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Quantification of fructo-oligosaccharides based on the evaluation of oligomer ratios using an artificial neural network
Analytica Chimica Acta 638 (2009) 191–197
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Quantification of fructo-oligosaccharides based on the evaluation of oligomer ratios using an artificial neural network Lucia Onofrejová, Marta Farková, Jan Preisler ∗ Department of Chemistry, Faculty of Science, Masaryk University, Kotláˇrská 2, 611 37 Brno, Czech Republic
a r t i c l e
i n f o
Article history: Received 24 November 2008 Received in revised form 17 January 2009 Accepted 19 February 2009 Available online 2 March 2009 Keywords: Quantification Artificial neural networks (ANN) Matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry (MALDI TOF MS) Fructo-oligosaccharides Internal standard
a b s t r a c t The application of an internal standard in quantitative analysis is desirable in order to correct for variations in sample preparation and instrumental response. In mass spectrometry of organic compounds, the internal standard is preferably labelled with a stable isotope, such as 18 O, 15 N or 13 C. In this study, a method for the quantification of fructo-oligosaccharides using matrix-assisted laser desorption/ionisation timeof-flight mass spectrometry (MALDI TOF MS) was proposed and tested on raftilose, a partially hydrolysed inulin with a degree of polymeration 2–7. A tetraoligosaccharide nystose, which is chemically identical to the raftilose tetramer, was used as an internal standard rather than an isotope-labelled analyte. Two mathematical approaches used for data processing, conventional calculations and artificial neural networks (ANN), were compared. The conventional data processing relies on the assumption that a constant oligomer dispersion profile will change after the addition of the internal standard and some simple numerical calculations. On the other hand, ANN was found to compensate for a non-linear MALDI response and variations in the oligomer dispersion profile with raftilose concentration. As a result, the application of ANN led to lower quantification errors and excellent day-to-day repeatability compared to the conventional data analysis. The developed method is feasible for MS quantification of raftilose in the range of 10–750 pg with errors below 7%. The content of raftilose was determined in dietary cream; application can be extended to other similar polymers. It should be stressed that no special optimisation of the MALDI process was carried out. A common MALDI matrix and sample preparation were used and only the basic parameters, such as sampling and laser energy, were optimised prior to quantification. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Fructo-oligosaccharides (FOS) are a subgroup of inulin, specifically those fructose polymers with a degree of polymeration (DP) < 10 found in certain plants, such as in the Jerusalem artichoke tuber, chicory root, leek, onion, garlic, oats, barley and rye [1]. For their nutritional properties, FOS are sometimes called soluble fibre. Because they are not digested by enzymes, such as ␣-amylase and maltase, in the small intestine, they arrive intact at the colon where they are fermented by colonic flora. This means that FOS represent a selective nutrient for micro organisms in the large intestine especially important for children and young animals. In addition, other benefits are observed with FOS supplementation, i.e. increasing absorption of different minerals (such as magnesium and calcium) in the intestine, improving the elimination of toxic compounds, preventing and treating infection, diarrhoea, diseases and supporting the immune system [1–4]. Due to the qualities mentioned above, FOS are of great interest in food, pharmaceutical and veterinary studies.
∗ Corresponding author. Tel.: +420 5 49496629; fax: +420 5 49492494. E-mail address: [email protected] (J. Preisler). 0003-2670/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.aca.2009.02.034
For the analysis of FOS, matrix-assisted desorption/ionisation time-of-flight mass spectrometry (MALDI TOF MS), a proven method for study of polymers, can be employed. This method allows rapid determination and/or confirmation of the FOS masses and oligomer dispersion. Furthermore, MALDI is known to exhibit large tolerance to salts, detergents and inorganic buffers. Unlike electrospray, the domain of which is on-line coupling to liquid-phase column separations, MALDI is routinely used for off-line highthroughput analysis of large series of samples. The disadvantage of MALDI MS may be poor signal reproducibility because the signal intensity is a very complex function of many parameters, such as sample morphology and laser energy, that strongly influence desorption and ionisation efficiencies. This usually leads to large errors in quantification. MALDI MS quantification was based on the use of internal standards labelled with isotopes, such as 18 O, 15 N or 13 C. These internal standards exhibit a high physicochemical similarity to analytes and many of them were developed especially for use in global proteome profiling [5–7] and also for the quantification of other biomolecules [8–10]. Analyte quantity is calculated from the peak ratio of analyte and standard, which differ in mass. Examples of these techniques include SILAC (Stable Isotope Labelling with Amino Acid in Cell Culture) [11] for in vivo labelling and in
