Unified representation of high- and low-resolution spectra to facilitate application of mass spectrometric techniques in clinical practice

Highlights

• •Strategy for thresholding and denoising spectra for conversion is proposed.
• •Intelligent thresholding to maximize number of shared peaks in different resolutions.
• •Algorithm unifies high- and low-resolution mass spectra is presented.
• •Algorithm facilitates the translation of mass spectrometric assays to clinical use.

Abstract

The majority of research in the biomedical sciences is carried out with the highest resolution accessible to the scientist, but, in the clinic, cost constraints necessitate the use of low-resolution devices. Here, we compare high- and low-resolution direct mass spectrometry profiling data and propose a simple pre-processing technique that makes high-resolution data suitable for the development of classification and regression techniques applicable to low-resolution data, while retaining high accuracy of analysis. This work demonstrates an approach to de-noising spectra to make the same representation for both high- and low-resolution spectra. This approach uses noise threshold detection based on the Tversky index, which compares spectra with different resolutions, and minimizes the percentage of resolution-specific peaks. The presented method provides an avenue for the development of analytical algorithms using high-resolution mass spectrometry data, while applying these algorithms in the clinic using low-resolution mass spectrometers.

1. Introduction

The mass spectrometric methods of direct tissue profiling have gained increasing attention over the past decade [1], [2], [3], [4], [5], [6], especially due to development of ambient ionization methods [7], [8], [9], [10]. Removing chromatography significantly increases throughput, but this direct spray (shotgun) approach also makes the spectra less interpretable without high-resolution devices [11]. Currently, high-resolution mass spectrometry is widely used in research, but to make assays applicable in a clinical setting they must be accurate and precise when run on low-resolution devices. The vast body of data that is collected and analyzed during the research stage of assay development could be applied to solving various clinical questions by training appropriate machine learning algorithms. However, the direct application of these research-derived algorithms in the clinic would likely create erroneous output, since the clinical data that would be inputted is usually low-resolution [12]. Thus, methods for the transformation of high-resolution data, so that classifiers or regressors obtained from this data are directly applicable to low-resolution spectra with high accuracy, is required.

The problems of comparing and mapping tissue profiling data obtained by different mass spectrometric methods, such as REIMS [10], DESI [1], MALDI, etc., have been recently considered by Golf et al [13]. However, all results in their work were on high-resolution spectra, and the major challenge was to reduce the variation caused by differences in ionization methods and instrumental platforms. Here, we approach a less ambitious task. We propose an algorithm for mapping high-resolution mass spectra to a lower resolution that is suitable for the development of clinically applicable machine learning algorithms.

For practical application of machine learning techniques, such as automatic classification, the spectra must be represented as an array of features [14], [15], [16], [17]. So, if such arrays from high- and low-resolution signals are the same, application of the classifier would give the same result. However, in practice, high- and low-resolution spectra, even if obtained by similar instruments, are not as similar as would be expected. Differences in the sensitivity and dynamic range of different mass analyzers not only make high-resolution data richer, but can also alter peak intensities and/or move them below the noise level, especially for the low intensity peaks. So, the high-resolution data should be transformed to lower resolution and the appropriate thresholds should be found to apply to the high- and low-resolution spectra.

In our work, we demonstrate an analytical approach to determine the optimal parameters for high-resolution data processing for conversion into a dataset suitable for training classification methods that will be applied to low-resolution datasets targeted for clinical application.

2. Methods

All experiments were performed on a Thermo LTQ Orbitrap XL instrument. Mass spectrometric data were obtained using the direct-spray-from-tissue approach ion source in negative ion mode. Spectra were obtained via online liquid extraction of lipids from mouse (i.e., wild-type mus musculus) brain cortex tissue using needle electrospray ionization (NESI) [18]. Frozen mouse brain was received from the local vivarium, defrosted at room temperature and samples were dissected from the left hemisphere cortex. All experiments were carried out in accordance with guidelines approved by the local ethics committee. For registration of high-resolution spectra (resolution 24,000 at m/z = 744) the Orbitrap analyzer was used and low-resolution spectra (resolution 2000 at m/z = 744) were obtained using an LTQ analyzer from the same instrument. All spectra were measured in the m/z 500–1000 range.

Spectra from each sample were measured for 10 s, with 20 scans in low-resolution mode and 20 in high-resolution mode. The low- and high-resolution spectra were obtained by averaging measurement scans in the low- and high-resolution modes, respectively.

Binning of mass spectrum data is a common technique for spectra storage and analysis, especially automated analysis. High-resolution data was binned at bin widths of m/z = 0.25 or m/z = 0.02. The bin width was chosen according to the precision of the spectra at different resolution settings. The wide bin was used for preliminary convolution of high-resolution data with the Gaussian function, with FWHM corresponding to low-resolution peak width. For baseline correction, the median in the sliding m/z window (window width m/z = 0.5 for high- and m/z = 2 for low-resolution) was calculated and applied to the spectra. Then, peak-picking was carried out in the binned spectra, and peak losses were estimated.

