inducer to repressor proteins are also considered.
By applying the findings from the stability analysis to the modeling equations, we obtain the following prediction graphs:
From the graph, when a pulse of inducer 2 is introduced to the system, mRNA 2 and reporter protein 2 respond afterwards with concentrations increase from 0 to a high level, and the outputs (mRNA 2 and reporter protein 2) maintain at ‘on-state’ (i.e. high level of output) without decreasing back to ‘off-state’ (i.e. zero output level). In conclusion, from the prediction model, by applying suitable parameter values obtained from the stability analysis, it is simulated that upon addition of inducers, the corresponding state is switched on, which is indicated by the high and steady output level of the reporter protein. This behavior fits the design of Tristable Switch.
| Parameters | Notation | Value |
|---|---|---|
| Maximum transcription rate 1 | $k_{tx,\;1}$ | 1 |
| Maximum transcription rate 2 | $k_{tx,\;2}$ | 1 |
| Maximum transcription rate 3 | $k_{tx,\;3}$ | 1 |
| mRNA degradation rate 1 | $d_1$ | 0.12 |
| mRNA degradation rate 2 | $d_2$ | 0.12 |
| mRNA degradation rate 3 | $d_3$ | 0.12 |
| Maximum translation rate 1 | $k_{tl,\;1}$ | 1 |
| Maximum translation rate 2 | $k_{tl,\;2}$ | 1 |
| Maximum translation rate 3 | $k_{tl,\;3}$ | 1 |
| Degradation of repressor protein 1 | $k_{deg3}$ | 0.12 |
| Degradation of repressor protein 2 | $k_{deg2}$ | 0.12 |
| Degradation of repressor protein 3 | $k_{deg1}$ | 0.12 |
| Degradation of reporter protein 1 | - | 0.12 |
| Degradation of reporter protein 2 | - | 0.12 |
| Degradation of reporter protein 3 | - | 0.12 |
| Dissociation Constant for DNA-Repressor Protein 1 interaction | $K_1$ | 1e-8 |
| Dissociation Constant for DNA-Repressor Protein 2 interaction | $K_2$ | 1e-8 |
| Dissociation Constant for DNA-Repressor Protein 3 interaction | $ø_1$ | 1.5e-8 |
| Dissociation Constant for DNA-Repressor Protein 1 interaction | $ø_1$ | 1.5e-8 |
| Dissociation Constant for DNA-Repressor Protein 2 interaction | $ø_2$ | 1.5e-8 |
| Dissociation Constant for DNA-Repressor Protein 3 interaction | $ø_3$ | 1e-8 |
| Hill Coefficient of Repressor 1 (DNA-Repressor) | $n_1$ | 3 |
| Hill Coefficient of Repressor 2 (DNA-Repressor) | $n_2$ | 3 |
| Hill Coefficient of Repressor 3 (DNA-Repressor) | $n_3$ | 3 |
| Hill Coefficient of Inducer 1 | $m_1$ | 2 |
| Hill Coefficient of Inducer 2 | $m_2$ | 2 |
| Hill Coefficient of Inducer 3 | $m_3$ | 2 |
| Variables | Notation |
|---|---|
| mRNA 1 concentration | $r_x$ |
| mRNA 2 concentration | $r_y$ |
| mRNA 3 concentration | $r_z$ |
| Repressor 1 concentration | x |
| Repressor 2 concentration | y |
| Repressor 3 concentration | z |
| Inducer 1 concentration | $u_1$ |
| Inducer 2 concentration | $u_2$ |
| Inducer 3 concentration | $u_3$ |
To view the codes we employed in our model programming, please click here.
REFERENCE
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