Mass recalibration for mass spectrometry data

Abstract

The invention relates to the generation and use of a machine-learned or trained algorithm, as derived by (supervised) training of a multi-layered or convolutional neural network using a mass-refined training spectrum, for mass recalibration of mass spectrometry data, in particular for mass spectrometry data based on matrix-assisted laser desorption / ionization (MALDI) as an ionization mechanism, the method is applied to mass spectrometry data, and further particularly to mass spectrometry imaging (MSI) data, and further particularly comprises subjecting the mass spectrometry data to a mass defect analysis, such as a Kenderke mass defect analysis. In this way, the quality of mass spectrum data can be improved in a timely manner.

Description

Technical Field

[0001] The present disclosure relates to generating and using machine - learned or trained algorithms, such as those obtained by (supervised) training of a multi - layer or convolutional neural network using mass - fine - tuned training spectra, for mass - spectrometry data quality recalibration, particularly applied to mass - spectrometry data based on matrix - assisted laser desorption / ionization (MALDI) as the ionization mechanism, further particularly applied to mass - spectrometry imaging (MSI) data, and further particularly including subjecting the mass - spectrometry data to mass - defect analysis, such as Kendrick mass - defect analysis. By doing so, the quality of mass - spectrometry data can be improved in a timely manner. Background Art

[0002] The prior art is explained below with reference to specific aspects. However, this should not be construed as limiting. Useful further developments and modifications known from the prior art can also be applied outside the relatively narrow scope presented here, and will be apparent to those skilled in the art after reading the disclosure following this introduction.

[0003] Mass - spectrometry imaging is a technique that enables visualization of the spatial distribution of molecules by measuring the mass - to - charge ratio m / z of molecules on a surface, such as on a biological tissue section. MSI can detect a variety of molecules, such as metabolites, peptides, proteins, lipids, or drugs, without the need for labeling or extraction, and can provide valuable information about the molecular composition, structure, and function of cells and tissues, as well as their changes in response to disease or treatment.

[0004] MSI works by scanning a sample with a focused ionization beam, such as a laser or an ion beam, and recording the mass spectrum at each point. The mass spectrum contains signals of the molecules desorbed and ionized from the sample point. By selecting specific signals corresponding to the molecule of interest, the intensity of that signal can be plotted on the sample, generating an image showing the spatial distribution of the molecule. MSI can generate multiple images for different molecules from the same sample because each mass spectrum contains many signals.

[0005] There are different types of ionization techniques available for MSI, such as matrix - assisted laser desorption / ionization, secondary ion mass spectrometry (SIMS), desorption electrospray ionization (DESI), or laser ablation electrospray ionization (LAESI). Each technique has its own advantages and limitations, depending on the type of sample, the size of the molecule, the spatial resolution, the sensitivity, and the specificity. MSI also requires careful sample preparation, data acquisition, and data analysis to ensure the quality and reliability of the results.

[0006] MSI has many applications in various fields, such as biology, medicine, pharmacology, food, and environmental science, and can reveal the molecular heterogeneity, complexity, and dynamics of biological systems, as well as the interactions and functions of different molecules. MSI can also help identify biomarkers, diagnose diseases, monitor drug delivery and metabolism, and evaluate treatment effects.

[0007] The mass accuracy of mass spectrometry data, especially MALDI MSI data, may depend on many different factors, including the sample type, the type of mass analyzer instrument, and the preparation and acquisition protocols. Low mass accuracy may make it difficult or even impossible to analyze the mass spectrometry data and correctly interpret the experimental results. Therefore, achieving high mass accuracy is a prerequisite for many applications of mass spectrometry, especially MALDI MSI.

[0008] There are several methods to perform recalibration of mass spectrometry data, including methods based on the detection of specific calibrant peaks and comparing the measured mass with a priori known theoretical masses. Such methods may fail in cases where the calibrant peaks cannot be detected due to, for example, low signal-to-noise ratio in the spectrum or non-uniform spatial distribution of the calibrant. In addition, adding a calibrant to the sample under study, such as a tissue sample for MALDI MSI, may have an impact on the ionization of analyte molecules from the sample, thus altering the experimental results. There are other methods that do not rely on calibrant peak detection, but these methods are also applicable only under certain premises or they require high computational effort.

[0009] Below, the literature of the prior art that may be relevant to the present disclosure will be briefly cited, without requiring completeness:

[0010] The study by Assaf Wool et al. (Proteomics 2002, 2, 1365 - 1373) concerns the pre-calibration of matrix-assisted laser desorption / ionization time-of-flight spectra of peptide mass fingerprints.

[0011] Patent publication US2018 / 0019110 A1 concerns a method for mass spectrometry data analysis for analyzing a sample composed of two different reference chemical structures A and B, each of which repeats. It includes: obtaining the exact mass information of each peak in the sample mass spectrum by mass spectrometry; obtaining Kendrick mass defect information D A and D B , where the fractional part is extracted from the mass information obtained by performing Kendrick mass conversion calculation processing on the exact mass information of each peak; obtaining mass defect information d B and d A , where the fractional part is extracted from the mass information of reference chemical structures A and B, A-based B, and B-based A; for D A , D B , dA , and d B , calculate

[0012] n A = D B / d A , n B = D A / d B

[0013] and obtain the degree of polymerization information n A and n B ; and display a graph corresponding to each peak on a two-dimensional coordinate, where n A and n B are axes.

[0014] Patent Publication US2019 / 0257839 A1 (the entire content of which is incorporated herein by reference) relates to a method for evaluating mass spectrometry data for analyzing peptides from biological samples, the mass spectrometry data being particularly MALDI-TOF mass spectrometry data, and comprising the following steps: a) providing an expected mass defect; b) determining a measured mass defect, i.e., the mass defect generated from the mass spectrometry data; c) comparing the measured mass defect with the expected mass defect.