The high- and low-resolution spectra were compared in the following way: To find which high-resolution peaks overlap with the low-resolution ones, the low-resolution spectrum was normalized to 1 for every peak [19]; the normalized low-resolution spectrum was linearly interpolated on the m/z grid of the high-resolution spectrum; then all the entities of the interpolated spectrum greater than 0.5 were set to 1, and the rest were set to zero. For each peak in the low-resolution spectrum, the maximal coincident peak from high-resolution was tagged as a shared, or common, peak; all other peaks in the overlap were tagged as only high-resolution peaks. Peaks in low-resolution that had no matching high-resolution pairs were tagged as only low-resolution peaks. This approach is illustrated in Fig. 1.

Fig. 1.

Illustration of peak tagging and comparison of high- and low-resolution mass spectra, when the bin width of the data is not the same.

All calculations and visualizations were made using code written by the authors using MATLAB or Python. This code is available on request.

3. Results and discussions

The application of statistical and machine learning techniques, such as classification or regression of mass spectrometric data, requires that it be converted into numerical vectors. The standard technique for this is binning, when the entire m/z range is split into a set of “bins” of a fixed width, and the intensity of each bin is the aggregated value of the signal within its boundaries [20]. The bin width is chosen so that, despite the variations in the peak position due to measurement errors, it never crosses the bin boundaries.

To use existing data analysis techniques with a dataset measured on a different instrument, specific data preprocessing techniques that would convert the new data to the same binned form are required. To ensure that methods trained on high-resolution data are applicable to low-resolution data one needs a transformation that maps the position and intensity of the most essential peaks in the high-resolution spectra to the low-resolution binned representation. The most straightforward and naive mapping technique is to increase the bin width so it corresponds to the bin width in low-resolution.

3.1. Low- and high-resolution data with different binning widths

Comparison of high- and low-resolution with bin widths of m/z = 0.02 and m/z = 0.25, respectively, and corresponding Venn diagrams that show peaks shared by low- and high-resolution mass spectra of 3 samples are presented in Fig. 2. It can be seen that major peaks in both spectra have a high overlap similarity.

Fig. 2.

Binned spectra of high- (lower spectrum) and low- (upper spectrum) resolution and corresponding Venn diagrams. A, B – first sample, C, D – second sample, E, F – third sample.

The majority of peaks specific to only high- or low-resolution spectra that comprise half of the low- and two thirds of high-resolution peaks are low-intensity noise, as demonstrated by histograms in Fig. 3.

Fig. 3.

Histograms of intensities of shared peaks and those present in only high- or low- resolution spectra for sample 1 (Fig. 2. B) in logarithmic scale. A – histogram of intensities of shared peaks in the low-resolution spectrum; B – histogram of intensities of shared peaks in the high-resolution spectrum; C – histogram of intensities of peaks unique for the low-resolution spectrum; D – histogram of intensities of peaks unique for the high-resolution spectrum.

Peaks that are present only in either high- or low-resolution mostly have intensities below 10% of the highest peak and most of them may be discarded as noise (Fig. 3). So, in order to create a mapping algorithm, a threshold level that only retains peaks present in both high- and low-resolution spectra and discards all resolution-specific peaks must be defined.

3.2. Different binning widths for same high-resolution spectra

As was mentioned earlier, the naive mapping approach is to increase the bin width for high-resolution spectra. Here, we will consider how such coarse-grained representation influences the position and intensity of peaks in the peak array. An estimate of peaks lost when transferring high-resolution data to the low-resolution representation is shown in Fig. 4.

Fig. 4.

High-resolution spectra with different bin widths (upper – m/z = 0.02 fine, and lower – m/z = 0.25 rough) and corresponding Venn diagrams. A, B – first sample, C, D – second sample, E, F – third sample.

High-resolution spectra were convoluted with the Gaussian function and then binned to the same grid as low-resolution spectra (bin width m/z = 0.25). Then, in a manner similar to that described above, these convoluted (rough) spectra were compared to the high-resolution originals (fine), considering them as low- and high-resolution spectra, respectively. Each sample lost about half of the peaks as a result of the transformation to this coarse-grained representation, and, at the same time, each spectrum acquired a few new ones due to the mismatches in the position of bin boundaries. It should also be noted that the number of mismatched peaks in this analysis is almost identical to that of the high-resolution-only category from Fig. 2, which agrees with the assumption that high-resolution peaks that do not correspond to anything in low-resolution spectra appear mainly due to the difference in spectra resolution rather than peculiarities of the detection techniques.