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vitro isotope labelling of target peptides at N/C terminal, such as protein-AQUATM [7,12]. Accuracy of the MS quantification methods mentioned above is usually in the range of 5–10% [5–9]. The use of compounds not chemically identical with the analyte has limited applicability in MS quantification [13]. MALDI TOF MS quantification performance has been improved by employing a high rate repetition laser [13–16]. The high repetition rate laser allows the accumulation of a large number of shots from a single spot and increases sample throughput. The error between the experimental result and the manufacturer’s certified values was less than 5% using an internal standard [13]. A high repetition rate laser can also reduce analysis time if used with other instruments, such as a triple quadrupole mass spectrometer [17]. Wang’s group first reported MS-quantification of FOS [18] and malto/polysaccharides [19,20] using the addition of a pure oligosaccharide as an internal standard (a pentafructo-oligosaccharide or maltooligosaccharide with DP = 7), but few details on the quantification were given. FOS quantification was based on the relative ratio of two peaks. In the MS spectrum, the contents of the oligosaccharides were calculated from the potassium adduct [18] or from the sum of the MALDI MS responses of [M+Na]+ , [M+K]+ and [M−H2 O+Na]+ [19,20]. In this work, the quantification of the raftilose with a pure monodisperse tetraoligosaccharide nystose as the internal standard is based on evaluating the peak intensity of four oligomers with DP = 3–6 and assumes a constant oligomer dispersion profile. In addition to the conventional data processing, artificial neural networks (ANN) [21–24] are employed to increase robustness of the raftilose quantification. ANN is an information-processing paradigm, which simulates biological neural networks. ANN can qualify non-linear MALDI responses and include other factors, such as sample-to-sample variation and dependence of oligomer dispersion profile on total raftilose concentration. 2. Experimental 2.1. Chemicals Beneo P95, dietetic product containing raftilose, a fructooligosaccharide with DP = 3–7, was obtained from Orafti (Belgium). Nystose, MALDI matrices 2,5-dihydroxybenzoic acid (DHB); 2,4,6trihydroxyacetofenon (THAP) and sodium acetate (source of sodium ions) were purchased from Sigma–Aldrich (Germany). Acetonitrile (HPLC grade) from Scharlau (Germany) was used. All chemicals were of analytical-reagent grade. Water redistilled in the quartz apparatus from Heraeus (Germany) was used for stock solution preparation. 2.2. Mass spectrometry All MALDI MS analyses were carried out on a time-of-flight mass spectrometer Shimadzu/Kratos (model Axima CFR, Great Britain) equipped with a nitrogen laser emitting at 337 nm. A stainless steel target with 384 positions was used for sample preparation. The m/z scale was calibrated using oligomers with DP = 3–7. Auto calibration on m/z of oligomer peaks confirmed the ion composition [GFn +Na]+ and was used to ensure high mass accuracy. Mass spectra were accumulated for 1000 laser pulses using automatic TV raster. 2.3. Sample preparation Stock solutions at a concentration of 1 mg mL−1 of raftilose, nystose and sodium acetate were prepared in redistilled water. The stock solutions at a concentration of 10 mg mL−1 DHB and THAP in acetonitrile (50%) were prepared. A sample solution for MALDI MS was prepared by mixing 20 L in volume of the raftilose standard,
MALDI matrix and sodium acetate solutions. 2 L of mixed sample solution were deposited on the MALDI target and allowed to dry at room temperature. For quantification using the internal standard, two sets of the sample solutions were prepared as mentioned above. In this case, 20 L water or nystose solution were added to the first or second set of solutions, respectively. All solutions were deposited in five replicates. Amount of 0.1 g of a commercially available dietary cream Transit (Orafti, Oreye, Belgium) was placed into a reaction cell (50 mL). Extraction was carried out in a Soxhlet extractor fex IKA Werke 50 (IKA-werke, Staufen, Germany) at 120 ◦ C with 10% ethanol for 1 h and cooled to 30 ◦ C. 1 L of supernatant was used for quantification using MALDI MS [25]. 2.4. Artificial neural network (ANN) The data was processed on a Pentium PC computer using Trajan 3.0 software package (Trajan Neural Network Simulator 1996–1998) [26]. 3. Results and discussion 3.1. Selection of experimental conditions The aim of this work was to prove the above-mentioned concept of quantification using conventional fructo-oligosaccharide samples and to optimise the data processing. Intentionally, only normal sample preparation and basic optimisation of MALDI TOF MS conditions were carried out. 3.1.1. Optimisation of MALDI MS First, optimum conditions for MALDI MS of the raftilose standard were found. The investigated analysis parameters included selection of MALDI matrix, alkali ion and instrument mode. Based on previous reports [18,20], two MALDI matrices, DHB and THAP were selected for the analysis of raftilose. MALDI MS performance with the matrices was evaluated with 670 pg of the raftilose standard in linear mode. Samples were prepared using the dried droplet procedure [25]. This sample preparation method was selected for several reasons: it is simple, rapid and it does not require special tools. DHB was chosen as the MALDI matrix because it exhibited a better spot-to-spot and sample-to-sample repeatability and signalto-noise ratio. Generally, saccharides tend to be ionised in the form of adducts with an alkali metal [18]. To ensure proper cationisation of raftilose, sodium acetate (1 mg mL−1 ) was added to the raftilose standard which resulted in a dominant single molecular ion peak for each raftilose oligomer. The feasibility of reflector and linear modes was also investigated. The spectra of raftilose recorded in reflector mode provided a better signal-to-noise ratio and contained less peaks of fragments/adducts. To summarise, the optimum conditions for MALDI MS of the raftilose standard involved measurement in the positive reflector mode and using DHB (10 mg mL−1 ) with the addition of sodium acetate (1 mg mL−1 ). Fig. 1A shows a MALDI spectrum of 125 pg raftilose measured at optimum conditions, which was characterized by peaks of [GFn +Na]+ ions with m/z 527.16 (trimer), 689.21 (tetramer), 851.26 (pentamer) and 1013.32 (hexamer); minor peak with m/z 11754.37 (heptamer) is not displayed in the m/z range of the spectra. The relative intensity of oligomer peaks with DP = 4–7 with respect to the trimer peak increases with raftilose concentration. Peaks of potassium adducts [GFn +K]+ as well as the peak at m/z = 551.0, noticeable particularly in Fig. 1B–D originating from the matrix, were not important for quantification. The profile of the oligomer peak envelope, however, depends on the amount of raftilose as can be seen from the comparison of Fig. 1A and B for 125 and 25 pg raftilose, respectively. This phenomenon may
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Fig. 1. MALDI mass spectra of (A) 125 pg raftilose, (B) 25 pg raftilose, (C) 40 pg nystose and (D) 125 pg raftilose with 40 pg nystose. Spectra recorded under optimised conditions with 10 mg mL−1 DHB and 1 mg mL−1 sodium acetate, see text for details.