[0015] Patent Publication US2020 / 0328069 A1 (the entire content of which is incorporated herein by reference) relates to a method that is applicable to the quality control and signal correction of mass spectrometry data of biological tissue samples and is based on the analysis of chemical background signals observed in the spectrum. It utilizes the fact that chemical background signals contain components from multiple polymer molecules, the chemical structures of which have strong regularities. These regularities imply that the observed masses are subject to certain statistical distributions, each of which is characteristic of a molecular class. By analyzing these statistical properties, any possible mass drift can be detected and corrected.

[0016] Patent Publication US2021 / 0065849 A1 relates to a pre-processor that extracts multiple spectra to be processed from a total mass spectrum. A simulated spectrum generator with a learned model generates simulated spectra with peak discrimination actions from each mass spectrum. A post-processor generates a combined simulated spectrum based on the multiple simulated spectra. A peak filter performs peak discrimination on a peak list using the combined simulated spectrum.

[0017] In view of the above, there is still a need for accurate and improved mass recalibration of mass spectrometry data, particularly using machine learning methods. Summary of the Invention

[0018] According to a first aspect, the present disclosure relates to a mass spectrometry method, comprising: - obtaining or providing a mass spectrum comprising a plurality of measured ion abundance values, each measured ion abundance value from the plurality of measured ion abundance values being associated with a value or range of values on a first mass-related scale; - applying an algorithm to the mass spectrum, the algorithm comprising a mapping of ion abundance values to a second mass-related scale, the mapping comprising at least one of the following steps: (i) identifying when the second mass-related scale substantially coincides with the first mass-related scale, and (ii) revising when the second mass-related scale does not substantially coincide with the first mass-related scale; and - processing the mass spectrum to have a mass-related scale that is at least one of the identified and the revised; wherein the algorithm implements the result of training using machine learning on a plurality of data sets, wherein each data set from the plurality of data sets comprises a mass-curated training spectrum and / or is derived from the mass-curated training spectrum, the mass-curated training spectrum having undergone one or more intentional mass-related scale modifications, and wherein the training is intended to provide the mapping to substantially undo or substantially compensate for the one or more intentional mass-related scale modifications. In a particular embodiment, the training may be intended to provide the mapping to substantially undo or substantially compensate for any, each, and every intentional mass-related scale modification.

[0019] A mass spectrum may represent a structure that records and stores the relative abundances and masses of charged molecules or ions in the gas phase generated from a sample. The representation of a mass spectrum typically shows the mass-related scale as the horizontal axis and the ion abundance-related scale as the vertical axis. Within the scope of the present disclosure, peak lists should also be included in the definition of a mass spectrum, which are data sets of such abundance-mass pairs that do not necessarily have a continuous and contiguous mass-related scale and in which noise is mostly absent if not completely absent.

[0020] In the context of the present disclosure, the term "mass-curated" as used in the term "mass-curated training spectrum" means that the training spectrum has been mass-calibrated or has been mass-calibrated using a method with a high level of accuracy and precision.

[0021] It is possible to perform the training of a machine learning model and / or the application of an algorithm implementing the results of machine learning on a mass spectrum by considering only the ion behavior on the mass-related scale, such as only observing signal peaks along the mass-related scale, such as centroids, and substantially ignoring any actual ion abundance or ion intensity associated with each signal peak along such a mass-related scale. Ion abundance information can also be used as a weighting factor so that, in the training and / or recalibration phase, stronger signal components are favored over weaker signal components.

[0022] When applying an algorithm that implements the results of machine learning, the mass spectrum can be processed in such a way that its overall mass-related scale is modified compared to a first quality-related scale. For example, when each and every mass-related interval or mass-related range along the mass-related scale in the mass spectrum suffers from a mass-related inaccuracy exceeding a tolerance level, such as a deviation greater than or equal to X parts per million (ppm), where X can be taken from the following group, which includes: 10, 9, 8, 7, 6, 5, 4, 3, 2, 1. It is also considered that the processing of the mass spectrum can lead to its mass-related scale being partially modified and partially confirmed, and the latter can be applied, for example, in cases where the mass-related inaccuracies determined in one or more mass-related intervals or mass-related ranges along its mass-related scale remain within the tolerance level defined by way of example above. Finally, for example, when there are no mass-related inaccuracies exceeding the tolerance level defined by way of example above in all mass-related intervals or all mass-related ranges along the mass-related scale, the processing of the mass spectrum may also lead to the confirmation of its mass-related scale along its entire range.

[0023] In various embodiments, an analyzer operating according to a principle selected from the following group can be used to perform the acquisition of the mass spectrum, the group including: time-of-flight analyzer, ion cyclotron resonance analyzer, Kingdon-type analyzer, for example A time-of-flight analyzer in which ions can be axially or orthogonally accelerated has the following advantages: (i) high transmission efficiency, which means it can detect most of the ions entering the analyzer without losing them, resulting in higher sensitivity and lower detection limits; (ii) no upper m / z limit, which means it can measure the masses of very large molecules, such as proteins or polymers, without fragmenting them into smaller pieces, thus enabling the analysis of intact biomolecules and complex mixtures; (iii) fast scan rate, which means it can acquire a complete mass spectrum in a very short time, typically within a few microseconds, enabling the analysis of transient or dynamic phenomena, such as chemical reactions or biological processes; and (iv) compatibility with various ion sources and techniques, ion sources such as electron ionization (EI), chemical ionization (CI), matrix-assisted laser desorption / ionization (MALDI), electrospray ionization (ESI), and techniques such as ion mobility spectrometry (IMS) and collision-induced dissociation (CID), thus providing versatility and flexibility for different applications and fields.

[0024] In various embodiments, the mass-related scale may include one of a mass scale m and a mass-to-charge ratio scale m / z. Working with the mass-to-charge ratio m / z rather than the mass m does not require inferring or determining the charge state of each signal peak in the mass spectrometry data, which can introduce uncertainty and can also be a computationally lengthy process, especially when the number of such signal peaks is large. Certain ionization mechanisms are known to predominantly produce ions with a single charge, such as MALDI, which further simplifies the data processing regarding the mass-related scale.

