Difference between revisions of "Team:USTC/Measurement"

Overview

In this part, we establish a bio-calibration of the concentration of antibiotics and do experiments to comfirm constants in the formula. Using modeling prediction and results developed in previous work, we propose a transform formula between concentration and deformation. We also get the deformation of film from interference fringes using the interference analyzing program.

Building the Calibration

Basic hypotheses

Let's assume that bacteria response on antibiotic is linear to antibiotic concentration to a supposing n power. That is \(K=CA^{n}\)

And let's show the variable lists before we get started:

[A]: Concentration of antibiotics.
m: Percentage of moving bacteria.(%)
M: Exact movement number of bacteria.
h: Deformation length of the film.
m0:Percentage of moving bacteria at the time we start the test.

Concentration→Motility

The motility of bacteria can be divided into two parts: original motility and
induced motility (by antibiotics). According to our previous work, Adhesion Dynamics, we conclude the relationship between the motility and time. That is
\(m(t)=\frac{K+(m_{0}k-(1-m_{0})K)\ e^{ -(K+k)t}}{K+k}\)

More information about the formula please refer to Github:2015USTCiGEM

Because we assume the effect of antibiotics on motility is n power, we can define\(K=CA^{n}\) .

When the movement percentage reaches a steady state, that means \(m=\frac{K}{K+k}\), we can infer that \(m=\frac{CA^{n}}{CA^{n}+k}\).

And due to the concentration of bacteria solutions we used are almost the same(OD~0.3), the AA-B-CS will be almost the same as well. That means the total number 'N' and the 'k' will be almost the same, which is very important in our standardized operation.

Motility→Deformation

According to the analysis in Film Candidate we can know the relation between deformation and bacteria's movement.That is

\(f=MF_{0}\)

\(f=2F\times \frac{h}{b}\)

\(\frac{F}{ac}=\frac{\Delta b}{b}G\)

\(\Delta b=\frac{b}{2}\times (\frac{h}{b})^{2}\)

So \(f=acG(\frac{h}{b})^{3}\)

Now we can substitute each equations and predict the relationship between deformation 'h' and concentration 'A':
\(\frac{CA^{^{n}}}{CA^{n}+k}N=acG(\frac{h}{b})^{3}\)

'N' is the total number of sticked bacteria.

Get the reciprocal of the upper equation:

\(\frac{acG}{Nb^{3}}(1+\frac{k}{CA^{n}})=\frac{1}{h^{3}}\)

That means \(\frac{1}{h^{3}}\)is linear to \(\frac{1}{A^{n}}\).

Deformation→Fringes

According to the modeling of fringes analysis we conclude the relationship between deformation 'h' and the changes of number of fringes on y axis (\(\Delta N\)) is: \(\Delta N=\frac{2h}{\lambda }\)

So replace 'h' with 'ΔN' in equations and we will get:

\(\frac{acG\lambda ^{3}}{8Nb^{3}}(1+\frac{k}{CA^{n}})=\frac{1}{\Delta N^{3}}\)

Define \(\frac{acG\lambda ^{3}}{8Nb^{3}}\) as a complex constant \(A_{0}\), \(\frac{ackG\lambda ^{3}}{8NCb^{3}}\) as another complex constant \(B_{0}\), and simplify the formula as below:

\(A_{0}+\frac{B_{0}}{A^{n}}=\frac{1}{\Delta N^{3}}\)

So if we measure the two constants \(A_{0}\)&\(B_{0}\), we can build a calibration on concentration detecting. And when we get a solution with unknown concentration, we can test it and find the concentration in calibration!

Confirm Constants

According to our modeling in calibration we need to confirm three constants \(A_{0}\), \(B_{0}\), 'n'. That means we need to test at least three point to confirm the formula.

In this case we use engineered bacteria(specific operation need to be added later) to build a calibration on chloramphenicol.
The engineered bacteria(specific operation need to be added later) was more sensitive to chloramphenicol (add link to specific experiment and show the fluorescence result here).

And according to adhesion pre-experiment we choose the concentration range with 0.5ug/ml~5ug/ml in the experiment.
The changes of fringe number and test concentration shown below(take three pictures in a row with the time interval 20s):

time(s)	5.0ug/ml(Fringe number)	1.0ug/ml(Fringe number)	0.5ug/ml(Fringe number)
0	42/43	51/49/52	44/43
20	-	50/51/50	-
40	-	50/46	-
60	-	48/48/50	45
80	-	48/49/49	-
100	-	51/53/49	45
120	42/43	-	-
140	-	51/48/52	-
160	-	-	41
180	-	48/52/54	-
200	48	55/47/49	43/43
220	43/47	51/52	45
240	48/46	53/51	44
starting average	42.5	50.5	43.5
ending average	46.4	51.75	44.2
ΔN	3.9	1.25	0.7

And we can fitting this data with calibration formula, assume n=3(through trying different value of n get the best value of n) then get the simplified formula:

\(A_{0}+\frac{B_{0}}{A}=\frac{1}{\Delta N }\)

Fitting result:

The fitting result indicate that our modeling and normalization operation was correct and effective. And we can get the value of unknown constants:

constant	value
A0	0.1339
B0	0.6513

Testing the Calibration

In order to test whether the calibration is correct and to confirm the coefficients, we choose two concentration as check point.
And use SPRING to measure its concentration.

Methods

1.Use matlab recognize the number of fringes in each image.
2.Collect the output information from program and calculate the change fringe numbers in average.
3.Find the concentration in calibration.

More details on coding please refer to Github:2015USTCiGEM

Result

The real concentration and experiment results shown in table:

time(s)	1.8ug/ml(Fringe number)	3.2ug/ml(Fringe number)
0	78/80	77/76/77
20	77/77	79/77
40	78	75/72
60	79	74
80	81	75/75
100	75	72/73
120	80	74/74
140	83/82	71/75
160	81/79	72/76
180	82/82	75/74
200	82/81	75
220	80/82	74/74/75
240	81/80	74/75/74
starting average	79	77.2
ending average	81	74.3
ΔN	2.0	2.9
experiment concentration	1.80ug/ml	3.09ug/ml

The result shows that the experiment concentration is very close to real concentration. That means the calibration is correct and effective!
And Spring is unbelievably fast- it only take 100s! That's tens of times quicker than current method.