have substantial negative impact on the results from conventional methods for the quantification of raftilose, which assume a constant ratio of peak heights among the raftilose oligomers. A limit of detection (LOD) of 0.94 pg was obtained with raftilose using MALDI TOF MS. The calculation of the LOD (3) was based on the response of the pentamer for 6.7 pg of raftilose deposited on target. 3.1.2. Internal standard For the quantification of raftilose, the addition of nystose as the internal standard was proposed. Nystose is a tetrafructo-
oligosaccharide, combining one molecule of glucose with three molecules of fructose (GF3 ). Presumably, the chemical properties of nystose are very similar to that of raftilose oligomers with DP = 3–7. The nystose spectrum on Fig. 1C shows a single major peak at m/z = 688.21. 3.1.3. Representative sampling The prime criterion for high repeatability is the MALDI matrix morphology, which reflects homogenous embedding of the analyte molecules in the matrix. Most inhomogeneities of the samples were due to the fact that DHB crystals generally formed near the
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edge of the spot, while few crystals could be found in the middle of the spot. This inhomogeneity of the DHB matrix resulted in different oligomer peak ratios for spectra accumulated from the middle of the spot and those near the spot rims. For desorption from the edge of the spot, the peak intensity of oligomers went down monotonously with DP increasing from 3 to 7, while the tetramer peak dominated the spectra generated from the spot centre. In order to achieve reproducible results, representative sampling covering the entire sample area was essential. Such sampling was ensured by defining automatic “TV raster”. The shape of the raster was a regular square with 1024 points that covered the well area 1.0 mm × 1.0 mm; the signal was only accumulated for the first 1000 positions. The accumulated MALDI spectra were smoothed using the moving average method with a window width of four points. This data acquisition scheme resulted in reproducible spectra with a constant oligomer peak dispersion profile for samples with a given raftilose amount and was used in the rest of the work. 3.1.4. Laser power Laser power determines the degree of desorption, ionisation and fragmentation of analytes in MALDI mass spectrometry. While low laser power may lead to insufficient signal-to-noise ratio, an increase in laser power results in the generation of more fragments of analyte and matrix ions and the resolution deteriorates. Also, the intensity of the major peaks may be cut-off and the microchannel plate detector may become saturated at high ion flux leading to distortion of measured oligomer peak dispersion profiles. The level of laser power is expressed in arbitrary units on the scale 0–180 at the mass spectrometer employed in this work. Because the power of a nitrogen laser varies significantly on dayto-day basis, an adjustment of a constant power value on the scale 0–180 did not guarantee reproducible intensities of raftilose peaks. Therefore, an adjustment of laser power according to the intensity of the dominant peak (raftilose trimer) was preferred for keeping the laser power value constant. Performance of the instrument was investigated with 125 pg raftilose sample at two power levels with intensities of the dominant peak in the range of 50–90 mV (low power level) or 100–200 mV (high power level). To assess the feasibility of the two power levels, the measured isotope ratios of the M+1 peak (1 × 13 C) to the monoisotopic (no 13 C) peak of raftilose oligomers with DP 3–6 were compared to the theoretical ones, assuming 1.1% 13 C abundance. From Table 1 it is apparent that there was a large (−40% to −22%) negative systematic deviation of the ratio for each oligomer unit at the low laser power. On the other hand, the experimental isotope ratio approximated the theoretical value in the case of the high power level, although the intensity of major peaks was occasionally (in ∼5% cases) cut-off. The relative error of the ratio was in all cases less than 7% at the high power level. Therefore the higher laser power was chosen for the quantification experiments. Further increases of the laser power resulted in serious major peak cut-offs. It should be stressed that this relative error (∼7%) represents the limit of MALDI MS instrument perfor-
Table 2 Selection of nystose amount for quantitative analysis of raftilose. Signal/noise ratio of tetramer peak
Raftilose amount (pg)
Nystose amount (pg)
<10 10–50 >50
<40 40–250 >250
10 50 150
mance for quantification under these conditions (laser power and number of laser shots). Additional improvements would have to include accumulation of more laser shots or more laborious sample preparation. 3.2. Quantification 3.2.1. Conventional data processing Quantification was investigated at three raftilose levels: 22.5, 125 and 720 pg. Because the added amount of nystose should be comparable to the amount of raftilose tetramer, determination of the amount of added nystose was based on the comparison of the signal-to-noise ratio of the raftilose tetramer. Table 2 shows the amount of added nystose, which roughly follows the trend of the amount of raftilose. Raftilose samples and samples with the added internal standard were spotted in five replicas on the MALDI target. Prior to measurement the laser power was set to the high level, i.e. to achieve the intensity of the highest peak in the MALDI spectrum of 125 pg raftilose sample between 100 and 200 mV. Fig. 1D shows a spectrum of 125 pg raftilose with the addition of 40 pg nystose and the corresponding change in oligomer dispersion profile. Relative peak heights were determined for oligomer units with DP = 3–6 from normalized MALDI spectra. The heptamer peak was not included in the quantification of raftilose; it did not considerably affect the result of the raftilose content because of its low intensity in the MALDI spectra. Conventional data processing assumes that the intensity of the raftilose peaks is linearly proportional to its concentration and the ratio of the oligomer peak heights with DP = 3–6 is constant. First, the ratio of the tetramer peak height to the sum of peak heights of the remaining oligomers (DP = 3, 5 and 6) was calculated according to r1 =
h4r h3r + h5r + h6r
where hir are the peak heights of raftilose i-mers determined from the MALDI mass spectra of raftilose. Second, a portion of tetramer the peak height originating from raftilose, h4r , was calculated using peak heights h3r , h5r and h6r from the MALDI mass spectra of raftilose with the nystose addition and ratio r1 . The remaining portion of the peak height, h4n , calculated as the difference of the total tetramer peak height h4 and the raftilose portion h4r , corresponds to the added nystose. For correct determination of the analyte contents, attention has to be paid to the right transformation of the oligomer peak heights.
Table 1 Peak height ratio (2nd peak (M+1)/monoisotopic peak (M)) of raftilose oligomers (for 125 pg raftilose, sample volume 2 L). Oligomers Theoretical ratio Lower energy of laser (intensity: 50–90 mV) Experimental ratioa Relative errorb (%) Higher energy of laser (intensity: 100–200 mV) Experimental ratioa Relative errorb (%) a
Trimer 0.2111
Tetramer
Pentamer
Hexamer
0.2810
0.3512
0.4215
0.126 −40.3
0.166 −40.9
0.273 −22.3
0.327 −22.4
0.195 −7.6
0.289 2.8
0.358 1.9
0.443 5.1
The ratios were determined from five sample wells. The relative error was determined as the relative difference between the peak heights of the measured and the theoretical isotope ratios of the M+1 peak (1 × 13 C) to the peak height of the monoisotopic (no 13 C) peak of raftilose. b
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The ion intensities are not corrected with regard to m/z by the instrument software. Due to the quadratic dependence of m/z on √ time of flight, the measured peak heights should be divided by m. On the other hand, the response is a function of the number of ions and, to receive analyte contents in weight units, the result has to be multiplied by the analyte molar weight M, which is approximately equal to m. To summarise, the contents of the analyte, w √ is proportional to the peak height multiplied by m. To determine raftilose contents from the known contents of the raftilose tetramer, the ratio of the transformed tetramer peak height to the sum of the transformed peak heights of all major oligomers was established as √ w4 h4r m4 r2 = = √ √ √ √ w3 + w4 + w5 + w6 h3r m3 + h4r m4 + h5r m5 + h6r m6 where wi and mi are the contents and mass of raftilose i-mer, respectively. Thus, the contents of raftilose, wr can be determined from wr =