[0025] In various embodiments, machine learning may include methods selected from the group consisting of: multi-layer machine learning, supervised machine learning, deep learning, neural networks, such as convolutional neural networks. Preferably, the neural network may have an architecture including an initial block that includes a plurality of convolutional layers, followed by a second block that includes a plurality of fully connected layers. This design of the neural network facilitates (i) more effective and efficient processing of high-dimensional inputs, such as images, because the convolutional layers reduce the number of parameters and weights by applying filters to local regions of the input, (ii) the ability to learn hierarchical and spatial features from the input, because the convolutional layers capture local patterns and the pooling layers aggregate them into higher-level features, (iii) avoiding dead neurons, because the convolutional layers use activation functions like ReLU or LeakyReLU, which allow small gradients for negative inputs and do not saturate the gradients and eliminate them as in the case of fully connected layers using sigmoid or tanh functions, and (iv) achieving higher accuracy and performance in tasks such as image classification, object detection, and segmentation, because the convolutional layers can assign importance to different features and the fully connected layers can learn their non-linear combinations.

[0026] In various embodiments, the first mass-related scale may be pre-mass calibrated using the raw mass spectrometry data and a method selected from the group consisting of: internal lock mass calibrant, external lock mass calibrant, statistical assessment of molecular content, may be applied thereto. The principle of internal lock mass calibration is generally to select a signal peak present in the mass spectrometry data that has known properties and a mass-to-charge ratio (m / z). In a MALDI sample, this may include one or more signal peaks originating from or coming from the MALDI matrix material, such as α-cyano-4-hydroxycinnamic acid (CHCA). This peak is referred to as the "lock mass" and is used to map the proxy parameter observed during acquisition, such as the flight time, on the mass-related scale. The principle of external lock mass calibration is to introduce a small amount of calibration compound into the ion source together with any analyte compound. This can be done, for example, during the sample preparation step. The calibrant compound preferably has a well-defined and stable mass-to-charge ratio (m / z) that is different from any analyte compound.

[0027] In various embodiments, the application algorithm may include mass defect analysis of a mass spectrum. Preferably, mass defect analysis is performed on signal peaks in the mass spectrometry data having a single isotope mass. To this end, the mass spectrometry data, in particular the mass spectrum, may be subjected to a de-isotoping algorithm.

[0028] In various embodiments, the data set may include mass defect data derived from underlying mass-refined training spectra. Preferably, the mass defect data may be given by pairs of (m, δ λ (m)), where the mass defect δ λ (m) is calculated using the following formula (Kendrick mass defect data),

[0029] where denotes the floor function, λ is a scaling factor, m N is the closest nominal mass, which is given by and m is replaced by the mass-related value included in the mass spectrum.

[0030] In various embodiments, the mass defect data may be represented as a two-dimensional histogram H on a mass-related axis and a mass defect-related axis, accumulating the ion abundance values at the mass-related value m in the two-dimensional histogram interval containing the point (m, δ λ (m)). Preferably, the data set includes i = 1,..., N histograms H i and deliberately made mass-related scale modifications Δ i of {H i , Δ i}, and the training is performed by finding a parameter vector θ that minimizes the expression where f θ is the mapping of the histogram H to the mass-related scale modification Δ, and the mapping is parameterized by the parameter vector θ.

[0031] In various embodiments, the mass-related axis may be divided into K mass-related intervals, and the mass defect-related axis may be divided into L mass defect-related intervals, where K may be selected from the group consisting of: 5, 10, 15, 20, 25, 30, 40, 50, and any other natural number greater than or equal to 5, and where L may be selected from the group consisting of: 100, 150, 200, 250, 300, 350, 400, 500, and any other natural number greater than or equal to 100. The lower limit of the number of intervals provides a reliable data pool allowing robust and reliable statistical analysis.

[0032] In various embodiments, the quality-refined training spectra can include one of computer-simulated generated synthetic mass spectra and measured and calibrated mass spectra. A synthetic mass spectrum can be a mass spectrum generated by a computer program or a mathematical model, rather than by a real mass spectrometer. It can be used to simulate the expected mass spectrum of a known or hypothesized compound. Synthetic mass spectra can be advantageous because their generation can save time and resources as they do not require the preparation and analysis of real samples, or the operation and maintenance of a mass spectrometer, and they can serve as a reference or standard for comparison as they can represent the ideal or optimal mass spectrum of a compound without any noise, interference, or error. In the context of training, this can mean that a machine learning model can be trained to purely identify and correct deviations in mass or mass-related parameters, without being affected by other artifacts that may be present in a real-measured mass spectrum. On the other hand, measured and calibrated mass spectra can represent physical reality more accurately than computer simulations, including side effects and mass analyzer responses that go beyond theoretical scientific descriptions, making the results more relevant and closer to physical reality. It is conceivable that the body of training spectra for training, such as for creating multiple data sets, can consist of synthetic mass spectra as well as measured and calibrated mass spectra.

[0033] In various embodiments, intentional mass-related scale modifications can be selected from the group including: linear or non-linear stretching, linear or non-linear squeezing, offset. Preferably, the intentional mass-related scale modification can be parameterized as Δ(m) = a × m q + b, where Δ represents a mass shift, a and b are random real-valued parameters, m is a mass-related parameter, q is a power coefficient, where q is preferably one of one and 0.5, one meaning a linear modification and 0.5 being an example of a non-linear modification.

[0034] In various embodiments, the number of several quality-refined training spectra employed during training can be selected from the group including: 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, and any other natural number greater than 50. Having a specific minimum number of quality-refined training spectra included in or used to derive multiple datasets can be beneficial and advantageous because the larger the number, the better the generalization ability of the algorithm, which means the performance of the algorithm on new and unseen data, rather than just the data on which the machine learning model is trained, can be improved. Additionally, a large number of datasets can capture more diversity and variability in the data and reduce the risk of overfitting or underfitting. Moreover, using a large number of quality-refined training spectra can increase the accuracy and reliability of the algorithm, which means the algorithm can produce correct and consistent results and avoid errors or biases. This is because a large number of datasets can provide more evidence and support for the machine learning model to learn from and reduce the impact of noise or outliers that the quality-refined training spectra may otherwise harbor.

