Difference between revisions of "Team:USTC/Model/5"

A wide range of bacteria species are known to communicate through the so called quorum sensing (QS) mechanism by means of which the produce a small molecule that can freely diffuse in environment and in the cells.^[1] Acyl-Homoserine lactone (AHL) and a family of N-acylhomoserine lactones (AHLs) is an important class of “quormones,” or autoinducers.^[5] We used external AHL to stimulate the expression of CysDes protein, and choose arabinose to stimulate the expression of CmCR protein.

For the first part, we built an ODE model by using MATLAB code to simulate protein expression process, by solving ODEs, we can predict the express rate(d[P]/dt) and concentration of target protein([P]) during the several hours after inducer was added to the medium. To identify the stability and reliability of our QS system, we also add some noise to our ODEs, which correspond to the disturbance in biology system. The result proved that our QS system can run stably in a quite big disturbance environment.

For the second part, we introduced a Universal Protein Expression Platform(UPEP) to modeling the process of gene transcription and translation switch on or off quantitively and output the suitable inducer concentration and induced time, which helps us obtain a best induced result and guide our experiment.

By using this platform, you need to input the type of QS system or inducer type used in your system, and some other information about your plasmid, include target gene sequence length and self-degradation rate of the target protein. By solving ODE based on biochemical reaction process, the platform returns a figure shows the time cost in induce process with different inducer concentration. You can choose a maximum time cost that accepted in your wet-lab experiment, then decide the concentration of inducer adds to the medium. What's more, once you decide your inducer concentration, our platform will output two figures show the product concentration([P]) and product generate rate(d[P]/dt) at a different time.

Acyl-Homoserine lactone(AHL) is an important class of “quormones,” or autoinducers widely used in bacterial quorum sensing(QS) systems.[5] And the mechanism of AHL inducer are studied clearly in the previous reserch. Firstly, we write down the chemical porcess of reaction shown in appandix A, then we can write down the ODEs in appandix B. By slove these ODEs in MATLAB result of the express rate(d[P]/dt) and concentration of target protein([P]) - time curve are shown in Fig.1 below.

Fig. 1 | [P]-time and d[P]/d[t]-time curve of CysDes

Then we choose the function to fit [P]-time curve, and fit rusult are shown in Fig.2. By using fit result, we can define 2 parameters to characterize the protein expression process, the first one is y_m, which means the balance concentration of protein. And the second one is t₉₀, which means the time cost to reach 90% expression.

Fig. 2 | fit curve of [P] time

For the result of simulation are closely related to plasmid's copy number and concentration of inducer added, we changed these two numbers and simulate respectively to each number, and find different y_m and t₉₀ at different conditions, shown in Fig.3 and Fig.4.

Fig. 3 | y_m result with inducer added and [DNA]

Fig. 4 | t₉₀ result with inducer added and [DNA]

Furthermore, to identify the stability and reliability of our QS system, we also add some noise to our ODEs, which means each chemicals' concentration was add a random disturbance to ODE solver. result of [P]-t curve was shown in Fig.5 below, black curve is ODE's solution at noise = 0, and 4 other curves are other solutions when noise added. When we try to solve ODE in a loop code, and count the possibility of route to obtain the probability density on the curve, result is shown in Fig.6.

Fig. 5 | [P]-time curve after noise added

Fig. 6 | Probability Density of [P]-time curve

Appandix A | Biochemical reaction equations of AHL induced QS system

Appandix B | ODEs of AHL induced QS system

Appandix C | Biochemical Reaction constant of AHL induced QS system