1 Introduction

The fast growing application of metabolomics in biological research has resulted in the development of large-scale analytical techniques, which mostly employ mass spectrometers as detectors. The ideal result of a metabolomics analysis would be a complete metabolite profile that consists of a list of all compounds and their abundance in the sample studied, giving way to subsequent biological interpretation. The actual result of such an analysis is currently far from this, not only due to analytical and ‘informational’ limitations, but also resulting from the complexity of biological samples. These are generally composed of a highly diverse mixture of (macro) molecules in a very broad range of concentrations (Moco et al. 2007).

Technical advances in mass spectrometry, resulting in increased mass resolution and accuracy, enable the (putative) identification of metabolites simply by their accurate mass determinations (Aharoni et al. 2002; Lim et al. 2007; Murch et al. 2004; Thurman et al. 2005). For instance, Fourier transform ion cyclotron mass spectrometry (cyclotron FTMS) and Orbitrap FTMS (Olsen et al. 2005) typically analyse the masses of ions with an ultra high accuracy of less than 1 ppm deviation from the calculated masses. Such high mass accuracies considerably decrease the number of possible solutions to the elemental composition of the detected ion. However, even accuracies of 1 ppm or better are not considered to be sufficient for the unequivocal de novo identification of unknown metabolites solely on the basis of elemental composition calculations (Kind and Fiehn 2006; Verhoeven et al. 2006). Nevertheless, high mass accuracy will still significantly narrow down the chemical solution space, enabling efficient and batch-wise searching in databases of previously identified metabolites. Data on retention time, MS/MS fragmentation, and UV/Vis spectra can additionally be used for the putative or unambiguous identification of the mass signals (Moco et al. 2006).

A widely-used analytical approach to obtain extensive metabolite profiles from crude extracts is based on liquid chromatography for analyte separation, coupled to high resolution time-of-flight mass spectrometry (LC-TOF-MS) for detection (De Vos et al. 2007; Idborg et al. 2005; Peterman et al. 2006; Saghatelian et al. 2004). The accuracy and the precision of a TOF-MS depend on a number of technical parameters (Chernushevich et al. 2001). It is a common practice to calibrate the system by automatically alternating the analysis of the sample with the analysis of a compound of known accurate mass (lock-mass). The latter serves as a calibration standard with which the observed m/z value can be corrected on-line (Eckers et al. 2000). With the present generation of TOF mass spectrometers and by using an on-line lock-mass calibration, mass accuracies within 3–5 ppm are routinely obtained in the 100–1,000 Da range (Chernushevich et al. 2001). The calibration can also be performed off-line by using internal standards or low intensity ions as shown by (Makarov et al. 2006) and (Olsen et al. 2005).

Although the lock-mass correction will compensate for random drifts in the mass measurement, a considerable number of TOF instruments is equipped with a time-to-digital converter (TDC), which brings about another limitation: a relatively small dynamic range for accurate mass measurements. The under-estimation of accurate masses at higher ion intensities as a result of TDC functioning is a recognized problem known as the ‘dead time effect’ (Gedcke 2001). Consequently, when using a lock-mass reference in accurate mass measurements, the mass error will be minimal at an intensity ratio of analyte and calibrant of 1, but systematic over-estimation of the accurate mass will occur at analyte intensities less than the lock-mass intensity, and systematic under-estimation at intensities higher than that of the lock-mass (Colombo et al. 2004). In addition, the problem of stochastic noise due to low count rates arises at low signal intensity (Gu et al. 2005). To overcome these effects, a correction function can be derived using internal standards measured at different ratio’s, which can then be applied to the subsequent analytical runs (Kofeler and Gross 2005). This typically improves accuracy from 5 to 2–3 ppm. The experimental setup requires individual calibration runs with 13C labeled standard for each series of experiments in order to determine the correction function. This seriously limits the applicability of the method, given the expense and availability of the 13C labeled standard.

