Model

Section 1: Model — Twelve-days Person P. acne Tracking

According to electrophoresis film, our team use application ImageJ to estimate the greyscale of 500 bp, 400 bp, and 300 bp. The result, written in a matrix below, donated as γ:

Define a new matrix as

The matrix ρ:

Construct the experiment time into a matrix τ:

By using the Matlab , we can find the best fit line between τ and ρ:

From the model, we can see that the amount of P. acne diminishes as the day of using BS cleanser increases. Based on the slope of the best-fit line, we can infer that the amount of P. acne decreases by 7.8375% each day. By the end of 10 days, the amount of P. acne is roughly 20% of the original amount.

Section 2: Model — Bactria Growth

To demonstrate that the protein cafe can indeed limit Bactria growth, we used OD techniques to estimate Bactria growth. OD index can show the optical density of bacterial suspension and reflect the relative number of bacteria. OD index of control group and experimental group at 0h, 1h, 2h, 4h, 6h, 8h and 12h were recorded. Here, the time matrix is

The OD Index of normal bacteria growth is

Each row of N represents a group experiments, so that the average normal growth of bacteria is

The OD Index of control group (with Turbol-ID) is

The OD Index of first experiment group (with Caf) is

The OD Index of second experiment group (with Caf) is

We donate the average OD Index of Ε1 and Ε2 as follow:

In order to find the best fit logistic line of the Bactria Growth in Experiment Group and Control Group, we use the CURVE FITTING application in MATLAB to do this job:

The normal growth of bacteria is

This curve suggests the growth rate of the E. coli under normal conditions. In theory, the maximum increasing speed of the growth of the E. coli is within the log phase, and as we can tell from the graph, the inflection point of the curve in this period is where the E. coli experiences the greatest reproduction rate. In this case, the point where y=0.8, time taken (x) is lesser than 4 hours, is the inflection point and we further set this position as the standard to carry on the following analysis.

The growth curve of control group is

This is the growth curve of E. coli after inserting our turboID-SP synthetic plasmid. This time, when y=0.8, the x value which indicates the time taken is greater than 4 hours (around 4.7 hours) which means that the growth rate of the E. coli after adding turboID-SP plasmid indeed had a relatively decrease. But, in terms of the final stationary phase, the total amount of the E. coli indicating by the OD600 value is slightly higher than that in normal condition (higher than 1.6 A compare with 1.6 A). Therefore, overall, we can conclude that the influence to the E. coli of adding turboID-SP synthetic plasmid is acceptable.

And the growth curve of experiment group is

This is the growth curve of the E. coli after inserting our Caf1-AMP synthetic plasmid. This is an experiment that we previously concerned most about. As we are not 100% sure that AMP as an antimicrobial peptide would not pose threats to the life of the E. coli. Thus, we set this test as the experiment group, and the previous one (inserting of turboID-SP synthetic plasmid) as the control group. This time, the time taken for the E. coli to reach the point when y=0.8 is around 4.4 hours which is actually lower than the time taken in the control group (4.7 hours). Therefore, we can finally come out the conclusion that our Caf1-AMP synthetic plasmid will not cause harmful effects to the growth of the E. coli.

Although from the regression model, we can see a slightly harmful effect of Caf1-AMP on our engineering bacteria by contrasting the control and experiment group, the total amount of the bacteria does not change. This further corroborates the idea that we should purify Caf1-AMP expressed by the bacteria for maximum yield of protein expression.

Section 3: Model — qL-RCA

According to the data, we can create 6 matrix as follow:

The matrix t is the times series matrix; the matrix P is the record data of P. acne DNA; the matrix R is the record data of Random DNA; the matrix S1 is the record data of Sample 1; the matrix S2 is the record data of Sample 2; the matrix S3 is the record data of Sample 3. The plot graph is shown below.

We can build a exponential model of the initial stage for P. acne DNA, Random DNA, Sample 1, Sample 2, and Sample 3. Regarded 0.5 is the threshold of the growth, we can solve the initial growth point of the curve:

We scored the samples based on how badly they were infected:

So, we can build a linear regression model as:

which indicates that the more infected a sample is, the faster it is detected.

From the graph, we can see that all the student sample groups lie between the pure P. acne DNA group and the control group, demonstrating the reasonable and reliable result of qL-RCA. Furthermore, student sample group 2, 3, and 1 with the order have decreasing rates of growth, corresponding to the actual frequencies each student get acne vulgaris, in which student sample 2 most frequently get acne vulgaris and in which student sample 1 least frequently get acne vulgaris.