CN108802251B - Method for rapidly determining chiral substances based on restricted alternation trilinear decomposition algorithm and HPLC-DAD instrument - Google Patents

Method for rapidly determining chiral substances based on restricted alternation trilinear decomposition algorithm and HPLC-DAD instrument Download PDF

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CN108802251B
CN108802251B CN201810729047.XA CN201810729047A CN108802251B CN 108802251 B CN108802251 B CN 108802251B CN 201810729047 A CN201810729047 A CN 201810729047A CN 108802251 B CN108802251 B CN 108802251B
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李勇
余向阳
张猛
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Jiangsu Academy of Agricultural Sciences
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Abstract

The invention discloses a method for determining chiral substances based on a restricted alternative trilinear decomposition algorithm and an HPLC-DAD instrument, which comprises the following steps: firstly, respectively preparing a correction set sample, a verification set sample and a prediction set sample, detecting the samples by using an HPLC-DAD instrument, then establishing a correction model and carrying out regression analysis, namely firstly forming HPLC-DAD data of the correction set sample, the verification set sample and the prediction set sample into a three-dimensional data arrayXDetermining the number of system factors by using vector subspace projection and combining a Monte Carlo simulation method, decomposing a three-dimensional data array by using a restricted alternative trilinear decomposition algorithm, establishing a correction model, performing regression analysis on the concentrations of chiral substances in a verification sample and a prediction sample, and finally measuring the concentration of the chiral substances in the system; the method can effectively solve the problem of chiral substance co-outflow peak, avoids wasting a large amount of time to screen the chiral column type and the mobile phase, and has the characteristics of rapidness, greenness and environmental protection.

Description

Method for rapidly determining chiral substances based on restricted alternation trilinear decomposition algorithm and HPLC-DAD instrument
Background
Chirality is an essential attribute of natural substances, and the difference of activity and toxicity between enantiomers of chiral pesticides is obvious and is closely related to the environment. About 40% of the pesticides currently used in china are chiral substances, and the proportion tends to increase gradually with the introduction of complex structures. Therefore, the method for rapidly detecting the chiral pesticide is established, so that the production cost of the pesticide can be effectively reduced, the input amount of the pesticide into a natural ecological system can be reduced, and the harm of the pesticide to the ecological environment and animals and plants is reduced or avoided.
The common chiral substance analysis methods at present comprise a chemical resolution method, an enzyme or microorganism method and a chromatographic resolution method, wherein the chromatographic resolution method has a plurality of obvious advantages, can meet the requirements of enantiomer separation and determination under various conditions, can carry out simple, convenient and quick qualitative and quantitative analysis, and can also carry out preparation-scale separation and micro-determination. The chromatographic resolution method can be divided into a chiral derivatization method, a chiral mobile phase method and a chiral stationary phase method. Among them, chromatographic resolution based on chiral stationary phase is the most common. The chiral stationary phase method is based on the energy difference or stability difference of the temporary diastereomer complex formed by the chiral selector on the surface of the stationary phase and the sample, and can achieve manual separation without direct resolution of converting into diastereomer. The method has the advantages of simple mobile phase composition, good reproducibility, convenient operation and wide application range. However, the chiral stationary phase method has strong specificity, one type of stationary phase can only split one type or a plurality of types of enantiomers, and a plurality of chiral columns with different functions are developed at present. Therefore, the chiral pesticide is detected by using a high performance liquid chromatography-diode array ultraviolet detector instrument (HPLC-DAD) method, and a large amount of time is spent for screening a proper column type and a proper mobile phase, so that the chiral substance has a separation effect on a chiral column; moreover, even if the chiral substance has a separation effect on a chiral column, a long-time exploration of a proper instrument and method is needed to ensure that the chiral substance is completely separated on the chiral column and cannot be overlapped with unknown interference during the chromatographic outflow time, so that accurate quantification can be realized. Therefore, the development of a universal and rapid chiral compound detection method based on an HPLC-DAD instrument becomes a technical problem to be solved in the field.
Disclosure of Invention
Aiming at the problems, the invention develops a restricted alternative trilinear decomposition algorithm (RATLD) aiming at a special system of chiral substance analysis based on the thinking of 'mathematical separation' enhanced 'chromatographic separation' and combines an HPLC-DAD instrument based on a chiral column to carry out rapid quantitative analysis on chiral substances in a complex sample. The technical method is realized by the following steps:
1) preparation of correction set samples: purchasing chiral substance standard to be detected, respectively preparing working solutions of chiral substances by using appropriate organic solvents (such as hexane), preparing chiral substance mixed solutions with different gradient concentrations in a concentration linear range to serve as a calibration set sample, wherein the concentration ratio can be set according to methods such as conventional orthogonal experimental design and uniform experimental design in the field (for example, refer to the tenth book of analytical chemistry handbook (second edition) -chemometrics, chemical industry publishers);
taking the determination of R-dinotefuran and S-dinotefuran in a rice sample as an example, n-hexane is used for respectively dissolving R-dinotefuran and S-dinotefuran standards to prepare 10.0mg/L working solution, then 6 groups of chiral substance mixed solutions with different concentration gradients are prepared by using the working solution to serve as calibration samples, the n-hexane is used for fixing the volume to 1mL, and in 6 calibration concentrated samples after the volume fixing, the R-dinotefuran concentration is 4.0, 2.0, 1.0, 0.5, 0.2 and 0.0mg/L in sequence, and the S-dinotefuran concentration is 0.0, 0.2, 0.5, 1.0, 2.0 and 4.0mg/L in sequence.
2) Preparation of validation set samples: weighing a sample to be detected without chiral substances, adding a certain amount of standard solution of the chiral substances to be detected, and extracting the sample to be detected according to a conventional sample processing method in the field (such as the literature, the technical standard compilation of liquid chromatography, China Standard Press) to ensure that the extract of the sample to be detected meets the sampling standard of a chromatograph. Wherein, the concentration of the sample extracting solution is verified to be within the concentration range of the chiral substances in the sample of the calibration set.
Taking the determination of R-dinotefuran and S-dinotefuran in a rice sample as an example, taking rice which is not polluted by dinotefuran, crushing and uniformly mixing the rice by using a food mashing machine, accurately weighing 1.0g of the rice into a 5mL disposable plastic tube with a cover, respectively adding a certain amount of chiral standard substance solution to ensure that the adding concentrations of two chiral substances are 0.1mg/kg, 0.5mg/kg and 1.5mg/kg respectively, adding 5.0mL of acetonitrile, oscillating for 30min, adding 1.0g of sodium chloride, swirling for 1min, centrifuging for 10min at the rotating speed of 5000R/min, taking 2.5mL of supernatant into the 5mL of disposable plastic tube, adding 30mg of graphite carbon black, 100mg of n-Propylethylenediamine (PSA), 100mg of anhydrous magnesium sulfate, swirling for 1min, centrifuging for 5min at the rotating speed of 8000R/min, taking 1mL of the supernatant, drying the supernatant by adding 1mL of n-hexane for dissolving, filtering with 0.22 μm organic filter membrane to obtain the sample of the verification set to be tested;
3) preparation of prediction set samples: and (4) processing the samples to be detected in the prediction set and the samples in the verification set in a consistent way, but adding no chiral substance standard substance.
4) And (3) screening a chiral column with separation effect and a mobile phase (chiral substances do not need to be completely separated on the chiral column) based on an HPLC-DAD instrument, and detecting a calibration sample, a verification sample and a prediction sample.
In the present example, a xylonite-bonded chiral chromatographic column (
Figure BDA0001720408420000021
IB-3), the high performance liquid chromatography parameters are set as follows: the instrument comprises the following steps: a high performance liquid chromatograph; a chromatographic column: xylonite IB-3; mobile phase: n-hexane (a) -ethanol (B); flow rate: 0.6 mL/min; sample introduction amount: 30 uL; a detector: diode Array Detector (DAD), scanning range 230-400nm, spaced 2nm apart. Under the condition, the co-outflow problem of R-dinotefuran and S-dinotefuran is measured.
5) Establishing a correction model and carrying out regression analysis: firstly, forming a three-dimensional data array X by HPLC-DAD data of a correction set sample, a verification set sample and a prediction set sample, determining the component number of a system by using vector subspace projection and a Monte Carlo simulation method, decomposing the three-dimensional data array by using a restricted alternative trilinear decomposition algorithm, establishing a correction model by using the correction set, and performing regression analysis on the concentrations of chiral substances in the verification sample and the prediction sample.
In step 5), the HPLC-DAD data of the correction set sample, the verification set sample and the prediction set sample are two-dimensional data arrays, the size of the two-dimensional data arrays is I × J, wherein I is time dimension, the size of the two-dimensional data arrays is the number of data points acquired by the time dimension, J is spectral dimension, the size of the J is the number of data points acquired by the spectral dimension, and the two-dimensional data of each sample are stacked to form the three-dimensional data arrayXWhich isThe size is I × J × K, wherein K is the dimension of the sample, and the value of K is the number of the sample.
In the step 5), the process of determining the number of system factors by using vector subspace projection and combining a Monte Carlo simulation method is as follows:
a) in a three-dimensional data arrayXIn the first direction, a pseudo sample array R is obtained1：
Figure BDA0001720408420000031
In the above formula, Xi..For three-dimensional data arraysXThe ith slice matrix in the I direction;
wiis random data generated by Monte Carlo simulation method, with size of 0-1, and X is selected by Singular Value Decomposition (SVD) method..kThe first N principal components to construct a sample array M..k：
[U,S,V]＝svds(X..k,N) (2)
M..k＝USVT(3)
Wherein, X..kA K-th slice matrix in the K direction is taken as the three-dimensional data array X;
b) constructing a pseudo matrix R2:
Figure BDA0001720408420000032
wherein, wiAnd w in equation (1)iThe same;
then two pseudo-matrices R are processed by singular value decomposition1And R2：
[U1,S1,V1]＝svd(R1) (5)
[U2,S2,V2]＝svd(R2) (6)
Calculate U according to the following equation1And U2The projection residuals of the corresponding vectors in (1):
Figure BDA0001720408420000041
in the above formula, DI(n)Representing the projection residual, U1(n)And U2(n)Are respectively U1And U2Of the nth column vector, IJDenotes an identity matrix, superscript, of size J × J+Is Moore-Penrose generalized inverse matrix with DI as vector of 1 × N | | |FIs the F norm of the matrix or Frobenius modulus;
c) randomly generating at least 50 groups w using a Monte Carlo simulation methodiNumerically repeating steps a) -b) calculating the mean value DI of the corresponding projection residualsN(DINVector with size of 1 × N), factor number determination standard, wherein when the factor number exceeds the real system group number, the corresponding projection residual error value will jump from a very small value to a relatively large value, and the projection residual error values of the following factors are all relatively large, so the factor number N corresponding to the jump point is largeIIs the pre-estimated system component number;
d) determining projection residual DJ along J directionNAnd estimate another component number NJ(ii) a From NIAnd NJJudging the final system component number;
the projection into quantum space incorporates the specific steps of the Monte Carlo simulation method (Yong Li, the electronic, the chemical rank of the thread-way fluorescence data by vector sub-space project with Monte Carlo simulation Systems,2014,136: 15-23).
In step 5), a restricted alternating trilinear decomposition new method (RATLD) is developed based on the restricted trilinear model. For a chiral system, although chiral substances have spatial steric hindrance difference, ultraviolet spectrums of the chiral substances are basically consistent, and severe collinearity exists, so that correct results cannot be analyzed by using a conventional second-order correction method. Therefore, there is a need to develop more robust methods to handle this type of data. According to a two-substance chiral system and the thought of a trilinear model, a limit trilinear model can be provided:
Figure BDA0001720408420000042
with the proviso of bj1＝bj2(j＝1，2，...，J)
Wherein x isijkIs a three-dimensional data arrayXThe elements (A) and (B) in (B),Xhas a size of I × J × K and ain、bjnAnd cknElements in a chromatographic matrix A of size I × N, a spectral matrix B of size J × N, and a relative concentration matrix C of size K × N, respectively, eijkIs a three-dimensional residual arrayEThe elements of (1); n represents the number of factors that are the sum of the physically significant component of interest and the interfering and background components. Based on the constrained trilinear model, the following equation holds:
Xi..＝[B(:,1),B(:,1),B(:,3:N)]diag(A(i,:))CT+Ei..(i＝1,2,...,I) (17)
X.j.＝Cdiag([B(j,1),B(j,1),B(j,3:N)])AT+E.j.(j＝1,2,...,J) (18)
X..k＝Adiag(C(k,:))[B(:,1),B(:,1),B(:,3:N)]T+E..k(k＝1,2,...,K) (19)
