Download Uncertainty calculation

Annex 1. Uncertainty calculations
Detailed information of the uncertainty calculations used to determine the results
quoted within this paper for the four methods described (EM-IDMS, standard
addition, ICAT, iTRAQ) is given in this annex.
All standard and combined uncertainties for the results described were calculated in
accordance with Eurachem and with the ISO Guide to the Expression of Uncertainty
Measurements (GUM, 1st ed., Geneva, Switzerland: International Organisation for
Standardisation, 1995).
Somatropin EM-IDMS uncertainty
Use of the EM-IDMS method described in the paper enables SI-traceability for the
value-assignment of protein standards via the specific peptides chosen provided the
criteria of complete release of the peptides of interest and stability of labelled and
natural peptides during tryptic digestion are satisfied.
The uncertainty of the individual EM-IDMS measurements for each of the two
somatropin peptides in the repeat digestions corresponding to the concentration of
each protein standard was calculated by using equation 2.
Equation 2
u  Cx
 uC z

 Cz
2
2
 uR
 u Rb 

   bc
  

 RB

 RB 
 c
2
2

 um y 
 um yc


   um x   
   um z   
 m 
 m 
 m 
 m

 z 
 x 
 y 
 yc

2
2




2
Where, uCz is the standard uncertainty associated with the preparation of the stock
standard, Cz is the molar fraction of the peptide stock standard, umx is the uncertainty
associated with the mass of protein solution used, mx is the mass of protein solution
used, umy is the uncertainty associated with the mass of labelled peptide solution
added to the sample, my is the mass of labelled peptide solution added to the sample,
umz is the uncertainty associated with the mass of natural peptide solution added to the
calibration blend, mz is the mass of natural peptide solution added to the calibration
blend, umyc is the uncertainty associated with the mass of labelled peptide solution
added to the calibration blend, myc is the mass of labelled peptide solution added to
the calibration blend, Rb is the mean measured natural to labelled peptide ratio in the
sample blend (n=5), uRb is the standard deviation of ratio RB, RBc is the mean
measured natural to labelled peptide ratio in the calibration blend (n=5), and uRbc is
the standard deviation of ratio RBc.
The final IDMS value for each standard material was the average of six repeat
measurements as the entire procedure from weighing to digestion was repeated three
times with two peptide measurements for each repeat analysis. The associated
uncertainty was calculated by combining the average uncertainty of the uncertainties
associated with each of the six values (u) with the variation associated with the
digestion (bvar, the standard deviation of the six values over
6 ) as described by
equation 3.
Equation 3
utotal   u  bvar
2
2
This total uncertainty associated with the molar fraction of the 22 kDa form of
somatropin contains a component associated with the between blend digestions to
account for the global variability of the digestion between repeat samples due to
multiple digestions. Additionally, the total uncertainty contains a component
associated with the multiple pairs of peptides used to infer protein concentration,
ensuring any variability associated with the extent of digestion is also encompassed.
Equimolar release of multiple peptides inferring completion of digestion has been
shown previously using isotopically labelled peptides and monitoring the release of
natural peptides from the protein over time. [Arsene C, Ohlendorf R, Burkitt WI,
Pritchard C, Henrion A, O'Connor G, et al. Protein quantification by isotope dilution
mass spectrometry of proteolytic fragments: cleavage rate and accuracy. Anal Chem
2008;80:4154-60]
Somatropin standard addition uncertainty
The potential for discrepancies in protein digestion between the two somatropin
samples analysed, possibly due to different material preparations, was investigated by
standard additions using a separate well-characterised somatropin preparation.
The uncertainty of the individual measurements from the calibration curves
determined for each of the two peptides per digestion was calculated using equation 4.
Equation 4
s
u x det , y   var x det  
b1
s
 y  b
j
1 1 x det  x 
 
