Team:BIT/MO1
Model of Biosensor
Abstract
As we all know, it is difficult to detect macromolecules with synthetic biological methods. The hardest problem is that it is difficult for macromolecules to enter the gene machine - cell body, that leads to follow-up work out of the question. For this problem, we propose a model that replaces the substance with another substance. Alpha-fetoprotein (AFP) is the substance that our project wants to detect, but alpha-fetoprotein is a macromolecule and is difficult to enter the body of engineering bacteria. So we use lysine, an easily detectable substance, to establish a mathematical relationship with our target concentration to detect the concentration of AFP indirectly.
If we can prove that the amount of lysine separated at different AFP concentrations is different, then we can prove that our project is feasible. At the same time the aim of our project is detection, if the lysine detection quantity has linear relationship with AFP concentration, then our project will have obvious advantages in detection.
Introduction
We divided the modeling part of the sensor work into two steps: First, AFP and aptamer combined, so leading to hydrogen bond fracture process. Second, lysine molecules and DNA complementary strand separate.
As the picture shows：
In order to simplify the model, we explore the ideal conditions and put forward the following assumptions:
1、Lysine is coupled with complementary strand 1:1.
2、AFP binds to aptamer 1:1.
3、The first step is that AFP binds with the aptamer and the second step is that lysine with the complementary strand complex separate in the time and space. The time is recorded as t1 and t2.
The first step
AFP has a good affinity with the aptamer. This conclusion has been proved through the experiment and the specific content can be seen in Design-biosensor part. A large number of literatures show that the affinity of proteins with aptamers is much greater than that of hydrogen bonds. When AFP binds to aptamers, it will result in a hydrogen bond breakage between the aptamer and DNA. Thus releasing lysine and DNA complementary complex, we referred to as Complex.
This process can be seen as a base reaction, which follows the law of mass action. So the reaction rate V can be expressed as following.
k1 refers to the rate constant, [AFP] and [Aptamer] refer to the concentration of themselves.
[AFP]0 is the initial concentration of AFP and is also the target of our detection. We assume that [Complex] is also zero when the response time t is zero. The ordinary differential equation yields the following results.
In the actual case, k1、[Aptamer]、t1 are constants. Therefore, after analyzing the first process, the relationship between the released lysine-complementary strand complex and the initial AFP concentration [AFP]0 should be proportional.
Considering that this step is validated by experiment, the concentration of lysine-DNA complementary strand complex is difficult to detect due to technical conditions，We used the complementary chain of fluorescence instead of lysine-DNA complementary strand complex (Complex), through the detection of fluorescence values, to measure the concentration of the complementary strand. The results show that there is a clear linear relationship between the concentration of the complementary strand and the concentration of AFP. (Please read the Design-biosensor section for details).
The secend step
The Complex, which is separated from the first step, will enter the next chamber of our microfluidic chip where the lysine molecules will be removed from the DNA complementary strand and will be able to enter our engineered cells. So, in the second step we will build the model on the decomposition reaction of the lysine-DNA complementary strand complex.
This is an enzymatic reaction, and its reaction rate satisfies the Michaelis-Menten equation. So we set the expression of the reaction rate:
[Complex] is the concentration of the complex; Vmax is the maximum reaction rate, which is expected to be measured experimentally. Km is the Michaelis-Menten constant of the enzymatic reaction.
We solve this ordinary differential equation for time t, we get
In order for the model to better guide our project, we use this model to predict the relationship between substance concentrations. Based on the literature knowledge we have consulted and the experience of the lab, we have roughly estimated several sets of values for the constant parameters in the equation and have the following curves:
Obviously, when the detected lysine concentration is in the range of 3 μg/ml, the complex concentration is very linearly related to the lysine concentration, and can be well fitted as a linear relationship, which is what a diagnostic item is required.
Finally, putting the two models together, we found that in the detection range, there is a good fit out of the linear relationship curve. This is a relationship curve in typical condition, the reaction time t1 = 2h, t2 = 1h.
There are some parameters and initial values of variables for equations:
Summary
On the one hand, the modeling work of sensing part has an important guiding significance to biosensor experimental work and the whole project principle design. We have theoretically put forward the scientific and reasonable scheme, and have set out a goal and standard for other work in the team. project's design is based on insight we have gained from modeling. On the other hand, we have made an assessment of the whole of our project. As a project located in the diagnosis category, we use the model to predict the linear relationship between the material concentration, which is a good proof of our project is feasible, and has obvious advantages -- template.
