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Transcript
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 utotal 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 n2 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 ucombined 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.