[0035] In various embodiments, the number of several intentional quality-related scaling modifications to which the quality-refined training spectra are subjected can be selected from the group including: 1, 500, 1000, 1500, 2000, 2500, 3000, 4000, 5000, and any other natural number greater than or equal to 1. It may be beneficial and preferred to subject each quality-refined training spectrum to different types of intentional quality-related scaling modifications, such as various squeezing and / or stretching and / or drifting operations, in order to provide multiple scenarios that have been found to potentially occur in actual measurements for training.

[0036] In various embodiments, mass spectra or quality-refined training spectra can be acquired during a measurement run of mass spectrometry imaging. Mass spectrometry imaging provides a large amount of mass spectrometry data from a single source, which can exhibit a high degree of molecular homogeneity, generally making them very suitable for statistical evaluation purposes.

[0037] In various embodiments, a mass spectrum or a quality-refined training spectrum can include measured ion abundance values derived from a matrix material suitable for matrix-assisted ionization, such as matrix-assisted laser desorption / ionization. MALDI enables the ionization of large molecules, such as proteins, without any significant degree of fragmentation, and since the vast majority of ions are singly charged, it makes the mass-related scale easy to interpret.

[0038] In various embodiments, a mass spectrum or a mass-refined training spectrum may include measured ion abundance values derived from molecules selected from the group consisting of: peptides, proteins, lipids, polysaccharides, oligonucleotides, polymers. All elements from the foregoing group include organic molecules, which means they contain carbon atoms, usually bonded to hydrogen, oxygen, nitrogen, or other elements. In addition, all elements from the foregoing group include macromolecules, which means they are large molecules composed of smaller subunits or building blocks (called monomers). All elements from the foregoing group include polymers, which means they are chains of monomers linked by covalent bonds. The monomers may be the same or different, depending on the type of polymer. For example, peptides and proteins are composed of amino acids, lipids are composed of a head structure and one or more aliphatic hydrocarbon chains, polysaccharides are composed of sugars, and oligonucleotides are composed of nucleotides. The bonds between monomers can be of various types. For example, peptides and proteins have peptide bonds, lipids have ester bonds, polysaccharides have glycosidic bonds, and oligonucleotides have phosphodiester bonds. Elements from the foregoing group may have different structures and properties. For example, peptides and proteins can have complex three-dimensional shapes, lipids are mostly hydrophobic, polysaccharides can be linear or branched, and oligonucleotides can form double helices. Generally, polymers can have different degrees of flexibility and rigidity.

[0039] In another aspect, the present disclosure relates to a method for generating a mass recalibration algorithm suitable for mass spectrometry data, which includes: - obtaining or providing a plurality of mass-refined training spectra; - applying one or more intentional mass-related scale modifications to each of the plurality of mass-refined training spectra; - generating a plurality of data sets from the plurality of mass-refined training spectra with intentional mass-related scale modifications by subjecting the plurality of mass-refined training spectra with intentional mass-related scale modifications to mass defect analysis; - training by subjecting the plurality of data sets to machine learning to substantially undo or substantially compensate for the one or more intentional mass-related scale modifications to achieve at least one of the following purposes, namely, confirming and correcting the mass-related scale of the mass spectrometry; and - using the training results to generate a mass recalibration algorithm.

[0040] Those skilled in the art will readily understand that any element and any explanation previously disclosed in connection with the first aspect of the present disclosure can be compatible with and applicable to another aspect of the present disclosure, such that they can be combined and implemented as the skilled person deems appropriate. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The present invention can be better understood by reference to the following drawings. The elements in the drawings are not necessarily drawn to scale, but rather the emphasis is placed on illustrating the principles of the present invention (usually schematically):

[0042] Figure 1 Shows the Kendrick mass defect plot of the observed, pre-mass calibrated spectrum, Figure a), and the corresponding re-calibrated spectrum, Figure b). The solid line represents the estimated mass drift function, which is approximately zero after re-calibration. The crosses represent the expected masses of the MALDI matrix cluster molecules from the prior model. Close-up Figures c) and d) show how the difference between the observed matrix peak positions and the expected matrix peak positions is reduced by re-calibration.

[0043] Figure 2 Shows examples of randomly generated mass drift functions and the Kendrick mass defect plots of the corresponding training spectra. Figures a) and b) show a random mass drift proportional to the mass, Figure a), and its square root, Figure b). Figure c) shows the mass drift function obtained by adding a random offset to the true observed mass drift function.

[0044] Figure 3 Presents a schematic overview of a neural network architecture according to the principles of the present disclosure.

[0045] Figure 4 Shows the relative mass dispersion of the first 50 local maxima of the original average spectrum. The horizontal dashed line represents the respective median standard deviation for all 31 MSI FFPE tissue sample datasets, which is the same data used in the following study by Tobias Boskamp et al.: Using the chemical noise background in MALDI mass spectrometry imaging for mass alignment and calibration (Using the chemical noise background in MALDI mass spectrometry imaging for mass alignment and calibration). Analytical Chemistry 2019, 92, 1301 - 1308.

[0046] Figure 5 Shows the median mass error for nine known MALDI matrix peaks (vertical axis, m / z) for pre-mass calibrated data and for data re-calibrated using the method according to the principles of the present disclosure. Detailed Description

[0047] Although the present invention has been shown and described with reference to several different embodiments of the present invention, those skilled in the art will recognize that various changes in form and detail may be made herein without departing from the scope of the present invention as defined by the appended claims.

[0048] Describes a method for mass re-calibration of mass spectrometry data, particularly in matrix-assisted laser desorption / ionization (MALDI) mass spectrometry imaging (MSI) data.

