High-resolution D-glucose structure analysis method based on nuclear magnetic resonance spectrum

By adopting selective multi-quantum filtering module and improved CLIP-COSY module in NMR spectroscopy technology, combining chemical shift coding and phase coding, the problems of signal congestion and overlap in the prior art are solved, and high-resolution D-glucose is achieved Structure analysis and phase-sensitive correlation spectrum display.

CN119492770AActive Publication Date: 2025-02-21XIAMEN UNIV

Patent Information

Application Number
CN202411623741.5
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-14
Publication Date
2025-02-21
Estimated Expiration
2044-11-14

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Abstract

The invention relates to a high-resolution D-glucose structure analysis method based on a nuclear magnetic resonance spectrum, which comprises the following steps: placing a 2-5% D-glucose deuterium aqueous solution in a magnetic resonance spectrometer, and applying a 90-degree hard pulse to obtain a 1H spectrum; chemical shift information and 90-degree pulse time width of the proton pair are determined through a 1H spectrum, multi-frequency-point pulse selective filtering is executed, and a signal in a chemical shift area of the proton pair is obtained; separation and phase correction of multi-quantum signals are carried out through a multi-quantum filtering module and a CLIP-COSY module, and two one-dimensional nuclear magnetic resonance phase-sensitive correlation spectrums are obtained; and analyzing the phase-coded signal through Hardman coding to reveal the molecular structure of D-glucose. Through selective filtering and phase encoding, the invention provides an efficient and lossless nuclear magnetic resonance detection method for analyzing a D-glucose molecular structure.
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Description

Technical Field

[0001] The invention relates to the field of nuclear magnetic resonance spectroscopy detection, and in particular to a high-resolution D-glucose structure analysis method based on nuclear magnetic resonance spectroscopy. Background Art

[0002] Glucose is the most common and important colorless monosaccharide in organisms, with a molecular formula of C6H 12 O6, it is the main source of energy for life activities. The human body digests and absorbs carbohydrates in food, converts them into glucose, and then transports them to various tissues and organs through the blood to provide energy for cells. Glucose is also an intermediate product in many biochemical reactions and participates in the metabolism of fat and protein. The structural analysis of glucose is crucial to understanding its function and metabolic pathway. Understanding its molecular structure helps to explain its function in cell metabolism, energy production, etc.

[0003] One-dimensional selective proton homonuclear correlation spectroscopy (one-dimensional COSY) is a key technology for demonstrating direct coupling relationships between atomic nuclei and analyzing molecular structures in nuclear magnetic resonance spectroscopy. However, the current one-dimensional nuclear magnetic resonance correlation spectroscopy technology still cannot completely overcome the problems of spectrum crowding and signal overlap caused by complex signal J coupling splitting, or cannot achieve phase-sensitive display, because its selective pulse is difficult to accurately select the required signal, and lacks the corresponding phase encoding strategy to achieve phase-sensitive correlation spectroscopy display. Summary of the invention

[0004] In order to solve the above problems, the present invention proposes a high-resolution D-glucose structural analysis method based on nuclear magnetic resonance spectroscopy, a method for selectively observing the direct coupling network of D-glucose directly coupled proton pairs, and using filtering technology in combination with phase encoding to obtain the phase-sensitive correlation spectrum of the direct coupling network of glucose coupled proton pairs without losing the signal-to-noise ratio, thereby realizing the molecular structure analysis of glucose.

[0005] The specific plan is as follows:

[0006] A high-resolution D-glucose structure analysis method based on nuclear magnetic resonance spectroscopy, comprising:

[0007] S1, placing the pre-prepared deuterated aqueous solution of D-glucose in a magnetic resonance spectrometer;

[0008] S2, in the magnetic resonance spectrometer, a 90° hard pulse is applied to the deuterated aqueous solution of D-glucose to obtain the D-glucose molecule 1 H spectrum;

[0009] S3, through D-glucose molecules 1The H spectrum determines the chemical shift information of the proton pairs with direct coupling relationship in the D-glucose molecule, and determines the 90° pulse time width required to excite the proton pairs with direct coupling relationship;

[0010] S4, based on the 90° pulse time width and chemical shift information, performing a first selective filtering through a first multi-frequency pulse to obtain a signal in a chemical shift region of a proton pair having a direct coupling relationship;