3.3. Same binning for high- and low-resolution spectra

Additionally, the low-resolution spectra were compared with the coarse-grained (rough) representation of the high-resolution spectra obtained with the same grid as that used for low-resolution (bin width m/z = 0.25), as described in Fig. 4. Fig. 5 demonstrates that the rough representation of the spectra keeps the number of shared peaks almost the same as in Fig. 2. However, the number of peaks found only in low-resolution spectra is a bit higher.

Fig. 5.

Spectra of high- (lower spectrum) and low- (upper spectrum) resolution with the m/z = 0.25 bin width and corresponding Venn diagrams. A, B – first sample, C, D – second sample, E, F – third sample.

From analysis of data presented in Fig. 2, Fig. 3, Fig. 4, Fig. 5, Fig. 6, it can be seen that a properly chosen threshold will minimize noise, as well as unreliable and random peaks, while retaining the meaningful peaks. Moreover, the thresholds for low- and high-resolution spectra should be different and algorithms for their determination required.

Fig. 6.

Histograms of intensities in logarithmic scale for different areas of the Venn diagram of low- and high-resolution spectra with the same bin width of m/z = 0.25. A – histogram of intensities of peaks unique for the low-resolution spectrum; B – histogram of intensities of peaks unique for the high-resolution spectrum; C – histogram of intensities for shared peaks in the low-resolution spectrum; D – histogram of intensities for shared peaks in the high-resolution spectrum.

3.4. Dice coefficient and Tversky index for optimal threshold selection

To search for proper threshold pairs, there is a need for a measure of the quality of the match between two spectra for particular threshold values. One such metric is the Dice coefficient, which can be calculated as

$$d=2\left|X\cap Y\right|/\left(\left|X\right|+\left|Y\right|\right),$$ (1)

where |X| - is the total number of high-resolution spectrum peaks, |Y| - is the total number of low-resolution spectrum peaks, and |X ∩ Y| is the number of peaks shared by the two spectra. The Dice coefficient measures the overlap significance of the two sets of values. It varies from zero to one, where zero corresponds to no overlap, and one to the case when the two sets are the same. If the two sets are of different sizes the Dice coefficient reaches the maximum value equal to the ratio of the set sizes and stays below one.

This metric was applied to different thresholds for each spectrum (Fig. 7A). The relationship between the Dice coefficient and the threshold values set for the high- (vertical axis) and low-resolution (horizontal axis) spectra in logarithmic scale is presented as a colormap in Fig. 7A. Optimal thresholds were chosen that corresponded to the local maximum on the diagram — 0.06 for the high-resolution data and 0.083 for the low-resolution data.

Fig. 7.

Optimization of threshold values using the Dice coefficient. A. Colormap of the Dice coefficient, X axis – threshold for the low-resolution spectrum, Y axis – threshold for the high-resolution spectra. B. Spectra representation with the applied thresholds for noise peaks cutoff. C – corresponding Venn diagram.

After threshold application, a significant decrease in the number of peaks was observed (spectra and Venn diagram in Fig. 7B and C, respectively), but this is the price for a reliable spectrum, which can be used for both low- and high-resolution systems. Moreover, the visual structure of the spectrum does not change much compared to that in Fig. 2A, meaning that data transformation preserves the key features of the spectra.

The Dice coefficient punishes peak mismatching equally both in high- and low-resolution spectra. However, as mentioned earlier from Fig. 4 the majority of unmatched peaks in high-resolution spectra can be attributed to the fine bin width. Thus, it is of greater interest to reduce the number of unmatched peaks in low-resolution spectra, which are also smaller in size. Thus, the applied metrics should treat the classes asymmetrically. The Tversky index is one such metric. It uses different weights for mismatches in low- and high-resolution peaks. By changing the weights, the value (cost) of the data mismatch in low- or high-resolution data can be varied. The Tversky index is calculated as

$$t=\left|X\cap Y\right|/\left(\left|X\cap Y\right|+\alpha \left|X-Y\right|-\left(1-\alpha \right)\left|Y-X\right|\right),$$ (2)

where α is the weight coefficient, |X-Y| - is the number of high-resolution peaks that are not found in the low-resolution spectrum, and |Y-X| - is the number of low-resolution peaks that are absent in the high-resolution spectrum, and |X ∩ Y| is the number of peaks shared by the two spectra. The weight coefficient α defines how important is the non-matching set of peaks in high- and low-resolution spectra. When α is set to 0, the Tversky index becomes equal to one when all peaks from the low-resolution spectra are found in high-resolution spectra. And if α is set to 1, the maximal value of the Tversky index is less than one, since there are always more peaks in high-resolution versus low-resolution spectra.