[0049] In the following, an embodiment of a mass calibration method is described, which includes (supervised) training of a multi-layer machine learning model, such as a neural network, to extract the mass error of an observed spectrum from its so-called Kendrick mass defect plot. Once the mass drift function, i.e., the mass error as a function of mass, is obtained, it is quite straightforward to recalibrate the spectrum or adjust its mass axis or mass-related axis.

[0050] For training a machine learning model, such as a neural network, only a relatively small number of mass-refined, i.e., accurately and precisely mass-calibrated, training spectra need to be available. Such mass-refined training spectra can be generated in different ways, such as, for example, from a prior model that describes the expected signal components of an actually measured spectrum. Alternatively, existing mass calibration methods can be applied only to a small subset of the measured mass spectra, such that computationally expensive algorithms, or methods that are not applicable to every spectrum for other reasons, can be utilized for this purpose.

[0051] Mass spectrometry imaging (MSI)

[0052] As previously elaborated, in a typical mass spectrometry imaging experiment, a series of mass spectra are acquired from a plurality of positions (points) uniformly distributed over a sample extending in two dimensions. For each point, molecules are extracted from the sample, ionized, and detected in a mass analyzer. The resulting mass spectra include a sequence of mass-intensity pairs.

[0053] Note: The actual physical quantity measured by the mass detector of a mass analyzer is the mass-to-charge ratio, denoted as m / z. Thus, strictly speaking, the spectrum includes m / z values and intensity values. However, for simplicity, the term "mass" is used below and throughout this disclosure as a synonym for the mass-to-charge ratio.

[0054] Kendrick mass defect plot

[0055] The m / z values or molecular masses are given in daltons (Da) as multiples of the atomic mass unit (1 Da = 1 amu). The mass in daltons approximately corresponds to the total number of protons and neutrons including the atomic nucleus of the molecule. The difference between this integer nominal mass and the actual mass is called the mass defect (sometimes also referred to as mass excess). The mass defect of a molecule is the sum of the mass defects of the individual atoms, and for each chemical element or isotope, the mass defects of the individual atoms are different.

[0056] A similar concept is the so-called Kendrick mass defect, which describes the mass defect of a molecular mass relative to a properly chosen Kendrick scale (Edward Kendrick: A mass scale based on CH2=14.0000 for high resolution mass spectrometry of organic compounds, Analytical Chemistry 1963, 35, 2146-2154). The Kendrick scale is appropriately chosen according to the molecular class under consideration and its corresponding typical repeating unit. In the classical case, for example, the Kendrick scale corresponds to the repeating unit CH2. Alternative scales can be selected for the analysis of lipids, peptides, or glycans.

[0057] More specifically, for a given molecular mass m, the (central) Kendrick mass defect relative to a reference λ is defined as

[0058]

[0059] According to this definition, the central Kendrick mass defect is always in the range of [-0.5, 0.5]. The evaluation of the Kendrick mass defect for all observed masses m in the spectrum defines the mass defect plot (m, δ λ (m)), which can be plotted in a graph where the abscissa corresponds to the mass m (or m / z value), and the Kendrick mass defect δ λ (m) is plotted on the ordinate, see Figure 1 . Note that the mass defect axis has a circular structure: mass defects greater than 0.5 wrap around to the other side of the -0.5 defect at higher mass values.

[0060] The Kendrick mass defect plot of the spectrum reveals specific patterns depending on the type of analyte under consideration. Deviations from these patterns can be attributed to mass drift, and thus the mass defect plot can be used to estimate the mass drift function. In Figure 1shows a mass defect plot of a peptide measurement example. For these analytes, the averagine peptide model can be used, which is based on the observation that peptides cluster around equidistant masses with a spacing slightly greater than 1 Da (see Michael W. Senko et al.: Determination of monoisotopic masses and ion populations for large biomolecules from resolved isotopic distributions. Journal of the American Society for Mass Spectrometry 1995, 6, 229 - 233). The exact mass m of a peptide is approximately proportional to its nominal mass m N i.e., m≈λm N , where λ≈1.000495, and as a result, δ λ (m) is approximately zero for the exact peptide mass. Thus, for the observed spectrum, the clusters formed by peptide masses directly correspond to the deviation of the line with δ λ (m)=0 in the Kendrick mass defect plot from the effective mass drift function (see Tobias Boskamp et al.: Using the chemical noise background in MALDI mass spectrometry imaging for mass alignment and calibration. Analytical Chemistry 2019, 92, 1301 - 1308). Other biopolymers may have other scaling parameters, e.g., for N - glycans λ≈1.0035.

[0061] Figure 1 The Kendrick mass defect plot shown includes another signal pattern that is not generated by peptide molecules but by MALDI matrix clusters. The matrix pattern has a different and more complex structure than the peptide pattern, reflecting the different chemical reactions and variations that MALDI matrix molecules may participate in. Similarly, other molecular classes, such as glycans, lipids, or polymers, each show their own characteristic patterns in the Kendrick mass defect plot. In the case where the measured spectrum is affected by some effective mass drift, this mass drift is reflected by the distortion of the Kendrick mass defect plot in a manner similar to that of the Figure 1 peptides shown. However, due to the higher complexity of these patterns, the effective mass drift cannot be easily detected from the Kendrick mass defect plot.

[0062] The Kendrick mass defect plot of the spectrum can be represented as a two - dimensional histogram H on the mass and mass defect axes, containing the points (m,δλ (m)) in the two-dimensional histogram interval to accumulate spectral intensity at mass m. To this end, the mass and mass defect axes are each subdivided into K and L intervals, so that H can be represented as a matrix with K columns and L rows. A typical choice is to subdivide the mass axis or mass-related axis into K ≈ 25 intervals and the mass defect axis into L = 256 intervals. This representation is robust in the presence of strong noise, as is typically observed in a single spectrum, while allowing the Kendrick mass defect plot to be encoded by a fixed number of variables, e.g., allowing it to be used as an input to a neural network.

[0063] Description of a preferred embodiment

[0064] The proposed method may include the following steps:

[0065] 1. Generate a set of training spectra that are accurately mass-calibrated, i.e., mass-refined, with high mass accuracy.