[0011] S5, based on the signal in the chemical shift region of the proton pair, a filtering operation is performed through a multi-quantum filtering module to obtain a multi-quantum signal obtained by the evolution of the proton pair with a direct coupling relationship, and a second selective filtering is performed on the multi-quantum signal obtained by the evolution of the proton pair with a direct coupling relationship through a second multi-frequency point pulse to obtain a multi-quantum signal after phase information correction;

[0012] S6, by chemically shift encoding the first 180° hard pulse in the CLIP-COSY module to separate the multi-quantum signals after phase information correction, the multi-quantum signal peaks of D-glucose with direct coupling relationship at different phases are obtained, and the multi-quantum signal peaks are extended by J coupling evolution to obtain a one-dimensional NMR phase-sensitive correlation spectrum;

[0013] S7, changing the evolution time, executing S4-S6 again, obtaining two one-dimensional nuclear magnetic resonance phase-sensitive correlation spectra with different phases, performing phase encoding on the two one-dimensional nuclear magnetic resonance phase-sensitive correlation spectra, and obtaining one-dimensional nuclear magnetic resonance phase-sensitive correlation spectra of two signals in the multi-quantum signal peak of D-glucose with a direct coupling relationship;

[0014] S8, through the one-dimensional nuclear magnetic resonance phase-sensitive correlation spectrum of each of the two signals in the multi-quantum signal peak of D-glucose, the direct coupling information of the two signals in the proton pairs with a direct coupling relationship in D-glucose is obtained, and different coupled proton pairs are selected for excitation through the direct coupling information, thereby tracking all coupled proton pairs and revealing the entire molecular structure of D-glucose.

[0015] Furthermore, in S1, the mass concentration of the deuterium aqueous solution of D-glucose pre-configured is 2%-5%.

[0016] Further, in S4, performing a first selective filtering by using a first multi-frequency pulse to obtain a signal in a proton pair chemical shift region having a direct coupling relationship specifically includes:

[0017] A first gradient field and a second gradient field are added on the left and right sides of the first multi-frequency pulse, coherent path selection is performed through the first gradient field and the second gradient field, and selective filtering is achieved in conjunction with the first multi-frequency pulse to obtain signals in the chemical shift region of proton pairs with a direct coupling relationship; the first gradient field and the second gradient field have equal strength and direction.

[0018] Further, in S5, the multi-quantum filtering module includes a first group of 90° hard pulses, a second group of 90° hard pulses, a third gradient field and a fourth gradient field; the intensity ratio of the third gradient field after the first group of 90° hard pulses to the intensity ratio of the fourth gradient field after the second group of 90° hard pulses is -1:2.

[0019] Furthermore, in S6, the CLIP-COSY module has two single-scan z filter elements on both sides of the mixing period, which ensure the in-phase to in-phase coherent transfer between directly coupled spins in the multi-quantum signal after phase information correction, and eliminate the anti-phase and zero quantum contributions in the multi-quantum signal after phase information correction.

[0020] Further, in S6, the signal model after chemical shift encoding is:

[0021]

[0022] Among them, ω I and ω S represents chemical shift; I and S represent spin operators; the up operator I + and reduction operator I - Respectively represent +1 and -1 quantum orders; Δ1 and Δ2 represent two different evolution times.

[0023] Furthermore, in S7, the specific implementation method of phase encoding the two one-dimensional nuclear magnetic resonance phase-sensitive correlation spectra is Hademann coding.

[0024] The present invention adopts the above technical solution and has the following beneficial effects:

[0025] (1) The present invention uses a selective multi-quantum filtering module, combined with an improved CLIP-COSY module with chemical shift encoding and phase encoding to obtain the direct coupling network information of the selected D-glucose hydrogen nuclei, and displays it in a phase-sensitive mode, which has the advantages of higher sensitivity and resolution, strong anti-interference ability, good selectivity, short experimental time, etc., and will not cause damage to the experimental samples, which can facilitate subsequent other measurement purposes;

[0026] (2) The present invention selectively detects only the selected hydrogen nuclei and obtains their direct coupling network information, and no other signals interfere with the spectrum results;

[0027] (3) The present invention does not require separation of the D-glucose to be tested before the test and can be directly used for molecular structure detection in mixed samples;