The coefficient α was varied from 0 to 1 in increments of 0.1. After analysis of index distribution (Figs. S1–S11), we chose 0.2 as the optimal α value (Fig. 8A). The threshold for the optimal value of the Tversky index at α 0.2 for high-resolution was 0.0239, and for low-resolution — 0.0891 (Fig. 8).

Fig. 8.

Optimization of threshold values using the Tversky index. A. Colormap of the Tversky index, X axis – threshold for the low-resolution spectrum, Y axis – threshold for the high-resolution spectra. B. Spectra with applied thresholds for noise peaks cutoff. C –corresponding Venn diagram.

Threshold values found by the algorithm described above are optimal for data conversion between high- and low-resolution spectra.

The last stage of construction of the peak array that could be used for training machine learning algorithms applicable to both high- and low-resolution data is to map the intensities of peaks retained after threshold application.

Intensities of peaks common for low- and high-resolution are compared in one plane (Fig. 9)

Fig. 9.

Correlation of high- and low-resolution peak intensities. Plane of intensities of low- and high-resolution peaks in logarithmic scale for each of the common peaks with and without thresholds.

There is good correlation between peak intensities in high- and low-resolution spectra and it is even higher for peaks common for both resolution settings after threshold application.

To summarize, there are many different mass spectrometers used for a broad range of problems. For some purposes, high-resolution mass spectrometers should be used; for others, low-resolution instruments are better [12]. For example, high- or ultrahigh-resolution mass spectrometry is typically used in scientific research for reliable identification of molecules. For these purposes, tandem mass spectrometry coupled with liquid chromatography separation provides more reliable identification. Routine mass spectra measurements for clinical applications are conducted with low-resolution mass spectrometers for economic reasons. Though their analytical characteristics are worse in comparison to high-resolution instruments, they are less expensive and more widely available. One of the analytical characteristics, the SNR, varies for different instruments and different methods of ion detection. Time-of-flight instruments and quadrupole instruments usually have electron multiplier systems for ion detection, which have a lower SNR, and ICR-based and Orbitrap spectrometers use image current detection systems which require Fourier transform for spectrum measurement and result in higher SNR. Due to the differences in sensitivity and SNR of the devices, different optimal thresholds should be applied for data analysis.

Since this paper describes only the approach for the transfer from high- to low-resolution mass spectra, a model experiment was carried out with mouse brain tissue as a well-characterized biological tissue type [10], [21]. Further work on high- and low-resolution mass spectra comparison will be carried out with samples of different human brain tumors provided by the N.N. Burdenko NSPCN to validate these preliminary results. The proposed algorithm of data transformation could be validated by comparing low-resolution data measured in the clinic on a Bruker Esquire 4000 instrument with the high-resolution spectra measured on the same tissues using a Thermo LTQ Orbitrap XL instrument in laboratory conditions.

Together with the recently published algorithm [13], this method can convert all of the mass spectrometric data obtained on different instruments, using different ionization methods, to a unified standard data form that could be analyzed as a single data type. This approach could merge the data from MALDI- or DESI-imaging and data obtained with direct spray ionization methods and different instruments with different analytical characteristics, such as resolution, sensitivity, and SNR.

4. Conclusions

• 1We proposed an algorithm that makes it possible to transform high-resolution data into a representation resembling the low-resolution spectrum structure, which is suitable for application of machine learning techniques in a way that greatly reduces the need for low-resolution experimental data when proceeding to the clinic.
• 2Low- and high-resolution spectra with different binning due to the accuracy of spectra measurements have significant differences – more than 50% of peaks are lost during the conversion from high- to low-resolution, and vice versa. These differences mostly correspond to low intensity noise peaks. Also, the excessive bin width could explain the majority of peaks lost in high-resolution spectra during the transformation. Application of the same binning widths to both high- and low-resolution spectra reduces the amount of unique peaks in high-resolution spectra.
• 3Application of thresholds derived by maximization of the Dice coefficient reduces the number of unique peaks in both resolution settings, while increasing the fraction of shared peaks relative to the unique ones. However, since the Dice coefficient treats both sets of peaks identically, it is not possible to adjust the optimization procedure to take into account the difference in the importance of the unique peaks for high- and low-resolution spectra.
• 4The Tversky index was introduced to decrease the weights of unique high-resolution peaks and increase the score of unmatched peaks in low-resolution spectra. The optimal value of the asymmetry parameter α was found to be 0.2. The application of the Tversky index leads to lower threshold values and preserves more high-resolution unique peaks in comparison to the Dice coefficient maximization method.
• 5The intensities of peaks remaining after cutoff threshold application are rather linear in both low- and high- resolution spectra. The differences could be explained by possible aggregation of the intensities of several high-resolution peaks in one low-resolution peak.
• 6The developed approach is one possible strategy for converting high- and low-resolution data to the same unified representation.

Conflict of interest

None.

Appendix A. Supplementary data

The following are the Supplementary data to this article: