The impact of background expression

       In the search for the relationship between the initial concentration of AHL and the time at which the threshold is reached, we found that when we changed the background expression only, we can see that when the background is expressed as a certain value, the concentration of added AHL can be linearly related to the time at which the threshold is reached. By analyzing the data, we determined the optimal background expression in a highe range, where the concentration of AHL can be linearly related to the reached threshold time, that is, when the background expression of the system is expressed within this range, it is considered that the concentration of added AHL (concentration range (0,1000)) is linearly related to the time , through the linear treatment, we can calculate the actual production of the initial concentration of AHL better. At the same time, it also lay the theoretical basis for elimination of background expression through AiiA hydrolase later and optimization system.

Effects of Bacterial Growth on Threshold Time

       We expect to build a system that can work after Stable Period. But in the experiment we found that when the bacteria grow to a stable period, the number of intracellular LuxR protein is not enough to make the system work. We introduce a growth curve based on the logistic equation to construct a model that takes into account the growth of bacteria in order to analysis the current stage of the experiment, although we will solve this problem in the fulture.
       Compare to the previous AHL-t map, we can see that the time to reach threshold is increased significantly after we consider the growth and extend our time of detection then, which is what we do not expect. So it is more advantages that we initially chose to open the system in a smooth period.

The Influence of Introducing Sensor on System Detection

       According to the following comparison chart, we can see that when the sensor is introduced, the linear range of the concentration of AHL and time reached threshold is greatly reduced, and cause 2 problems: (1) When the concentration of addde AHL is low, the time to reach the threshold will be greatly extended; (2) When the concentration is haigh, the time to reach the threshold will be no significant gap. This is why we get this result: no fluorescence or fluorescence is too strong after we add AHL. But it is certain that the introduction of the sensor can reduce the time to reach the threshold. Thus we add AiiA to offset this part and the background expression produced by the AHL later.

 

      The transfer of metabolic molecules [1] as fig1.Specified P is AHL molecule, Pn is LuxR-AHL polymer, GR inhibitory promoter, GA activated promoter, M is LuxI.First LuxR and AHL combine to form a complex,which dimerize into a transcrip -tional activator, LuxR-AHL.According to the theory of system biology [3-4],We can get the formula: The above process is described by ordinary differential equations: When the system is balanced:       The number of solutions is related to the parameters.n> 1, there are 1-3 solutions;Whenδ₂<δ ₃. δ=δ₂orδ₃,the system has two equilibrium solutions.when δ< δ₂ or δ > ₃，.The system has only one equilibrium solution.Whenδ₂ < δ < δ₃, the system has three equilibrium solutions.When the eigenvalue satisfies Re <0, the equilibrium point is stable, but only if the Re satisfies <0, the positive feedback system is stable and the system does not need to convert high and low steady state. The parameters in the program are Re <0, so we can think that the expression of our system is stable.

references:

[1]Haseltine E L, Arnold F H. Implications of Rewiring Bacterial Quorum Sensing[J]. Applied & Environmental Microbiology, 2008, 74(2):437.
[2]Wang H O, Abed E H. Bifurcation control of a chaotic system ☆[J]. Automatica, 1995, 31(9):1213-1226.
[3]PEI YU, GUANRONG CHEN. HOPF BIFURCATION CONTROL USING NONLINEAR FEEDBACK WITH POLYNOMIAL FUNCTIONS[J]. International Journal of Bifurcation & Chaos, 2004, 14(05):1683-1704.
[4]Le H N, Hong K S. Hopf bifurcation control via a dynamic state-feedback control[J]. Physics Letters A, 2012, 376(4):442-446.

 

clear
i=1;
yc1=0.0000001;        % The rate of LuxI molecules produced by background expression
n=2;        % Hill factor
v1=0.001;        % The rate at which a AHL-LuxR molecule produces LuxI molecules per unit of time
Kd=100;        % Dissociation constant
R=100;        % The content of LuxR in a cell
v2=0.001;        % LuxI catalyzes the generation of AHL
N=1.73772;        % Total number of cells
for        L=0.001:0.001:1 % Initial AHL molecule
t=1;
L(1)=L;
I(1)=0;        % Initial LuxI value
LR=0;
t=2;
while        L<3
if        t>7200
% M=I1(t-7200);% Green fluorescent protein (LuxI) attenuation
M=0;
else
M=0;
end
% Y=N/(1+exp((-1.29336)*((0.001*t)-4.35987)));% The cell growth curve corresponds to the number of cells
Y=N;
I(t)=R*v1*(L(t-1).^n/(Kd+L(t-1).^n))+I(t-1)+yc1-M;% The amount of LuxI molecule in unit cells +L(1)/v2
L(t)=I(t)*v2*(Y/N)+L(t-1); % The amount of AHL molecule in unit cells
LR=R*(L(t).^n/(Kd+L(t).^n));% The amount of LuxR-AHL molecule in unit cells
t=t+1;
end
tt(i)=t-1;
i=i+1;
end
figure
plot(tt)
xlabel('Initial AHL concentration')
ylabel('t')
grid on;