[0066] 2. Generate a set of training data by applying a known mass drift function to the mass-refined training spectra.

[0067] 3. Train a machine learning model, such as a neural network, to map the Kendrick mass defect histogram to the corresponding known mass drift function for each mass-refined training spectrum.

[0068] 4. Apply the trained algorithm that implements the machine learning results to the Kendrick mass defect histogram of a new pre-calibrated mass spectrum to obtain an estimate of the effective mass drift function for this measured mass spectrum.

[0069] 5. Use the mass drift function estimated by the algorithm that implements the machine learning results to re-calibrate the mass spectrum.

[0070] These steps are described in more detail by way of example as follows:

[0071] Generate mass-refined training spectra

[0072] To train a machine learning model, such as a neural network, a relatively small number (usually no more than 150) of mass-refined training spectra are required. These mass-refined training spectra need to be similar to the actual mass spectra to be processed, i.e., the actually measured mass spectra that should later be re-calibrated using the trained algorithm that implements the machine learning results. Ideally, they include signal components from molecules of the same class, including the analyte molecules under study and, optionally, MALDI matrix molecules. In addition, the type and level of spectral noise in the mass-refined training spectra should be comparable to the noise in the actual mass spectra to be processed.

[0073] One option for obtaining such a mass-refined training spectrum is to use a prior model of spectral components and the expected noise in the actual mass spectrum to be processed. For example, the Averagine model for the above peptides can achieve statistical prediction of the exact expected mass of peptides in biological tissues and thus generate any number of random peptide masses. In addition, a chemical model of the MALDI matrix used for ionization in the experiment can achieve prediction of matrix cluster peaks observed in the real mass spectrum (see Bernd O. Keller et al.: Discerning matrix-cluster peaks in matrix-assisted laser desorption / ionization time-of-flight mass spectra of dilute peptide mixtures. Journal of the American Society for Mass Spectrometry 2000, 11, 88 - 93). In a particularly advantageous embodiment, the two models together can be used to randomly generate synthetic mass spectra similar to the true measured mass spectra of peptides, with near-perfect mass scale accuracy and precision.

[0074] Another option for obtaining a mass-refined training spectrum is to apply an auxiliary mass recalibration method to the real, measured, and pre-mass-calibrated spectrum. Since only a small set of mass-refined training spectra is needed, it is feasible to use an auxiliary recalibration method that is restricted to only a small number of spectra. This restriction may be due to the high computational complexity of the auxiliary method. For example, the prior model of the above spectral components can be employed in the auxiliary recalibration method to approximate the measured mass spectrum by appropriately parameterized model components and their respective mass drifts. Then, the resulting mass drift function can be used to accurately and precisely mass-calibrate the training spectrum.

[0075] A different type of auxiliary recalibration method requires detection of a priori known calibrant signals in the measured mass spectrum. Depending on the choice of calibrant, such a method may be limited by the fact that the calibrant can only be reliably detected in a small fraction of the measured mass spectrum. In the case of applying a specific calibrant mixture to the sample, it may also be desirable to apply the mixture to only a small fraction of the sample to avoid contaminating the sample with the calibrant, which may have an adverse effect on subsequent ionization and mass detection processes. All these situations can make it cumbersome and time-consuming to apply the auxiliary recalibration method to the complete set of measured mass spectra, but still allow accurate and precise mass calibration of a sufficient number of training spectra.

[0076] Generate training data from mass-refined training spectra

[0077] To train the machine learning models, especially neural networks, described in the next section, mass-refined training spectra with known mass drifts are required, which are similar to the types of mass drifts observed in real measured mass spectra. For a given mass-refined spectrum S with mass-intensity pairs (m k , s k ), and a mass drift function Δ(m) that describes the effective mass drift at mass m, the distorted spectrum S′ contains the mass-intensity pairs (m k + Δ(m k ), s k ). To generate the training data, each mass-refined training spectrum S generated in the previous step n is combined with a large number (usually up to 2500) of mass drift functions Δ n,i to produce the same number of distorted training spectra S′ n,i . Here, the label n represents the set of mass-refined training spectra, and the label i represents different mass drift functions. The entire set of training data may contain all pairs (S′ n,i , Δ n,i ).

[0078] Two different methods can be used to generate the mass drift function Δ n,i : either by a random linear function of m or a suitable power of m, and by randomly scaling the actually observed mass drift functions, which are obtained, for example, using an auxiliary mass recalibration method together with the mass-refined training spectra, as described above.

[0079] For the first option, a purely synthetic mass drift function is generated as Δ(m) = a × m q + b, where the real-valued parameters a and b are randomly selected from within a suitable range of values for each mass drift function. The exponent q is a fixed choice depending on the type of mass drift function typically expected for the mass analyzer used. For example, for a time-of-flight (TOF) instrument, the observed mass drift is known to be proportional to m or sqrt(m), so q = 1 and q = 1 / 2 are suitable, as shown in Figure 2 , charts a) and b).

[0080] For the second option, the true, observed mass drift function Δ(m) is randomly transformed into a scaled function Δ′(m) = cΔ(am + b) + d, again using randomly selected real-valued scaling parameters a, b, c, and d, as shown in Figure 2, Chart c). Note that this choice requires recalibrating the mass drift function extracted from the observed mass spectrum using an auxiliary mass. To obtain a set of mass-refined training spectra covering a wide range of potential mass drift functions, these two options for generating the mass drift function can be combined when creating the training data.

[0081] Machine learning models, such as neural networks, for estimating the effective mass drift of spectra

[0082] The core element of the proposed mass recalibration method can be implemented as a neural network that takes the Kendrick mass defect histogram of the spectrum as input and calculates the effective mass drift function of the spectrum. Figure 3 The architecture of such a proposed neural network is shown. Since the input to this network, i.e., the mass defect histogram H, can be interpreted as an image, a convolutional neural network (CNN) can be used, which has been successfully applied to many imaging problems. More specifically, the neural network architecture can have an initial feature extraction block with several convolutional layers, followed by a fully connected prediction network.