wn h4r h4n r2
where wn is the content of added nystose in weight units. The described calculation assumes a constant oligomer dispersion profile and mass-independent ionisation efficiency and detector sensitivity. The calculation was rapidly carried out using Microsoft Excel, showing errors of up to 9.5% (Table 3). 3.2.2. Data processing using ANN The main reason for the large errors above is the incorrect assumption that the ratio of oligomer peak heights is constant. In fact, the relative intensity of the oligomer is a function of the total amount of raftilose as can be seen by comparing Fig. 1A with B. Additionally, the response is not linear and also depends on the sample topology, laser power and instrument parameters. To determine the quantity of analyte in such a complex system, we propose the use of ANN. There are many different neural network architectures, but one of the most common is the feedforward neural network. This network consists of artificial neurones sorted in input layer, one or more hidden layer(s) and an output layer. The neurons are arranged so that each node in one layer is connected with each node in the next layer. The strength of a
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connection between two neurones is called the weight. Each hidden and output neuron also has a single bias value. Weights and biases are modified in the course of network training. The ANN architecture was searched for automatically by the Trajan program computation and then used further for the training process and the prediction as well. Architectures with one or two hidden layers and 1–10 or 1–20 neurons per hidden layer, respectively, were examined. We have also tried a “manual” search for the best architecture; the same result was obtained as with the Trajan Automatic Network Designer. The architectures with one hidden layer containing a different numbers of nodes were found unacceptable. A relatively complex architecture consisting of four layers (input layer, two hidden layers and output layer) was selected because more simple architectures were not able to describe the system satisfactorily. The structure of the optimal model 10:7:7:1 (number of input neurons:number of hidden neurons in the first layer:number of hidden neurons in the second layer:number of output neurons) was used (Fig. 2). The calibration sample set should be representative and accurate and contain a sufficient number of samples. A calibration model was established with the training set (15 samples, each in 5 replicas) using input and hidden nodes. Samples in the training set contained an amount of raftilose ranging from 10 to 750 pg as given in Table 3 with corresponding nystose additions, the volumes of all samples were 2 L. Each raftilose level was measured for five spots with and without addition of the internal standard. Input neurons for the ANN contained the peak heights of oligomers with DP = 4–6 with and without the nystose addition, intensity of MALDI spectra with and without the nystose addition in mV and the amount of the nystose addition with the corresponding outputs – amount of the raftilose levels. The raftilose trimer without addition of the internal standard was not included in the data processing because its intensity in normalized spectra was 100% at all concentration levels. We have used Back Propagation (BP) as the training algorithm. Other training algorithms were also tried (Conjugate Gradients, Levenberg-Marquardt, and Quick Propagation) but the same results were obtained. The number of epochs needed was 2000. The average relative error for the training set was 2.6%. Accuracy was excellent in most cases (around 0.1%); the error was larger than 10% only for three samples of the training set with low raftilose amounts (Table 3). In the case of the conventional data
Table 3 MS quantification of raftilose using conventional and ANN calculations. Amount expected (pg) Calibration set 10 15 20 25 30 40 50 75 100 150 200 300 450 600 750 Test sample set 1 720 125 22.5 Test sample set 2 720 125 22.5 a
Amount found, conventional calculation (pg)
Errora , conventional calculation (%)
Amount found, ANN (pg)
Errora , ANN (%)
7 13 18 24.5 16.5 28.5 42 83.5 95.5 115 180.5 235.5 442.5 447.5 725.5
−28.6 −13.4 −9.4 −1.4 −44.9 −28.5 −16.1 11.5 −4.7 −23.4 −9.8 −21.6 −1.7 −25.5 −3.2
14 17 20 26 24.5 40 49.5 75 100 150 200 300 449.5 600 749
40.5 13.4 0.1 4.8 −18.3 0.1 −1.4 0.2 −0.2 −0.1 0.0 −0.1 −0.1 0.0 −0.1
691 135 24.5
−4.6 7.9 9.5
725 132.5 21
0.7 6.1 −7.0
582 111.8 19.2
−19.1 −10.5 −11.9
687 117 24
−4.6 −5.8 6.4
The error was determined as the relative difference between the calculated and actual analyte amount.
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Fig. 2. ANN architecture used for MS quantification of raftilose (10:7:7:1, number of input neurons:number of hidden neurons in the first layer:number of hidden neurons in the second layer:number of output neurons).
processing, the absolute value of relative error was higher than 10% for nine samples of the training set. To improve raftilose quantification in the low end of the range, more samples with low raftilose amounts could be added to the training set of ANN. After the training phase, the network was used to predict the outputs from an arbitrary set of inputs. The amounts of raftilose for the test set were predicted with an error lower than 7%; average absolute error was 4.6%. Moreover, the data obtained for the samples could be directly compared with the conventional data processing also used in this study. In the case of the conventional data processing, the error was above 7% for two of the samples; average absolute error was 7.3%. Repeatability of MS-quantification was tested after one week with three test samples prepared with and without the addition of nystose. The same network was used for the prediction. Again, ANN data processing yielded errors of raftilose contents lower than 7%; average absolute error was 5.6% (Table 3). Repeatability was also examined for the conventional data processing using the same set of tested samples. As shown in Table 3, the conventional data processing resulted in significantly larger errors than the ANN approach; average absolute error 13.8%. Finally, a dietary cream with known content of raftilose was selected as a sample of food products for quantification because the content of raftilose could not be changed during food processing, such as baking etc. MALDI process is extremely sensitive to matrix composition, therefore Soxhlet extraction was carried out to avoid possible interferences. Using the ANN, the dietary cream was found to contain 85 g raftilose in 100 g of the product, which is in agreement with the value declared by the manufacturer (94 g/100 g). Sample treatment and extraction recovery may contribute to the resulting negative error −9.6%.
tion. Thus, ANN lead to better results; the achieved accuracy was better than 7%, which is comparable to that of quantification methods based on the use of stable isotope labels and approaches the practical accuracy limitations of the instrument under the given conditions. It should be stressed that general dried droplet sample preparation with a common matrix and minimal MALDI TOF MS optimisation and acceptable sampling (five replicates of each sample, averaging of 1000 laser shots) were employed. Although a relatively large calibration set was used for training ANN, the calibration was stable and did not have to be repeated. Thus, ANN data processing compared to conventional data processing leads to better day-to-day repeatability. The content of raftilose was determined in a food product. The technique should be generally applicable for MS quantification. Acquisition of five 1000-shot spectra for a sample with the current TOF MS equipped with a 10-Hz nitrogen laser lasted almost 10 min. Using a TOF MS with a highrepetition laser and automated spot raster, the same data can be acquired within seconds [27]. With a suitable extraction and/or concentration technique, the quantification method may be applied for the determination of disperse polymers where a pure monodisperse oligomer/polymer is available, e.g. oligosaccharides in food supplements, glycans in barley malt etc.