It is current practice in untargeted metabolic profiling to calculate the average accurate mass from a single chromatographic mass peak over multiple scans (Smith et al. 2006), without taking into account the intensity-dependent mass error. The systematic error in mass measurements using TDC-based TOF-MS can only be avoided by careful and time-consuming manual analysis, limiting the exact mass calculations to those chromatographic scans that display an analyte mass intensity similar to the lock-mass intensity. For instance, in untargeted LC/TOF-MS based metabolomics studies, mass signals identified as being significantly different between (groups of) samples are usually identified by manually retrieving the accurate masses and corresponding elemental compositions from the raw data (Bino et al. 2004; von Roepenack-Lahaye et al. 2004; Vorst et al. 2005; Wilson et al. 2005). Although dedicated software is available to align and compare high mass resolution LC/TOF-MS datasets, e.g. Markerlynx (available from Waters), MetAlign (www.metalign.nl), MZmine (Katajamaa et al. 2006), AnalyzerPro (www.spectralworks.com), and XCMS (open source) (Smith et al. 2006), these tools currently lack an automated intensity-dependent accurate mass correction. As a result, accurate masses generated by these software tools can deviate strongly from the real masses of the compounds detected when used to process TDC-based TOF-MS data. This hampers automated elemental composition calculation and compound annotation.

In a previous study (Moco et al. 2006) we have described a procedure, called metAccure, which allowed us to obtain a mass error of 2 ppm or less from tomato extracts on a QTOF Ultima MS, containing a TDC. After the reconstruction of the chromatographic mass peak over consecutive scans, the accurate mass was obtained by averaging the observed masses with signal intensity of 0.25–2.0 times the local lock-mass intensity. However, this approach could only be successfully applied to about 10% of the collected mass signals, as the rest of the signals were too low compared to the corresponding lock-mass intensity.

Here we describe the intensity-dependent error in TOF-MS based mass measurements in the context of a large metabolomics data set. A mathematical method to obtain improved accurate masses based on estimation of the intensity-dependent mass error is presented. First, mass specific trails are reconstructed of all observed instances across the chromatographic profile of a number of known metabolites. The latter were present in a large number of samples and served as training set for the procedure. Subsequently, the mass error is described as a function of the ratio of the metabolite signal intensity in each scan to the most closely associated lock-mass intensity. The correction is then applied to both low and high intensity mass signals. We show that this approach results in an improved mass accuracy of better than 1 ppm compared to the standard 5 ppm deviation. The procedure has been implemented in a Python 2.4 script, which reads NetCDF data, corrects them and returns a corrected NetCDF file for subsequent processing.

2 Materials and methods

2.1 HPLC-QTOF-MS analysis of crude plant extracts

Crude aqueous methanol extracts were prepared from seedlings of genotypes of Arabidopsis thaliana (Keurentjes et al. 2006) and from potato tubers at different developmental stages. The conditioning and calibration of the HPLC and the MS systems were as described recently (De Vos et al. 2007). The analysis of the 166 Arabidopsis samples was done using electrospray ionization (ESI) in negative mode and an HPLC run of 30 min. ESI in positive mode was used for the 24 potato samples with an HPLC run of 60 min. In both analysis series, an Alliance HPLC (Waters) and a QTOF Ultima MS (Waters) equipped with a TDC were used. The mass resolution of the QTOF-MS was 10,000. Masses between m/z 100 and 1,500 were recorded each at scan rate of 1 per second, with an ion collection time of 0.9 s and an interscan delay of 0.1 s. All mass data were recorded in centroid mode. Leucine enkephalin (C28H37N5O7) was used as a lock-mass, sampled through a separate source every 10 s, with ion intensities ranging from 400 to 4,000 (Arabidopsis series) and from 600 to 1,200 (potato series). At the beginning of each series of analyses, the lock mass concentration was set at an intensity of about 1,500 counts per scan. However, due to variations in pump performance and spray efficiency of the capillary needle, the actual lock mass intensity per measurement can vary considerably over a large series of samples.

2.2 Data handling

The MassLynx 4.0 software package (Waters) was used to collect lock-mass corrected mass data in centroid mode and to store them in RAW-format. MassLynx data were then converted into the NetCDF format using MassLynx’s DataBridge utility. Next, a Python 2.4 procedure was used to extract intensity and m/z values for each mass signal in each scan and subsequently to combine mass peaks in consecutive scans into trails when the accurate mass difference was below a user-defined threshold (here set at 50 mDa). In the next step, results from multiple runs for a set of metabolites characterized both by their m/z value and retention time expressed in scan number were integrated. All trails containing m/z values within 50 mDa differences from the required exact accurate mass were collected. Then the trails were selected based on retention time allowing 20 scan numbers deviation. The data were then used for statistical analysis.