p n
S xx
2
 b1 x j 
2
0
n2
S xx   x j  x 
2
Where xdet is the number of moles of protein present in the sample as determined by
the calibration curve, yj is the measured peak area ratio at each calibration point, b1 is
the calculated best fit gradient, b0 is the calculated intercept, n is the total number of
data points used for the calculation, p is the number of measurements made to
determine a particular value, x is the mean concentration value of the different
calibration standards and xj is the number of moles of protein for each calibration
standard present at each calibration point, as calculated by gravimetric preparation.
The final standard addition molar concentration for each standard material was the
average of six repeat measurements, three from each of the two peptides used. The
associated uncertainty was calculated by combining the average uncertainty of the
uncertainties associated with each of the six values (u) with the variation associated
with the digestion (bvar, the standard deviation of the six values divided by
6 ) as
described by equation 3 above.
This total uncertainty associated with the molar fraction of the 22 kDa form of
somatropin contains a component associated with the global variability of the
digestion between repeat samples due to multiple digestions across the concentration
range of interest. It also contains a component associated with the linearity of the
digestion method over the concentration range of interest, assessing the comparability
of the digestion method for the two reference materials in the presence of potentially
different excipients. Additionally, there is a component associated with the multiple
pairs of peptides used to infer protein concentration, ensuring any variability
associated with the extent of digestion is also encompassed.
Somatropin ICAT uncertainty
To further investigate the potential for discrepancies in protein digestion between the
two somatropin samples analysed, possibly due to different material preparations, the
labelling technique of ICAT, enabling digestion under identical conditions was used.
The uncertainty of the individual measurements for ICAT corresponding to the
concentration of protein in each sample was determined for each of the three ICATlabelled peptides identified per digestion and calculated using equation 5.
Equation 5
2
2
u  u  u 
u C  R   P   m 
R P m
2
Where C is the mean molar fraction calculated from the values obtained by
considering the individual ratios observed, R is the mean ratio measurement of the
heavy and light labelled ICAT pairs (n=3), uR is the standard deviation of ratio R, P is
the concentration of the protein solution standard, uP is the uncertainty associated with
the concentration of the protein solution standard, m is the mass of sample used, and
um is the uncertainty associated with the amount of sample used.
The final ICAT molar concentration for each standard material was the mean of the
molar concentrations of the three peptides used. The associated uncertainty was
calculated by combining the average uncertainty of the uncertainties associated with
each of the three values (u) with the variation between samples associated with the
digestion (bvar, the standard deviation of the three values divided by
3 ) as described
by equation 3 above.
The total uncertainty associated with the molar fraction of the 22 kDa form of
somatropin via ICAT contains a component due to the differences within the digestion
between the standard materials (EP/WHO), which contain a variety of excipients, and
the purified in-house standard (IS), which does not. The uncertainty associated with
the between blend digestions for the EM-IDMS method to account for the global
variability of the digestion has been eliminated here as the samples are digested in a
single vessel.
Somatropin iTRAQ uncertainty
The uncertainty associated with the individual iTRAQ results corresponding to the
concentration of protein in each sample from all the observed iTRAQ-labelled
peptides identified per digestion was calculated by applying Equation 5 above. For
iTRAQ, the value of R used was the mean of the repeat ratio measurements of all the
115 (WHO) or 116 (EP)-labelled peptides to the 114-labelled peptides of the
independent standard, n=5.
The combined uncertainty was then calculated in the same manner as described
previously, by combining the average uncertainty of the uncertainties associated with
each of the three values (u) with the variation associated with the digestion (bvar, the
standard deviation of the three values divided by
3 ), equation 3 above.
This total uncertainty associated with the molar fraction of the 22 kDa form of
somatropin via iTRAQ contains a component associated across with a significant
number of tryptic peptides (>16) from across the protein sequence used to infer
protein concentration, ensuring any variability associated with the extent of digestion
is also encompassed.
Combined results - uncertainty
Results of the independent methods EM-IDMS, standard addition and iTRAQ were
combined to give a final value for the standards. The total measurement uncertainty
for this final result was calculated by combining the variation between the three
methods and the uncertainty associated with the independent protein standard used, as
shown in the equation below (equation 6).
Equation 6
u
ucombined all methods    IS
 C IS
2

  bvar 2

Where uIS is the uncertainty of the independent standard, CIS is the mole fraction of
the independent standard, and bvar is the standard deviation of the final values from
each of the three methods divided by
3.
Within this final result, all components of uncertainty, including the variability of
digestion, uncertainty associated with the mass fraction assignment of the peptide
standards and instrument variability have been encompassed.