Team:USTC/Model/System Analysis/m

System analysis

Purpose of analysis

In our project, the whole gene circuit is composed of three parts: sensing system, regulation system and degradation system. The function of sensing system is to detect the existence of nicotine and transform the chemical signal (6-Hydroxynicotine) to fluorescence signal (GFP). After receiving the chemical signal, the regulation system can activate the expression of degradation system by increasing the concentration of AHL. In this way, nicotine can be detected by the bacteria and it is economical for bacteria to spare some energy from expressing degradation enzymes to normal growth after sensing. At the same time, adequate metabolic enzymes can be synthesized for nicotine transformation. To reach the target of design, we need to insure low expression of GFP/NicA2 without nicotine, but sufficient quantity of effective or signal proteins when sensing nicotine. The level of expression is under the control of their promoter strengths and DNA copy numbers. This part we will talk about the impact of these two factors to the whole system and help the experiment design to choose the appropriate gene elements for optimizing.

Promoter strength

There are three important promoters controlling the expression and signal processing in the circuit:

(1) Promoter1 controls expression of Vppa. Vppa catalyzes the reaction from nicotine to 6-Hydroxynicotine.

(2) Promoter2 controls expression of hdnoR which binds to pHdno and represses 6Hlno/GFP/LuxI expression. 6-Hydroxynicotine is the inducer to release hdnoR repression. 6Hlno is responsible for 6-Hydroxynicotine degradation. LuxI catalyzes the reaction of AHL synthesis.

(3) Promoter3 controls expression of LuxR. A certain amount of LuxR-AHL dimer can activate the transcription of NicA22.

To describe the strength of promoter, we define variable ‘s’ as the strength of promoter. ‘s’ can be any real number in the region of [0,1]. The transcription rate of three promoters can be described as below:

Equation 1 Transcription rate and promoter strength

Initial steady state

The combination of promoter strengths need to meet the requirements of the design:

(1) Low concentration of GFP under detection limit.

(2) Low concentration of AHL to lower the basal expression of degradation system.

(3) Low concentration of NicA2 to save energy for normal growth.

Figure 1 Initial GFP expression with s1

Figure 2 Initial GFP expression with s2

Figure 3 Initial AHL expression with s2, s3

Figure 4 Initial NicA expression with s2, s3

The range of strength value in the simulation is from 1e-2 to 1. The simulation time is 200000 s to guarantee that all species reach equilibrium state at last. From figure1 and figure2, we can find that the change of Vppa and GFP concentration is mainly follow the exponential function. However, the index of Vppa is positive but negative in the condition of GFP. It is reasonable because Vppa expression is promoted by promoter1 and promoter2 represses GFP expression. Considering that the small amount of GFP is difficult to be detected, we can conclude that s2 over 1e-2 is appropriate for repression of GFP expression. Figure3 shows the tendency of AHL concentration change with variable ‘s2’ and ‘s3’. It is obvious that s3 has little impact to AHL concentration but s2 plays a vital role in regulating AHL concentration. Within our parameter region, AHL concentration is much smaller than 0.1 nM, so the expression of degradation system is very low. This phenomenon can clearly be observed from figure 4. When s2 is lower than 1e-1.5 and s3 is higher than 1e-0.5, only about 5-20 M of NicA2 is generated but this concentration range is enough low to satisfy the design.

Adding nicotine

From the simulation result of initial steady state, we can find that range of promoter strength from 0.1 to 1 for both promoters satisfies our requirements of low expression of GFP and NicA2. So, to simplify the simulation, we set the parameter interval of s1 and s2 to [0.1,1]. Under these settings, the difference among initial states under control of various s1/s2 combinations is not very significant. Based on this fact, we set the same initial condition for all simulation to reduce the amount and time of calculation.