### Overview

The iTRAQ™ protocol uses four reporter ions of 114.1, 115.1, 116.1 and 117.1 Da. These are singly-charged and so found in the region 114 - 117 m/z in the mass spectra. Relative quantitation is performed by comparing the peak areas of each of these reporter ions in the mass spectrum. The default setting for i-Tracker assumes that the bulk of the peak will occur in the region of the reporter ion mass ± 0.05 Da. Each ion peak within this region is captured. The area of each reporter ion is then calculated by summing the areas of the trapezoids formed between each captured peak. This can be user-adjusted to suit the characteristics of the mass analyser used.

The reagents supplied by ABI are not 100% pure, but come with a datasheet by batch indicating the percentages of each reporter ion reagent that differ by -2, -1, +1 and +2 Da from the quoted mass. This quality control measure is taken into account by the i-Tracker software by adjusting each peak area as appropriate. The simultaneous equations needed for making this adjustment are solved using Cramer's rule. If the determinant of the initial matrix of coefficients is zero, or if no purity information is supplied, the software will output a warning and proceed without purity correction.

Following any purity correction, the peak areas are normalized. These normalized areas are used to calculate the quantitative ratios between each reporter ion. If the maximum peak height of any reporter ion is below the user-defined threshold for consideration, the string "UT" for under-threshold is the output. If there is no peak in the spectrum associated with a reporter ion as comparator (i.e. the denominator of the ratio calculation) the string "NA" is output.

Very low peaks in the mass spectra may suffer from large errors due to the quantized nature of the ion current. In order to provide some idea as to the potential magnitude of this error, a set of ratio-errors is reported which represent the maximum percentage error due to quantization. It should be noted that this reported error does not account for errors in detection of the ion current nor systematic error, such as background noise, in the measurement, but merely serves as a warning against placing too high confidence in reported ratios when these have been based on peaks with low ion counts.

### Detailed description

Items in this section are presented in the order in which data is processed by the software with one exception: The calculation for the determinant of coefficients, for purity correction, is performed very early in the processing sequence, in order to minimise repetitive calculation, whereas here it is presented as part of the purity correction section. Other than for this the following may be considered in parallel to the Perl code (i-Tracker.pl), which contains similar headings and flags for straightforward comparison.

#### Data input

Spectra must be non-centroided as the peak area calculations rely on the presence of all the peaks that would otherwise be combined in a centroided output.

i-Tracker can read spectra in.dta or.mgf formats. The two formats differ in the title information they contain and slightly in the format of the precursor ion information. However, the main difference in the way i-Tracker handles these files is that.dta files, which represent a single spectrum, are read into memory before processing whilst.mgf files are read in to memory spectrum by spectrum whilst keeping the input file open. Once a spectrum's information has been read, further processing is identical between input file formats.

#### Reporter ion peak collection

All peaks in the ranges:

114.1 ± 0.05

115.1 ± 0.05

116.1 ± 0.05

117.1 ± 0.05

are collected as a {mass}->intensity pair (hash). The default range of ± 0.05 was identified by considering the mass accuracy of the mass spectrometer and through manual inspection of a number of these peaks in the output files. This can be user-adjusted through an option presented at run-time.

#### Reporter ion area calculation

For each reporter ion peak range, the total area is calculated by summing the areas between ion peak pairs using the trapezoid approximation for calculating the area under a curve.

For example, a reporter ion peak may be comprised of four ions within the range considered. Here a, b, c and d are ion masses and a', b', c' and d' are their intensities. The total area (A) of this reporter ion peak is therefore:

A = (*b*-*a*) * 0.5 * (*a*'+*b*') + (*c*-*b*) * 0.5 * (*b*'+*c*') + (*d*-*c*) * 0.5 * (*c*'+*d*')

The maximum ion peak intensity is also identified at this point for comparison with the user-entered ion intensity threshold and for the calculation of quantisation errors.

#### Purity correction

Each batch of iTRAQ reagents supplied by ABI is labelled with sixteen purity values indicating the percentages of each reporter ion that have masses differing by -2, -1, +1 and +2 Da from the nominal reporter ion mass due to isotopic variants. This information can be used to correct the peak areas calculated for each reporter ion to account for the losses to, and gains from, other reporter ions. Losses to ion peaks not in the reporter ion range are also accounted for in this method.

The simultaneous equations needed to solve this problem are fairly complicated, but can be framed such that Cramer's rule may be applied. A detailed explanation of how to use Cramer's rule to solve simultaneous equations may be found in [8]. Briefly, if the determinant of the matrix of coefficients for the simultaneous equation is non-zero, the solution in each variable may be found. The four-way simultaneous equation for purity correction may be written as:

a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p are the sixteen purity correction values (as percentages) in the order:

114.1 - 2 Da, 115.1 - 2 Da, 116.1 - 2 Da, 117.1 - 2 Da, 114.1 - 1 Da, etc...

(NB This is a different logical order to that in which the user enters the values, they are rearranged within the program).

w,x,y,z represent the percentage of each peak expected to be present at the mass of the reporter ion associated with that peak. Here, w is for 114.1, x for 115.1 etc.:

w = (100 - (a + e + i + m))

x = (100 - (b + f + j + n))

y = (100 - (c + g + k + o))

z = (100 - (d + h + l + p))

The area (A_{r}) of each reporter ion peak (_{r}), as calculated above, can now be written in terms of the true areas of peaks (T_{r}):

The task is now to calculate each T_{r} according to these equations.

The determinant of the matrix of coefficients can be found:

If |C| is zero, then there is either an infinity of solutions or there are no solutions to these equations and so the purity correction module is skipped. If |C| is non-zero, purity correction proceeds:

The *Cramer determinants*, Δ_{r}, are found to be:

The true areas, T_{r}, can now be found:

T_{r} = Δ_{r}/|C|

#### Peak normalisation

Providing that the sum of the total areas is non-zero, normalised areas (N_{r}) are calculated as:

N_{r} = T_{r} / (T_{114.1} + T_{115.1} + T_{116.1} + T_{117.1})

If the sum of all areas is zero, then each normalised area is also considered to be zero.

#### Under threshold checking

If the maximum ion peak intensity for any reporter ion peak area is equal to or less than the user-entered threshold, a flag of "UT" for "Under Threshold" is reported.

#### Ratio calculation

All ratios of true areas are calculated to three decimal places provided that the denominator is non-zero. If the denominator in any ratio calculation is zero, an "NA" flag is reported.

#### Quantisation error calculation

Very low ion counts may introduce a significant quantisation error. To some extent this is mitigated against by a sensible user-entered threshold of around 20 ion counts, but even so, comparing two reporter ion peaks that just pass such threshold could introduce an error of around 2.5% into the final ratios:

Eg. The user-entered ion count threshold is set to 19. The "correct" areas of peaks 1 and 2 should have been based on intensities of 20.5 and 19.5 respectively, but the reported ratio is 1:1 due to the quantum nature of ion counts. A quantisation error of 2.5% has been introduced in this case. For ion counts lower than this, the potential quantisation error will be much greater, but their ratios in this case would have been masked by the user-entered threshold.

These potential quantisation errors are reported alongside the peak ratios to highlight instances where results might be compromised by this effect. They are calculated as a percentage error between two ratios thus:

Err(1,2) = (100 * ((0.5 / Peak1Max) + (0.5 / Peak2Max))

these are output in the errors matrix for each ratio.

Similar potential quantisation errors in the normalised areas are calculated as:

Err(1) = (100 * (0.5 * Peak1Max))

these are output in the left-right diagonal of the quantisation errors matrix.