[0028] (4) The present invention is highly robust and has no dependence on nuclear magnetic resonance equipment. It can be implemented on various types of nuclear magnetic resonance instruments. 1 The information obtained from the H spectrum can be used to obtain the parameter data required for subsequent multi-frequency pulse generation;

[0029] (5) The present invention has a high signal-to-noise ratio and a wide range of applications. It can accurately analyze the molecular structure of specific substances in complex chemical and biological systems. In addition to D-glucose, it can also be used to analyze any system with coupling. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 A high-resolution D-glucose structure analysis method based on nuclear magnetic resonance spectroscopy according to an embodiment of the present invention;

[0031] Figure 2 A schematic diagram of a pulse sequence used in a high-resolution D-glucose structure analysis method based on nuclear magnetic resonance spectroscopy according to an embodiment of the present invention;

[0032] Figure 3 This is a diagram showing the experimental results of testing β-D-glucose using a high-resolution D-glucose structure analysis method based on nuclear magnetic resonance spectroscopy technology according to an example of the present invention. DETAILED DESCRIPTION

[0033] The present invention is further described in detail below in conjunction with embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0034] like Figure 1 As shown, the present invention provides a high-resolution D-glucose structure analysis method based on nuclear magnetic resonance spectroscopy, comprising:

[0035] S1, pre-preparing a deuterium aqueous solution of D-glucose, and placing the pre-prepared deuterium aqueous solution of D-glucose in a magnetic resonance spectrometer.

[0036] Specifically, the mass concentration of the deuterium aqueous solution of D-glucose pre-configured is 2%-5%;

[0037] S2, applying a 90° hard pulse to the pre-configured deuterium aqueous solution of D-glucose to obtain the D-glucose molecule 1 H spectrum.

[0038] Specifically, Figure 3 (a) shows that in this embodiment, the D-glucose molecule 1 H spectrum, including:

[0039] The double peak at 4.62ppm is the signal of H on carbon 1 of β-D-glucose, the triple peak at 3.22ppm is the signal of H on carbon 2 of β-D-glucose, the quartet at 3.70ppm is the signal of H on carbon 5 of β-D-glucose, and the double peak at 3.87ppm is the signal of H on carbon 6 of β-D-glucose; the H signal on carbon 1 of β-D-glucose and the H signal on carbon 2 directly coupled thereto are selected as target peaks, and the H signal on carbon 5 of β-D-glucose and the H signal on carbon 6 directly coupled thereto are selected as target peaks.

[0040] Specifically, in this embodiment, the instrument used for high-resolution structural analysis of glucose is a Varian 500 MHz nuclear magnetic resonance spectrometer.

[0041] S3, through D-glucose molecules 1 The H spectrum determines the chemical shift information of the proton pairs with direct coupling relationship in the D-glucose molecule and determines the 90° pulse time width required to excite the proton pairs with direct coupling relationship.

[0042] Specifically, in this embodiment, the D-glucose molecule 1 The H spectrum acquisition process uses a single pulse consisting of a 90° RF hard pulse and a signal sampling period to collect 1 After the H spectrum, the 90° pulse time width pw required to excite the target signal is measured, and the calibration substance in the solution is calibrated to fix the chemical shift information and prevent the occurrence of inconsistent chemical shifts in multiple experiments of the same substance due to reasons such as unstable instrument magnetic field.

[0043] S4, based on the 90° pulse time width and chemical shift information, a first selective filtering is performed by using a first multi-frequency pulse to obtain a signal in a chemical shift region of a proton pair having a direct coupling relationship.

[0044] Specifically, performing the first selective filtering by the first multi-frequency pulse to obtain a signal in the chemical shift region of the proton pair having a direct coupling relationship specifically includes:

[0045] A first gradient field and a second gradient field are added on the left and right sides of the first multi-frequency pulse, coherent path selection is performed through the first gradient field and the second gradient field, and selective filtering is achieved in conjunction with the first multi-frequency pulse to obtain signals in the chemical shift region of proton pairs with a direct coupling relationship; the first gradient field and the second gradient field have equal strength and direction.

[0046] The first multi-frequency pulse is used to excite the proton pair signal having a direct coupling relationship in D-glucose;

[0047] By applying a 180° first multi-frequency pulse in the y direction for a time of τ and an excitation frequency of two different chemical shifts of a pair of proton pairs with a direct coupling relationship to a deuterium aqueous solution of glucose, and performing vector addition calculation on a vector formed by the parameters of a single-frequency excitation pulse, and coordinating a first gradient field and a second gradient field with equal intensity and in the z direction, signals of two different chemical shift regions corresponding to the target signal can be filtered from the full spectrum signal;

[0048] Specifically, Figure 2 As shown, firstly, a 90° hard pulse is used to excite a full spectrum signal, and a 180° multi-frequency pulse (first multi-frequency pulse) required for excitation is generated according to the chemical shift information of the target signal to be extracted and the measured time width pw of the 90° pulse; after the 180° multi-frequency pulse is input with the chemical shift information of the glucose hydrogen nuclei to be excited, a multi-frequency pulse capable of simultaneously exciting two frequencies is generated by referring to the time width pw of the 90° pulse through the vector addition principle; selective filtering is achieved by combining the 180° multi-frequency pulse with the first gradient field and the second gradient field to filter out signals in the two chemical shift regions of the glucose hydrogen nuclei; wherein, the action time of the 90° hard pulse is 12.25μs, and the first multi-frequency pulse used is of the rsnob type with a bandwidth of 40Hz;

[0049] After the density operator derivation, taking a pair of weakly coupled AX nuclei with spin -1 / 2 as an example, their spin operators are I and S, the coupling constant is JIS, and the chemical shifts are ω I With ω S In order to conveniently describe the order of quantum signals, the raising and lowering operator I is introduced + and I - Represent +1 and -1 quantum orders respectively. In the magnetic resonance spectrometer, under thermal equilibrium, the initial density operator can be written as:

[0050] δ1=I z +S z

[0051] Among them, I z and S z The operator expression for angular momentum in the z direction, I y and S y The operator expression for the angular momentum in the y direction is:

[0052]

[0053] The first 180° dual-color pulse with two gradient pulses is applied simultaneously to two different chemical shift sites of the target coupled spin pairs of I and S. The signals near the two chemical shift frequencies are retained through the coherent path selection of the gradient pulses. During τ, under the action of J coupling, the magnetization of I and S evolves into the antiphase single quantum coherence (SQC) term 2I ± S z and 2I z S ± .

[0054] S5, based on the signal in the chemical shift region of the proton pair, a filtering operation is performed through the multi-quantum filtering module to obtain a multi-quantum signal obtained by the evolution of the proton pair with a direct coupling relationship, and a second selective filtering is performed on the multi-quantum signal obtained by the evolution of the proton pair with a direct coupling relationship through a second multi-frequency point pulse to obtain a multi-quantum signal after phase information correction.

[0055] Specifically, the multi-quantum filtering module includes a first group of 90° hard pulses, a second group of 90° hard pulses, a third gradient field and a fourth gradient field; the intensity ratio of the third gradient field after the first group of 90° hard pulses to the intensity ratio of the fourth gradient field after the second group of 90° hard pulses is -1:2.

[0056] like Figure 2 As shown, in the first 180° multi-frequency pulse (first multi-frequency pulse) and its corresponding first gradient field and second gradient field, the multi-quantum signal obtained by the evolution of glucose hydrogen nuclei is filtered out through the multi-quantum filtering module, and the second 180° multi-frequency pulse (second multi-frequency pulse) and its corresponding third gradient field and fourth gradient field are used to achieve the effect of re-coupling, adjust the signal phase information, filter out the selected signal, suppress the remaining background signals, and the signal expression returns to δ2=I + +I - +S + +S - ; Where δ2 represents the signal evolution form after the second multi-frequency pulse.

[0057] S6, by chemically shift encoding the first 180° hard pulse in the CLIP-COSY module to separate the multi-quantum signals after phase information correction, the multi-quantum signal peaks of D-glucose with direct coupling relationship at different phases are obtained, and the multi-quantum signal peaks are extended by J-coupling evolution to obtain a one-dimensional NMR phase-sensitive correlation spectrum.

[0058] Specifically, the CLIP-COSY module has two single-scan z filter elements on both sides of the mixing period, which ensure the in-phase to in-phase coherent transfer between directly coupled spins in the multi-quantum signal after phase information correction, and eliminate the anti-phase and zero quantum contributions in the multi-quantum signal after phase information correction.

[0059] Two different evolution times Δ1 and Δ2 were set before and after the first 180° hard pulse of the perfect echo sequence; wherein Δ is a constant evolution time; two experiments were performed according to the two different evolution times to obtain two coupling network information spectra with different phases of the proton pair signal peak of D-glucose with a direct coupling relationship.

[0060] Specifically, refer to Figure 2 In this embodiment, the CLIP-COSY module uses a modified perfect echo sequence in conjunction with two front and rear z filters to act on the sample to be tested, chemical shift encoding is performed on the first 180° hard pulse in CLIP-COSY, the two signals after regrouping are separated, and two different evolution times Δ1 and Δ2 are set before and after the 180° hard pulse; chemical shift encoding mainly allows the chemical shift to evolve by setting different evolution times in the two experimental samplings, so that the signal extracted after the selective multi-quantum filtering module obtains different phases; the evolution times Δ1 and Δ2 of the coupled signals β1 and β2 of β-D-glucose are 14.75ms and 15.25ms respectively; the evolution times Δ1 and Δ2 of the coupled signals β5 and β6 of β-D-glucose are 13.16ms and 16.84ms respectively; by setting different evolution times in the two experiments, the signals obtained by the selective multi-quantum filtering module are in different phases, so that the spectra of the two experiments can be transformed and processed later to obtain one of the signals respectively.

[0061] S7, change the evolution time, execute S4-S6 again, obtain two one-dimensional nuclear magnetic resonance phase-sensitive correlation spectra with different phases, phase encode the two one-dimensional nuclear magnetic resonance phase-sensitive correlation spectra, and obtain the one-dimensional nuclear magnetic resonance phase-sensitive correlation spectra of the two signals in the multi-quantum signal peak of D-glucose with a direct coupling relationship.

[0062] Specifically, the specific implementation method of phase encoding the two one-dimensional nuclear magnetic resonance phase-sensitive correlation spectra is Hartmann encoding.

[0063] In the CLIP-COSY module, the simplified signal model of the density operator after chemical shift encoding is:

[0064]

[0065] From the signal expression, it can be seen that after juxtaposing the two experimental spectra and performing Hadamard coding processing in the F1 dimension, separate spectra of the two signals can be obtained.

[0066] S8, through the one-dimensional nuclear magnetic resonance phase-sensitive correlation spectrum of each of the two signals in the multi-quantum signal peak of D-glucose, the direct coupling information of the two signals in the proton pairs with a direct coupling relationship in D-glucose is obtained, and different coupled proton pairs are selected for excitation through the direct coupling information, thereby tracking all coupled proton pairs and revealing the entire molecular structure of D-glucose.

[0067] Specifically, the disclosure of the entire molecular structure of D-glucose specifically includes: repeating the experiment multiple times to select different hydrogen nuclei for excitation based on the direct coupling information displayed by the phase-sensitive correlation spectrum, and obtaining the coupling network information of all coupled proton pairs to reveal the entire molecular structure of D-glucose.

[0068] pass Figure 3 As can be seen from the experimental results of (b)-(e), the embodiments of the present invention can accurately extract the coupling network information of specific atomic nuclei of D-glucose from the nuclear magnetic resonance spectra overlapped by J coupling splitting, and present it in a phase-sensitive form. The arrows in the figure represent the selected hydrogen nucleus signals, and the other marked signals are its coupling network information.

[0069] Although the present invention has been specifically shown and described in conjunction with the preferred embodiments, it should be understood by those skilled in the art that various changes may be made to the present invention in form and details without departing from the spirit and scope of the present invention as defined by the appended claims, all of which are within the scope of protection of the present invention.

Claims

1. A high-resolution D-glucose structure analysis method based on nuclear magnetic resonance spectroscopy, characterized in that: include: S1, placing the pre-prepared deuterated aqueous solution of D-glucose in a magnetic resonance spectrometer; S2, in the magnetic resonance spectrometer, a 90° hard pulse is applied to the deuterated aqueous solution of D-glucose to obtain the 1 H spectrum; S3, through D-glucose molecules 1 The H spectrum determines the chemical shift information of the proton pairs with direct coupling relationship in the D-glucose molecule, and determines the 90° pulse time width required to excite the proton pairs with direct coupling relationship; S4, performing a first selective filtering based on the 90° pulse time width and chemical shift information through the first multi-frequency pulse to obtain a signal in the chemical shift region of the proton pair having a direct coupling relationship; S5, based on the signal in the chemical shift region of the proton pair, a filtering operation is performed through a multi-quantum filtering module to obtain a multi-quantum signal obtained by the evolution of the proton pair with a direct coupling relationship, and a second selective filtering is performed on the multi-quantum signal obtained by the evolution of the proton pair with a direct coupling relationship through a second multi-frequency point pulse to obtain a multi-quantum signal after phase information correction; S6, by chemically shift encoding the first 180° hard pulse in the CLIP-COSY module to separate the multi-quantum signals after phase information correction, the multi-quantum signal peaks of D-glucose with direct coupling relationship at different phases are obtained, and the multi-quantum signal peaks are extended by J coupling evolution to obtain a one-dimensional NMR phase-sensitive correlation spectrum; S7, changing the evolution time, executing S4-S6 again, obtaining two one-dimensional nuclear magnetic resonance phase-sensitive correlation spectra with different phases, performing phase encoding on the two one-dimensional nuclear magnetic resonance phase-sensitive correlation spectra, and obtaining one-dimensional nuclear magnetic resonance phase-sensitive correlation spectra of two signals in the multi-quantum signal peak of D-glucose with a direct coupling relationship; S8, through the one-dimensional nuclear magnetic resonance phase-sensitive correlation spectrum of each of the two signals in the multi-quantum signal peak of D-glucose, the direct coupling information of the two signals in the proton pairs with a direct coupling relationship in D-glucose is obtained, and different coupled proton pairs are selected for excitation through the direct coupling information, thereby tracking all coupled proton pairs and revealing the entire molecular structure of D-glucose.

2. The high-resolution D-glucose structure analysis method based on nuclear magnetic resonance spectroscopy according to claim 1, characterized in that: In S1, the mass concentration of the deuterium aqueous solution of D-glucose pre-prepared is 2%-5%.

3. The high-resolution D-glucose structure analysis method based on nuclear magnetic resonance spectroscopy according to claim 1, characterized in that: In S4, performing the first selective filtering by the first multi-frequency pulse to obtain a signal in the chemical shift region of the proton pair having a direct coupling relationship specifically includes: A first gradient field and a second gradient field are added on the left and right sides of the first multi-frequency pulse, coherent path selection is performed through the first gradient field and the second gradient field, and selective filtering is achieved in conjunction with the first multi-frequency pulse to obtain signals in the chemical shift region of proton pairs with a direct coupling relationship; the first gradient field and the second gradient field have equal strength and direction.

4. The high-resolution D-glucose structure analysis method based on nuclear magnetic resonance spectroscopy according to claim 1, characterized in that: In S5, the multi-quantum filtering module includes a first group of 90° hard pulses, a second group of 90° hard pulses, a third gradient field and a fourth gradient field; the intensity ratio of the third gradient field after the first group of 90° hard pulses to the intensity ratio of the fourth gradient field after the second group of 90° hard pulses is -1:

2.

5. The high-resolution D-glucose structure analysis method based on nuclear magnetic resonance spectroscopy according to claim 1, characterized in that: In S6, the CLIP-COSY module mixing period is flanked by two single-scan z filter elements, which ensure the in-phase to in-phase coherent transfer between directly coupled spins in the multi-quantum signal after phase information correction and eliminate the anti-phase and zero quantum contributions in the multi-quantum signal after phase information correction.

6. The high-resolution D-glucose structure analysis method based on nuclear magnetic resonance spectroscopy according to claim 1, characterized in that: In S6, the signal model after chemical shift encoding is: Among them, ω I and ω S represents chemical shift; I and S represent spin operators; the up operator I + and reduction operator I - Respectively represent +1 and -1 quantum orders; Δ1 and Δ2 represent two different evolution times.

7. The high-resolution D-glucose structure analysis method based on nuclear magnetic resonance spectroscopy according to claim 1, characterized in that: In S7, the specific implementation method of phase encoding the two one-dimensional nuclear magnetic resonance phase-sensitive correlation spectra is Hardman encoding.

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