4. Conclusions
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The concept of using the addition of a pure oligomer for quantification of disperse polymers has been proven in this work. The content of raftilose was calculated from a change of tetramer abundance after the addition of nystose. In order to assess the content of raftilose from the content of the raftilose tetramer, conventional data processing assumes the same ionisation efficiency and detector sensitivity for all raftilose oligomers and neglects the presence of higher oligomers. ANN data processing does not suffer from these constrains that can lead to systematic errors in the resulting oligosaccharide contents. Furthermore, ANN can take into consideration non-linear responses and a significant variation of the oligomer dispersion profile within the total raftilose concentra-
Acknowledgements We gratefully acknowledge financial support of the Czech Science Foundation (grant no. 525/06/0663) and the Ministry of Education, Youth and Sports of the Czech Republic (LC06035 and MSM0021622415). References
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Analytica Chimica Acta journal homepage: www.elsevier.com/locate/aca
Quantification of fructo-oligosaccharides based on the evaluation of oligomer ratios using an artificial neural network Lucia Onofrejová, Marta Farková, Jan Preisler ∗ Department of Chemistry, Faculty of Science, Masaryk University, Kotláˇrská 2, 611 37 Brno, Czech Republic
a r t i c l e
i n f o
Article history: Received 24 November 2008 Received in revised form 17 January 2009 Accepted 19 February 2009 Available online 2 March 2009 Keywords: Quantification Artificial neural networks (ANN) Matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry (MALDI TOF MS) Fructo-oligosaccharides Internal standard
a b s t r a c t The application of an internal standard in quantitative analysis is desirable in order to correct for variations in sample preparation and instrumental response. In mass spectrometry of organic compounds, the internal standard is preferably labelled with a stable isotope, such as 18 O, 15 N or 13 C. In this study, a method for the quantification of fructo-oligosaccharides using matrix-assisted laser desorption/ionisation timeof-flight mass spectrometry (MALDI TOF MS) was proposed and tested on raftilose, a partially hydrolysed inulin with a degree of polymeration 2–7. A tetraoligosaccharide nystose, which is chemically identical to the raftilose tetramer, was used as an internal standard rather than an isotope-labelled analyte. Two mathematical approaches used for data processing, conventional calculations and artificial neural networks (ANN), were compared. The conventional data processing relies on the assumption that a constant oligomer dispersion profile will change after the addition of the internal standard and some simple numerical calculations. On the other hand, ANN was found to compensate for a non-linear MALDI response and variations in the oligomer dispersion profile with raftilose concentration. As a result, the application of ANN led to lower quantification errors and excellent day-to-day repeatability compared to the conventional data analysis. The developed method is feasible for MS quantification of raftilose in the range of 10–750 pg with errors below 7%. The content of raftilose was determined in dietary cream; application can be extended to other similar polymers. It should be stressed that no special optimisation of the MALDI process was carried out. A common MALDI matrix and sample preparation were used and only the basic parameters, such as sampling and laser energy, were optimised prior to quantification. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Fructo-oligosaccharides (FOS) are a subgroup of inulin, specifically those fructose polymers with a degree of polymeration (DP) < 10 found in certain plants, such as in the Jerusalem artichoke tuber, chicory root, leek, onion, garlic, oats, barley and rye [1]. For their nutritional properties, FOS are sometimes called soluble fibre. Because they are not digested by enzymes, such as ␣-amylase and maltase, in the small intestine, they arrive intact at the colon where they are fermented by colonic flora. This means that FOS represent a selective nutrient for micro organisms in the large intestine especially important for children and young animals. In addition, other benefits are observed with FOS supplementation, i.e. increasing absorption of different minerals (such as magnesium and calcium) in the intestine, improving the elimination of toxic compounds, preventing and treating infection, diarrhoea, diseases and supporting the immune system [1–4]. Due to the qualities mentioned above, FOS are of great interest in food, pharmaceutical and veterinary studies.
∗ Corresponding author. Tel.: +420 5 49496629; fax: +420 5 49492494. E-mail address: [email protected] (J. Preisler). 0003-2670/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.aca.2009.02.034
For the analysis of FOS, matrix-assisted desorption/ionisation time-of-flight mass spectrometry (MALDI TOF MS), a proven method for study of polymers, can be employed. This method allows rapid determination and/or confirmation of the FOS masses and oligomer dispersion. Furthermore, MALDI is known to exhibit large tolerance to salts, detergents and inorganic buffers. Unlike electrospray, the domain of which is on-line coupling to liquid-phase column separations, MALDI is routinely used for off-line highthroughput analysis of large series of samples. The disadvantage of MALDI MS may be poor signal reproducibility because the signal intensity is a very complex function of many parameters, such as sample morphology and laser energy, that strongly influence desorption and ionisation efficiencies. This usually leads to large errors in quantification. MALDI MS quantification was based on the use of internal standards labelled with isotopes, such as 18 O, 15 N or 13 C. These internal standards exhibit a high physicochemical similarity to analytes and many of them were developed especially for use in global proteome profiling [5–7] and also for the quantification of other biomolecules [8–10]. Analyte quantity is calculated from the peak ratio of analyte and standard, which differ in mass. Examples of these techniques include SILAC (Stable Isotope Labelling with Amino Acid in Cell Culture) [11] for in vivo labelling and in
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vitro isotope labelling of target peptides at N/C terminal, such as protein-AQUATM [7,12]. Accuracy of the MS quantification methods mentioned above is usually in the range of 5–10% [5–9]. The use of compounds not chemically identical with the analyte has limited applicability in MS quantification [13]. MALDI TOF MS quantification performance has been improved by employing a high rate repetition laser [13–16]. The high repetition rate laser allows the accumulation of a large number of shots from a single spot and increases sample throughput. The error between the experimental result and the manufacturer’s certified values was less than 5% using an internal standard [13]. A high repetition rate laser can also reduce analysis time if used with other instruments, such as a triple quadrupole mass spectrometer [17]. Wang’s group first reported MS-quantification of FOS [18] and malto/polysaccharides [19,20] using the addition of a pure oligosaccharide as an internal standard (a pentafructo-oligosaccharide or maltooligosaccharide with DP = 7), but few details on the quantification were given. FOS quantification was based on the relative ratio of two peaks. In the MS spectrum, the contents of the oligosaccharides were calculated from the potassium adduct [18] or from the sum of the MALDI MS responses of [M+Na]+ , [M+K]+ and [M−H2 O+Na]+ [19,20]. In this work, the quantification of the raftilose with a pure monodisperse tetraoligosaccharide nystose as the internal standard is based on evaluating the peak intensity of four oligomers with DP = 3–6 and assumes a constant oligomer dispersion profile. In addition to the conventional data processing, artificial neural networks (ANN) [21–24] are employed to increase robustness of the raftilose quantification. ANN is an information-processing paradigm, which simulates biological neural networks. ANN can qualify non-linear MALDI responses and include other factors, such as sample-to-sample variation and dependence of oligomer dispersion profile on total raftilose concentration. 