M O D E L

Model

The establishment of mathematical models can help us describe the relationship between different parameters and variables in the project process by using a set of mathematical equations.In our project, UV-inducible promoters control the expression of GFP and toxin proteins, and we use mathematical models to describe the relationship between incubation time and fluorescence intensity under different durations of UV-induced induction.

Ultraviolet irradiation will increase the expression of fluorescent proteins per unit, making the overall fluorescence intensity stronger, but at the same time, the accumulation of toxin proteins in bacteria will also lead to a decrease in bacterial biomass (OD value) and weaken the overall fluorescence intensity.Through the whole model, we can know the change of fluorescence intensity under different UV irradiation time and incubation time.The model parameters are obtained by fitting our experimental data, and referring to some literatures and the work of other iGEM teams.Our assay can help us better understand the relationship between bacterial death and fluorescence intensity within the assay.

1.Model Hypothesis

1 The resources in the environment where strains are cultivated are limited, and the population cannot grow infinitely

2.After UV irradiation, GFP and RelE under the control of UV-sensitive promoters start to express simultaneously

2 Parameter Description

3.Modeling and Solving

1 in the absence of toxic proteins When given different times of UV light (2-20min), the fluorescence intensity emitted by bacteria cultured for the same time has an exponential relationship with UV light:

[Experimental results, replaceable scatter plots]

F=a〖T_uv〗^b(1)

When T_uv = 1, F = a and is related to T_c. When given a certain period of UV irradiation, the relationship between the fluorescence intensity and the incubation time can be expressed by the logistic equation:

[Experimental results, replaceable scatter plots]

Substituting (2) into (1), we get:

Using the experimental data between T_c, T_uv and F for three-dimensional fitting, we can get:

[0.5 <= T_uv <= 20]

[1 <= T_uv <= 20]

[2 <= T_uv <= 20]

It can be seen that when 1min <= T_uv <= 20min, the model can effectively fit the experimental data. Finally, we can get the functional relationship of F on T_c and T_uv.

2 In the presence of toxic proteins The growth of the E.coli follows a logistic curve, which is indicated by the following equation:

When the E.coli expressed the bacterial virulence protein relE, the growth of it still followed the logisticstic curve, which could be indicated by the following equation（ref：https://parts.igem.org/Part:BBa_K3036004）：

Since both RelE and GFP are under the control of the same UV-sensitive promoter element, it is assumed that the survival pressure β brought by the expression of toxic proteins is positively correlated with the protein expression D, which is correlated with the UV irradiation time T_uv, therefore:

So there is

When a' is taken as 1, 5,10, respectively, the changes of F with UV irradiation time and incubation time are as follows:

[a’=1]

[a’=5]

[a’=10]