METHOD FOR PREDICTING CHEMICAL SHIFT VALUES OF NMR SPIN SYSTEMS IN A SAMPLE OF A FLUID CLASS, IN PARTICULAR IN A SAMPLE OF A BIOFLUID

Abstract

Correlation information between captured characteristics and chemical shift values of captured NMR spin systems is provided by a model appliance for a fluid class. An NMR spectrum of a sample of the fluid class is recorded. Peaks in the recorded NMR spectrum which belong to defined reference NMR spin systems are identified, and experimental chemical shift values of the peaks from the recorded NMR spectrum are determined. A chemical shift value of at least one of the captured NMR spin systems not belonging to the reference NMR spin systems is predicted by applying the model appliance onto the experimental chemical shift values of the reference NMR spin systems. Peaks in an NMR spectrum of a sample of a fluid class are attributed more quickly and reliably to NMR spins systems of compounds contained in the sample.

Claims

1. A method for predicting chemical shift values of nuclear magnetic resonance (NMR) spin systems belonging to compounds contained in a sample of a fluid class using NMR spectroscopy comprising: a) providing a model appliance representing an information of correlation between captured characteristics of the fluid class, wherein the captured characteristics include concentrations of captured substances contained in the fluid class, and chemical shift values of captured NMR spin systems belonging to compounds contained in the fluid class, wherein the compounds are among the captured substances, wherein the model appliance comprises a definition of reference NMR spin systems, wherein the reference NMR spin systems are a subset of the captured NMR spin systems, and wherein the reference NMR spin systems belong to compounds which are omnipresent in the fluid class; b) recording an NMR spectrum of the sample of the fluid class; c) identifying peaks in the recorded NMR spectrum which belong to the defined reference NMR spin systems of the model appliance, and determining experimental chemical shift values of the peaks from the recorded NMR spectrum; and d) predicting a chemical shift value of at least one of the captured NMR spin systems not belonging to the reference NMR spin systems by applying the model appliance onto the experimental chemical shift values of the reference NMR spin systems.

2. The method according to claim 1, wherein the reference NMR spin systems are chosen from a subset of the captured NMR spin systems for which the chemical shift values are of significance for an above-average amount of the concentrations of the captured substances, as determined by the model appliance.

3. The method according to claim 1, wherein the reference NMR spin systems are determined using a statistical correlation analysis method selected from the group consisting of: an Analysis of Variance (ANOVA) decomposition, a Spearman's rank correlation, a Kendall's Rank correlation, a spurious calculation, and a canonical correlation analysis.

4. The method according to claim 1, wherein the model appliance comprises a 1R sub-model of reduced type which indicates the captured characteristics x.sub.j as a function f of the chemical shift values δ.sub.i of the reference NMR spin systems only, with
x.sub.j=f.sub.j(δ.sub.1, . . . , δ.sub.R), with j: index of captured characteristics, with j=1, . . . , C and C: number of captured characteristics, and with i: index of reference NMR spin systems, with i=1, . . . , R and R: number of reference NMR spin systems.

5. The method according to claim 1, wherein the model appliance comprises a 2R sub-model of reduced type which indicates the chemical shift values δ.sub.k of the non-reference NMR spin systems as a function f of the chemical shift values δ.sub.i of the reference NMR spin systems only, with
δ.sub.k=f.sub.k(δ.sub.1, . . . , δ.sub.R), with k: index of non-reference NMR spin systems, with k=1, . . . , N and N: number of captured non-reference NMR spin systems, and with i: index of reference NMR spin systems, with i=1, . . . , R and R: number of reference NMR spin systems.

6. The method according to claim 1, wherein the model appliance comprises a 1F sub-model of full type which indicates the chemical shift values δ.sub.1 of the non-reference NMR spin systems or all captured NMR spin systems, as a function f of the captured characteristics x.sub.j, with
δ.sub.1=f.sub.1(x.sub.1, . . . , x.sub.C), with 1: index of NMR spin systems, with 1=1, . . . , N and N: number of non-reference NMR spin systems or with 1=1, . . . , S and S: number of all captured NMR spin systems, and with j: index of captured characteristics, with j=1, . . . , C and C: number of captured characteristics.

7. The method according to claim 1, wherein the model appliance comprises a 2F sub-model of full type which indicates the characteristics x.sub.j as a function f of the chemical shift values δ.sub.1 of the captured NMR spin systems, with
x.sub.j=f.sub.j(δ.sub.1, . . . δ.sub.S), with j: index of captured characteristics, with j=1, . . . , C and C: number of captured characteristics, and with 1: index of captured NMR spin systems, with 1=1, . . . , S and S: number of captured NMR spin systems.

8. The method according to claim 4, wherein the model appliance comprises a 1F sub-model of full type which indicates the chemical shift values δ.sub.1 of the non-reference NMR spin systems or all captured NMR spin systems, as a function f of the captured characteristics x.sub.j, with
δ.sub.1=f.sub.1(x.sub.1, . . . , x.sub.C) with 1: index of NMR spin systems, with 1=1, . . . , N and N: number of non-reference NMR spin systems or with 1=1, . . . , S and S: number of all captured NMR spin systems, and with j: index of captured characteristics, with j=1, . . . , C and C: number of captured characteristics; and wherein the model appliance comprises a 2F sub-model of full type which indicates the characteristics x.sub.j as a function f of the chemical shift values δ.sub.1 of the captured NMR spin systems, with
x.sub.j=f.sub.j(δ.sub.1, . . . , δ.sub.S), with j: index of captured characteristics, with j=1, . . . , C and C: number of captured characteristics, and with 1: index of captured NMR spin systems, with 1=1, . . . , S and S: number of captured NMR spin systems.

9. The method according to claim 8, further comprising: d1) applying the 1R sub-model of reduced type onto the experimental chemical shift values of the reference NMR spin systems to obtain predicted characteristics; d2) applying the 1F sub-model of full type onto the predicted characteristics obtained in previous substep d1) to obtain predicted chemical shift values of the non-reference NMR spin systems; d3) applying the 2F sub-model of full type onto the experimental chemical shift values of the reference NMR spin systems and the predicted chemical shift values of the non-reference NMR spin systems obtained in previous substep d2) to obtain predicted characteristics; d4) applying the 1F sub-model of full type onto the predicted characteristics obtained in previous substep d3) to obtain predicted chemical shift values of the non-reference NMR spin systems.

10. The method according to claim 5, wherein the model appliance comprises a 1F sub-model of full type which indicates the chemical shift values δ.sub.1 of the non-reference NMR spin systems or all captured NMR spin systems, as a function f of the captured characteristics x.sub.j, with
δ.sub.1=f.sub.1(x.sub.1, . . . , x.sub.C) with 1: index of NMR spin systems, with 1=1, . . . , N and N: number of non-reference NMR spin systems or with 1=1, . . . , S and S: number of all captured NMR spin systems, and with j: index of captured characteristics, with j=1, . . . , C and C: number of captured characteristics; and wherein the model appliance comprises a 2F sub-model of full type which indicates the characteristics x.sub.j as a function f of the chemical shift values δ.sub.1 of the captured NMR spin systems, with
x.sub.j=f.sub.j(δ.sub.1, . . . , δ.sub.S), with j: index of captured characteristics, with j=1, . . . , C and C: number of captured characteristics, and with 1: index of captured NMR spin systems, with 1=1, . . . , S and S: number of captured NMR spin systems.

11. The method according to claim 10, further comprising: d1′) applying the 2R sub-model of reduced type onto the experimental chemical shift values of the reference NMR spin systems to obtain predicted chemical shift values of the non-reference NMR spin systems; d2′) applying the 2F sub-model of full type onto the experimental chemical shift values of the reference NMR spin systems and the predicted chemical shift values of the non-reference NMR spin systems obtained in previous substep d1′) to obtain predicted characteristics; d3’) applying the 1F sub-model of full type onto the predicted characteristics obtained in previous substep d2′) to obtain predicted chemical shift values of the non-reference NMR spin systems.

12. The method according to claim 1, wherein the model appliance is derived from a teaching database, the teaching database comprising for each of a plurality of teaching samples of the fluid class values of the captured characteristics, including values for the concentrations of the captured substances, and chemical shift values of the captured NMR spin systems, obtained through use of a teaching NMR spectrum recorded of the respective teaching sample and assignment of peaks in the teaching NMR spectrum to the captured NMR spin systems and determining the chemical shift values of the peaks.

13. The method according to claim 12, wherein the captured characteristics include a temperature (T), and wherein, for each set of the concentrations of substances, teaching samples of at least two different temperatures (T) are included.

14. The method according to claim 12, wherein the model appliance, or at least one sub-model (1R, 2R, 1F, 2F) of the model appliance, is derived from the teaching database through use of a multivariate statistical algorithm, and wherein the multivariate statistical algorithm is a self-learning algorithm.

15. The method according to claim 1, wherein the fluid class is chosen as a biofluid, and wherein the captured substances are metabolites.

16. The method according to claim 15, wherein the biofluid is selected from urine, blood serum, sweat, saliva, cerebrospinal fluid (CSF), or another body fluid, or is selected from fruit juice, chyle, nectar, or another plant fluid.

17. The method according to claim 1, wherein the fluid class is selected from wine, honey, condiments, a plant derived product, or a naturally derived product.

18. A method for determining a concentration of at least one substance contained in a sample of a fluid class by NMR spectroscopy comprising: a) providing a model appliance representing an information of correlation between captured characteristics of the fluid class, wherein the captured characteristics include concentrations of captured substances contained in the fluid class, and chemical shift values of captured NMR spin systems belonging to compounds contained in the fluid class, wherein the compounds are among the captured substances, wherein the model appliance comprises a definition of reference NMR spin systems, wherein the reference NMR spin systems are a subset of the captured NMR spin systems, and wherein the reference NMR spin systems belong to compounds which are omnipresent in the fluid class; b) recording an NMR spectrum of the sample of the fluid class; c) identifying peaks in the recorded NMR spectrum which belong to the defined reference NMR spin systems of the model appliance, and determining experimental chemical shift values of the peaks from the recorded NMR spectrum; and aa) predicting chemical shift values of non-reference NMR spin systems of the captured NMR spin systems by applying the model appliance onto the experimental chemical shift values of the reference NMR spin systems; bb) identifying peaks in the recorded NMR spectrum which belong to the non-reference NMR spin systems through use of the predicted chemical shift values, and determining experimental chemical shift values of the peaks from the recorded NMR spectrum; cc) calculating the concentration of the at least one substance by applying the model appliance onto the experimental chemical shift values of the reference NMR spin systems and non-reference NMR spin systems, by applying a 2F sub-model of full type which indicates the characteristics x.sub.j as a function f of the chemical shift values δ.sub.1 of the captured NMR spin systems, with x.sub.j=f.sub.j(δ.sub.1, . . . , δ.sub.S), with j: index of captured characteristics, with j=1, . . . , C and C: number of captured characteristics, and with 1: index of captured NMR spin systems, with 1=1, . . . , S and S: number of captured NMR spin systems.

19. A method for determining a concentration of at least one substance contained in a sample of a fluid class by NMR spectroscopy comprising: a) providing a model appliance representing an information of correlation between captured characteristics of the fluid class, wherein the captured characteristics include concentrations of captured substances contained in the fluid class, and chemical shift values of captured NMR spin systems belonging to compounds contained in the fluid class, wherein the compounds are among the captured substances, wherein the model appliance comprises a definition of reference NMR spin systems, wherein the reference NMR spin systems are a subset of the captured NMR spin systems, and wherein the reference NMR spin systems belong to compounds which are omnipresent in the fluid class; b) recording an NMR spectrum of the sample of the fluid class; c) identifying peaks in the recorded NMR spectrum which belong to the defined reference NMR spin systems of the model appliance, and determining experimental chemical shift values of the peaks from the recorded NMR spectrum; and aa′) predicting chemical shift values of non-reference NMR spin systems of the captured NMR spin systems by applying the model appliance onto the experimental chemical shift values of the reference NMR spin systems; bb′) calculating the concentration of the at least one substance by applying the model appliance onto the experimental chemical shift values of the reference NMR spin systems and the predicted chemical shift values of the non-reference NMR spin systems obtained in step aa′), by applying a 2F sub-model of full type which indicates the characteristics x.sub.j=as a function f of the chemical shift values δ.sub.1 of the captured NMR spin systems, with x.sub.j=f.sub.j(δ.sub.1, . , δ.sub.S), with j: index of captured characteristics, with j=1, . . . , C and C: number of captured characteristics, and with 1: index of captured NMR spin systems, with 1=1, . . . , S and S: number of captured NMR spin systems.

20. A method according to claim 18, wherein the at least one substance, the concentration of which is determined by NMR spectroscopy, comprises an ion or other NMR inactive sub stance.

21. A method for determining the concentration of at least one compound contained in a sample of a fluid class comprising: a) providing a model appliance representing an information of correlation between captured characteristics of the fluid class, wherein the captured characteristics include concentrations of captured substances contained in the fluid class, and chemical shift values of captured NMR spin systems belonging to compounds contained in the fluid class, wherein the compounds are among the captured substances, wherein the model appliance comprises a definition of reference NMR spin systems, wherein the reference NMR spin systems are a subset of the captured NMR spin systems, and wherein the reference NMR spin systems belong to compounds which are omnipresent in the fluid class; b) recording an NMR spectrum of the sample of the fluid class; c) identifying peaks in the recorded NMR spectrum which belong to the defined reference NMR spin systems of the model appliance, and determining experimental chemical shift values of the peaks from the recorded NMR spectrum; and aa′) predicting a chemical shift value of at least one of the captured NMR spin systems, with the at least one NMR spin system belonging to the compound, by applying the model appliance onto the experimental chemical shift values of the reference NMR spin systems, wherein the at least one NMR spin system is a non-reference NMR spin system; bb′) identifying at least one peak in the recorded NMR spectrum of the sample which belongs to the at least one NMR spin system though use of the predicted chemical shift value; cc′) calculating the concentration of the compound based on the shape and/or size of the identified at least one peak in the recorded NMR spectrum of the sample.

22. The method of claim 9, starting with the predicted chemical shift values of the non-reference NMR spin systems of substep d4), and further comprising iteratively repeating: applying the 2F sub-model of full type onto the experimental chemical shift values of the reference NMR spin systems and the predicted chemical shift values of the non-reference NMR spin systems to obtain predicted characteristics; applying the 1F sub-model of full type onto the predicted characteristics to obtain predicted chemical shift values of the non-reference NMR spin systems.

23. The method of claim 11, starting with the predicted chemical shift values of the non-reference NMR spin systems of substep d3′), and further comprising iteratively repeating: applying the 2F sub-model of full type onto the experimental chemical shift values of the reference NMR spin systems and the predicted chemical shift values of the non-reference NMR spin systems to obtain predicted characteristics; applying the 1F sub-model of full type onto the predicted characteristics to obtain predicted chemical shift values of the non-reference NMR spin systems.

24. A method according to claim 19, wherein the at least one substance, the concentration of which is determined by NMR spectroscopy, comprises an ion or other NMR inactive sub stance.

25. The method according to claim 21, wherein in step cc′), the concentration of the compound is calculated through use of peak integration and/or lineshape fitting.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0075] The invention is shown in the drawing.

[0076] FIG. 1 L-Asparagine's spin system —CH.sub.2 multiplet δ.sub.O chemical shift values interpolation by its fitted model as pH and chloride ions concentration (mM) change in artificial urine mixtures.

[0077] FIG. 2 Variables/characteristics (metabolite concentrations, pH, T) contribution to 41 .sup.1H-NMR (partial) models. Bars indicate in how many models each variable is weighted (significant) for the fitting.

[0078] FIG. 3 Variables/chemical shift values (41 .sup.1H spin systems NMR chemical shifts) contribution to the 38 metabolite concentrations, pH and T (partial) models. Bars indicate in how many models each variable is weighted (significant) for the fitting. Arrows point out the bars that correspond to the variables that are significant for the highest number of models.

[0079] FIG. 4 Workflow of the presented embodiment of the inventive method for predicting chemical shift values, in a variant starting with a first sub-model of reduced type (top line) calculating sample characteristics from experimental chemical shift values of reference NMR spin systems, and in a variant starting with a second sub-model of reduced type (second to top line), calculating predicted chemical shift values from experimental chemical shift values of reference NMR spin systems, and further of three optional subsequent variants for determination of metabolite concentrations.

[0080] FIG. 5 Chemical shifts distributions in 20 randomly prepared artificial urine mixtures (top figure) and their corresponding predictions errors distribution in the presented embodiment of the inventive method.

[0081] FIG. 6 17 metabolites concentrations and pH values distributions in 20 randomly prepared artificial urine mixtures (top figure) and their corresponding predictions errors distribution in the presented embodiment of the inventive method.

[0082] FIG. 7 12 metabolites concentrations distributions in 20 randomly prepared artificial urine mixtures (top figure) and their corresponding predictions errors distribution in the presented embodiment of the inventive method.

[0083] FIG. 8 7 metabolites concentrations distributions in 20 randomly prepared artificial urine mixtures (top figure) and their corresponding predictions errors distribution in the presented embodiment of the inventive method.

[0084] FIG. 9 Chemical shifts distribution in 20 real urine samples (top figure) and their corresponding predictions errors distribution in the presented embodiment of the inventive method.

[0085] FIG. 10 δ prediction errors of 36 .sup.1H spin systems in 60 real urine biofluids samples in the presented embodiment of the inventive method.

[0086] FIG. 11 TMAO .sup.1H-NMR peak assignment by the presented embodiment of the inventive method, BQuant, BATMAN and Chenomx NMR profiler.

[0087] FIG. 12 The 7 metabolites' 10 .sup.1H spin systems NMR chemical shifts (indicated by the arrows) that appear as significant variables for concentrations, pH and T models. The dashed circles highlight the most easily assigned in urine biofluid NMR profiles.

DETAILED DESCRIPTION

[0088] In the following, the inventive method is explained in more detail by way of an embodiment wherein a particular biofluid, namely human urine, has been chosen as the fluid class to which the model appliance and test samples, as well as the samples to be investigated relate. Accordingly, in this embodiment, the captured substances of the model appliances are metabolites. However, it should be stressed that the invention is also applicable to other fluid classes, in particular other types of biofluid such as blood serum, or types of artificial products such as shower gels, or types of nature or plant derived artificial products such as ketchup, for example.

[0089] The growth of metabolomics and other “omics” fields indicates their significance in modern system biology studies, due to their ability to extract detailed information of the organisms' metabolome, proteome and genome..sup.1,2 In the framework of metabolomics, various spectroscopic, spectrometric or biochemical techniques are employed. Among them is NMR spectroscopy—in general through 1D-NMR experiments—because of its rapid, accurate and nondestructive features..sup.3

[0090] Metabolomics studies require the identification of metabolites in complex mixtures such as biofluids..sup.4-6 The difficulty arises from the large number of metabolites. In the NMR spectra of biofluids, many metabolites' signals are overlapped due to magnetically equivalent .sup.1H nuclei and/or some of them are hidden by the peaks of more abundant metabolites of the biofluid's matrix. However, the biggest challenge arises from NMR chemical shifts variations due to pH, ionic strength as well as chemical-electrostatic interactions among metabolites..sup.7 This problem is particularly serious for the biofluids that exhibit a high variety of metabolites' content, ionic strength and pH variability, such as urine. Urine composition is not regulated by homeostasis rules as are plasma/serum and CSF biofluids; yet, it is probably the most valuable biofluid for metabolomics, due to its collection—sample preparation simplicity, abundance and rich content of metabolic information..sup.8 So far, more than 3000 substances (organic, inorganic, ionic substances, as well as proteins in small amounts),.sup.9 are detected in human urine and, among them, around 300 metabolites have been detected-quantified by means of NMR spectroscopy..sup.10

[0091] To assign and quantify metabolites the following approaches are commonly employed: [0092] i) manual assignment-quantification. This approach consists of compounds spiking in the biofluid sample and peak integration, use of software such as Chenomx NMR Suite, exhaustive inquiry in metabolites NMR spectra databases and/or spectra binning. Spiking many metabolites is costly and time consuming, and could significantly alter the composition of the biofluid matrix, thus contributing to peaks shifting due to previously non-existing interactions, and the other manual assignment procedures require extensive NMR experience on working with biofluids. [0093] ii) use of semi-automated computational tools. Bayesil,.sup.11 MetaboMiner,.sup.12 etc. are some of the most known software tools, which provide several metabolites (around 50 for serum/plasma samples by Bayesil) quantification from a .sup.1H-NMR spectrum, while allowing the user to improve the assignment-fitting of the metabolites' .sup.1H-NMR peaks. However, the use of a specific protocol is required for the sample preparation and NMR acquisition, and experience in NMR analysis of biofluids is still a prerequisite for the accurate metabolites assignment. [0094] iii) use of automated computational approaches like the BATMAN algorithm,.sup.6 Dolphin.sup.5 and BQuant..sup.13 BATMAN (the same applies for BQuant) is an almost automated tool. In general, it uses a MCMC estimation of the Bayesian model for the best fitting of a metabolite's .sup.1H spin system, with a view to its quantification. A significant amount of computational power, prior knowledge of metabolites' NMR peaks position range, as well as prior database construction are usually required to get as many true positive results as possible. Yet, several false positive results are obtained due to wrong NMR peak assignments. The Dolphin software package appears computationally “lighter” than BATMAN, it is still based upon databases information (i.e. HMDB, BMRB, etc.), while taking advantage of the 2D-JRES spectra increases the accuracy of the metabolites' assignment and consequently their quantification. Apart from the need of high resolution 2D-JRES spectra, the user should define a list of metabolites to quantify. However, not all metabolites contain coupled .sup.1H nuclei and many of them exhibit only singlet(s), and often their NMR signals resonate in the same spectral region, again leading to false positive assignments.

[0095] In conclusion, the key prerequisite for a successful and accurate metabolites' concentration determination is the flawless assignment of their signals. The previous approaches require computational time or computational power or extra NMR experiments or user's high NMR experience, and still do not guarantee 100% metabolites' assignment (therefore quantification) success.

[0096] The present invention presents a new approach for assigning compounds, here metabolites, or their NMR spin systems, respectively, to their peaks in an NMR spectrum. The inventive method, or its model appliance, respectively, can be implemented in a fully automated computational tool.

[0097] The model appliance has already built in position models for each of a number of NMR spin systems, made previously through use of mixtures (test samples), and each time works totally automated (blind). It does not use any fitting procedures for the quantification and/or assignment of NMR signals. However, quantification may be done by integration or lineshape fitting by a downstream software, if desired. In practice, the model appliance simply solves an “equation” depending on sensor (reference) NMR signals ppm values and provides the output of compounds (here metabolites) NMR peaks positions as well as an estimation of their concentrations.

[0098] In the embodiment presented, the model appliance or the computational tool, respectively, automatically assigns 41 .sup.1H NMR spin systems of 21 metabolites/compounds in a urine NMR sample, while providing an estimation of 5 further (molecular) metabolites/substances and 10 major ions concentrations with small relative error (<10%), of sample's pH value with <±0.1 error, as well as its temperature (T) during the NMR acquisition with ±0.1 K. An NMR spectrum may be analysed by the model appliance on the order of 10 seconds for providing a full set of predicted chemical shift values and sample characteristics, in particular, compound concentrations.

[0099] From the basics of NMR, it is known that the observed chemical shift (δ.sub.O) value of a spin system (here of .sup.1H nuclei) of a compound in a solution mixture is the precise picture of the chemical environment around the nucleus, and it is highly affected by all kinds of molecular interactions that the compound experiences inside the solution mixture. However, the details of the effects of these multiple weak interactions on the chemical shifts are not predictable a priori. In general, under fast exchange conditions, the δ.sub.O value can be related to the mole fraction of the corresponding compound molecules in the mixture, existing in numerous equilibrium states, namely those molecules that form any possible (self-) interaction with any context (n number of metabolites) of urine matrix (X′.sub.C), and those that do not participate in the interaction (X.sub.f):

[00001]$\begin{array}{cc}{\delta }_O=X_f.Math.{\delta }_f+\underset{n=1}{\overset{i}{.Math.}}.Math..Math.X_C^{.Math.n}.Math.{\delta }_C^{.Math.n},& \left(1\right)\end{array}$

where δ.sub.f and δ.sub.C′ are the chemical shift values of the spin system of a metabolite in its interactions within itself and with n other metabolites (including all existing compounds in (here) the urine matrix), respectively. From eq. (1), it is clearly indicated that the δ.sub.O values are directly correlated to the concentration of the interacting compounds. As previously mentioned, pH and T changes cause chemical shifts variations; consequently, each .sup.1H-NMR δ.sub.O value from any wine compound that contains .sup.1H nuclei could be described by the following function:

δ.sub.o=f(x.sub.1, . . . , x.sub.n),   (2)

where variables x are the concentrations of each possible interacting compound, the pH and the T (also referred to as the sample's characteristics), whose contributions to each .sup.1H nuclei NMR chemical shift rebound to its δ.sub.o value.

[0100] In order to construct eq. 2, the mapping of all above mentioned contributions to each δ.sub.o is needed. To achieve this, simulation of the real urine's content matrix states is obtained by constructing numerous mixtures of urine metabolites in various concentrations, acquiring their 1D .sup.1H-NMR spectra and recording each .sup.1H-NMR δ.sub.o from each metabolite .sup.1H spin system. For improving the simulation of urine, criteria have been applied for the selection of metabolites for the artificial urine samples construction. To do this, the most abundant 26 urine metabolites (of molecular type) as well as 10 ions (or metabolites of ion type) were selected according to HMDB (human metabolomics database) and other bibliographic reported concentrations and occurrence in urine biofluid (see, Example). Namely, the applied criteria were based upon 100% occurrence and high abundance of the molecular metabolites and ions as measured by NMR, MS, LC and other techniques in thousands of urine samples of healthy individuals..sup.14 Accordingly, the mixtures were prepared by changing in each mixture the concentration of one metabolite, using as starting point its lowest reported concentration until the mean one here (note that alternatively, also an interval from the lowest abnormal value to the highest abnormal value may be used), with typically 4 intermediate values. The same experimental scheme was followed for the pH adjustment of each mixture after the addition of the common urine buffer for .sup.1H-NMR based metabolomics (see, Example). In Table 1, the designed structure of the mixtures is presented. In total 1235 mixtures were created.

TABLE-US-00001 TABLE 1 Alanine Serine Na.sup.+ n.sup.th pH (mM) (mM) (mM) . . . compound (5 values) Mixture 1 0.0050 0.0035 1.0000 . . . 0.0070 6.80-7.20 Mixture 2 0.0100 0.0025 1.0000 0.0070 6.80-7.20 Mixture 3 0.0050 0.0025 1.5000 0.0070 6.80-7.20 . 0.0050 0.0025 1.0000 0.0070 6.80-7.20 . . Mixture n.sup.th 0.0050 0.0025 1.0000 0.0040 6.80-7.20

[0101] Based upon Table 1, an artificial urine matrix was composed, where each row of the matrix contains the metabolites (molecular and ions) concentrations information, pH and the T of each artificial urine mixture, namely the x variables of eq. 2. The mixtures matrix (or first part of a teaching database) of the presented embodiment had the size of 1235×38, where 38 is the total number of variables (26 molecular metabolites/substances and 10 ion metabolites/substances concentrations plus pH and T values, i.e. the total number of captured characteristics C is 38). The 1H-NMR acquisition of each mixture (or test sample) produced one—reasonably simpler—spectrum compared to that of real urine, from which 41 .sup.1H spin systems δ.sub.O from 21 metabolites (compounds)—out of 26 metabolites—were manually assigned, i.e. the total number of captures spin systems S is 41. Based on their recorded chemical shift values (to the 4.sup.th decimal of ppm), a novel 1235×41 matrix (or second part of a teaching database) was composed, where each column contains the δ.sub.o values of each spin system for 1235 artificial urine cases.

[0102] To the inventors' knowledge there has been neither such a systematic study for real biofluids simulation nor this kind of matrices (databases) construction based upon the NMR of simulated biofluids. Athersuch et al..sup.15 proposed that mixing different biofluid samples in known proportions according to a mixture design could improve some metabolites with overlapping NMR signals quantification. Sokolenko et al..sup.16 using the Plackett-Burman experimental design approach created some synthetic mixtures of 20 metabolites in order to deconvolute overlapped .sup.1H-NMR resonances. In no case, was it considered that chemical shift changes due to changes in metabolite composition could be predicted.

[0103] As mentioned above, in general 6 different concentrations (from the low to the mean range in the presented embodiment) of each substance (molecular or ion metabolite), 5 pH values (6.8-7.2 range after buffer addition) and 2 temperature values (300.0 and 302.7 K) were used for the artificial urine content matrix. In order to derive the best correlation function (eq. 2) between each studied spin system δ.sub.o values and all 38 variables (concentrations, pH, T), a multivariate statistical machine learning approach was employed, providing the best fitting as well as interpolation of the data. Multivariate adaptive regression (linear and cubic) splines models.sup.17 (MARS models) (a number of similar machine learning multivariate approaches were tested, including artificial neural networks) exhibited the best cross-validated R.sup.2 values and the lowest root mean square errors (RMSE) as well as the best predictability tested by various test datasets (see Example). In summary, the eq. 2 for each studied .sup.1H spin system took the form of:

[00002]$\begin{array}{cc}{\delta }_O=c_0+\underset{m=1}{\overset{M}{.Math.}}.Math.c_m.Math.B_m\left(x\right),& \left(3\right)\end{array}$

where, c.sub.0 is the calculated constant value of the derived regression model, M is the number of linear or cubic spline basis function that are exploited for the best fitting model production, c.sub.m is the coefficient of the m.sup.th linear or cubic spline basis function, and B.sub.m (x) is the linear or cubic spline basis function. The calculated cross validated R.sup.2 and RMSE values for the 41 (partial) model spin systems studied were >0.98 and <le-04, respectively. In FIG. 1, the interpolation of the δ.sub.O values of the L-Asparagine spin system —CH.sub.2 multiplet (1 out of the 2) is depicted as a function of pH and chloride ions concentration.

[0104] By performing an ANOVA decomposition of each (partial) model it was possible to detect all weighted variables, namely the variables that were significant for the construction of each model. As depicted in FIG. 2, the concentration of all ions (ion metabolites), of specific metabolites (such as urea, hippurate and creatinine), pH and T appear in almost all 41 models as significant variables. Bibliographic data' as well as primary chemical knowledge confirm the previous results, especially for the pH, T and ions impact on chemical shifts variations. In addition, the high concentration that creatinine, hippurate and urea usually exhibit in urine biofluid (as in the mixtures used here),.sup.9 compared to all other metabolites, is the likely origin of the importance of these metabolites in determining the chemical shifts of many others, and in turn this finding corroborates the choice of selecting the most abundant metabolites in the initial metabolite panel.

[0105] At this point, the implementation requires to build a reverse function that, given the chemical shift values, could reconstruct the concentrations of (molecular) metabolites and ions (ion type metabolites) that were providing those values. The same mathematical approach was employed for the construction of the reverse (partial) models. In this case the response (y) values were the concentrations of each substance/metabolite (including ion), pH and T (i.e. the sample characteristics), whereas the variables were the 41 studied NMR spin systems. The 38 produced (partial) models exhibited lower cross validated R.sup.2 values (>0.90) than the δ.sub.O (partial) models, however reasonably, the ions, creatinine, urea, hippurate, pH and temperature were perfectly fitted (R.sup.2>0.98). ANOVA decomposition of the 38 models revealed which .sup.1H spin systems NMR signals from the 41 studied could act as “sensors” for the prediction of the matrix of concentrations of the artificial urines. The highest score was exhibited by the .sup.1H nuclei of the metabolites highlighted by arrows in FIG. 12 and by arrows in FIG. 3.

[0106] In urine, citrate, creatinine as well as glycine are always present in high concentration with respect to other metabolites, and their .sup.1H-NMR signals are quite distinctive, allowing for a facile assignment compared to the aspartic acid, asparagine, taurine and threonine NMR signals. Taking under consideration this criterion, the reduction of all concentrations, pH, and T (partial) models took place. The 38 reduced (partial) models were constructed using only 5 variables (i.e. the number of reference NMR systems R is 5 here): the two singlets of creatinine, the two doublets of citrate and the singlet of glycine, which are highlighted in FIG. 12 by dashed circles. Apparently, the cross validated R.sup.2 and RMSE values of the new fitted models were worse than those of the full models (see Table 2 for some examples); however the knowledge of the previously mentioned NMR signals positions of the 5 sensors (or reference NMR spin systems) could predict quite sufficiently (as a starting point) the concentration of the (molecular) metabolites and ions (ion metabolites) as well as the pH and T values in each artificial urine mixture via its NMR profile, without using any fitting procedure and/or relying on metabolite NMR signature templates from databases or NMR signals integration.

TABLE-US-00002 TABLE 2 Metabolites concentration, Cross pH and T Cross validated R.sup.2 RMSE models validated R.sup.2 (reduced RMSE (reduced (4 examples) (full model) model) (full model) model) Chloride ions 0.99 0.98 0.07 (mM) 0.15 (mM) Sulfate Ions 0.98 0.96 0.05 (mM) 0.12 (mM) Creatinine 0.99 0.95 0.08 (mM) 0.28 (mM) pH 0.99 0.95 0.02 0.04

[0107] The detection of the 5 sensor NMR signals offered the opportunity to explore the correlation between them and each one of the above mentioned studied NMR signals of the rest of the metabolites. Namely, 36 new δ.sub.O (partial) models were created (following the same mathematical approach) using the 5 sensor peak positions in the 1235 mixtures as variables (examples of their R.sup.2 and RMSE values are reported in Table 3), i.e. the number of non-reference NMR spin systems N is 36 here. The fitted δ.sub.O reduced (partial) models (functions) showed high R.sup.2 and low RMSE values, demonstrating that 36 .sup.1H spin systems NMR signals positions could be predicted via the positions of the 5 sensor peak positions.

[0108] In conclusion, 4 different types of models (or, to be more exact, sub-models of the model appliance) were created: [0109] i) 2 kinds of full models. The first kind (also referred to as first sub-model of full type) includes the prediction of 41 .sup.1H spin systems NMR peaks positions by the knowledge of mixture's substance/metabolite concentrations, pH and T values (38 variables), and the second kind (also referred to as second sub-model of full type) includes the prediction of 36 substance/metabolite concentrations, pH and T through the 41 .sup.1H spin systems NMR peaks positions. [0110] ii) 2 kinds of reduced models. The 38 predictive (partial) models of substance/metabolite concentrations, pH and Tby the 5 sensor NMR signals positions (together representing a first sub-model of reduced type), and the predictive (partial) models of 36 .sup.1H spin systems δ.sub.O values based upon the 5 sensor NMR peaks positions (together representing a second sub-model of reduced type).