[0083] Feature extraction sub-network

[0084] The feature extraction sub-network can have two parts. The first part can employ a series of K 1D convolutional layers, each convolutional layer operating on a single mass bin in the input histogram, i.e., operating on a column of the matrix H. For each column, different sets of 1D convolutional filters are applied, and each convolutional filter integrates the circular padding to account for the circular structure of the Kendrick mass defect. After each 1D convolutional layer, 1D batch normalization and the LeakyReLU activation function can be used. In summary, this part consists of six 1D convolutional layers with batch normalization and activation functions.

[0085] In the second part, four 2D convolutional layers can be used, which allows for information exchange between the mass bins. Here, 2D batch normalization and the LeakyReLU activation function are used after each 2D convolutional layer.

[0086] Prediction sub-network

[0087] In the prediction sub-network, first an initial 1D convolution can be applied to reduce the number of channels to one. For each mass bin, then a multi-layer perceptron (MLP) is used to produce the final mass drift estimate for that bin. Each MLP is implemented as a fully connected layer with the LeakyReLU activation function. For the final output, a tangent hyperbolic (tanh) activation function scaled by 0.5 can be used to ensure that the output is always in the interval [-0.5, 0.5].

[0088] Neural network training

[0089] Training is performed in multiple iterations using pre-generated training data (see below). In each iteration, different sets of mass-refined training spectra are used, along with the corresponding known mass drift functions. The Kendrick mass defect histograms of the mass-refined training spectra are fed into a neural network, and the network parameters are modified to minimize the difference between the neural network output and the expected mass drift function. The training can use the Adam optimizer with a learning rate of 1e-4 and a batch size of 64.

[0090] Apply an algorithm implementing the neural network training results to recalibrate the mass spectrometry

[0091] To recalibrate the measured mass spectrum, the Kendrick mass defect histogram of the spectrum is fed into the trained network. The output of the network is an estimate of the effective mass drift function for the measured mass spectrum. To recalibrate the spectrum, a negative mass drift is applied to the mass axis or mass-related axis of the mass spectrum.

[0092] Evaluation results

[0093] To demonstrate the effectiveness of the new recalibration method, the method is applied and evaluated on a set of 31 formalin-fixed paraffin-embedded (FFPE) tissue samples in peptide MALDI MSI measurements. The total training takes about 40 minutes for each FFPE tissue sample data, which is divided into 3 minutes for generating training data and 37 minutes for machine learning itself. It takes about 0.039 seconds to recalibrate a mass spectrum from a sample point using a graphics processing unit (GPU) of the GeForce RTX2080 type. Due to the lack of ground truth data containing perfectly mass-calibrated spectra, it poses a challenge to evaluate the accuracy of the mass drift calibration method. Below, two different mass metrics are reported: the relative mass dispersion of high-intensity peaks in the average spectrum, and the absolute mass drift of selected known MALDI matrix peaks.

[0094] Relative mass dispersion

[0095] For each of the 31 tissue sample datasets, 50 of the highest-intensity average spectrum peaks are considered. For each of these 50 highest peaks, the closest peak in all individual spectra is calculated. Those peaks among the 50 highest peaks that cannot be present in at least 10% of all spectra at a signal-to-noise ratio of at least 2.5:1 are discarded. Finally, the median mass dispersion of all remaining average spectrum peaks is calculated, where the mass dispersion of an average spectrum peak is defined as the standard deviation of the corresponding peak positions in the individual spectra, expressed in parts per million (ppm) relative to the m / z value (e.g., its centroid) of the peak.

[0096] Figure 4The results of this evaluation for all tissue sample datasets are shown, comparing the new recalibration method with the original pre-quality-calibrated data and with data recalibrated using the statistical recalibration method of the previously cited Tobias Boskamp et al. Since the latter was explicitly designed to be applied only to spectra with a sufficiently low level of MALDI matrix signal peaks, additional results were obtained when this method was applied only to such low matrix spectra.

[0097] The new method according to the principles of the present disclosure achieved a lowest median mass dispersion of 11.27 ppm, which is better than the 12.96 ppm mass dispersion obtained for the statistical recalibration evaluated on low matrix spectra. When the statistical recalibration was evaluated on all spectra in a way that significantly increased the computation time, the mass dispersion increased to 18.64 ppm, making the performance gap even wider. Thus, contrary to the statistical recalibration, the new method according to the principles of the present disclosure can be applied to mass spectra containing strong MALDI matrix signals while increasing the robustness of the recalibration.

[0098] Absolute mass error

[0099] To quantify the absolute mass error, the absolute mass drift (vertical axis, m / z) of nine selected known MALDI matrix peaks was considered. For this purpose, a combined model of the aforementioned matrix molecules was used, allowing the mass error to be assessed as the distance between the measured peak and the closest theoretical matrix peak. For each matrix peak and each tissue sample dataset, the median mass error of all spectra was calculated.

[0100] The results are shown in Figure 5 and represent the median mass error of all tissue sample datasets for each of the nine matrix peaks individually. Averaged over all nine matrix peaks, the new method according to the principles of the present disclosure yielded a median mass error of -28.70 ppm compared to 63.88 ppm observed in the original pre-quality-calibrated data. This shows the mass gain provided by performing the method according to the principles of the present disclosure.

[0101] The present invention has been shown and described above with reference to various different embodiments of the present invention. However, those skilled in the art will understand that, without departing from the scope of the present invention, if feasible, various aspects or details of the present invention can be changed, or the aspects or details of different embodiments can be arbitrarily combined. For example, the method according to the present disclosure has been described above with reference to mass spectrometry data that has only one or at least only one major signal component, namely a peptide. However, those skilled in the art will recognize that the principles of the present disclosure can be extended to cases where not only one or only one major signal component appears, but also two or even more appear. Methods for how to handle such more complex data structures are disclosed by the applicant, for example, in US2020 / 0328069 A1, which is incorporated herein by reference in its entirety. Generally, the foregoing description is for illustrative purposes only and not for the purpose of limiting the present invention, which is defined only by the appended claims, including any equivalent embodiments, as the case may be.