2. Experimental 2.1. Chemicals Beneo P95, dietetic product containing raftilose, a fructooligosaccharide with DP = 3–7, was obtained from Orafti (Belgium). Nystose, MALDI matrices 2,5-dihydroxybenzoic acid (DHB); 2,4,6trihydroxyacetofenon (THAP) and sodium acetate (source of sodium ions) were purchased from Sigma–Aldrich (Germany). Acetonitrile (HPLC grade) from Scharlau (Germany) was used. All chemicals were of analytical-reagent grade. Water redistilled in the quartz apparatus from Heraeus (Germany) was used for stock solution preparation. 2.2. Mass spectrometry All MALDI MS analyses were carried out on a time-of-flight mass spectrometer Shimadzu/Kratos (model Axima CFR, Great Britain) equipped with a nitrogen laser emitting at 337 nm. A stainless steel target with 384 positions was used for sample preparation. The m/z scale was calibrated using oligomers with DP = 3–7. Auto calibration on m/z of oligomer peaks confirmed the ion composition [GFn +Na]+ and was used to ensure high mass accuracy. Mass spectra were accumulated for 1000 laser pulses using automatic TV raster. 2.3. Sample preparation Stock solutions at a concentration of 1 mg mL−1 of raftilose, nystose and sodium acetate were prepared in redistilled water. The stock solutions at a concentration of 10 mg mL−1 DHB and THAP in acetonitrile (50%) were prepared. A sample solution for MALDI MS was prepared by mixing 20 L in volume of the raftilose standard,
MALDI matrix and sodium acetate solutions. 2 L of mixed sample solution were deposited on the MALDI target and allowed to dry at room temperature. For quantification using the internal standard, two sets of the sample solutions were prepared as mentioned above. In this case, 20 L water or nystose solution were added to the first or second set of solutions, respectively. All solutions were deposited in five replicates. Amount of 0.1 g of a commercially available dietary cream Transit (Orafti, Oreye, Belgium) was placed into a reaction cell (50 mL). Extraction was carried out in a Soxhlet extractor fex IKA Werke 50 (IKA-werke, Staufen, Germany) at 120 ◦ C with 10% ethanol for 1 h and cooled to 30 ◦ C. 1 L of supernatant was used for quantification using MALDI MS [25]. 2.4. Artificial neural network (ANN) The data was processed on a Pentium PC computer using Trajan 3.0 software package (Trajan Neural Network Simulator 1996–1998) [26]. 3. Results and discussion 3.1. Selection of experimental conditions The aim of this work was to prove the above-mentioned concept of quantification using conventional fructo-oligosaccharide samples and to optimise the data processing. Intentionally, only normal sample preparation and basic optimisation of MALDI TOF MS conditions were carried out. 3.1.1. Optimisation of MALDI MS First, optimum conditions for MALDI MS of the raftilose standard were found. The investigated analysis parameters included selection of MALDI matrix, alkali ion and instrument mode. Based on previous reports [18,20], two MALDI matrices, DHB and THAP were selected for the analysis of raftilose. MALDI MS performance with the matrices was evaluated with 670 pg of the raftilose standard in linear mode. Samples were prepared using the dried droplet procedure [25]. This sample preparation method was selected for several reasons: it is simple, rapid and it does not require special tools. DHB was chosen as the MALDI matrix because it exhibited a better spot-to-spot and sample-to-sample repeatability and signalto-noise ratio. Generally, saccharides tend to be ionised in the form of adducts with an alkali metal [18]. To ensure proper cationisation of raftilose, sodium acetate (1 mg mL−1 ) was added to the raftilose standard which resulted in a dominant single molecular ion peak for each raftilose oligomer. The feasibility of reflector and linear modes was also investigated. The spectra of raftilose recorded in reflector mode provided a better signal-to-noise ratio and contained less peaks of fragments/adducts. To summarise, the optimum conditions for MALDI MS of the raftilose standard involved measurement in the positive reflector mode and using DHB (10 mg mL−1 ) with the addition of sodium acetate (1 mg mL−1 ). Fig. 1A shows a MALDI spectrum of 125 pg raftilose measured at optimum conditions, which was characterized by peaks of [GFn +Na]+ ions with m/z 527.16 (trimer), 689.21 (tetramer), 851.26 (pentamer) and 1013.32 (hexamer); minor peak with m/z 11754.37 (heptamer) is not displayed in the m/z range of the spectra. The relative intensity of oligomer peaks with DP = 4–7 with respect to the trimer peak increases with raftilose concentration. Peaks of potassium adducts [GFn +K]+ as well as the peak at m/z = 551.0, noticeable particularly in Fig. 1B–D originating from the matrix, were not important for quantification. The profile of the oligomer peak envelope, however, depends on the amount of raftilose as can be seen from the comparison of Fig. 1A and B for 125 and 25 pg raftilose, respectively. This phenomenon may
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Fig. 1. MALDI mass spectra of (A) 125 pg raftilose, (B) 25 pg raftilose, (C) 40 pg nystose and (D) 125 pg raftilose with 40 pg nystose. Spectra recorded under optimised conditions with 10 mg mL−1 DHB and 1 mg mL−1 sodium acetate, see text for details.
have substantial negative impact on the results from conventional methods for the quantification of raftilose, which assume a constant ratio of peak heights among the raftilose oligomers. A limit of detection (LOD) of 0.94 pg was obtained with raftilose using MALDI TOF MS. The calculation of the LOD (3) was based on the response of the pentamer for 6.7 pg of raftilose deposited on target. 3.1.2. Internal standard For the quantification of raftilose, the addition of nystose as the internal standard was proposed. Nystose is a tetrafructo-
oligosaccharide, combining one molecule of glucose with three molecules of fructose (GF3 ). Presumably, the chemical properties of nystose are very similar to that of raftilose oligomers with DP = 3–7. The nystose spectrum on Fig. 1C shows a single major peak at m/z = 688.21. 3.1.3. Representative sampling The prime criterion for high repeatability is the MALDI matrix morphology, which reflects homogenous embedding of the analyte molecules in the matrix. Most inhomogeneities of the samples were due to the fact that DHB crystals generally formed near the