wherein, Xi..、X.j.、X..kAre respectively asXA slice matrix along three directions of i, j and k; ei..、E.j.、E..kRespectively are slice matrixes of E along three directions of i, j and k; b is(:,n)The nth column vector of B; b is(:,3:N)For a matrix consisting of the 3 rd to last column vectors of matrix B, if N is 3, then B is(:,3:N)The 3 rd column vector of B; a. the(i,:)Is A ith column vector; c(k,:)The kth column vector of C; diag (A)(i,:)) And diag ([ B ](j,1),B(j,1),B(j,3:N)]) Is a diagonal matrix whose diagonal elements are respectively corresponding to A(i,:)And [ B(j,1),B(j,1),B(j,3:N)]Corresponding; upper labelTIs a matrix transposition operation. Based on the restricted trilinear model, restricted alternating three can be constructedLinear decomposition algorithm (RATLD), the objective function of which is constructed as follows:
Figure BDA0001720408420000051
Figure BDA0001720408420000052
wherein | |. calo | |)FThe F-norm of the matrix, or Frobenius modulus. B is(:,1)The ultraviolet spectrogram of the pure chiral substance can be obtained by directly measuring the pure substance by HPLC-DAD. A, B can be solved according to the above objective function(:,3:N)And C:
A(i,:)＝diagm([B(:,1),B(:,1),B(:,3:N)]+Xi..(CT)+)(i＝1,2,...,I) (10)
Figure BDA0001720408420000053
Figure BDA0001720408420000054
where diagm (.) extracts the elements on the diagonal of the matrix and arranges them into a column vector. The computation process of the RATLD algorithm is as follows:
a) determination of chiral ultraviolet Spectrum B(:,1)And carrying out normalization;
b) random initialization matrices A and B(:,3:N)；
c) C is calculated according to the formula (12), and non-negative restriction is carried out on C
d) Calculating A according to the formula (10), carrying out non-negative constraint on A, and carrying out column-by-column normalization on A;
e) calculating B according to equation (11)(:,3:N)To B, pair(:,3:N)Performing non-negative restriction, and for B(:,3:N)Performing column-by-column normalization;
f) calculating C according to the formula (12), and carrying out non-negative restraint on C;
g) repeating steps d) -f) until a convergence criterion is met:
Figure BDA0001720408420000061
Figure BDA0001720408420000062
in the above formula, m is the current iteration number, SSR is the sum of squares of residuals, and the maximum value of m is 1000.
After the chromatographic matrix A, the spectral matrix B and the concentration matrix C are obtained, determining the position of the chiral substance to be detected in the matrix by utilizing the chromatogram and the spectrogram of the chiral substance to be detected, and then sequentially carrying out regression analysis on the two chiral substances.
Regression analysis was performed as for R-dinotefuran: firstly, the position of the R-dinotefuran in the analytic matrix is determined (such as the first column), and the analytic concentration C of the correction set sample is determined in the analytic concentration matrix1By using C1And the true concentration vector C0Establishing a correction model:
C0＝C1*b (15)
wherein b is a regression coefficient and can be obtained by using a least square method; obtaining a correction model, and analyzing the concentration C of the verification set2And the analytic concentration C of the prediction set sample3And (5) bringing the test sample into a correction model to obtain the concentration of the R-dinotefuran in the test sample and the prediction sample.
Compared with the prior art, the invention has lower selection requirements on the chiral column and the mobile phase, only needs the separation effect, and does not need to completely separate the chiral substances on the chiral column. The invention can realize the rapid detection of the specific chiral substance under the coexistence of unknown interference. The method avoids the problem that a large amount of time is wasted in a conventional method for screening the columnar phase and the mobile phase, and has the characteristics of rapidness, greenness and environmental protection.
Drawings
FIG. 1R-dinotefuran and S-dinotefuran chromatograms.
FIG. 2 is a UV spectrum of R-dinotefuran and S-dinotefuran measured by HPLC-DAD.
FIG. 3 component fraction estimation of HPLC-DAD data using vector subspace projection in combination with Monte Carlo simulation: (a) projecting a residual error in the direction I; (b) is the J direction projection residual.
Fig. 4 shows the ralld analysis results when the group score is selected to be 3: (a) is a chromatogram; (b) is a spectrogram.
Detailed Description
The technical scheme of the invention is further described by combining the specific embodiment as follows:
reagents referred to in the following examples:
s-dinotefuran and R-dinotefuran were analytically pure and purchased from Guangzhou Bo chemical research, Inc. Sodium chloride (a.r., chemical corporation, west longa); acetonitrile (HPLC, Merck, germany); n-hexane (HPLC, Merck, germany); ethanol (HPLC, Merck, germany); (N-propylethylenediamine (Agela Technologies Co.); anhydrous magnesium sulfate (A.R., Douduo chemical reagent plant), baking at 550 deg.C for 5h, and cooling;
example 1S-dinotefuran and R-dinotefuran detection assay
a. Preparing a correction set sample: respectively dissolving S-dinotefuran and R-dinotefuran standard substance by using normal hexane to prepare working solution with the concentration of 10mg/L, mixing according to the concentration shown in the table 1,
TABLE 1 concentrations of R-dinotefuran and S-dinotefuran in the calibration set samples
Figure BDA0001720408420000071
b. Preparing a verification set sample:
taking rice which is not polluted by dinotefuran, crushing and uniformly mixing the rice by a food mashing machine, accurately weighing 1.0g of the rice in a 5mL disposable plastic tube with a cover, adding a certain amount of chiral substance standard solution to make the addition concentrations of chiral substances respectively 0.1mg/kg, 0.5mg/kg and 1.5mg/kg, adding 5.0mL acetonitrile, oscillating for 30min, adding 1.0g sodium chloride, vortexing for 1min, centrifuging at 5000r/min for 10min, collecting supernatant 2.5mL in 5mL disposable plastic tube, adding 30mg of graphite carbon black, 100mg of N-Propylethylenediamine (PSA), 100mg of anhydrous magnesium sulfate, vortexing for 1min, centrifuging at 8000r/min for 5min, collecting supernatant 1mL, blowing with nitrogen, adding 1mL of n-hexane for dissolution, filtering by a 0.22-micron filter membrane to obtain a to-be-detected verification set sample, and repeating each concentration level for 3 times;
c. preparing a prediction set sample:
taking a rice plant sample to be detected, crushing and uniformly mixing the rice plant sample by using a food mashing machine, accurately weighing 1.0g of the sample in a 5mL disposable plastic tube with a cover, adding 5.0mL of acetonitrile, oscillating for 30min, adding 1.0g of sodium chloride, whirling for 1min, centrifuging for 10min at the rotating speed of 5000r/min, taking 2.5mL of supernatant in the 5mL disposable plastic tube, adding 30mg of graphite carbon black, 100mg of N-propyl ethylenediamine (PSA), 100mg of anhydrous magnesium sulfate, whirling for 1min, centrifuging for 5min at the rotating speed of 8000r/min, taking 1mL of supernatant again, blowing nitrogen for drying, adding 1mL of n-hexane for dissolving, filtering by using a 0.22 mu m filter membrane to obtain the sample to be detected, and setting three parallel samples for each sample to be detected.
d. Instrumentation and chromatographic conditions
And (3) screening a chiral column with separation effect and a mobile phase (chiral substances do not need to be completely separated on the chiral column) based on an HPLC-DAD instrument, and detecting a calibration sample, a verification sample and a prediction sample.
The high performance liquid chromatography parameters were set as follows: the instrument is a high performance liquid chromatograph (Agilent 1260); the chromatographic column is selected from xylonite IB-3 (solvent-resistant chiral column with cellulose-tris (3, 5-dimethylphenyl carbamate) covalently bonded on the surface of silica gel), the mobile phase is selected from n-hexane (A) -ethanol (B), the flow rate is set to 0.6mL/min, the temperature of the column oven is 40 ℃, and the sample injection amount is 30 uL.
The detector is a Diode Array Detector (DAD) with a scanning range of 230-400nm and 2nm intervals.
Before injection, the sample was filtered through a 0.22 μm organic filter.
As shown in FIG. 1, the chromatographic outflow time of S-dinotefuran is 11.3-11.9min (FIG. 1(a)) and the chromatographic outflow time of R-dinotefuran is 11.4-12.0min (FIG. 1(b)), so that when two chiral substances are detected simultaneously, there is a serious problem of peak overlap, and at this time, the conventional method needs to search the instrument conditions again or try other chiral chromatographic columns and mobile phases to completely separate the two chiral substances, but this process is quite time-consuming and laborious, and when the peak of unknown interfering substance is discharged at the chiral outflow time, the quantitative result is also affected. However, the concept of 'mathematical separation' enhanced 'chromatographic separation' based on second-order correction of chemometrics can well solve the problem of chromatographic peak overlap, and can realize rapid quantitative analysis of the substances of interest under the interference of unknown interference co-effluent peaks.
e. Establishing a correction model and carrying out regression analysis: firstly, forming a three-dimensional data array X by HPLC-DAD data of a correction set sample, a verification set sample and a prediction set sample, determining the number of system factors by using vector subspace projection and Monte Carlo simulation, analyzing the three-dimensional data array by using a restricted alternative trilinear decomposition algorithm, establishing a correction model by using the correction set, and performing regression analysis on the concentrations of S-dinotefuran and R-dinotefuran in the verification sample and the prediction sample.
In step e, the HPLC-DAD data measured by each sample is a two-dimensional data array with the size of I × J, wherein I is a time dimension and the size of the I is the number of data points acquired by the time dimension, J is a spectrum dimension and the size of the J is the number of data points acquired by the spectrum dimension, and the two-dimensional data of each sample are stacked to form the three-dimensional data arrayXThe size of the sample is I × J × K, wherein K is the dimension of the sample, and the value of K is the number of the sample.