TABLE-US-00003 TABLE 3 Cross RMSE RMSE Cross validated R.sup.2 (ppm) (ppm) δ.sub.O models validated R.sup.2 (reduced (full (reduced (4 examples) (full model) model) model) model) Threonine, —CH (d, 0.99 0.98 0.0002 0.0004 3.59 ppm) Glycolate, —CH.sub.2 (s, 0.99 0.97 0.0001 0.0003 3.95 ppm) Aspartate, —CH.sub.2 (m, 0.99 0.98 0.0002 0.0004 2.68 ppm) Taurine, —CH.sub.2SO.sub.3 (t, 0.99 0.98 0.0001 0.0003 3.27 ppm)

[0111] The combination of the 4 kinds of models (compare FIG. 4) led to the construction of a final algorithm, based upon the best metabolite's NMR signals positions prediction (tested in 60 real urine samples and 20 randomly prepared artificial urine mixtures). The compound concentration predictions are focused only upon the random artificial mixtures, where the substance (metabolite including ion) concentrations were known.

[0112] The final algorithm shown in FIG. 4 can be performed in two variants. In a first variant, shown in the top line, the five sensor peaks (or experimental chemical shift values of reference NMR spin systems) 10 read from the recorded NMR spectrum are fed in a substep d1) into the first sub-model of reduced type 1R, resulting in an output 11 of predicted metabolite concentrations, pH and T values (i.e. here 38 predicted characteristics) for the sample. Upon these predicted characteristics, the first sub-model of full type 1F is applied in a substep d2), thus obtaining an output 12 of 36 predicted chemical shift values δ.sub.0 for the non-reference NMR spin systems. Together with the experimental chemical shift values 10 for the reference NMR spin systems, these are input into the second sub-model of full type 2F in a substep d3), resulting in predicted characteristics 13 again. In a substep d4), these are fed into the first sub-model of full type 1F again to obtain an output 14 of further predicted chemical shift values of second iteration (note that if desired, further iterations of substeps d3) and d4) may be applied). The resulting predicted chemical shift values may be used as final predicted chemical shift values 30.

[0113] In a second alternative variant, shown in the line below, the five sensor peaks (or experimental chemical shift values of reference NMR spin systems) 10 read from the recorded NMR spectrum are fed in a substep d1′) into the second sub-model of reduced type 2R, resulting in a an output 21 of 36 predicted chemical shift values δ.sub.0 for the non-reference NMR spin systems. Together with the experimental chemical shift values 10 for the reference NMR spin systems, these are input into the second sub-model of full type 2F in a substep d2′), resulting in predicted characteristics 22. In a substep d3′), these are fed into the first sub-model of full type 1F again to obtain an output 23 of further predicted chemical shift values. In the example shown, this output 23 together with the experimental chemical shift values 10 of the reference NMR spin systems are used in a second iteration of substeps d2′) and d3′), thus obtaining output 24 of predicted concentrations of second iteration and output 25 of predicted chemical shift values of second iteration (if desired, further iterations of steps d2′) and d3′) may be applied). The resulting predicted chemical shift values may be used as final predicted chemical shift values 30 again.

[0114] For (optional) further determining metabolite concentrations, the previously described algorithm can be considered as a first step aa) or aa′) or aa″) in which chemical shift values 30 of non-reference NMR spin systems have been determined.

[0115] If a quick estimate of metabolite concentrations is desired, with a coarse accuracy being enough, the final predicted chemical shift values 30 of the non-reference NMR spin systems (together with the experimental chemical shift values 10 of the reference NMR spin systems) can be used in a step bb′), applying second sub-model of full type 2F once more, resulting in an output 31 of predicted characteristics, including metabolite concentrations (note that if only specific concentrations are of interest, it may suffice to apply only partial models of the second sub-model of full type 2F). This approach is used further below (compare FIGS. 6-8 in particular) for concentration determination. Note that this procedure may be applied to derive concentrations of NMR inactive metabolites, if desired.

[0116] If a somewhat more accurate estimate is desired, but the efforts of peak integration or lineshape fitting are to be avoided, the final predicted chemical shift values 30 can be used to identify the peaks of the non-reference NMR spin systems in the NMR spectrum, and read out their experimental chemical shift values in a step bb). This input 32 may be used in a step cc) applying the second sub-model of full type 2F once more to obtain an output 33 of predicted characteristics, including metabolite concentrations (again note that if only specific concentrations are of interest, it may suffice to apply only partial models of the second sub-model of full type 2F). Note that this procedure may be applied to derive concentrations of NMR inactive metabolites, too, if desired.

[0117] Finally, if a high accuracy of compound (or NMR active metabolite) concentration is desired, the final predicted chemical shift values 30 can be used to identify the peaks of at least one (non-reference) NMR spin system of the compound in the NMR spectrum in a step bb″), and to derive concentration information from the size and shape of the identified peak (or peaks) 34, e.g. by peak integration or lineshape fitting.

EXAMPLE

[0118] A) Artificial Urine Mixture Tests.

[0119] Twenty artificial urine mixtures were produced, containing random substance/metabolite (molecular and ion) concentration values (calculated by a randomizer) and pH values, and their NMR spectra were acquired at different temperatures. All random values were within the limits of concentration, pH and T matrix of the applied models. In the 20 NMR spectra the 5 sensor signals lied inside the chemical shifts matrix limits.

[0120] The δ.sub.O prediction errors distribution is summarized in FIG. 5, where, as shown, the prediction accuracy is almost perfect. Namely, all 36 predicted .sup.1H spin systems NMR positions exhibit less or equal to ±0.0002 ppm error. Although the small errors are produced from artificial and not real urine samples, they validate the chosen mathematical-algorithmic approach for NMR peak position predictions.

[0121] Further, all ion, creatinine, hippurate, aspartate, asparagine and urea concentrations, pH and T predictions exhibited less than 2-4% relative errors, whereas all other metabolite concentrations were predicted with 5-15% relative errors. As depicted in FIGS. 6-8, the relative prediction errors distribution of the metabolites concentrations and pH is very small compared to the large distribution of the metabolites concentrations in the twenty artificial urine test mixtures. Namely, the presented algorithm could provide information of the urine sample metabolites concentrations range, without any NMR signals integration-deconvolution.

[0122] B) Tests on Real Urine Samples.

[0123] Sixty different real urine samples were selected for automatic signal prediction on condition that the 5 sensor chemical shifts (or experimental chemical shift values of the reference NMR systems) constituting the input file of the algorithm lied inside the limits of the chemical shifts matrix of the presented embodiment. This criterion was set because the model extrapolation efficiency is low, especially when the 5 values of the input file are very far from the chemical shifts matrix upper-lower limits. This limitation of the presented algorithm is due to the fact that it was constructed and trained by quite narrow metabolite/substance concentrations (bibliographic low and mean values), pH (6.8-7.2) ranges (note that for broader ranges of the teaching database, this limitation is overcome).

[0124] FIG. 9 depicts the δ.sub.O prediction errors distribution of 20 out of the 60 real urine samples which exhibited the highest errors distribution, and FIG. 10 summarizes the absolute prediction errors from all 60 real urine biofluids. The δ.sub.O prediction errors are ≦|10.0015| ppm, which—considering the used artificial urine metabolites mixtures formation—are more than satisfying. According to other semi-automatic targeted metabolite detection methods from 1D .sup.1H-NMR biofluids spectra (for example Bayesian approaches error: ≦|10.0020|) the algorithm's δ.sub.O predictions already exhibits lower error ranges. A comparison example is demonstrated in FIG. 11, where the inquiry is the assignment of TMAO metabolite in a healthy person's urine NMR profile. The NMR spectrum is loaded on the Chenomx NMR profiler console, 2015 edition. The manual assignment (by Chenomx) prompts the user to search the spectral range that is defined by the vertical lines 40a, 40b. In this relatively large spectral region (0.04 ppm) 3 peaks (marked by “?”) are candidates for the TMAO's .sup.1H-NMR singlet. The use of BQuant and BATMAN software for the assignment and quantification of TMAO (given the region 3.26-3.30 ppm) took about 15-20 min and their assignment result was the NMR peak 41 pointed by the right arrow. Our automated algorithm's .sup.1H-NMR TMAO ((CH.sub.3).sub.3NO) δ.sub.O prediction (performed in 10 sec) is pointed by the dotted vertical line and arrow.

[0125] The correct TMAO's .sup.1-NMR peak 42 according to the spiking result is pointed by the left arrow and the tick symbol. All automated approaches (except the inventive one) exhibited a false positive result, whereas the invention's prediction error was +0.0002 ppm, calculated within a few seconds by the use of an average laptop.

[0126] The inventive method allows fast δ.sub.O “accurate” predictions (so far ≦|0.0015| ppm); further a fast prediction of ion concentration (by NMR) and of other metabolite concentrations, pH and temperature, are feasible with very small relative error (≦2%) by mathematical procedures and no metabolite NMR pattern fitting procedures. The method has, in practice, no need for high computational power. The method is well suited for a totally automated procedure. There is no need for a specific NMR protocol like specific NMR spectrum resolution, number of scans or even specific sample preparation protocol with specific buffer capacity. Only TSP as a reference compound is needed.

[0127] Materials and Experimental Methods of the Example

[0128] 1) NMR Sample Preparation.

[0129] The 26 urine (molecular) metabolites were purchased by Sigma. These metabolites are listed in Table 4 as well as the salts from which the 10 studied ions were extracted. 10% of common urine buffer was used in each NMR sample final volume. The buffer contains 1.5 M KH.sub.2PO.sub.4, 2 mM NaN.sub.3 and 0.1% TSP as NMR reference compound which are dissolved in D.sub.2O, 99.8% .sup.2H. The pH of the NMR samples was adjusted by the addition of HCl or NaOH solutions of 4 N concentration and measured by a pH meter at 298 K.

TABLE-US-00004 TABLE 4 List of the metabolites and ions used in the artificial urine mixtures. Metabolites Salts (Ions) L-Alanine Na.sub.2SO.sub.4 L-Asparagine NaCl L-Aspartic acid LiCl L-Arabinose AlCl.sub.3 Betaine KCl Citrate Na.sub.3PO.sub.4 Creatine MgCl.sub.2 Creatinine CaCl.sub.2 L-Cysteine ZnCl.sub.2 D-Glucose Dimethyl Sulfone L-Glutamic acid L-Glutamine Glycerol L-Glycine Glycolic acid Guanidoacetic acid Hippuric acid Lactate Methanol Myoinositol L-Serine Taurine L-Threonine TMAO Urea

[0130] 2) NMR Experiments

[0131] One dimensional (1D) 1H-NMR spectra for all samples were acquired using a Bruker 600 MHz spectrometer (Bruker BioSpin) operating at 600.13 MHz proton Larmor frequency and equipped with a 5 mm CPTI 1H-13C/31P-2H cryo-probe including a z-axis gradient coil, an automatic tuning—matching (ATM) and an automatic sample changer. A PT 100 thermocouple provided temperature stabilization at the level of approximately 0.1 K at the sample. Before measurement, samples were kept for at least 3 min inside the NMR probehead, for temperature equilibration. A one-dimensional NMR spectrum was acquired with water peak suppression using a standard pulse sequence (NOESYpresat, Bruker), using 64 free induction decays (FIDs), 64 k data point, a spectral width of 12,019 Hz, an acquisition time of 2.7 s, a relaxation delay of 4 s, and a mixing time of 100 ms. The NOESYpresat pulse sequence is the standard for metabolomic analysis (Aranjbar, Ott, Roongta, & Mueller, 2006) since it provides very good water suppression together with quantitative information as demonstrated in Saude, Slupsky, and Sykes (2006).

[0132] 3) Computational Platforms

[0133] The algorithm was developed in MATLAB R2014a computing environment and needs MATLAB for its application. All MARS models-functions were produced by the use of free available ARESlab toolbox (Jekabsons G., ARESLab: Adaptive Regression Splines toolbox for Matlab/Octave, 2015, available at http://www.cs.rtu.lv/jekabsons/). All other features of the algorithm were developed by the inventors.

REFERENCES

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