2.3 Metabolite selection

A set of known metabolites, present in the majority of the samples and in broad range of concentrations, was selected for the calculation of the mass error. In plants, a wide variety of secondary metabolites is detected with LC-MS, including flavonoids, phenylpropanoids, and glucosinolates. The majority of the metabolites selected for the analysis of the Arabidopsis samples in this study were glucosinolates because they give unique ion masses, i.e. they are easy to extract from the raw data and are known to be present in many different genotypes (Kliebenstein et al. 2001; Reichelt et al. 2002). The same criteria were applied to the selection of the metabolites from the potato series.

2.4 Intensity-based accurate mass calculation

The relation between the mass error and the ratio of the intensity of the analyte (Int) and the nearby lock-mass intensity (Int lm ) was described as a linear function of the form \( M_{{corr}} = M_{{obs}} + c\log10(Int/Int_{{lm}} ) \), where M corr is the corrected accurate mass, M obs is the observed accurate mass, and c is the parameter estimated from measurements on the set of known metabolites. The analyte intensities were sorted and then grouped in groups of 100 data points each. The average intensity and the standard deviation of the corresponding masses within each group were calculated. The mass error estimation (M err ) was found to be a linear function of the inverse of the intensity. The corrected mass per trail was calculated as a weighted average using 1/M 2 err as a weight. The final value for the accurate mass was obtained as a grand average of the average mass of the individual samples. The trail building is the most time consuming step in the procedure. The time depends on the number of masses in the NetCDF file. A file containing 59,984 mass values was processed in 15 s whereas 1 min and 33 s were needed for 233,846 mass signals. The calculations were performed on a computer running Linux kernel 2.6 with an Intel Pentium 4 2.80 GHz processor and 2 GB of physical memory.

2.5 Software availability

MetAccure is primarily a procedure for intensity dependent mass error correction. The Python 2.4 implementation is available upon request.

3 Results and discussion

3.1 The influence of signal intensity on mass accuracy

To study the influence of the intensity of the analyte ion signal on the actual accurate mass measurement, a set of trails (intensity and accurate mass data derived from a single chromatographic mass peak in a series of consecutive scans) was automatically extracted from a metabolomics experiment on 166 extracts made from Arabidopsis seedlings. In this way, a large number of accurate mass measurements for a single compound, derived from multiple scans and extracts and at a wide range of signal intensities became available for analysis. For the most abundant compounds, which were often detected as being above background (i.e. 3 times local noise) in more than 30 scans per run, this resulted in a substantial collection of on average 4,500 data points per mass signal, allowing detailed statistical analysis. In total, the mass signals of 14 metabolites were collected. Their common names, molecular formulae, and theoretical accurate masses of the [M − H]- ions are listed in Table 1.

Table 1 Metabolites used in development and evaluation of the accurate mass correction procedure
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An example of a typical trail of the ion signal corresponding to sinapoyl malate ([M − H]− = 339.0719; Table 1) is shown in Fig. 1a. At higher signal intensities (>3,000 ion counts per scan), the measured mass was obviously underestimated as a result of the ‘dead time effect’ of the TDC-type of TOF-detector used. The systematic error reached up to 5.2 mDa (−15 ppm) at an intensity of 18,268 counts/scan. For comparison, the intensity of the lock-mass was in the range of 1,306–1,505 ion counts/scan. Figure 1b, where signal intensity has been plotted as a function of the detected accurate mass, shows the strong negative correlation between both parameters.

Fig. 1
figure 1

Example of a trail of an abundant mass signal given by sinapoyl malate. (left) Mass signal intensity [ion counts per scan] and the measured lock-mass corrected accurate mass of the parent ion [M − H]− are plotted for the elution from scan 567 to 585. The theoretical accurate mass of 339.0719 (acc_mass) is given by the dotted line. (right) Scatter plot of measured accurate mass versus mass signal intensity per scan for the same trail. Lock-mass intensity was 1,306 to 1,505 ion counts per scan

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In Fig. 2, the accurate mass error (measured mass–actual mass, in mDa) has been plotted against signal intensity in a large number of scans over a wide range of intensities of the major ions of kaempferol-glucoside-rhamnoside and glucohirsutin. The observed patterns are highly similar for these two ions, the main distinction being the amount of scatter around the average. For practical purposes, three different intensity ranges are discerned based on the above observations (Fig. 2b): (i) range I (intensity <150 ion counts per scan), where the accurate mass error is dominated by random effects overshadowing any systematic error; (ii) range II (150–20,000 counts), encompassing a region with a systematic intensity-dependent accurate mass error; (iii) range III (>20,000 counts) in which ion intensities are systematically underestimated resulting in a more complex correlation between mass error and intensity as a result of detector saturation. In untargeted LC/MS analyses, detector saturation is prevented as much as possible, so that range III data are normally rare and at most only observed for a few highly abundant ion species.