Claims

1. A mass spectrometry method comprising: - acquiring or providing a mass spectrum comprising a plurality of measured ion abundance values, each measured ion abundance value from the plurality of measured ion abundance values ​​being associated with a value or a range of values ​​on a first mass related scale; - applying an algorithm to the mass spectrum, the algorithm comprising a mapping of ion abundance values ​​to a second mass-related scale, the mapping comprising at least one of the following steps: (i) confirming when the second mass-related scale substantially coincides with the first mass-related scale, and (ii) correcting when the second mass-related scale does not substantially coincide with the first mass-related scale; and - processing the mass spectrum to have a mass-related scale that is at least one of validated and corrected; wherein the algorithm implements the results of training multiple data sets using machine learning, wherein each data set from the multiple data sets contains and / or is derived from a quality refined training spectrum, the quality refined training spectrum has undergone one or more intentional quality-related scale modifications, and wherein the training is intended to be provided to the mapping to substantially undo or substantially compensate for the one or more intentional quality-related scale modifications.

2. The method according to claim 1, wherein: The acquisition of the mass spectrum is performed using an analyser operating according to a principle selected from the group consisting of: a time of flight analyser, an ion cyclotron resonance analyser, a Kingdon type analyser, e.g.

3. The method according to claim 1, wherein: The mass-related scale includes one of a mass scale m and a mass-to-charge ratio scale m / z.

4. The method according to claim 1, wherein: The machine learning includes methods selected from the following group, the group including: multi-layer machine learning, supervised machine learning, deep learning, neural networks, such as convolutional neural networks.

5. The method according to claim 4, wherein: The neural network has an architecture including an initial block including a plurality of convolutional layers, followed by a second block including a plurality of fully connected layers.

6. The method according to claim 1, wherein: The first mass related scale is pre-mass calibrated using raw mass spectral data and applying thereto a method selected from the group consisting of: an internal lock mass calibrant, an external lock mass calibrant, a statistical evaluation of molecular content.

7. The method according to claim 1, wherein: Application of the algorithm includes mass defect analysis of mass spectra.

8. The method according to claim 1, wherein: The data set includes quality defect data derived from the underlying quality refined training spectra.

9. The method according to claim 8, wherein: The quality defect data consists of pairs of (m,δ λ (m)) is given by the mass defect δ λ (m) is calculated using the following formula in represents the floor function, λ is the scaling factor, and m N is the closest nominal mass, which is given by is given by , where m is replaced by the mass-related value contained in the mass spectrum.

10. The method according to claim 8, wherein: The quality defect data is represented as a two-dimensional histogram H on the quality-related axis and the quality defect-related axis, including the pair (m, δ λ The ion abundance value at the cumulative mass-related value m in the two-dimensional histogram interval (m)).

11. The method according to claim 10, wherein: The data set includes i=1,…,N histograms H i and intentional mass-dependent scale modification Δ i {H i ,Δ i }, and training is performed by finding a parameter vector θ that makes the expression Minimize, where f θ is a mapping of the histogram H to a quality-dependent scale modification Δ, parameterized by a parameter vector θ.

12. The method according to claim 10, wherein: The quality-related axis is divided into K quality-related intervals, and the quality-defect-related axis is divided into L quality-defect-related intervals, wherein K is selected from the following group, which includes: 5, 10, 15, 20, 25, 30, 40, 50, and any other natural number greater than or equal to 5, and wherein L is selected from the following group, which includes: 100, 150, 200, 250, 300, 350, 400, 500, and any other natural number greater than or equal to 100.

13. The method according to claim 1, wherein: The mass refined training spectrum comprises one of a computer generated synthetic mass spectrum and a measured and calibrated mass spectrum.

14. The method according to claim 1, wherein: The intentional mass-related scale modification is selected from the group consisting of: linear or non-linear stretching, linear or non-linear squeezing, drifting.

15. The method according to claim 1, wherein: The intentional mass-dependent scaling modification is parameterized as Δ(m)=a×m q +b, where Δ represents the mass drift, a and b are random real-valued parameters, m is a mass-related parameter, and q is a power coefficient, where q is preferably between unity and 0.

5.

16. The method according to claim 1, wherein: The number of quality refined training spectra used during the training is selected from the following group, which includes: 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, and any other natural number greater than 50.

17. The method according to claim 1, wherein: The number of intentional quality-related scale modifications to which the quality-refined training spectra are subjected is selected from the group consisting of: 1, 500, 1000, 1500, 2000, 2500, 3000, 4000, 5000, and any other natural number greater than or equal to 1.

18. The method according to claim 1, wherein: The mass spectrum or mass refined training spectrum is acquired during a measurement run of mass spectrometry imaging.

19. The method according to claim 1, wherein: The mass spectrum or mass refined training spectrum comprises measured ion abundance values ​​derived from a matrix material suitable for matrix-assisted ionization, such as matrix-assisted laser desorption / ionization.

20. The method according to claim 1, wherein: The mass spectrum or mass refined training spectrum comprises measured ion abundance values ​​originating from molecules selected from the group consisting of: peptides, proteins, lipids, polysaccharides, oligonucleotides, polymers.

21. A method of generating a mass recalibration algorithm for application to mass spectrometry data, comprising: - Obtain or provide a plurality of training spectra with refined quality; - applying one or more intentional quality-related scaling modifications to each quality refined training spectrum from the plurality of quality refined training spectra; - generating a plurality of data sets from said plurality of quality refined training spectra modified by intentional quality related scaling by subjecting said plurality of quality refined training spectra modified by intentional quality related scaling to a quality defect analysis; - in order to substantially undo or substantially compensate for the one or more intentional mass-related scale modifications, training by subjecting the plurality of data sets to machine learning to achieve at least one of the following purposes, namely, confirming and correcting the mass-related scale of the mass spectra; as well as -Use the training results to generate a quality recalibration algorithm.

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