Team:HUST-China/Modelling/Wet-lab data analysis

Fitting

In this part, we process data from our wetlab in two different parts: the first one is comparing whether pET-28a single transformed cells and cotransformed cells are different, the second one is that whether the oscillatory behavior of cotransformed cells is only the result of Brownian motion.
Furthermore, we make comparison between data from wetlab and drylab. In this process, our data from experiment and simulation matches well, which is a promising and satisfying result.

Methods

1.Tell the difference between single transformed cells and cotransformed cells using Q-Q plot and Kolmogorov-Smirnov test;
2.Use Shapiro-Wilk test and spline interpolation to confirm oscillatory florescent intensity is not a Brown movement;
3.Use Q-Q plot to find the correspodent time intervals in experiment data and simulation data; comparing them after normalization using Kolmogorov-Smirnov test.

Result

For the first step, a Q-Q plot is used to compare two groups of data explicitly. Q-Q plot is used to compare whether two groups of data come from same distribution regardless of time dimension. In other words, well-matched Q-Q plot is one of the necessary but not sufficient conditions for judging whether two groups of data are similar to each other. Here, we present the Q-Q plot between pET-28a single transformed cells and cotransformed cells:

Fig 1.Q-Q plot of single transformed cells and cotransformed cells.

Apparently, these are different. To make the result more reliable, we run two-sample Kolmogorov-Smirnov test (abbreviate as KS test in the following).
In KS test, the null hypothesis is that these two groups are same. We get the p-value of this test:p=2.0470e-10;
Thus we can conclude that null hypothesis is rejected, in other words, we can conclude that these two samples come from different population.
Then, in this part, we focus on discussion whether oscillatory behavior of cotransformed cells is only a Brown movement.
In this part, we use spline interpolation to get more data from the curve, which makes our analysis more precise, and there is little flaw doing it, since the presumption is that the curve should be smooth, which is obviously true.

Fig 2.Oscillaroty behavior of florescent intensity from experiment.

We then run Shapiro-Wilk test for the data. If the null hypothesis failed to be rejected, then the fluctuation of data would come from random variation. We use STATA to run the test, and we get the result, which the p-value is: p=0.00023.
Thus, null hypothesis is rejected, in other words, we can draw the conclusion that there is oscillatory behavior of this group of cells.