Modeling
Goal
The design involves utilizing alternative reading frames to express two sets of fluorescence proteins (Fluc/Rluc+Fluc) based on spliceosome activity. Since spliceosome abnormality is simulated using PB and splicing activity is monitored using fluorescence proteins, we would want to know (1) how fluorescence protein activity respond to PB concentration, (2) whether PB inhibition serves as an effective proxy for spliceosome abnormality, and (3) how initial plasmid concentration affects the fluorescence protein activity.
Hypothesis
There is a positive correlation between plasmid and luciferase activity.
There is a negative correlation between the amount of PB added and luciferase activity.
Assumptions
PB works perfectly
There is no degradation in plasmids
Method
Statistical testing
Linear regression
Cubic spline interpolation
Model and Results
PB and Luciferase activity:
In order to address the first question, we performed cubic spline interpolation and linear regression. Since spliceosome abnormality is simulated using PB, it is crucial that we know how luciferase activity responds to changes in PB concentration. Therefore, we collected data from experiments by measuring the luciferase activity of the expression system under different PB concentrations.
The original dataset contains only three data points per construct. To improve the statistical power of regression, we performed cubic spline interpolation. The y-axis is the relative luciferase activity. We calculated the relative activity by adding Rluc activity to Fluc activity and dividing the sum by Rluc activity.
The reason for calculating relative Luciferase activity instead of simply using Fluc activity was due to that the relative activity could reduce error. In this case, Rluc activity acts as an Internal reference. To further explain, when adding plasmid, we cannot promise that we add the same amount of plasmid to each well. Thus, by using the relative activity, we do not need to worry about this error.
The Python codes for performing the calculations are shown below. Plots of luciferase activity in MAP3K7 and ZNF91 plasmids are shown below the codes. Blue lines are interpolated curves, and the red points are the original data points obtained from experiment. In general, there is a difference in luciferase activity across the two plasmids, but they both respond negatively to PB concentration.
Figure 1. Codes and plots for cubic spline interpolation.
The interpolated values are then used for linear regression. The codes and plots are shown below. Blue scatter plots are the interpolated values, and the linear regression lines are plotted in red.
Figure 2. Codes, plot, and R2 value of MAP3K7 linear regression using cubic spline interpolated values.
Figure 3. Codes, plot, and R2 value of ZNF91 linear regression using cubic spline interpolated values.
Both R2 values are very close to 1. PB and Luciferase activity are negatively correlated.
PB as a proxy for spliceosome abnormality:
We performed statistical testing on the difference in luciferase activity under fixed PB concentration and varied input plasmid concentration. The null hypothesis and alternative hypothesis are constructed:
Null hypothesis: Adding PB does not change the luciferase activity, so PB does not effectively inhibit spliceosome and does not lead to differential translation of the proteins.
Alternative hypothesis: Adding PB significantly change the luciferase activity and leads to differential translation of proteins.
The statistical test was performed using excel. Assuming the differences follow t-distribution under the null hypothesis, the probability of observing a difference at least the values recorded was below 0.05 for all groups except for 0.5 ug of ZNF36 plasmid was transfected. Overall, PB does serve as a good proxy for spliceosome abnormality, and the plasmids can be used to detect splicing abnormalities.
Figure 4. T-test for relative luciferase activity of MAP3K7 with and without PB.
Figure 5. T-test for relative luciferase activity of ZNF36 with and without PB.
Luciferase activity and initial plasmid concentration:
Data was collected to measure the change in luciferase activity under varied initial plasmid concentrations. Three pairs of values were obtained, and we repeated cubic spline interpolation and linear regression on these data.
Figure 6. Codes and plots for cubic spline interpolation of ZNF36 with and without PB.
Figure 7. Codes and plots for linear regression of ZNF36 with and without PB using interpolated values.
Figure 8. R2 of linear regression of ZNF36 with and without PB using interpolated values.
Figure 9. Codes and plots for cubic spline interpolation of MAP3K7 with and without PB.
Figure 10. Codes and plots for linear regression of MAP3K7 with and without PB using interpolated values.
Figure 11. R2 of linear regression of MAP3K7 with and without PB using interpolated values.
The R2 values are very close to 1, this means that the linear regression fits the relationship between copies and relative luciferase activity. In other words, as the copy number increases, the relative luciferase activity increases linearly in our data range.
Conclusion:
In summary, PB is an effective proxy for spliceosome abnormality, while relative luciferase activity is negatively correlated to PB concentration and positively correlated to initial plasmid concentration. Since most initial plasmid concentration can generate statistically significant differences in relative fluorescence activity across with PB and without PB groups, the initial plasmid concentration can be toned to reduce cost for real-world implementation. Additionally, the negative correlation between PB concentration and relatively luciferase activity indicates that the test may show different fluorescence level based on the severity of spliceosome abnormality. Overall, the sensitivity of luciferase activity to change in input signal can be further toned for the optimal cost and fluorescence level.