Team:SCUT/Bioeffector
Measurement
Bio-effector
What our bio-effector manage to do is to keep the concentration of Cd2+ below the detection limit in order to maintain it in safe level. By doing so, we believe this could help us to achieve our first goal-wipe out the Cd2+ from environment. This device has a core, namely, the CsgA-EC component which is the unit of engineered curli in our project and its expression is connected with the concentration of the Cd2+ and after it is expressed, it will be secreted outside the cell. In extracellular environment, those components become curli by nucleation reaction and begin to chelate Cd2+ by its extra polypeptide.
To the whole Bio-effector Device, its power of adsorption directly links with the expression level of CsgA-EC and the length of ECs. In addition, if we take difference about the concentration of Cd2+ from the beginning of the adsorption to the end of it into consideration, we will see the capacity of its adsorption is also depend on the concentration of extracellular Cd2+. This fact inform us if we are going to get a precise model for the device, we do need to bring all factors connected into consideration.
Part 1: Cadmium Adsorption
I. Goal
We designed a quantitative experiment to measure the concentration of extracellular cadmium ion with length of ECs is different, initial concentration of cadmium ion and incubating time. Then we established a suitable mathematical model and work out the relationship between the concentration of extracellular cadmium ion, initial concentration of cadmium ion and incubating time. After this model was built, we could easily figure out the adsorption capacity of Bio-effector.
II. Principle
1) Principle of Fast Equilibrium
In general, the modeling method for interactions of two materials is based on law of mass action. According to the mechanism of adsorption,
[P] for the volume of non-adsorptive csgA-EC
[M] for the concentration of free cadmium ion
n for adsorption number of cadmium ion with each csgA-EC unit
[PMn] for the volume of adsorptive csgA-EC
According to law of mass action,
Adsorption rate
Disadsorption rate
We have done a series of preliminary experiment about cadmium adsorption and measured some useful quantitative data. [1] These data shows that the concentration of extracellular cadmium ion decreases quickly at the beginning of incubation and then reaches stationary phase. The process of quick decrease only need little time. Therefore, under the guidance of this experiment, we thought we could ignore this process and focused on the stationary phase.
According to the principle of fast equilibrium, we let v1 equal to v2 and make the adsorption constant Kd equal to k2/k1. Finally, we determined that the mathematical model was as follow: [2]
2) Optimization of Model and Determination of Data-available Variable
In the model mentioned above, Kd, n are constants. [P], [M], [PMn] are real-time variables. However, because the variable of incubating time was ignored, we had no idea how to determine the real-time value of these variables. So we need to optimize our model. As we know,Expression volume of CsgA-EC
Initial concentration of extracellular cadmium ion
Therefore,
This model is an implicit function.
In this model, [P]total is independent variable and [M] is dependent variable.
3) Different Length of ECs and Different value of Kd
In the preliminary experiment, the data we had measured was empirical data. In other words, we didn’t analyzed the concrete mechanism of cadmium adsorption. We could only work out the empirical value of Kd with these data. We couldn’t analyze the influencing factors of Kd with these data, let alone building a sub model.Thus, we could simply draw a conclusion that ECs with different length have different values of Kd.