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Animated presentation, we suggest to switch slideshow mode on (ie. by pressing F5) [Changing slides: cursors, space/backspace, mouse scroll, PageUp/PageDown]. Determination of the concentration. A quantitative property of an indicator refer s to the concentration: - PowerPoint PPT Presentation
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Animated presentation, we suggest to switch slideshow mode on (ie. by pressing F5)
[Changing slides: cursors, space/backspace, mouse scroll, PageUp/PageDown]
Determination of the concentrationA quantitative property of an indicator refers to the concentration:
color (absorbance, optical density) fluorescence cell number (e.g. in determination of growth factor concentration)
Quantified concentration can be obtained by comparison with known concentration sample (standard)
The principle of comparison:
equal absorbances equal concentrations
PARTIAL TRUTH !!!PARTIAL TRUTH !!!
concentration
10
00
50
0
25
0
12
5
62
31
16
7.8
3.9
1.9
0.9
7
0.4
9
0.2
4
0.1
2
0.0
30
0.0
61
0.0
07
0.0
15
0.0
04
0
The sample with unknown concentration
ODThe serial dilution of the standard
According to OD: it could be anyone
?
You should also dilute the unknown sample
This region could indicate the concentration
This region could indicate the concentration
ODEstimating the concentration with a „ruler”
conc. of the standard (µg/ml)
The
OD
are
pro
port
iona
l with
the
co
ncen
trat
ions
in t
his
ran
ge
2X 4X 8X 16X 32X 64X 128X 256XDilutions of the unknown sample
10
00
50
0
25
0
12
5
62
31
16
7.8
3.9
1.9
0.9
7
0.4
9
0.2
4
0.1
2
0.0
30
0.0
61
0.0
07
0.0
15
0.0
04
0.0
02
points with identical OD
The concentrations are equal in the tubes
The 1.9μg/ml diluted standard corresponds to the…
… 128-fold diluted unknown sample
So, the concentration of the (undiluted) unknown sample: 1.9x128 = 243.2μg/ml
OD
conc. of the standard (µg/ml)(two-fold dilution (log scale!))
2X 4X 8X 16X 32X 64X 128X 256XDilutions of the unknown sample
10
00
50
0
25
0
12
5
62
31
16
7.8
3.9
1.9
0.9
7
0.4
9
0.2
4
0.1
2
0.0
30
0.0
61
0.0
07
0.0
15
0.0
04
0.0
02
You can use linear regression (Least-squares analysis), and calculate the concentrations with the equations (formula) of the lines fitted on the
linear parts of the dilution curves
ystd=mx+b
Ysample=mx+b
Serious errorsYou must know the optical density range that you should use to calculate the
concentration with the equation(formula) of the dilution line!
Dilution curve
The fitted line with its equation(formula)y=mx+b OD=m(concentration)+b
OD
concentration
The OD of any highly diluted solutions will be located on this range of the dilution curve. If you insert this OD value
into the formula and calculate the concentration by multiplying it with the dilution, then you get enormous high
FALSE concentration.
This OD range results false concentrations also
The range of suitable OD values
dilution curve
OD
concentration
The range of suitable OD values
Don’t force fitting the line where it is unnecessary
Incorrectly fitted line
The line has to be fitted to these points too!
0
1
2
3
4
5
6
1 10 100 1000 10000hígítás
OD
Notice that the dilution curve is represented on logaritmic function!
Two different representations of the same results:
Normal (linear) dilution curve Logaritmic dilution curve
The correct representation helps to find the proper points of the curve
0
1
2
3
4
5
6
0 500 1000 1500 2000 2500hígítás
OD
1 2 4 8 16 32 64 128 256 512 1024 2048
Dilution:
0 1 2 3 4 5 6 7 8 9 10 11
dilution 2x:
0
1
2
3
4
5
6
1 10 100 1000 10000hígítás
OD
0
1
2
3
4
5
6
0 2 4 6 8 10 12hígítás 2x
OD
=
Good representation helps the correct data analysis
Try to find the proper points of the ‘sigmoid’ curve (even if it’s not represented in the function completely),
and fit the line to these proper points
In practice, it rarely happens that we are able to work with good standard dilution curves.
It is the same with the dilution curve of the unknown sample. Usually we only make 2-3 dilutions of the samples.
1x 2x 4x 8x 16x 32x 64x 128x
OD
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5 standard (1x: 100 g/ml)
dilution
Dilutions of the unknown
dilution 1x 10x 100x
OD 4.0 2.1 1.1
1.1Value around the
sensitivity threshold
2.1
Approx. 5 (in order to have the accurate value we could use the equation of the line between the two points)
100/5 = 20 g/ml
The unknown: 20x10 = 200 g/ml
In this example the OD value of the undiluted (1x) sample should not be used.
1x 2x 4x 8x 16x 32x 64x 128x
OD
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5 standard (1x: 100mg/ml)
dilution
Dilutions of the unknown
dilution 1x 10x 100x
OD 4.0 2.1 1.1
4.0 The OD 4.0 is the value around the most concentrated standard dilution value
It is possible that the dilution curve has other shape
For example if the missing 2 fold dilution value should be here
Than it is the starting point of the plateau of the dilution curve
Should we use the remaining OD value?
PresentationELISA plate with serially diluted IFNγ standard and Tcell culture supernatants
Which is the concentrated sample?
Try to calculate the concentration of the given ELISA data at home!• calculate the mean of the 3 parallel data• use the logarithm of the dilution to draw the dilution curves• try to use a computer with spreadsheet program
Calculate the concentration of the unknown sample.The concentration of the
standard is 100μg/ml.
Write these formulas:
the log of the dilution,…
the average of the parallel standards,…
and the average of the parallel samples
Select the cells with the formulas, click on the tiny square on the right bottom
corner of the selected square, and drag it (autofill)
into the next lines.
Click on the chart wizard
Choose the „XY Scatter” chart type
Choose the series tab
Add data
Write the name of the first data series
Click on the X values (dilution)Choose the dilution (log) values
Click on the Y values (OD values)
Choose the standard OD values
=Sheet1!$A$17:$A$28
=Sheet1!$C$17:$C$28
Do the same procedure with the unknown sample data also
Straight line can be fitted on point 5 to 8 of the standard curve, and the on point 3 to point 6 of the sample titration curve
Data of the standard curve linear part
Data of the sample curve linear part
You can use this data to draw the linear parts
!!
!!
Right click on the line and choose the „Add Trendline” option
Linear trendline
Display equation on chart
(Options tab)
The equation of the standard line
Do the same with the sample line
sample: y = -0.3778x + 2,8471 standard: y = -0.3678x + 3.5265
e.g. OD 1.2 x=4.359 OD 1.2 x=6.325
The 104.359=22856 –fold dilution of the sample has equal OD than….
…the 106.325=2113489 –fold diluted standard
You can calculate the dilutions of different OD solutions with the equations
The sample is 2113489/22856= app. 92x thinner than the 100µg/ml standard
1.08 μg/ml
Note
This is a demonstrative tutorial example!You can get the result easier!(eg. You need only the equation of the standard trend line compared to an appropriately chosen dilution and OD value of the sample for get the correct result)