Fig. 2
figure 2

Mass error versus signal intensity per scan for two abundant mass peaks belonging to kaempferol-glucoside-rhamnoside (a) and glucohirsutin (b); the roman numerals indicate the three intensity ranges discerned: I (<150 ion counts/scan), II (150–20,000) and III (>20,000)

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Instead of using the raw data, one can express intensity as a fraction of the local lock-mass intensity. This ensures that local fluctuations in the lock-mass intensity and hence, in the lock-mass assisted accurate mass measurements, are corrected for. The masses were sorted on the adjusted intensity for ranges I and II and the average mass error and average adjusted intensity per bin of size 100 masses were calculated. The results are presented in Fig. 3 and illustrate that the observed mass error is minimal at ion intensities close to the lock-mass intensity (Colombo et al. 2004). Because the observed mass error appears to be independent of the m/z and nature of the ion involved, the accuracy of experimentally-obtained accurate mass measures can in practice be enhanced by a simple arithmetic correction (based on the adjusted intensity only). This is true in particular for data in intensity range II, where the error is mainly systematic in nature. Although in the lower intensity range I the mass accuracy is strongly influenced by stochastic effects, accurate mass measurements in this range will benefit from the same correction function. At the high ion intensities of range III, the correlation between intensity and mass error is more complicated due to detector saturation effects, hindering a simple intensity-dependent correction of the accurate mass. In LC/MS, mass peaks with such high intensities will however always be accompanied by accurate mass data of the same compound in neighboring scans of the chromatographic peak that have mass signal intensities in range II. This eliminates the need for a correction, provided the high intensity signals can be masked during the automated correction.

Fig. 3
figure 3

Systematic mass error for the mass peaks observed in the training set of seven metabolites. Shown are the moving averages (window size = 100) of the mass error [mDa] over the intensity/lock-mass intensity ratio [counts/scan] in the intensity range (II). Abbreviations of compounds correspond to those given in Table 1

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3.2 Intensity-based accurate mass correction

3.2.1 Arabidopsis model derivation

To be able to correct for the observed systematic error in the accurate mass measurements in range II, we attempted to describe the mass error as a function of the adjusted intensity ratio (to the nearby lock-mass intensity). For the training set of seven compounds that covered data points in intensity range II (Table 1), we observed that a linear function of the logarithm of the adjusted intensity fitted this relationship quite well. The regression coefficients for the seven regression lines were very similar and explained about 90% of the variation. All seven curves passed close to the origin, which indicates that the calibration was properly performed. Therefore, a single linear relationship through the origin was fitted for all seven molecules, resulting in the mass correction function:

$$ M_{{corr}} = M_{{obs}} + 0.00806051\log10(Int/Int_{{lm}} ) $$

where M corr is the corrected mass [Da], M obs is the observed mass [Da], Int is the intensity of the analyte [ion counts], and Int lm the intensity of the nearby lock-mass [ion counts]. The regression line explained 90.8% of the variation. The regression coefficient had a standard error of 1.87E-05. The property of the mass correction functions was evaluated using a leave-one-out (LOO) cross-validation procedure: only six of the compounds were used to estimate the mass correction function, and applied to the left-out molecule. This was done in turn for all seven molecules, which resulted in an average mass error of −8.22E-05, an average absolute mass error of 1.21E-03 and a variance of the mass error of 2.54E-06, indicating a good prediction of the corrected mass values. The present correction function is based on 7 known metabolites. Although using a larger number of metabolites in principle is more appropriate to establish a reliable function, in practice samples, and especially plant extracts, may contain only a few unambiguously identified metabolites. We tested whether the correction function can be improved by using more metabolites. Therefore, the model was evaluated by carrying out the LOO cross-validation using 14 metabolites (Table 1). The values of the average mass error, the average absolute error, and the variance of the mass error were −11.88E-05, 1.19E-03, and 2.63E-06, respectively. The percentage of explained variance for all models was around 90%. These data indicate that the training set of only 7 metabolites was sufficient to accurately determine the correction function.

