Most assays have a linear range, I have seen instances where an individual
could not derive a linear protein versus color response, and it is true that at
very high levels of protein such as with coomassie blue that you get saturation
effects. I've seen this at very low concentrations of thick filaments from
C.elegans because the molecular weight is at 10E9 to 10E10. However for
globulins and globins, and most non-aggregated proteins the response will be
linear over a two to three magnitude range.
The individual who could not derive a linear range failed because he used three
pipettors to develop his assay. The first, the p20 failed because he was
recycling tips when pipetting proteinaceous solution. The second pipette he
loaned to a colleague, who we learned after the fact was trying to use a p200
to pipette 250 ul, this supershot the preset calibration (can only be done with
models made after 1990) and as a consequence was delivering 40 uls less that
desired. The third pipette, a p1000 failed because it was leaking. Once the two
pipetters were repaired he got a standard curve that was almost perfectly
linear. P20 and P200 can be used repeated pipetting of protein solutions (for
example if one is making triplicates) when the tip is equilibrated by plunging
back and forth in the reverse mode. This best example I can give is pippeting
mixtures of I-125 protein A in BSA. In the forward mode the counts are often 10
to 15% below expected and those found in the reverse mo!
de, drying the tip reveals the same amount of radioactivity remaining on the
sides of the tip. The reverse mode is found on the packaging equipment supplied
with a pippeter. For protein assays I recommend triplicates and using the
reverse mode since the surface area to volume for each tip changes with volume.
Certain assays often do not give linear responses, and one needs multiple
points, the ELISA development assays are frequently not linear.
In terms of the assay. The protein concentration is on the X-axis and the OD is
on the Y axis, however you will determine a X unknown using Y so it is
convenient to invert the linear regression. The slope of the line can be
derived using the LINEST function in MSEXCEL and this also provides one with
regression statistics. The correlation coefficient should be close to 1. Zar
(Biostatistical analysis, 1997) recommends not averaging values of equal X
component, but instead enter each data point unchanged. Protein determination
of unknowns should not be extrapolated beyond the assayed points, and the
estimates of line Y = mx + b is most accurate at the medium point of the assay
(close to the average X). This means that a unknown should be diluted several
ways, and the Y closest to the Y value derived from the medium X.
LINEST([Y-array], [X-array], TRUE, TRUE) after entering the mouse down on it
and select 2 columns and 5 rows (including the formula), [F2],
[control-shift-enter] and the statistics will show up. If you are really good
at pipetting replace 2nd TRUE with FALSE, since Y_sub_X=0 = 0).Note the Y array
and X-array _should_ be in adjacent columns with each X matched to each Y value
correctly. To do otherwise one may get a result but that result will have no
meaning.(I know they do not have to be exactly in adjacent columns, but if you
are unfamiliar with Linest best to have parallel columns)
To determine Y based on X use LINEST([protein concentration],[OD
values],TRUE,TRUE). To derive X then X = X intercept (second column top) +
slope(fist column top)*OD. Protein concentration is therefore = X * fold
dilution.
Here are the values of the linest function (That you care for a protein
standard):
- Columns - - 1 - - - 2
Rows
1 - - - - Slope - - - Y-Int (X-int if inverting the data arrays)
2 -SD of: Slope - - - Y-Int ("")
3 - - - - Cor.Coef. - Residual mean variance
4 - - - - F stat - - Residual degress of freedom
5 Variance:Regression - Residual
The probability of regression = FDIST(Row4Col1, 1, Row4,Col2)
The values of interest are R1C1, R1C2 and R3C1 relative to the equation cell
(R1C1)
If you have an equation that requires 2nd order fit, you can use also excel,
it's a bit trickier, but the rule is to minimize the sum of deviation square
(DEVSQ function in MSEXCEL) to determine the best fit. Again, I don't recommend
this, because the deviancy is generally at the high end and is a consequence of
saturation effects. I do use this 2nd order solving with my amino acid
composition analysis because some amino acids are often a magnitude more
abundant that others and so it is hard to center them. But to get a good
formula one needs at least 4 points, preferably 5 clean data points. If your
only analyzing doing a single sample, dilute your protein to best approximate
the mean Y value.
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Jayakumar, R
Sent: Monday, March 21, 2011 10:42 AM
To: WS; [email protected]
Subject: RE: Can anyone please tell about slope function
Hmmmm!! the protein concentrations are on the X-axis and OD on the Yaxis.
Always dependent variables on the Y-axis.
Jay
________________________________________
From: [email protected] [[email protected]]
On Behalf Of WS [[email protected]]
Sent: Monday, March 21, 2011 8:19 AM
To: [email protected]
Subject: Re: Can anyone please tell about slope function
Dear Sudheer,
the slope is the "m" in your equation. In real life, colorimetric
protein measurement standard curves sometimes get a bit far from
linear, so in times of computerized curve fits by eg excel,
sigma{plot, stat} or openoffice.org, you might be better off with a
2nd order fit (y=ax2 + bx + c); simply plot the OD readings on the x-
axis and the protein standard concentrations on the y-axis, then
you'll get directly the formula to calculate actual concentrations
from the OD values when performing a regression analysis.
By having a look at the R value you may compare various regression
methods (like linear vs 2nd order) and determine which one fits the
situation better.
BTW, the linear approximation is just an approximation which fits most
needs and is easily done when you have just a ruler and a sheet of
paper (when one wouldn't want to apply for mainframe computing time
just for a protein determination :). The chemistry that converts
protein into color is not really linear in respect of dose/response.
Have fun!
Wo
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