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edge of the spot, while few crystals could be found in the middle of the spot. This inhomogeneity of the DHB matrix resulted in different oligomer peak ratios for spectra accumulated from the middle of the spot and those near the spot rims. For desorption from the edge of the spot, the peak intensity of oligomers went down monotonously with DP increasing from 3 to 7, while the tetramer peak dominated the spectra generated from the spot centre. In order to achieve reproducible results, representative sampling covering the entire sample area was essential. Such sampling was ensured by defining automatic “TV raster”. The shape of the raster was a regular square with 1024 points that covered the well area 1.0 mm × 1.0 mm; the signal was only accumulated for the first 1000 positions. The accumulated MALDI spectra were smoothed using the moving average method with a window width of four points. This data acquisition scheme resulted in reproducible spectra with a constant oligomer peak dispersion profile for samples with a given raftilose amount and was used in the rest of the work. 3.1.4. Laser power Laser power determines the degree of desorption, ionisation and fragmentation of analytes in MALDI mass spectrometry. While low laser power may lead to insufficient signal-to-noise ratio, an increase in laser power results in the generation of more fragments of analyte and matrix ions and the resolution deteriorates. Also, the intensity of the major peaks may be cut-off and the microchannel plate detector may become saturated at high ion flux leading to distortion of measured oligomer peak dispersion profiles. The level of laser power is expressed in arbitrary units on the scale 0–180 at the mass spectrometer employed in this work. Because the power of a nitrogen laser varies significantly on dayto-day basis, an adjustment of a constant power value on the scale 0–180 did not guarantee reproducible intensities of raftilose peaks. Therefore, an adjustment of laser power according to the intensity of the dominant peak (raftilose trimer) was preferred for keeping the laser power value constant. Performance of the instrument was investigated with 125 pg raftilose sample at two power levels with intensities of the dominant peak in the range of 50–90 mV (low power level) or 100–200 mV (high power level). To assess the feasibility of the two power levels, the measured isotope ratios of the M+1 peak (1 × 13 C) to the monoisotopic (no 13 C) peak of raftilose oligomers with DP 3–6 were compared to the theoretical ones, assuming 1.1% 13 C abundance. From Table 1 it is apparent that there was a large (−40% to −22%) negative systematic deviation of the ratio for each oligomer unit at the low laser power. On the other hand, the experimental isotope ratio approximated the theoretical value in the case of the high power level, although the intensity of major peaks was occasionally (in ∼5% cases) cut-off. The relative error of the ratio was in all cases less than 7% at the high power level. Therefore the higher laser power was chosen for the quantification experiments. Further increases of the laser power resulted in serious major peak cut-offs. It should be stressed that this relative error (∼7%) represents the limit of MALDI MS instrument perfor-
Table 2 Selection of nystose amount for quantitative analysis of raftilose. Signal/noise ratio of tetramer peak
Raftilose amount (pg)
Nystose amount (pg)
<10 10–50 >50
<40 40–250 >250
10 50 150
mance for quantification under these conditions (laser power and number of laser shots). Additional improvements would have to include accumulation of more laser shots or more laborious sample preparation. 3.2. Quantification 3.2.1. Conventional data processing Quantification was investigated at three raftilose levels: 22.5, 125 and 720 pg. Because the added amount of nystose should be comparable to the amount of raftilose tetramer, determination of the amount of added nystose was based on the comparison of the signal-to-noise ratio of the raftilose tetramer. Table 2 shows the amount of added nystose, which roughly follows the trend of the amount of raftilose. Raftilose samples and samples with the added internal standard were spotted in five replicas on the MALDI target. Prior to measurement the laser power was set to the high level, i.e. to achieve the intensity of the highest peak in the MALDI spectrum of 125 pg raftilose sample between 100 and 200 mV. Fig. 1D shows a spectrum of 125 pg raftilose with the addition of 40 pg nystose and the corresponding change in oligomer dispersion profile. Relative peak heights were determined for oligomer units with DP = 3–6 from normalized MALDI spectra. The heptamer peak was not included in the quantification of raftilose; it did not considerably affect the result of the raftilose content because of its low intensity in the MALDI spectra. Conventional data processing assumes that the intensity of the raftilose peaks is linearly proportional to its concentration and the ratio of the oligomer peak heights with DP = 3–6 is constant. First, the ratio of the tetramer peak height to the sum of peak heights of the remaining oligomers (DP = 3, 5 and 6) was calculated according to r1 =
h4r h3r + h5r + h6r
where hir are the peak heights of raftilose i-mers determined from the MALDI mass spectra of raftilose. Second, a portion of tetramer the peak height originating from raftilose, h4r , was calculated using peak heights h3r , h5r and h6r from the MALDI mass spectra of raftilose with the nystose addition and ratio r1 . The remaining portion of the peak height, h4n , calculated as the difference of the total tetramer peak height h4 and the raftilose portion h4r , corresponds to the added nystose. For correct determination of the analyte contents, attention has to be paid to the right transformation of the oligomer peak heights.
Table 1 Peak height ratio (2nd peak (M+1)/monoisotopic peak (M)) of raftilose oligomers (for 125 pg raftilose, sample volume 2 L). Oligomers Theoretical ratio Lower energy of laser (intensity: 50–90 mV) Experimental ratioa Relative errorb (%) Higher energy of laser (intensity: 100–200 mV) Experimental ratioa Relative errorb (%) a
Trimer 0.2111
Tetramer
Pentamer
Hexamer
0.2810
0.3512
0.4215
0.126 −40.3
0.166 −40.9
0.273 −22.3
0.327 −22.4
0.195 −7.6
0.289 2.8
0.358 1.9
0.443 5.1
The ratios were determined from five sample wells. The relative error was determined as the relative difference between the peak heights of the measured and the theoretical isotope ratios of the M+1 peak (1 × 13 C) to the peak height of the monoisotopic (no 13 C) peak of raftilose. b
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The ion intensities are not corrected with regard to m/z by the instrument software. Due to the quadratic dependence of m/z on √ time of flight, the measured peak heights should be divided by m. On the other hand, the response is a function of the number of ions and, to receive analyte contents in weight units, the result has to be multiplied by the analyte molar weight M, which is approximately equal to m. To summarise, the contents of the analyte, w √ is proportional to the peak height multiplied by m. To determine raftilose contents from the known contents of the raftilose tetramer, the ratio of the transformed tetramer peak height to the sum of the transformed peak heights of all major oligomers was established as √ w4 h4r m4 r2 = = √ √ √ √ w3 + w4 + w5 + w6 h3r m3 + h4r m4 + h5r m5 + h6r m6 where wi and mi are the contents and mass of raftilose i-mer, respectively. Thus, the contents of raftilose, wr can be determined from wr =
wn h4r h4n r2
where wn is the content of added nystose in weight units. The described calculation assumes a constant oligomer dispersion profile and mass-independent ionisation efficiency and detector sensitivity. The calculation was rapidly carried out using Microsoft Excel, showing errors of up to 9.5% (Table 3). 3.2.2. Data processing using ANN The main reason for the large errors above is the incorrect assumption that the ratio of oligomer peak heights is constant. In fact, the relative intensity of the oligomer is a function of the total amount of raftilose as can be seen by comparing Fig. 1A with B. Additionally, the response is not linear and also depends on the sample topology, laser power and instrument parameters. To determine the quantity of analyte in such a complex system, we propose the use of ANN. There are many different neural network architectures, but one of the most common is the feedforward neural network. This network consists of artificial neurones sorted in input layer, one or more hidden layer(s) and an output layer. The neurons are arranged so that each node in one layer is connected with each node in the next layer. The strength of a