The process of determining the number of system factors by using vector subspace projection in combination with the Monte Carlo simulation method (VSPMCS) is as follows:
a) in a three-dimensional data arrayXIn the first direction, a pseudo sample array R is obtained1：
Figure BDA0001720408420000091
In the above formula, Xi..For three-dimensional data arraysXThe ith slice matrix in the I direction;
wiis random data generated by Monte Carlo simulation method, and its size is between 0 and 1Taking X by Singular Value Decomposition (SVD) method..kThe first N principal components to construct a sample array M..k：
[U,S,V]＝svds(X..k,N) (2)
M..k＝USVT(3)
Wherein, X..kA K-th slice matrix in the K direction is taken as the three-dimensional data array X;
b) constructing a pseudo matrix R2:
Figure BDA0001720408420000092
wherein, wiAnd w in equation (1)iThe same;
then two pseudo-matrices R are processed by singular value decomposition1And R2：
[U1,S1,V1]＝svd(R1) (5)
[U2,S2,V2]＝svd(R2) (6)
Calculate U according to the following equation1And U2The projection residuals of the corresponding vectors in (1):
Figure BDA0001720408420000101
in the above formula, DI(n)Representing the projection residual, U1(n)And U2(n)Are respectively U1And U2Of the nth column vector, IJDenotes an identity matrix, superscript, of size J × J+Is Moore-Penrose generalized inverse matrix, and DI is vector with the size of 1 × N;
c) randomly generating at least 50 groups w using a Monte Carlo simulation methodiNumerically repeating steps a) -b) calculating the mean value DI of the corresponding projection residualsN(DINVector of size 1 × N), pair DINThe factor N corresponding to the sudden jump point which is suddenly changed from small to bigINamely the pre-estimated system component number;
d) determining projection residual DJ along J directionNAnd estimate another component number NJ(ii) a From NIAnd NJJudging the final system component number;
the projection into quantum space incorporates the specific steps of the Monte Carlo simulation method (Yong Li, the electronic, the chemical rank of the thread-way fluorescence data by vector sub-space project with Monte Carlo simulation Systems,2014,136: 15-23).
Fig. 3 shows the estimation result of the system component score by combining vector subspace projection with the monte carlo simulation method, and it can be found that the first three projection residuals are all equal to 0 or close to 0, and the projection residual of the 4 th factor is suddenly increased, which indicates that the system component score should be estimated to be 3.
In step e, based on the restricted trilinear model, a restricted alternating trilinear decomposition method (RATLD) can be constructed, and the objective function is constructed as follows:
Figure BDA0001720408420000102
Figure BDA0001720408420000103
wherein | |. calo | |)FThe F norm or Frobenius norm of the matrix;
B(:,1)the ultraviolet spectrogram of the pure chiral substance can be obtained by directly measuring the pure substance by HPLC-DAD, and can be solved according to the above objective function to obtain A, B(:,3:N)And C:
A(i,:)＝diagm([B(:,1),B(:,1),B(:,3:N)]+Xi..(CT)+)(i＝1,2,...,I) (10)
Figure BDA0001720408420000111
Figure BDA0001720408420000112
wherein diagm (.) extracts the elements on the diagonal of the matrix and arranges them into a column vector;
the computation process of the RATLD algorithm is as follows:
a) determination of chiral ultraviolet Spectrum B(:,1)And carrying out normalization;
b) initializing matrices A and B(:,3:N)；
c) C is calculated according to the formula (12), and non-negative restriction is carried out on C
d) Calculating A according to the formula (10), carrying out non-negative constraint on A, and carrying out column-by-column normalization on A;
e) calculating B according to equation (11)(:,3:N)To B, pair(:,3:N)Performing non-negative restriction, and for B(:,3:N)Performing column-by-column normalization;
f) calculating C according to the formula (12), and carrying out non-negative restraint on C;
g) repeating steps d) -f) until a convergence criterion is met:
Figure BDA0001720408420000113
Figure BDA0001720408420000114
in the formula, m is the current iteration number, SSR is the sum of squares of residual errors, and the maximum value of m is 1000;
after obtaining the chromatographic matrix A, the spectral matrix B and the concentration matrix C, determining the position of the component to be detected in the matrix by utilizing the chromatogram and the spectrogram of the component to be detected (R-and S-dinotefuran), and then sequentially performing regression analysis on the two components. Taking R-dinotefuran as an example, regression analysis is carried out: firstly, the position of the R-dinotefuran in the analytic matrix is determined (such as the first column), and the analytic concentration C of the correction set sample is determined in the analytic concentration matrix1By using C1And the true concentration vector C0Establishing a correction model:
C0＝C1*b (15)
wherein b is a regression coefficient and can be obtained by using a least square method; after obtaining the correction model, the correction model is processedAnalytical concentration C of validation set2And the analytic concentration C of the prediction set sample3And (5) bringing the test sample into a correction model to obtain the concentration of the R-dinotefuran in the test sample and the prediction sample. The same can be used to obtain the verification set and predict the concentration of S-dinotefuran in the set. Specific regression procedures can be found in the literature (Fundamentals and analytical applications of multi-way catalysis, Alejandro c.oliviri, Graciela m.escandra,
Figure BDA0001720408420000121
C.Goicoechea,Arsenio
Figure BDA0001720408420000122
ozde la
Figure BDA0001720408420000123
a,Editors.2015，Chapter 4-Practical Analytical Applications ofMultiway Calibration Methods Based on Alternating Multilinear Decomposition)。
FIG. 3 is a chromatogram and a spectrogram analyzed by the RATLD algorithm with a factor of 3, and it can be seen from the chromatogram and the real chromatogram that the S-dinotefuran and R-dinotefuran chromatograms are analyzed by the RATLD algorithm are basically overlapped, and the qualitative result is satisfactory. In addition, an interfering substance is analyzed by the RATLD, and the RATLD algorithm can realize the interested rapid determination under the coexistence of unknown interference. The results of the correction model on the prediction of the sample in the verification set are shown in Table 2, the average recovery rate of S-and R-dinotefuran is satisfactory, and the development method is feasible. In the predicted sample, the chiral concentration of S-dinotefuran and R-dinotefuran is determined to be 0.7 + -0.1 mg/kg and 1.0 + -0.1 mg/kg.
TABLE 2 prediction of sample concentration and average recovery
Figure BDA0001720408420000124
The foregoing is only a preferred embodiment of this invention and it should be noted that modifications can be made by those skilled in the art without departing from the principle of the invention and these modifications should also be considered as the protection scope of the invention.

Claims (2)

1. A method for determining chiral substances based on a restricted alternation trilinear decomposition algorithm and an HPLC-DAD instrument comprises the following specific steps:
1) preparing a correction set sample: preparing a mixed solution of chiral substances with gradient concentration to be used as a correction set sample;
2) preparing a verification set sample: adding a chiral object standard product into a sample to be detected without chiral objects, and extracting the sample to be detected according to a conventional sample processing method in the field;
3) preparing a prediction set sample: processing steps of the samples to be detected in the prediction set and the samples in the verification set are consistent unless the chiral standard is added;
4) screening a chiral column and a mobile phase with a separation effect based on an HPLC-DAD instrument, and detecting a correction set sample, a verification set sample and a prediction set sample;
5) establishing a correction model and carrying out regression analysis: firstly, the HPLC-DAD data of a correction set sample, a verification set sample and a prediction set sample are combined into a three-dimensional data arrayXDetermining system component number by using vector subspace projection and combining a Monte Carlo simulation method, decomposing the three-dimensional data array by using a restricted alternative trilinear decomposition algorithm, establishing a correction model by using a correction set, and performing regression analysis on the concentrations of chiral substances in the verification sample and the prediction sample;
5.1) the process for determining the number of system factors by using the vector subspace projection and combining the Monte Carlo simulation method is as follows:
5.1.1) in three-dimensional data arraysXIn the first direction, a pseudo sample array R is obtained1：
Figure FDA0002409719850000011
In the above formula, Xi..For three-dimensional data arraysXThe ith slice matrix in the I direction;
wiis random data generated by a monte carlo simulation method, has a size between 0 and 1,taking X by Singular Value Decomposition (SVD) method..kThe first N principal components to construct a sample array M..k：
[U,S,V]＝svds(X..k,N) (2)
M..k＝USVT(3)
Wherein, X..kFor three-dimensional data arraysXA K-th slice matrix in a K-direction;
5.1.2) construction of the pseudo-matrix R2：
Figure FDA0002409719850000012
Wherein, wiAnd w in equation (1)iThe same;
then two pseudo-matrices R are processed by singular value decomposition1And R2：
[U1,S1,V1]＝svd(R1) (5)
[U2,S2,V2]＝svd(R2) (6)
Calculating U according to equation (7)1And U2The projection residuals of the corresponding vectors in (1):
Figure FDA0002409719850000021
in the above formula, DI(n)Representing the projection residual, U1(n)And U2(n)Are respectively U1And U2Of the nth column vector, IJDenotes an identity matrix, superscript, of size J × J+Is Moore-Penrose generalized inverse matrix with DI as vector of 1 × N | | |FIs the F norm of the matrix;
5.1.3) random Generation of at least 50 groups w Using Monte Carlo simulation methodiNumerical value repeating steps 5.1.1) -5.1.2), calculating the average value DI of the corresponding projection residualsN，DINAs vectors, DINIs taken as 1 × N and a pre-estimated system component number N is obtainedI；
5.1.4) determining the projection residual DJ in the J directionNAnd estimate the otherGroup number NJ(ii) a From NIAnd NJJudging the final system component number;
5.2) the objective function of the constrained alternating trilinear decomposition algorithm is constructed as follows:
Figure FDA0002409719850000022
Figure FDA0002409719850000023
wherein, Xi..、X.j.Are respectively asXSlice matrix along i and J directions, A is a chromatographic matrix with size J × N, B(:,1),B(:,1),B(:,3:N)]Is a relative spectrum matrix B with a size of K × N, C is a relative concentration matrix with a size of K × N, B(:,n)The nth column vector of B; b is(:,3:N)Is a matrix composed of the 3 rd to the last column vectors of the matrix B; a. the(i,:)Is A ith column vector; diag (A)(i,:)) And diag ([ B ](j,1),B(j,1),B(j,3:N)]) Is a diagonal matrix whose diagonal elements are respectively corresponding to A(i,:)And [ B(j,1),B(j,1),B(j,3:N)]Corresponding; upper labelTPerforming matrix transposition operation; b is(:,1)Is an ultraviolet spectrogram of a homochiral substance; solving A, B according to the above objective function(:,3:N)And C:
A(i,:)＝diagm([B(:,1),B(:,1),B(:,3:N)]+Xi..(CT)+) (i＝1,2,...,I) (10)
B(j,3:N)＝diagm((C(:,3:N))+(X.j.-C(:,1:2)diag([B(j,1),B(j,1)])A(:,1:2) T)(A(:,3:N) T)+) (11)
(j＝1,2,...,J)
Figure FDA0002409719850000031
wherein diagm (.) extracts the elements on the diagonal of the matrix and arranges them into a column vector;
5.3) the computation process of the restricted alternating trilinear decomposition algorithm is as follows:
5.3.1) determination of the ultraviolet spectrum B of the chiral substance(:,1)And carrying out normalization;
5.3.2) random initialization matrices A and B(:,3:N)；
5.3.3) calculating C according to the formula (12), and carrying out non-negative restriction on C;
5.3.4) calculating A according to the formula (10), carrying out non-negative restriction on A, and carrying out column-by-column normalization on A;
5.3.5) calculating B according to equation (11)(:,3:N)To B, pair(:,3:N)Performing non-negative restriction, and for B(:,3:N)Performing column-by-column normalization;
5.3.6) calculating C according to formula (12), and performing non-negative restriction on C;
5.3.7) repeat steps 5.3.4-5.3.6 until the following convergence criterion is met:
Figure FDA0002409719850000032
Figure FDA0002409719850000033
in the formula, m is the current iteration number, SSR is the sum of squares of residual errors, and the maximum value of m is 1000; finally obtaining a chromatographic matrix A, a spectral matrix B and a concentration matrix C;
5.4) after obtaining the chromatographic matrix A, the spectral matrix B and the concentration matrix C, determining the position of the chiral substance in the matrix by using a chromatogram and a spectrogram of the chiral substance, and then sequentially carrying out regression analysis on the two chiral substances;
5.4.1) establishing a correction model:
C0＝C1*b (15)
wherein, C0As a true concentration vector, C1For analytical concentration of calibration set samplesB is a regression coefficient;
5.4.2) analytical concentration C of the validation set samples2And the analytic concentration C of the prediction set sample3And (5) bringing the test sample into a correction model to obtain the concentrations of the chiral substances in the verification set sample and the prediction set sample.
2. The method for determining chiral substances based on the restricted alternation trilinear decomposition algorithm and the HPLC-DAD instrument as claimed in claim 1, wherein the HPLC-DAD data of the correction set sample, the validation set sample and the prediction set sample in step 5) are all two-dimensional data arrays with the size of I × J, wherein I is time dimension, I is the number of data points acquired in time dimension, J is spectral dimension, J is the number of data points acquired in spectral dimension, and the two-dimensional data of each sample are stacked to form the three-dimensional data arrayXThe size of the sample is I × J × K, wherein K is the dimension of the sample, and the value of K is the number of the samples.
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