Team:XMU-China/modeling

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Modeling

1. Introduction
Ordinary differential equation(s) (ODE) is one of the most popular methods in modeling. Frank R. Giordano and other scientists have introduced it exhaustively. ^[1] In many computational biological researching, researchers often use it to simulate the dynamics part of biological process. The concentrations of RNA, proteins, and other molecules are represented by time-dependent variables. ^[2] We used the same method to construct our model.

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2. Modeling
First of all, there are 4 variables and 4 parameters in this experience. Their names and meanings are listed below.

Those functions about describing the rate equations of biochemical reactions in the circuit P_cIGLT are:

The initial condition is

Equation (1) represents the course of growth of E.coli.^[3] Equation (2) represents the course of producing and decomposing GFP. OD₀ and flu₀ is value of OD and flu when t=0. Then, we changed the parameters and figured out the best value for fitting the data of fluorescence intensity.

Figure 1: Fitting line and data of fluorescence intensity

Those functions about describing the rate equations of biochemical reactions in the circuit P_cIGLT are:

The initial condition is

Equation (3) represents the course of growth of E.coli.. Equation (4) represents the course of producing and decomposing GFP. Equation (5) represents the arabinose utilized for inducing. OD₀, flu₀ and Arc0 is value of OD, flu and Arc when t=0. After that, we changed the parameters and then found out the value fitting the data of fluorescence intensity most.

Figure 2: Fitting line and data of fluorescence intensity (Value Arc=0.1).

Figure 2: Fitting line and data of fluorescence intensity (Value Arc=0.1).

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3. Result
According to Figure (1-3), we can draw a conclusion that the model we constructed can simulate the process of dynamic change in fluorescence intensity. We can figure out how those parameters work in this model if we have more experience data.

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4. Reference

[1] Frank R. Giordano, Maurice D. Weir, William P. Fox, A First Course in Mathematical Modeling, Third Edition, Thomson Learning, 2003, 297-329
[2] RON WEISS, SUBHAYU BASU, SARA HOOSHANGI, ABIGAIL KALMBACH, DAVID KARIG, RISHABH MEHREJA and ILKA NETRAVALI Genetic circuit building blocks for cellular computation, communications, and signal processing, Natural Computing, 2003, 2: 47–84.
[3]You L, Cox RS, Weiss R, Arnold FH. Programmed population control by cell-cell communication and regulated killing[J]. Nature, 2004, 428(6985): 868-871.