Due to stochastic effects that result from the small number of ion counts at low intensities, the variance of the mass error increases with diminishing ion intensities (Fig. 2). Figure 4 describes this effect in more detail. The corrected masses were sorted on intensity and bins of mass points for each were made. For each bin, the standard deviation of the observed mass and the average intensity were calculated. The curves for 6 out of the 7 molecules (exception sinapoyl glucoside) were very similar. The larger the bin size the smoother the curves were. Varying the bin size from 10 to 150 showed that bin size of at least 100 is needed to obtain a smooth curve. This means that many data points (many samples) are needed in order to obtain a reliable estimation of the mass error. When expressed in relative terms (as proportion of the exact ion mass [ppm]), the standard deviation in the corrected mass is clearly a function of the intensity and largely independent of the nature of the ion involved. At higher intensities, the standard deviation approaches a minimum (about 3 ppm). The observed relative standard deviation (M err ) [ppm] can be described as a function of the intensity:

$$ M_{{err}} {\text{ = 2}}{\text{.52 + 298}}{\text{.44/}}Int $$
Fig. 4
figure 4

Relative standard deviation for the mass peaks in the training set of seven metabolites. Shown are the relative standard deviation [ppm] and average intensity [counts/scan] of bins of 100 data points with similar intensities

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The regression explained 78.5% of the variance.

The procedure to calculate a single corrected mass for a complete mass trail, would then include the following steps:

  • Masking data points in range III (Int > 20,000 ion counts/scan);

  • Selecting a set of known masses from the data points in range II, and determining the coefficients for fitting the mass error and the relative standard deviation;

  • Calculating corrected mass (M corr ) and error estimate (M err ) for each data point;

  • Averaging the available corrected masses within a trail using 1/M 2 err as weighing factor.

A critical condition in the procedure is that the experimental samples contain known metabolites that, furthermore, cover a broad range of intensities. In practice, 5–10 known masses suffice. The model needs to be determined for each set of samples, even if the same set of metabolites is used, as the concentration of the metabolites can vary.

3.2.2 Arabidopsis model evaluation

The performance of the proposed procedure was evaluated on the compounds from the test set that were not used in the derivation of the regression coefficients. The grand average mass error using all raw masses in a trail is given in Table 1. Prior to correction, high accuracy was found for sinapoyl glucoside and 7-methylthioheptyl glucosinolate. In general, for compounds with saturated peaks (intensity maximum up to 34,000 ion counts/scan) the mass error had a large negative value. An exception was 7-methylthioheptyl glucosinolate for which the mass error was 0.8 ppm. The median of the adjusted intensity ratio (to the associated lock-mass intensity) calculated over the samples for this compound was 1.3, whereas for 8-methylthiooctyl glucosinolate the corresponding value was 13.5. The large value of the median indicates that, for the latter compound, a large number of mass points had much higher signal intensity than the lock-mass intensity, hence the high overall mass error of −22.6 ppm for this compound. The mean mass error for the compounds in the test set varied between +5.0 and +14.1 ppm. The mass peaks for the majority of the compounds in this set had moderate intensities, which may explain the positive value of the mean mass error of all data points. Next, each mass point with signal intensity in the ranges I and II was corrected. To check the influence of the number of data points used for the estimations of the mass error, three different sets of mass points were used to calculate the sample mean. The sets were defined as follows: mass data points within intensity range II only, data points within range I only, and data points within an intensity window of 0.5–2 times the lock-mass. The mass errors were calculated based on the corrected accurate mass and on the raw observed accurate mass (Table 2).

