"
Team:OUC-China/Magnetic Analysis
From 2013.igem.org
Magnetic Analysis
Abstract
We built a model to qualitatively and quantitatively analyze the magnetic detection ability of the sample bacteria, introducing a magnetism detection coefficient to quantify this ability. We were successful in using random function to simulate the movement process inside the microfluidic chip, thus comparing the modeling results with the experimental results, eliminating systematic error. The experimental results showed that although the membrane-producing gene cluster was inserted into the E.coli cells, it did not endow the cell with evident magnetic detection ability.Introduction
Because the distribution of the Magnetospirillum Magneticum AMB-1 and engineered bacteria in culture is random, it is difficult to detect Magnetospirillum Magneticum AMB-1 and engineered bacteria’s ability of feeling magnetism directly. We use microfluidic chip to make sure Magnetospirillum Magneticum AMB-1 and engineered bacteria move in a fixed direction. Then magnetic field in the vertical direction of the fixed direction can make Magnetospirillum Magneticum AMB-1 and engineered bacteria produce a orthogonal movement. We used mathematical modeling to qualitative and quantitative analyze the distance bacteria travelled in the vertical direction of the fixed direction by detecting distribution density of Magnetospirillum Magneticum AMB-1 and engineered bacteria in magnetic field. In order to quantify Magnetospirillum Magneticum AMB-1 and engineered bacteria’s ability of detecting magnetism ,we introduce a new parameter and manage to figure out the coefficient values .Models
Model assumption
Magnetospirillum MagneticumAMB-1 and engineered bacteria’s magnetism detection coefficient are both the same.Symbols description
Models
Microfluidic chip, as shown
Culture fluid enters into the microfluidic chip from the injection port. After passing though channel 2, sample bacteria broth remains in the filter in channel 3, while culture fluid issues from the sample outlet. The movement of sample bacteria in channel 2 can be divided into two parts, free movement along the channel and offset movement in the direction of the magnetic field.
Ignoring the trail of the sample bacteria’s movement, only considering the sample bacteria’s final position without magnetic field and offset in the magnetic field, we got the following results.
Under no magnetic field conditions, the sample bacteria’s distribution in the microfluidic chip shall meet:
When adding the magnetic field, the movement of sample bacteria is affected by the fixed magnetic field, resulting in a force parallel to the magnetic field and a certain dynamic acceleration.
These makes the sample bacteria tend to move towards the direction of the magnetic field. The sample bacteria’s movement is restricted by the size of the microfluidic chip, so the closer the bacteria gets to the border of the microfluidic chip, the more resistance the bacteria feels. And also, the drag acceleration resulting from the resistance changes with the bacteria’ position in the microfluidic chip. The drag acceleration meets this equation:
The resistance makes the sample bacteria form a certain density distribution, so we can observe the distribution of the bacteria in magnetic-free field and then work out the friction drag and the correspondent drag acceleration. From (1) and (2), we can get the functional relationship between the original position x1 and terminal position x2:
Because the speed is the derivative of the distance with respect to time.
And then work out the functional relationship between the distance and time:
And because the sample bacteria’s termination of the offset resulting from the magnetic field meets the following relationship:
We can take x0 into the equation one by one, and then define the corresponding point offset as well as the final sample bacteria’s density distribution function. Furthermore, the final density distribution function only depends on four parameters,x0,T,a1 and a2. As x0, T are certain parameters, a2 is dependant on the sample bacteria’s distribution function under no magnetic field conditions. Therefore, the corresponding point offset only depends on a1, namely the sample bacteria’s magnetism detection coefficient. So we can use the sample bacteria’s distribution function under two conditions, both with a magnetic field and without.
