Team:NWU-CHINA-B/Model

NWU-CHINA-B

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Our experiment was aimed at ginseng saponin CK, for which we were divided into two modules.The first module was the fermentation process: Pichia pastoris produce β-glucosidease. The second module was catalytic process:β- Glucosinase catalyzes the substrate to obtain ginseng saponin CK.

In order to better conduct and understand the experiment,we built three models. Our first model is to quantify enzyme activity and prepare for subsequent modeling. The second model can predict how much Pichia pastoris can produce β- glucosidease during fermentation processes. The third model is for catalytic processes to predict the yield of ginseng saponin CK under different conditions.

Model 1

Enzyme vitality model.

Model 2

The amount of β-glucosinase produced by Pichia pastoris .

Model 3

The amount of CK produced by β- glucosidease under different conditions.



  • Enzyme vitality model



    •   Enzyme vitality refers to the ability of enzymes to catalyze certain chemical reactions. The 1961 International Conference on Enzymes stipulated that one enzyme activity unit refers to the amount of enzymes that can convert 1 micromolar substrate within 1 minute under certain conditions (25 ℃, the other is the most appropriate condition), or the amount of enzymes that convert 1 micromolar in the substrate.


      By definition, we can measure the enzyme's activity by the concentration of pNP produced by enzymes in unit time and volume：




      However, pNP concentration is not easy to measure directly, and we indirectly derive pNP concentration by absorbing light:0,0.8,1.6, 3.2,4.0,4.8 mM pNP solution. Then take 10 microliter each to add 96 well plates, and add 80 sodium acetate buffer(50 mM, pH=6.0)and a solution of 100 μL NaOH (0.5 M) immediately after 30 min in a water bath at 80 degrees C, labeled with an enzyme in the the OD value is measured at 400 nm and the mean of three sets is measured. The standard curve of both is established with the OD value as the ordinate and the pNP concentration as the horizontal coordinate.






  • The amount of β-glucosinase produced by Pichia pastoris



    •   We built a model to predict the amount of protein produced by a certain amount of bacteria, and our idea was to find out the amount of protein that a bacteria could produce 𝛼𝑐, and then to find the number of bacteria under certain culture conditions 𝑁 ,then the total protein yield can be calculated as follows:





      The concentration of bacteria can be expressed in OD values, and we firstly determined the quantitative relationship between OD values and bacterial concentrations:

    The fitting equation is：
    2
    The result is a single bacterial protein production：

      As can be seen, the forecast is accurate.

      Then we determined the number of bacteria 𝑁 under different culture conditions.We found that the conditions that bacteria are suitable for growth are:

                Temperature: < 32 ℃
                dissolved oxygen (OTR):＞20%
                PH：5.0 to 6.0

      The survival state of bacteria is only dead and alive, so it can be seen as a two-category prediction problem, this kind of problem requires variables are numerical variables, so we think of the living state of bacteria as"1",the state of death as"0",and then simulated the growth status of bacteria under different living conditions:





      The data are then logistic regressed with SPSS to obtain the regression equation:









  • The amount of CK produced by β-glucosidease under different conditions



    •   When the substrate concentration is very thin (S is much smaller than Km) ,the Michaelis-Menten equation can be approximated to v=[E][S].At this point, Kcat/Km is an apparent secondary rate constant of the enzyme and substrate reactor, also known as a specific constant. The catalytic efficiency and perfection of an enzyme, as well as the best substrate of the enzyme, can be demonstrated from another angle.

      We looked at the Kcat/Km of the three substrates in the table below and we can see that from Rb1-F2,Kcat/Km is greatly increased. Theoretically, this transformation pathway will greatly increase the affinity of enzymes and substrates, and experiments have shown that this is indeed the case.



      To determine the best conditions for an experiment, multiple variables such as temperature ,PH, must be changed at the same time, which greatly increases the complexity of the experiment, so we use the TOPSIS method to determine the activity of CK under different reaction conditions to reduce the experimental workload.

      TOPSIS method (Technique for Order Preference by Similarity to Ideal Solution) is the method of distance solution is a common comprehensive evaluation method, in order to give a sort of many schemes, after giving all the schemes, according to these data, can construct an ideal optimal solution and the worst solution in a system composed of all the schemes. The idea of TOPSIS is to evaluate the combined distance between the ideal optimal solution and the worst solution of any one of the scheme systems by certain calculations. If a scheme is closer to the ideal optimal solution and the farther away from the worst solution, we have reason to think that the solution is better. What is the ideal optimal solution and the worst solution? Very simple, the ideal optimal solution is that the ideal optimal scheme of the value of each indicator is taken to the optimal value of the evaluation index in the system, the worst solution is that the ideal of the worst program of the value of each indicator is taken to the worst value of the evaluation index in the system.


      Step1. Forward the original data matrix. That is, those very small indicators, intermediate indicators, interval indicators corresponding to the data all into very large indicators, convenient for unified calculation and processing.

      Step 2. Standardize the forward-oriented matrix. That is, through standardization, eliminate the impact of the scale.

      Step 3. Calculate the score and predict CK activity compared to ideal conditions.

      Take the specific experiment as an example:
      Both temperature and PH are intermediate indicators with the best temperature values of T :Tbest and the best value of pH : pHbest.
      The result is a single bacterial protein production：

      Calculated：

    This model can also be used to predict the activity of CK under different T, pH conditions.



Enzymatic reaction：

Gene circuits：

Model results：



  • Enzymatic reaction：











  • Gene circuits：






    •   Suppose that the content of DNA, RNA, and protein corresponding to bgly is [dbgly] 、[rbgly] 、[bgly]。For the synthesis process of RNA, there is:



      Methanol has an effect on the 𝛼_𝐴𝑜𝑥1 protein synthesis process:







  • Model results：



    •   Create the file odefcn.m and enter the equations listed above.







      Then create the main file main.m, use ode45 to find the numerical solution of the differential equations, and draw the image.







      Finally get: