Model

Our ODE model simulates the key cellular processes involved in glucocorticoid-inducible transcriptional activation.

The whole process can be divided into 2 modules:

The glucocorticoid sensation module 

1. The natural growth of engineered cells.Equation (1)

2. Upon glucocorticoids stimulation, extracellular glucocorticoidspermeate the cell membrane by simple diffusion and then recognized by glucocorticoid receptor.  Equation (2) to (4)

3. The GC-receptor complex (TetR) is translocated into the nucleus and binds with Tet Operator, which initiate the expression of target gene. Equation (5)

The gene expression module 

1. It includes the transcription of SEAP and the translation of SEAP-mRNA(Xie et al., 2016).  Equation (6) and (7)

2.The growth and metabolic rates.  Equation (8) and (9)

3. The ODE modified from (6) with . This ODE led to two different paths in our modeling to meet different requirements of analysis respectively. the original one was named the pure ODE model, the (Quasi-steady state approximation) QSSA for the another.  Equation (10)

1.Modeling iteration: Integrated analysis of Simulation-experimental data

After that we established our ODE model, our wet-lab group have already obtained enough test data of glucocorticoid-inducible synthetic circuit, enabling us to estimate the unknown parameters in our model.

For instance, we first constructed a model consisting of only ODEs to simulate the whole signal transduction processes. However, we observed that the experimental data didn’t fit well with our simulation (Figure 3), which was attributable to the uncertainty that ODE model contained.

Therefore, we use QSSA instead, which assumes that  

Based on the fact that the protein-protein interaction/binding occurs in seconds, and transcription occurs in minutes to hours;

we can reasonably conclude that the glucocorticoids rapidly bind to the receptor and that this reaction reaches equilibrium very fast, whereas the subsequent transcription processes can be far slower.

The Michaelis-Menten equation derived from the above analysis largely enhance the precision of our model, the side-by-side comparison between the two model is shown in (Figure 3).

To validate the accuracy of our model, we used the model to predict the level of SEAP activity. As is shown in the figures above (Figure 3), the simulation showed that both ODE model predictions and QSSA model predictions match well with the corresponding wet-lab data (link related Results page), indicating that our model might have correctly reflected the whole processes of glucocorticoid-inducible transcriptional activation cascade.

Compared with ODE, QSSA achieved a better performance, particularly in the control group (Figure 3A) and in stimulation group between 12hr and 48hr (Figure 3B) . Clearly, the modified simulation is more accurate than the original simulation, suggesting that our hypotheses and reasoning are correct.

2.Sensitivity analysis of parameters in the whole process

As our wet-lab group need to further characterize and optimize the performance of the Tet_stress-based circuit (link to HP and related Results page), we utilized our model to quantitatively identify the factors (parameters) that have the most significant effect on the final level/activity of SEAP.

To address this issue, a built-in sensitivity analysis program of Simbiology was used to calculate the time dependence of SEAP production with respect to each potential parameter and its sensitivity.

By examining the computational sensitivity over time, we found out that k_inu (the efficiency of GC complex into the nucleus) , Compared with other potential parameters such as k_dm and k_sm , have the greatest impact on the output of GC complex and SEAP level.

To further verify the influence of k_inu on SEAP level, the initial value of k_inu was scanned in a range from 0 to 1, and the simulation showed that when the initial value of k_inu was 0.5, SEAP expression fits the experimental data well. The result is shown as below:

With the decrease in k_inu, the SEAP activity began to be significantly delayed, indicating that the synthetic circuit is largely dependent on the efficiency of nuclear import of Tet_stress upon glucocorticoid stimulation.

The results suggest that we can increase the glucocorticoid-responsiveness by enhancing the nuclear translocation of our synthetic transcriptional factor (Tet_stress).

As shown in our experimental results (Linked to Results Page). Our team then introduced a nuclear export signal (NES) into Tet_stress transcriptional factor (between TetR and GR_LBD) to manipulate the subcellular localization of the Tet_stress.  Wet-lab data showed that this improvement successfully enhanced the response of the glucocorticoid stimulation (Linked to Results Figures) .

In conclusion, we constructed a mathematical model to describe and predict the behavior of our stress sensor cell (the glucocorticoid-inducible transcriptional activation cascade). Our modeling achieves the following objectives:

1.An integrated simulation analysis in combination with experimental data demonstrated a good fit between our model and experimental data, which proves that our mathematical model is useful and effective, as well as heuristic. We believe our modeling and ideas is useful for other iGEM teams and synthetic circuit-based engineering of mammalian cells.

2.The sensitivity analysis showed that k_inu(the efficiency of GC complex in the nucleus) is the most sensitive parameter. This helped the wet-lab group to figure out how to improve the glucocorticoid-responsiveness of engineered stress-sensing cell, these model-assisted synthetic circuit design showed that mathematical modeling can provide a new outlet for further research. In our project, it did help us find the direction to further optimize our circuit design, which contributed to our engineering success and proof of the concept.