Table 2 Mass accuracy, expressed in ppm, obtained for different sets of ion intensity signals
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In general, without correction (i.e. the observed masses) the error of mass points within range II varied considerably between compounds, from 2.26 ppm for gluconapin to 10.37 ppm for glucoiberverin. The error of mass points in range I had large positive values: 21.1–25.6 ppm. The best result for these uncorrected data was obtained when selecting only mass intensity points within the window of 0.5–2 times the local lock-mass intensity. In this case, the mass error was <1 ppm, except for glucoiberverin and UDP-d-glucose. The mass errors in all intensity ranges decreased significantly when the corrected masses were used in the accurate mass calculations. For 6 out of 7 metabolites the mass error of data points within intensity range I was within 2 ppm, while the error for UDP-d-glucose was within 4 ppm. This demonstrates that the mass accuracy for metabolites with ion intensities of only 150 counts/scan or less (i.e. far below the lock mass intensity) can be significantly improved by the proposed correction procedure. The absolute mass errors were generally <1 ppm for mass points in intensity range II and within the window interval. An exception was progoitrin, for which the error was slightly higher: 1.83 ppm. Progoitrin was present in 40 samples of which 16 had no mass signal intensities in region II, and this might be the reason for the deviation of this metabolite from the rest of the compounds. Indeed, when data points from set range I and range II were combined for the calculation, the error for progoitrin decreased to 0.89 ppm while there was only a very slight change in the mass error for the rest of the metabolites (data not shown).

The correction function was currently defined and evaluated using a set of compounds with masses higher than 300 Da. In the current datasets, the majority of the signals with m/z values lower than 300 Da originated from polar metabolites. With the reversed phase C18-chromatography method used, these compounds mainly elute within the first 3 min, i.e. within the injection peak. This chromatographic region is therefore not well resolved. With the proposed trail-building procedure it was not possible to extract pure components, due to overlap in both retention time and m/z values of mass signals. Unintended fragmentation was the other source of low m/z values in this dataset, but the intensities of these mass signals unfortunately were very low and therefore could not be used in derivation of the correction function. An exception was the sinapate fragment, elemental composition C11H15O5, [M − H]− 223.0612. After correction, the mass error of this fragment within intensity region II decreased from −10.97 ppm to −2.45 ppm. This error value is slightly higher than that of the other compounds, but still significantly improved compared to using the observed mass values.

Compared to other methods (Clauwaert et al. 2003; Kofeler and Gross 2005) for obtaining TOF-MS mass accuracy <3 ppm deviation, the proposed method is simpler and does not require additional experiments. For the derivation of the intensity corrected accurate mass using the method of (Kofeler and Gross 2005), 13C labeled standards are needed. Internal mass calibrants for each mass range can be applied for local mass correction in the mass region of the calibrant (Clauwaert et al. 2003). This local mass correction is then applied in both MS and MS/MS modes by using the energy switching functions of the mass spectrometer to selectively fragment the unknown while keeping the reference ion intact. Although this is a suitable technique for use in (typically more targeted) pharmaceutical research, it is not practical for untargeted metabolomics applications, even if high mass accuracy can be achieved.

The present analysis was done using a large number of samples. The influence of the number of samples on the correction function was investigated by selecting randomly between 10 and 160 samples. The regression coefficient was determined for each subset and the average mass error of the sample was calculated using mass points from region II. In this experiment it was not possible to estimate the weights because of the small number of data points available when small sample numbers were selected. A minimum of 70 samples was required for convergence of the error of the regression coefficient. The mass error for the training set was within 1 ppm, independent of the number of samples. However, much larger mass deviations were found for the metabolites in the test set (listed in Table 2) when a small number of samples was used, indicating overfitting of the correction function.

Next, we investigated the intensity corrected mass error as function of the intensity of the analyte, by calculating the intensity ratio of metabolite signal versus lock-mass intensity over different ranges. The masses in each sample were sorted on the intensity ratio and the average mass error was calculated for each intensity ratio window size of 0.25 units. The results for the observed and corrected masses of 8-methylthiooctylglucosinolate are shown in Fig. 5. When the corrected masses were used, the mass error remained within 2 ppm for an analyte/lock-mass intensity ratio of up to 7. To achieve similar accuracy for the uncorrected (observed) masses, only a small intensity interval (ratio to lock-mass of 0.75–1.25) could be selected. This result shows that, after applying the intensity dependent mass correction, high mass accuracies can be obtained for a large range of signal intensities (dynamic range of about 2 orders of magnitude).

Fig. 5
figure 5

The effect of the intensity-dependent correction on the average mass error for 8-methylthiooctyl glucosinolate and sinapoyl malate in the intensity ranges I and II. Shown are the moving averages (window size = 0.25) of the mass error [ppm] over the intensity/lock-mass intensity ratio [counts/scan] using the observed and the corrected masses

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3.2.3 Potato model

The procedure was further tested on a second set of 24 samples obtained from potato tubers and recorded in ESI positive mode. The samples consisted of three replicate extracts from 8 different development stages of a single genotype and contained much less variation in metabolite concentration than the Arabidopsis data set described above. A set of 7 metabolites present in all potato samples is given in Table 1. The first 5 metabolites were used for the training. As test set β2-chaconine and β2-solanine were used. The regression coefficient of −8.83838E-03 was quite similar to that of the Arabidopsis samples. The error of the regression coefficient was 6.15E-05 and 82.7% of the variance was explained by the regression. In general, similar trends as for Arabidopsis were observed when comparing observed (raw) and corrected masses for data points with intensities in range I, range II, and in a window interval of 0.5–2.0 times the local lock-mass intensity. Although there was no large difference between the mass accuracy obtained for the corrected masses from range II and the window interval compared to the raw masses from the window interval, an intensity dependent correction greatly improved the mass accuracy for the low intensity signals (range I). In this particular experiment, the lock-mass intensity varied between 600 and 1,200 counts/scan. This means that for the low abundant metabolites (lower than 300 counts/scan in all samples) the window approach is not applicable.

3.3 Experiments with low lock-mass intensity

In non-targeted metabolomics studies, the aim is to obtain accurate masses for as many mass signals as possible over a broad range of ion signal intensities. Relatively high lock-mass intensity in combination with the window approach is not suitable for the accurate mass determination of low abundant metabolites. The intensity of the lock-mass can be lowered as much as possible so that low abundant metabolites can also be analysed. As for the high abundant metabolites, there will always be mass data points within the predefined intensity ratio window. To test this, an additional experiment was done in which 32 samples from the original 166 extracts of Arabidopsis were randomly selected and re-analyzed by LC/QTOF-MS in ESI negative mode, but now with a lock-mass intensity in the interval of 160–400 counts/scan, i.e. operating on the lower border of range II (Fig. 2b). The systematic under-estimation at high intensities was still present, whereas at low intensities the mass error was random around zero and confined within 20 mDa for most of the compounds. As a result, it was not possible to fit the data. As expected, the mass error was always negative for data points from region II and varied from −1.12 ppm (glucoiberverin) to −15.52 ppm (sinigrin). As for the window approach, the absolute mass error was within 2 ppm. However, when higher lock-mass intensity in combination with intensity dependent correction was used, the mass error was lower than 1 ppm and the dynamic range was of about 2 orders of magnitude, in contrast to the window approach.

3.4 Applicability of the model

The empirical method to correct the intensity-dependent mass-error outlined here is suited specifically for LC/MS based metabolomics analyses with TOF-mass spectrometers equipped with a time-to-digital converter (TDC). Many instruments, including most Waters Micromass and many Bruker machines (except the Bruker MicroTof, which is equipped with an ADC), which are widely used in (plant) metabolomics, are equipped with this type of detector. The TDC is also the detector of choice in low intensity analysis, because of its superior mass resolution and high noise insensitivity compared to analog-to-digital (ADC) converter based detector systems (Cajka and Hajslova 2007; Tamura 2002). Although recent modifications to the ion optics design of TDC based instruments have resulted in a much larger dynamic range, detector effects of intensity on mass accuracy are still present in the lower intensity ranges. This most recent generation of instruments will therefore also benefit from the described method. Added to the large base of Waters Micromass and Bruker instruments installed around the world and the long economic life of these costly instruments, we expect that the computational procedure for enhanced mass accuracy presented here will be useful for a very large user base.

4 Conclusions

This study has shown that the systematic under-estimation of the accurate mass at intensities higher than those of the lock-mass can be corrected very well, resulting in a drastic improvement of the mass accuracy from nearly 20 to <1 ppm deviation from the calculated mass. In addition, a significant improvement in the mass determination was obtained for low intensity signals, as the mass error remained within 1 ppm when mass points with intensities lower than 150 counts were included in the analysis. To our knowledge, the only previous numerical attempt at intensity-dependent error correction was based on using 13C labeled internal standards (Kofeler and Gross 2005). The method proposed here can be applied using endogenous metabolites and does not require additional measurements and expensive 13C labeling. An efficient way of establishing the specific regression coefficients for each sample series within an LC-MS based metabolomics experiment would be to routinely incorporate a number of runs with a dilution series of a standard sample. This will allow for a more standardized calculation of the correction function.