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connection between two neurones is called the weight. Each hidden and output neuron also has a single bias value. Weights and biases are modified in the course of network training. The ANN architecture was searched for automatically by the Trajan program computation and then used further for the training process and the prediction as well. Architectures with one or two hidden layers and 1–10 or 1–20 neurons per hidden layer, respectively, were examined. We have also tried a “manual” search for the best architecture; the same result was obtained as with the Trajan Automatic Network Designer. The architectures with one hidden layer containing a different numbers of nodes were found unacceptable. A relatively complex architecture consisting of four layers (input layer, two hidden layers and output layer) was selected because more simple architectures were not able to describe the system satisfactorily. The structure of the optimal model 10:7:7:1 (number of input neurons:number of hidden neurons in the first layer:number of hidden neurons in the second layer:number of output neurons) was used (Fig. 2). The calibration sample set should be representative and accurate and contain a sufficient number of samples. A calibration model was established with the training set (15 samples, each in 5 replicas) using input and hidden nodes. Samples in the training set contained an amount of raftilose ranging from 10 to 750 pg as given in Table 3 with corresponding nystose additions, the volumes of all samples were 2 L. Each raftilose level was measured for five spots with and without addition of the internal standard. Input neurons for the ANN contained the peak heights of oligomers with DP = 4–6 with and without the nystose addition, intensity of MALDI spectra with and without the nystose addition in mV and the amount of the nystose addition with the corresponding outputs – amount of the raftilose levels. The raftilose trimer without addition of the internal standard was not included in the data processing because its intensity in normalized spectra was 100% at all concentration levels. We have used Back Propagation (BP) as the training algorithm. Other training algorithms were also tried (Conjugate Gradients, Levenberg-Marquardt, and Quick Propagation) but the same results were obtained. The number of epochs needed was 2000. The average relative error for the training set was 2.6%. Accuracy was excellent in most cases (around 0.1%); the error was larger than 10% only for three samples of the training set with low raftilose amounts (Table 3). In the case of the conventional data
Table 3 MS quantification of raftilose using conventional and ANN calculations. Amount expected (pg) Calibration set 10 15 20 25 30 40 50 75 100 150 200 300 450 600 750 Test sample set 1 720 125 22.5 Test sample set 2 720 125 22.5 a
Amount found, conventional calculation (pg)
Errora , conventional calculation (%)
Amount found, ANN (pg)
Errora , ANN (%)
7 13 18 24.5 16.5 28.5 42 83.5 95.5 115 180.5 235.5 442.5 447.5 725.5
−28.6 −13.4 −9.4 −1.4 −44.9 −28.5 −16.1 11.5 −4.7 −23.4 −9.8 −21.6 −1.7 −25.5 −3.2
14 17 20 26 24.5 40 49.5 75 100 150 200 300 449.5 600 749
40.5 13.4 0.1 4.8 −18.3 0.1 −1.4 0.2 −0.2 −0.1 0.0 −0.1 −0.1 0.0 −0.1
691 135 24.5
−4.6 7.9 9.5
725 132.5 21
0.7 6.1 −7.0
582 111.8 19.2
−19.1 −10.5 −11.9
687 117 24
−4.6 −5.8 6.4
The error was determined as the relative difference between the calculated and actual analyte amount.
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Fig. 2. ANN architecture used for MS quantification of raftilose (10:7:7:1, number of input neurons:number of hidden neurons in the first layer:number of hidden neurons in the second layer:number of output neurons).
processing, the absolute value of relative error was higher than 10% for nine samples of the training set. To improve raftilose quantification in the low end of the range, more samples with low raftilose amounts could be added to the training set of ANN. After the training phase, the network was used to predict the outputs from an arbitrary set of inputs. The amounts of raftilose for the test set were predicted with an error lower than 7%; average absolute error was 4.6%. Moreover, the data obtained for the samples could be directly compared with the conventional data processing also used in this study. In the case of the conventional data processing, the error was above 7% for two of the samples; average absolute error was 7.3%. Repeatability of MS-quantification was tested after one week with three test samples prepared with and without the addition of nystose. The same network was used for the prediction. Again, ANN data processing yielded errors of raftilose contents lower than 7%; average absolute error was 5.6% (Table 3). Repeatability was also examined for the conventional data processing using the same set of tested samples. As shown in Table 3, the conventional data processing resulted in significantly larger errors than the ANN approach; average absolute error 13.8%. Finally, a dietary cream with known content of raftilose was selected as a sample of food products for quantification because the content of raftilose could not be changed during food processing, such as baking etc. MALDI process is extremely sensitive to matrix composition, therefore Soxhlet extraction was carried out to avoid possible interferences. Using the ANN, the dietary cream was found to contain 85 g raftilose in 100 g of the product, which is in agreement with the value declared by the manufacturer (94 g/100 g). Sample treatment and extraction recovery may contribute to the resulting negative error −9.6%.
tion. Thus, ANN lead to better results; the achieved accuracy was better than 7%, which is comparable to that of quantification methods based on the use of stable isotope labels and approaches the practical accuracy limitations of the instrument under the given conditions. It should be stressed that general dried droplet sample preparation with a common matrix and minimal MALDI TOF MS optimisation and acceptable sampling (five replicates of each sample, averaging of 1000 laser shots) were employed. Although a relatively large calibration set was used for training ANN, the calibration was stable and did not have to be repeated. Thus, ANN data processing compared to conventional data processing leads to better day-to-day repeatability. The content of raftilose was determined in a food product. The technique should be generally applicable for MS quantification. Acquisition of five 1000-shot spectra for a sample with the current TOF MS equipped with a 10-Hz nitrogen laser lasted almost 10 min. Using a TOF MS with a highrepetition laser and automated spot raster, the same data can be acquired within seconds [27]. With a suitable extraction and/or concentration technique, the quantification method may be applied for the determination of disperse polymers where a pure monodisperse oligomer/polymer is available, e.g. oligosaccharides in food supplements, glycans in barley malt etc.
4. Conclusions
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The concept of using the addition of a pure oligomer for quantification of disperse polymers has been proven in this work. The content of raftilose was calculated from a change of tetramer abundance after the addition of nystose. In order to assess the content of raftilose from the content of the raftilose tetramer, conventional data processing assumes the same ionisation efficiency and detector sensitivity for all raftilose oligomers and neglects the presence of higher oligomers. ANN data processing does not suffer from these constrains that can lead to systematic errors in the resulting oligosaccharide contents. Furthermore, ANN can take into consideration non-linear responses and a significant variation of the oligomer dispersion profile within the total raftilose concentra-
Acknowledgements We gratefully acknowledge financial support of the Czech Science Foundation (grant no. 525/06/0663) and the Ministry of Education, Youth and Sports of the Czech Republic (LC06035 and MSM0021622415). References
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