Team:Botchan Lab Tokyo/Model
Botchan Lab. Tokyo
Modeling
Multiple parts Model
We estimated the parameters of differential equations for determining the survival rate of E. coli when it was assumed that it experimented with a combination of multiple gene parts. Gene parts that are not inputted in the experiment, the differential equation can be set, the parameters for the repair mechanism is difficult to predict because there is no literature value.
First, write a differential equation for the survival rate of E. coli. The following relationship sisconsists of the model related to survival.
From now on, differential equations can be written as follows.
Table1. Description of Parameter and Variable
| N(variable) | Number of E.coli |
|---|---|
| K(parameter) | Maximum number of E.coli |
| r_(RecA+PprM)(parameter) | Parameter of survival function(RecA+PprM) |
| r_(PqqE) (parameter) | Parameter of survival function(PqqE) |
1.Predicting Parameters for RecA and PprM
The literature value we obtained is the survival rate when gamma rays are applied to E.coli WT.
However, the results of iGEM 2011 of Osaka University, and the survival rate of WT of E.coli when exposed to ultraviolet rays, recA, there is data of survival rate when put pprM.
Therefore, to determine the relationship between the unit of ultraviolet rays and gamma rays by comparing the WT, recA, the literature value containing pprM was an object to convert the data containing gamma rays.
In short, the ratio was determined.Among the literature values, the increase ratio of gamma rays and UV was in the following relationship.
Then, it was remade parameter fitting of the survival curve of E.coli (recA + pprM) when applying gamma rays.
In the nonlinear regression, the result(language of R) is as follows.
P-value is quite small,so Null hypothesis isn't rejected
2. Parameter Prediction of ppqE
There are the following literature.
From now on, it was found that the survival rate and gamma rays of E. coli (PqqE) are made up of linear relationships in one logarithm. From now on, when I write the survival curve, it became the following.
Perform simply parameter fitting in the same manner as 1 to this. The method is nonlinear regression. The results are as follows
P-value is quite small,so Null hypothesis isn't rejected
Now the parameters have been determined.
When the differential equation was solved, and the graph was written, it became the following.
Survival curve diagram of E.coli (RecA+PprM+PqqE)
3D Simulation
In our experiment, we planned to put a damage agent called Mitomycin C. The survival rate of E. coli varies depending on the amount of Mitomycin C. That is, the survival rate of E. coli will be represented by a two-variable function.
At this time, since it can not be represented in a two-dimensional graph, by visualizing the three-dimensional graph, it was aimed at making it easier to understand the survival rate of E. coli.
Mitomycin C has been found to vary greatly survival rate in a small amount than the literature value. The parameter was found to be 10.9867 in the estimated value. This can be thought of as an amount that varies depending on the amount of MMC in the exponential part of the survival curve, The expression is as follows. You can write a 3D graph by calling 3Dplot from Python's Sympy library. The results are as follows:
MMC showed the amount of Mitomycin C.Parameter c =10.9867. It caluculated by the same way of parameter fitting.
Source-Code
