Determination of HPLC method parameters using machine learning

Abstract

A computer implementation method for predicting the HPLC retention time of one or more compounds using a machine learning model is disclosed. In particular, the use of a machine learning model to identify a suitable set of HPLC method parameters for separating two or more compounds in a composition is disclosed. Related systems and products are also described.

Description

[Technical Field]

[0001] The present invention relates to a computer implementation method for predicting the HPLC retention time of one or more compounds using a machine learning model. In particular, the present invention relates to the use of a machine learning model to identify a set of HPLC method parameters suitable for the separation of two or more compounds in a composition, as well as related systems and apparatus. [Background technology]

[0002] High-performance liquid chromatography (HPLC) is the most commonly used analytical technique in the development of new drugs. From drug discovery and development to commercial manufacturing, HPLC is used for purity assays, stability testing, identification of degradation and by-products, genotoxicity limit testing, or preliminary separation (Dong & Guillarme, 2013; Snyder et al., 2009).

[0003] In the development process of HPLC methods, a wide range of parameters, including mobile phase (eluent), eluent pH, gradient program, flow rate, column oven temperature, and stationary phase (column) selection, must be optimized to achieve maximum separation between compounds. Currently, a time-consuming and costly "trial and error" approach is often applied to find the best settings, one element at a time.

[0004] Therefore, it is desirable to provide a method for addressing the aforementioned technical challenges. [Overview of the project]

[0005] More broadly, the present invention provides a machine learning model for predicting the HPLC retention time of one or more compounds and for identifying a set of HPLC method parameters suitable for separating two or more compounds in a composition.

[0006] Accordingly, the first aspect provides a method for predicting the HPLC retention time of one or more compounds, the method comprising (a) obtaining values ​​for one or more structural and / or physicochemical properties of the compounds and one or more HPLC method parameters, and (b) using a machine learning model to predict the retention time of each of the compounds when subjected to HPLC using one or more HPLC method parameters, the machine learning model being trained using a training dataset, the training dataset comprising molecular structural and / or physicochemical properties of one or more compounds, and for each compound, comprising one or more sets of chromatographic data including retention times for each compound and associated HPLC method parameters.

[0007] The inventors of the present invention have confirmed that it is possible to train a machine learning model to predict with high predictive accuracy chromatographic data, including the retention time of each compound when separated using relevant HPLC method parameters provided as input to the machine learning model. Furthermore, the inventors of the present invention have recognized that these highly accurate predictions of HPLC methods can be used to identify suitable HPLC method parameters for the separation of two or more compounds in a composition.

[0008] Accordingly, according to a second embodiment, a method for identifying a set of HPLC method parameters suitable for the separation of a compound in a composition comprising two or more compounds is also described herein, the method comprising (a) performing the method of the first embodiment for a plurality of sets of HPLC method parameters, (b) calculating one or more separation performance metrics using the results of step (a), and (c) identifying one or more sets of HPLC method parameters by applying one or more criteria to the separation performance metrics.

[0009] According to a third aspect, a method is provided for providing a tool for predicting the HPLC retention time of one or more compounds, the method comprising (a) obtaining a training dataset which includes one or more sets of chromatographic data for each compound, including retention times for each compound and associated HPLC method parameters, with respect to one or more structural and / or physicochemical property values ​​of one or more compounds; and (b) training a machine learning model to predict the retention time of a compound when subjected to HPLC using one or more HPLC method parameters, with respect to one or more structural and / or physicochemical property values ​​of the compounds and the values ​​of the HPLC method parameters as input. [Brief explanation of the drawing]

[0010] [Figure 1] This shows a schematic diagram of an HPLC system. [Figure 2A] This diagram shows an exemplary method flowchart for predicting HPLC retention times (A) and identifying a suitable set of HPLC method parameters for separating two or more compounds (B). The steps enclosed by dashed outlines are optional. [Figure 2B] This diagram shows an exemplary method flowchart for predicting HPLC retention times (A) and identifying a suitable set of HPLC method parameters for separating two or more compounds (B). The steps enclosed by dashed outlines are optional. [Figure 3] This shows the gradient of SAM-0200368 with time points labeled as tp_1, tp_2, and tp_3. [Figure 4] This is a star schema representing integrated data. [Figure 5]This diagram shows the definition and basic operation of a genetic algorithm based on one implementation of the method of this disclosure. In the diagram, Flow is the flow rate, Temp is the temperature and pH, Tp_1 is time point 1, Tp_2 is time point 2, Tp_3 is time point 3, Ep_1 is the elution force 1, Ep_2 is the elution force 2, Ep_3 is the elution force 3, Length is the column length, inner_diameter is the column inner diameter, Particle size is the column particle size, Pore_size is the column pore size, H is hydrophobicity, S is steric interaction, A is hydrogen bond acidity, B is hydrogen bond basicity, and c is ion exchange capacity. [Figure 6] This disclosure demonstrates the basic operation of a genetic algorithm based on one implementation of the method. [Figure 7-1] This shows a plot of the prediction error of an evaluated machine learning model before feature selection using random training-test splitting according to one embodiment of the method of this disclosure. [Figure 7-2] This shows a plot of the prediction error of an evaluated machine learning model before feature selection using random training-test splitting according to one embodiment of the method of this disclosure. [Figure 7-3] This shows a plot of the prediction error of an evaluated machine learning model before feature selection using random training-test splitting according to one embodiment of the method of this disclosure. [Figure 8] This shows a comparison of two splitting methods. The left side shows a random training-test split (80 / 20), and the right side shows a unified training-test split (80 / 20). Y_train and y_test relate to the training and test data, respectively. A "unified" sampling method was used to maintain an 80 / 20 ratio between training and test samples throughout the entire retention time range. [Figure 9] This shows the top 20 most important features of XGB models using a unified training-test split. The numbers are F-core values, also indicated by the length of the bars. [Figure 10]It shows the evaluation of the hyperparameters of the XGB model after using different learning rates and performing unified training-test splitting and feature selection. All models achieved good performance. When using learning_rate of 0.1 and 0.05, the models reached good performance with only a few hundred estimators. The plotted scores are the average test scores of 10-fold CV. [Figure 11] It shows the prediction error and residual plots of the final XGB model. The residual plot shows random errors over the full RT range indicating good fit of the model. This model functions best between 2 minutes and 20 minutes, probably due to the number of observations within this range. [Figure 12] It shows the prediction error and residual plots using molecular fingerprints and XGB. The histogram shows the distribution of the test set and the distribution of the predicted values. [Figure 13-1] It shows the comparison of KMeans clustering with 30 and 8 clusters using both ion exchange parameters (c). PCA was applied before clustering. "x" represents the cluster centers. [Figure 13-2] It shows the comparison of KMeans clustering with 30 and 8 clusters using both ion exchange parameters (c). PCA was applied before clustering. "x" represents the cluster centers. [Figure 14] It shows the comparison of different eps values for clustering of the analytical column using DBSCAN and c_28. [Figure 15] It shows the comparison of measured RT and predicted RT using an XGB model specially trained for the SAM method parameters and optimizer. The peak numbers are defined by the RT from the Empower data (i.e., measured RT, red peaks). [Figure 16] It shows the comparison of the predicted and measured results of molecules in an exemplary elution (labeled as SAM-XXXXX) using the method parameters from the optimizer. [Figure 17]The figure shows a comparison between the predicted and measured results of molecules in an exemplary elution (labeled SAM-0113392) using the recommended method parameters by the optimizer. [Figure 18] The figure shows a screenshot of the user interface for accessing the method of the present disclosure. **DETAILED DESCRIPTION OF THE INVENTION**

[0011] In the description of the present invention, the following terms are used and are intended to be defined as shown below.

[0012] As used herein, "and / or" shall be construed as a specific disclosure of each of the two features or components specified therein, and the other may or may not be present. For example, "A and / or B" shall be construed as a specific disclosure of each of (i) A, (ii) B, and (iii) A and B, as if each were individually described herein.

[0013] Furthermore, when used hereinafter, the terms "in particular", "more particularly", "specifically", "more specifically", or similar terms are used in conjunction with optional features without limiting the possibility of alternatives. Therefore, the features introduced by these terms are optional features and are not intended to limit the technical scope of the claims in any way. The present invention can be implemented, as will be appreciated by those skilled in the art, by using alternative features. Similarly, features introduced by "in an embodiment of the present invention" or similar expressions are intended to be optional features, without any limitation regarding alternative embodiments of the present invention, without any limitation regarding the scope of the present invention, and without any limitation regarding the possibility of combining such features with other optional or non-optional features of the present invention.

[0014] The compositions described herein may further comprise pharmaceutical compositions comprising pharmaceutically acceptable carriers, diluents, or excipients. The pharmaceutical compositions may optionally comprise one or more further pharmaceutically active polypeptides and / or compounds. Such formulations may be, for example, in a form suitable for intravenous injection.

[0015] The compounds described herein may be small molecules (e.g., small molecule inhibitors, activators, cofactors, etc.) or large molecules (e.g., biological therapeutic proteins or peptides, e.g., antibodies or antibody-derived compounds, nucleic acids, etc.). The compounds may be organic compounds. The compounds may be pharmaceutically active agents (also called drugs or therapeutic agents) or their degradation products.

[0016] The systems and methods described herein may be implemented in a computer system, including, or in addition to, the structural components and user interactions described herein. As used herein, the term “computer system” includes hardware, software, and data storage devices for embodying the systems according to the embodiments described above or for performing the methods. For example, a computer system may comprise processing units such as a central processing unit (CPU) and / or graphics processing unit (GPU), which may be embodied as one or more connected computing devices, input means, output means, and data storage devices. Preferably, a computer system comprises a computing device having a display or a display that provides a visual output display. Data storage devices may comprise RAM, disk drives, or other computer-readable media. A computer system may comprise a plurality of computing devices connected by a network and capable of communicating with each other through that network. It is expressly assumed that a computer system may consist of or include cloud computers.

[0017] The methods described herein may be provided as computer programs, or as computer program products or computer-readable media carrying computer programs configured to perform the methods described herein when executed on a computer. As used herein, the term “computer-readable media” includes, but is not limited to, any non-temporary media that are directly readable and accessible by a computer or computer system. Examples of media include, but are not limited to, magnetic storage media such as floppy disks, hard disk storage media, and magnetic tapes, optical storage media such as optical disks or CD-ROMs, electrical storage media such as RAM, ROM, and flash memory, and hybrids and combinations of the above, such as magnetic / optical storage media.

[0018] High-performance liquid chromatography (HPLC), also known as "high-pressure liquid chromatography," is the most commonly used analytical technique in the development of new drugs. HPLC's strength lies in its nearly universal applicability, as only a small number of samples cannot be measured using this technique. By combining HPLC with other techniques such as mass spectrometry (LC-MS), HPLC has gained even greater importance. From drug discovery and development to commercial manufacturing, HPLC is used for purity assays, stability testing, identification of degradation and by-products, genotoxicity limit testing, or preliminary separation (Dong & Guillarme, 2013; Snyder et al., 2009). The development process of an HPLC method requires setting a wide range of parameters. Several parameters, including the mobile phase (eluent), eluent pH, gradient program, flow rate, column oven temperature, and stationary phase (column), must be selected to achieve maximum separation performance between test substances. Currently, determining the optimal parameters requires extensive manual optimization involving several trial-and-error steps, which is time-consuming and costly, even though on-site guidelines can help shorten the process to some extent.

[0019] In the context of the present invention, the term HPLC is intended to encompass ultrahigh-performance liquid chromatography, as well as HPLC performed independently or as part of an analytical or separation process, such as as part of LC-MS.

[0020] Figure 1 shows a schematic diagram of an HPLC system. After the injection of a liquid sample using an autosampler, a flow of eluent from a pump carries the sample through the HPLC system. Once the sample enters the column, it is separated into its different components. The separation method is primarily determined by the column. Several types of HPLC exist, including reversed-phase chromatography (RPLC), normal-phase chromatography (NP-LC), hydrophilic interaction chromatography (HILIC), ion pair chromatography (IPC), size exclusion chromatography (SEC), and affinity chromatography. The methods described herein are applicable to all types of HPLC. Currently, RP-LC is the most commonly used separation method in the development process of novel small molecule drugs, particularly with respect to water-soluble samples (Dong, 2006). In some embodiments, HPLC may be RP-LC. In RP-LC, the stationary phase (called the column) is nonpolar. The column is a stainless steel tube packed with spherical particles made of porous modified silica. The most common modification in RP-LC is C-18. These C-18 groups bind to the surface of each particle, resulting in nonpolarity of the column. The mobile phase consists of a polar mixture of an organic solvent (common examples include acetonitrile or methanol) and water. Different migrations ("migration rates") of sample molecules (called kenshi) cause separation within the column. The migration of kenshi is determined by the equilibrium process between molecules of the same kenshi present in the mobile and stationary phases at any given time. The stronger the kenshi binds to the stationary phase, the stronger the retention by the stationary phase and the longer the retention time (RT). In addition to the chemical structure of the kenshi, the mobile and stationary phases, as well as temperature, affect the migration rate. The sample solvent, due to its polarity, does not bind to the column and exits the column first. Different molecules, after being separated on the column, exit the column and enter the detector. The most common type is the ultraviolet absorption detector (LC-UV). A UV detector measures the rate of light transmitted through the flow cell containing the sample as a function of time. The relationship between the percentage of transmitted light and the concentration of the test substance in the sample can be expressed using the Beer-Lambert-Law.The output of an LC-UV experiment is a chromatogram in which absorbance is plotted against retention time (RT).

[0021] In a first aspect, the present invention provides a method for predicting the HPLC retention time of one or more compounds, the method comprising (a) obtaining values ​​for one or more structural and / or physicochemical properties of the compounds and one or more HPLC method parameters, and (b) using a machine learning model to predict the retention time of each of the compounds when subjected to HPLC using one or more HPLC method parameters, the machine learning model being trained using a training dataset, the training dataset comprising molecular structural and / or physicochemical properties of one or more compounds, and for each compound, comprising one or more sets of chromatographic data including retention times for each compound and associated HPLC method parameters.

[0022] The method of this embodiment may have any of the features described in relation to any other embodiment.

[0023] The "get" step may include calculating properties, receiving them from a user interface, or receiving them from a computing device or database.

[0024] HPLC method parameters may include parameters related to the column (e.g., dimensions, particle size), parameters related to the eluent (e.g., pH of the eluent), or parameters related to the chromatography procedure (e.g., flow rate).

[0025] A schematic diagram is shown in Figure 2A. In step 100, values ​​for one or more structural and / or physicochemical properties of one or more compounds are obtained. This may optionally include obtaining the identity of the compounds, for example from a user, in step 102. This may optionally include step 104, which determines the values ​​of the structural / physicochemical properties. Alternatively, these may be received from a user, a computing device, or a database. The properties may include molecular fingerprints and / or one or more molecular descriptors. In some embodiments, the structural molecular descriptors and / or molecular fingerprints are 2D molecular descriptors or molecular fingerprints. In some embodiments, the molecular descriptor is selected from the group consisting of ABCIndex, AcidBase, AdjacencyMatrix, Aromatic, AtomCount, Autocorrelation, BCUT, BalabanJ, BaryszMatrix, BertzCT, BondCount, CarbonTypes, Chi, Constitutional, DetourMatrix, DistanceMatrix, EState, EccentricConnectivityIndex, ExtendedTopochemicalAtom, FragmentComplexity, Framework, HydrogenBond, InformationContent, KappaShapeIndex, Lipinski, McGowanVolume, MoeType, MolecularDistanceEdge, MolecularId, PathCount, Polarizability, RingCount, RotatableBond, SLogP, TopoPSA, TopologicalCharge, TopologicalIndex, VdwVolumeABC, VertexAdjacencyInformation, WalkCount, Weight, WienerIndex, and ZagrebIndex. In some embodiments, the parameters are calculated by the Mordred package.In some embodiments, the molecular descriptor is selected from the group consisting of SLogP, ATSC5v, ATSC8d, ATSC3Z, ABC, VSA_EState4, ATSC5dv, and ATSC6i.

[0026] In step 110, values ​​for one or more HPLC method parameters are obtained. These may be received from a user, a computing device, or a database. For example, they may be received from an optimization algorithm running on a processor. In some embodiments, a set of HPLC method parameters is generated by a genetic algorithm. In some embodiments, the genetic algorithm is run until one or more stopping criteria are met, optionally selected from i) a predetermined number of generations being reached, and ii) the difference between the separation performance metric for one or more sets of HPLC method parameters in the current iteration and the separation performance metric for one or more sets of HPLC method parameters in the previous iteration being less than a threshold. In some embodiments, the genetic algorithm is initialized with a randomly selected set of HPLC method parameters, the genetic algorithm is initialized with a set of HPLC method parameters selected from a predetermined set or range of each HPLC method parameter, and / or the genetic algorithm is initialized with a set of HPLC method parameters provided by the user. In some embodiments, one or more sets of HPLC method parameters are selected (e.g., by a genetic algorithm) from their respective predetermined sets and / or ranges.

[0027] In step 120, a machine learning model is used to predict the retention time of each compound when subjected to HPLC using one or more HPLC method parameters. Optionally, the machine learning model further predicts a metric representing peak width, and one or more sets of chromatographic data in the training dataset further include a metric representing the peak width of each compound.

[0028] In step 130, the predicted values ​​are presented to the user, for example, via a user interface, or to a computing device or database.

[0029] In one embodiment, the machine learning model further predicts a metric representing peak width. In such an embodiment, the machine learning model is trained using one or more sets of chromatographic data, each further including a metric representing the peak width of each compound.

[0030] In one embodiment, one or more compounds are individually selected from pharmaceutically active agents and their degradable organisms.

[0031] In one embodiment, the HPL method parameters are selected from the group consisting of HPLC type, flow rate, temperature, pH, column length, column inner diameter, column particle size, column pore size, column steric interaction, column hydrogen bond acidity, column hydrogen bond basicity, column ion exchange capacity (c_28), column ion exchange capacity (c_70), and one or more metrics that define the elution phase gradient. In one embodiment, the HPLC method parameters include one or more parameters selected from the group consisting of column length, column inner diameter, column particle size, column pore size, column steric interaction, column hydrogen bond acidity, column hydrogen bond basicity, column ion exchange capacity (c_28), column ion exchange capacity (c_70), and one or more metrics that define the elution phase gradient, and optionally include one or more parameters selected from the group consisting of HPLC type, flow rate, temperature, and pH. In one embodiment, the HPLC method parameters include one or more parameters selected from the group consisting of HPLC type, flow rate, temperature, pH, and one or more parameters selected from the group consisting of column length, column inner diameter, column particle size, column pore size, column steric interaction, column hydrogen bond acidity, column hydrogen bond basicity, column ion exchange capacity (c_28), column ion exchange capacity (c_70), and one or more metrics that define the elution phase gradient. In one embodiment, the HPLC method parameters include i) HPLC type, flow rate, temperature, one or more metrics that determine the elution phase gradient, pH, and ii) one or more parameters selected from the group consisting of column length, column inner diameter, column particle size, column pore size, column steric interaction, column hydrogen bond acidity, column hydrogen bond basicity, column ion exchange capacity (c_28), and column ion exchange capacity (c_70).

[0032] In some embodiments, the HPLC type may be, for example, normal-phase (NP) chromatography, reverse-phase (RP) chromatography, size exclusion chromatography, ion exchange chromatography, hydrophilic interaction chromatography (HILIC), and affinity chromatography. In some embodiments, the HPLC type is RP or NP chromatography. Specifically, the HPLC type may be RP chromatography.

[0033] In one embodiment, one or more metrics that define the elution phase gradient are: (i) the elution power of each of the multiple mobile phases, and / or (ii) a metric that defines the time-dependent change in the proportions of multiple mobile phases during elution (optionally, one or more metrics that define the time-dependent change in the proportions of multiple mobile phases during elution include one or more time point values ​​corresponding to the change in the rate of change of the mobile phase proportions, and / or values ​​for the rate of change of the mobile phase proportions at one or more time points during elution), and / or a metric that describes a function representing the change in the proportion of mobile phases in one or more regions (e.g., each of) of the gradient, and / or (iii) The elution power of the mobile phase at two or more (e.g., three) different time points (optionally, the mobile phase may include multiple mobile phases, and the elution power at a given time point is determined by summing the elution power of each of the multiple mobile phases, weighted according to their respective proportions). Includes.

[0034] In one embodiment, one or more physicochemical properties include one or more molecular descriptors, and further / or one or more molecular structural properties include a molecular fingerprint and / or one or more structural molecular descriptors. In some embodiments, one or more physicochemical properties and / or molecular structural properties are calculated by PaDEL-Descriptor, BlueDesc, ChemoPy, PyDPI, Rcpi, Cinfony, or Dragon software, preferably the Mordred package. Any package available in the art for calculating the physicochemical properties and / or molecular structural properties of a molecule, for example, starting from a molecular formula or a 2D or 3D structure, can be used.

[0035] In one embodiment, the structural molecular descriptor and / or molecular fingerprint is a 2D molecular descriptor or molecular fingerprint.

[0036] In one embodiment, the molecular descriptor is selected from the group consisting of ABCIndex, AcidBase, AdjacencyMatrix, Aromatic, AtomCount, Autocorrelation, BCUT, BalabanJ, BaryszMatrix, BertzCT, BondCount, CarbonTypes, Chi, Constitutional, DetourMatrix, DistanceMatrix, EState, EccentricConnectivityIndex, ExtendedTopochemicalAtom, FragmentComplexity, Framework, HydrogenBond, InformationContent, KappaShapeIndex, Lipinski, McGowanVolume, MoeType, MolecularDistanceEdge, MolecularId, PathCount, Polarizability, RingCount, RotatableBond, SLogP, TopoPSA, TopologicalCharge, TopologicalIndex, VdwVolumeABC, VertexAdjacencyInformation, WalkCount, Weight, WienerIndex, and ZagrebIndex. In some embodiments, the parameters are calculated by the Mordred package.

[0037] In one embodiment, one or more structural and / or physicochemical properties include a molecular descriptor selected from the group consisting of SLogP, ATSC5v, ATSC8d, ATSC3Z, ABC, VSA_EState4, ATSC5dv, and ATSC6i. In some embodiments, the parameters are calculated by the Mordred package.

[0038] In one embodiment, the elution phase gradient (in an HPLC method for which training data or retention time is predicted) is a fixed gradient. In some embodiments, the HPLC method represented in the training data and further / or for which RT is predicted has a flow rate of 0.2 ml / min and parameters selected from elution powers of approximately 1.05, 1.50, and 1.95 at three time points such as 0, 15, and 30 minutes (determined for the mobile phase or its components, for example, as a summary value for all components of the mobile phase at each time point).

[0039] In one embodiment, the HPLC method parameters whose retention time is predicted in step (b) are constrained to be within a predetermined range and / or selected from a predetermined set of values, and further / or the training dataset includes a set of chromatographic data obtained using the HPLC method parameters within the range and / or the respective sets of values, wherein the HPLC method parameters whose retention time is predicted in step (b) are within the range and / or selected from the set of values.

[0040] In one embodiment, the elution phase gradient is a non-fixed gradient.

[0041] In one embodiment, the machine learning model is an extreme gradient boosted model (e.g., an extreme gradient boosted tree), a gradient boosted model (e.g., a gradient boosted tree), a random forest model, a Lasso regression model, or a support vector machine, preferably an extreme gradient boosted model.

[0042] In one embodiment, the machine learning model is trained to minimize the difference between the predicted retention time and the corresponding retention time in the training data.

[0043] In one embodiment, the machine learning model is trained using a dataset containing data for at least 100, at least 200, at least 300, at least 400, at least 500, or at least 600 compounds.

[0044] In one embodiment, the dataset includes at least two, three, four, or five sets of chromatographic data, each containing the retention time of the compound and associated HPLC method parameters.

[0045] In some embodiments, the training data includes multiple data points (e.g., at least 100, 200, 500, 1000, 1500), each data point including the molecular / physicochemical properties of the compound, the corresponding retention time, and HPLC method parameters. In some embodiments, the data includes multiple data points for the same compound using the same HPLC method, multiple data points for the same compound using different HPLC methods, and multiple compounds using the same HPLC method. It is advantageous for the training dataset to include data for different compounds, such as at least 100, at least 200, at least 300, at least 400, at least 500, or at least 600 compounds. It is also advantageous for the training data to include data points for different HPLC methods, such as at least 10, at least 20, at least 50, at least 100, or at least 150, or at least 200 different sets of HPLC method parameters (a set of HPLC method parameters is different if at least one method parameter is different). In some embodiments, the training dataset includes a metric representing the width of the peak corresponding to each compound (i.e., the peak relating to the retention time of each compound).

[0046] In one embodiment, HPLC is reversed-phase chromatography, normal-phase chromatography, size exclusion chromatography, ion exchange chromatography, or hydrophilic interaction liquid chromatography, and optionally, HPLC is reversed-phase chromatography or normal-phase chromatography.

[0047] In one embodiment, a machine learning model is trained using a set of predictive features selected from a larger set through a feature selection process, each of which is selected from molecular structural or physicochemical properties (e.g., molecular descriptors or molecular fingerprints) as well as HPLC method parameters.

[0048] In a second aspect, the present invention provides a computer implementation method for identifying a set of HPLC method parameters suitable for the separation of a compound in a composition comprising two or more compounds, the method being: (a) Performing any of the methods of the embodiments of the first aspect for multiple sets of HPLC method parameters, (b) Using the results of step (a), calculate one or more isolation performance metrics, (c) Identifying one or more sets of HPLC method parameters by applying one or more criteria to the separation performance metric. Includes.

[0049] A schematic diagram is shown in Figure 2B. In step 140, values ​​for one or more sets of HPLC method parameters are obtained. This may include obtaining values ​​for one or more HPLC method parameters from an optimization algorithm. In step 150, retention times (and optionally, a metric representing peak width) are predicted by a method of the first embodiment (for example, as shown in Figure 2A). In step 160, one or more separation performance metrics are calculated using the results from step 150. In step 170, one or more sets of HPLC method parameters are identified by applying one or more criteria to the separation performance metrics. In step 180, the results are made available for output, for example, by outputting them to a user via a user interface, or to a computing device or database.

[0050] The method of this embodiment may have any of the features described in relation to any other embodiment.

[0051] In one embodiment, the separation performance metric includes one or more of the following: i) the mean retention time difference between adjacent peaks corresponding to the predicted retention times of two or more compounds, ii) the gradient duration, and iii) a predictive metric representing the peak width, and optionally includes both i) and ii).

[0052] In one embodiment, the separation performance metric includes i) the mean retention time difference between adjacent peaks corresponding to the predicted retention times of two or more compounds (where the criterion is to maximize this mean retention time difference), ii) the gradient duration (where the criterion is to minimize this gradient duration), and / or iii) the predicted peak width (where the criterion is to minimize this peak width).

[0053] In one embodiment, one or more sets of HPLC method parameters in step (a) are generated by an optimization algorithm and optionally by a genetic algorithm.

[0054] In one embodiment, step (a) includes running a genetic algorithm until one or more termination criteria are met, optionally selected from i) a predetermined number of generations being reached, and ii) the difference between the separation performance metric for one or more sets of HPLC method parameters of the current iteration and the separation performance metric for one or more sets of HPLC method parameters of the immediately preceding iteration being less than a threshold.

[0055] In one embodiment, the genetic algorithm is initialized with a randomly selected set of HPLC method parameters, the genetic algorithm is initialized with a set of HPLC method parameters selected from a predetermined set or range of each HPLC method parameter, and / or the genetic algorithm is initialized with a set of HPLC method parameters provided by the user.

[0056] In one embodiment, one or more sets of HPLC method parameters are selected from each predetermined set and / or range (e.g., by a genetic algorithm).

[0057] In one embodiment, the method includes presenting the user with one or more sets (e.g., five) of HPLC method parameters that satisfy one or more criteria for the separation performance metric. The presentation to the user may be, for example, via a user interface to a computing device or database.

[0058] According to a third aspect, a method is provided for providing a tool for predicting the HPLC retention time of one or more compounds, the method comprising (a) obtaining a training dataset which includes one or more sets of chromatographic data for each compound, including retention times for each compound and associated HPLC method parameters, with respect to one or more structural and / or physicochemical property values ​​of one or more compounds; and (b) training a machine learning model to predict the retention time of a compound when subjected to HPLC using one or more HPLC method parameters, with respect to one or more structural and / or physicochemical property values ​​of the compounds and the values ​​of the HPLC method parameters as input.

[0059] The method of this embodiment may have any of the features described in relation to any other embodiment.

[0060] In another embodiment, a computer program product is disclosed that includes computer-readable instructions that, when executed by one or more processors, cause one or more processors to perform any embodiment of the method described herein.

[0061] In another embodiment, a non-temporary computer-readable medium is disclosed that stores computer-readable instructions causing one or more processors to perform any of the embodiments of the method when executed by one or more processors.

[0062] In another embodiment, a system is disclosed comprising at least one processor and at least one non-temporary computer-readable medium containing instructions when executed by at least one of the processors.

[0063] The following are presented as examples, but should not be interpreted as limitations on the scope of the patent claims. [Examples]

[0064] Example 1 This study aims to evaluate the use of ML to improve the development process of HPLC methods. To increase efficiency, a recommendation tool is developed that suggests appropriate parameters for a given sample mixture. These parameters should serve as a starting point for trained analysts to fine-tune the precise values ​​of various HPLC parameters. This tool utilizes a supervised ML model to predict the RT of the test substance in the sample. The model is trained using the following input data: i) molecules and their molecular descriptors, ii) HPLC method parameters, iii) HPLC column parameters from a hydrophobic subtraction model, and iv) chromatographic data.

[0065] This tool uses RT prediction to evaluate different combinations of method parameters to maximize the separation between test substances. A single-page web application is implemented to provide easy access to the user.

[0066] A further objective of this research is to reduce the number of different HPLC columns required in the HPLC method development process. Since different vendors sell columns with similar properties, an unsupervised clustering algorithm is used to group columns with similar properties.

[0067] method Technical Implementation All code was written in Python version 3.9.7 (Rossum, 2021). The machine learning model was implemented using Scikit-Learn version 1.0.2 (Pedregosa et al., 2011). The extreme gradient boosting model was implemented using the Scikit-Learning wrapper interface of XGBoost version 1.5.0 (Chen & Guestrin, 2016). Mol files, chemical descriptors, and fingerprints were generated using RDKit version 2022.03.1 ("RDKit: Open-source cheminformatics", nd; https: / / www.rdkit.org). The genetic algorithm was implemented using PyGAD version 2.17.0 (Fawzy, 2021).

[0068] Data acquisition and preprocessing Chromatography data Chromatography data was collected from the Empower Chromatography Data System, a chromatography data software. The chromatography data was downloaded in JavaScript Object Notation (JSON) format. Since each injection can be processed multiple times by the analyst, multiple results exist for each injection. It was assumed that the peaks were properly integrated and labeled in the chromatogram with the most recent result_id. From these results, the RT and labels of all integrated peaks, as well as other relevant information such as the method, were extracted and saved in a CSV file for further processing.

[0069] After all integrated peaks were downloaded, the data from both Empower locations was merged. Many of the downloaded peaks did not have names that could be linked to internal molecular identifiers (e.g., Roche numbers). This could be used to download molecular files that identified the molecules. To link abbreviations to Roche numbers, information from Roche's internal small molecule impurity database (SMIDB) and late-stage methods database (Excel file) was used. Information from SMIDB could be retrieved using the SMIDB API. The data from the late-stage methods database had to be manually merged before exporting the Excel file to CSV format. Both data sources were merged and matched with the peak names from the Empower dataset.

[0070] HPLC equipment method The parameter settings that describe how to perform an HPLC experiment are stored in the instrumentation method. These parameter settings directly affect the retention time of the test substance in the sample. Therefore, the parameters of this method are required as input features for the ML model. Data corresponding to the following parameters were extracted: Method_id (SAM document number), column, temperature, mobile phase A, mobile phase B, mobile phase C, mobile phase D, pH, gradient (time point and composition), and flow rate.

[0071] mobile phase composition The variable elution_power was introduced. The greater the elution power of the mobile phase composition, the shorter the expected retention time of the test substance. To calculate the "elution power" of the mobile phase, each component of the mobile phase and its proportion were extracted from the SAM document. Using this information, the molar percentage of each component in the mobile phase was calculated. To obtain the elution powers shown in Table 1, only the main solvents, namely water, acetonitrile, methanol, and isopropyl alcohol, were considered. The elution power was obtained by multiplying the molar percentage of each solvent by its elution intensity. See Table 2 for the elution intensities of the solvents. In NP, water has the highest elution intensity (i.e., more water = shorter retention time), whereas in RP, water has the lowest elution intensity (i.e., more water = longer retention time). Since only values ​​for NP were available (Trappe, 1940), it was decided to adopt the inverse NP value as the elution intensity in RP-LC. The elution power of the mobile phase is the sum of the elution intensities of each component (for example, the elution power of mobile phase A in SAM-0200368 is 0.98 + 0.04 = 1.02). [Table 1]

[0072] Gradient information The variables time_point_1, time_point_2, and time_point_3 were introduced to describe the mobile phase at three different time points. For each instrumentation method, these time points were manually extracted along with the mobile phase composition at that time. Figure 3 shows the locations of these time points in SAM-0200368. At each time point, the dissolution force was calculated by multiplying the dissolution force of each portion of the mobile phase by its dissolution force and summing these values. For example, at time point 2 in SAM-0200368, the mobile phase consists of 60% A and 40% B. Therefore, the dissolution force at this time point is calculated as 0.60*1.02 + 0.40*2.00 = 1.41. Table 3 shows the time points and dissolution forces in SAM-0200368. These six variables were used as features for a machine learning model to represent the gradient and mobile phase. [Table 2] [Table 3]

[0073] HPLC column information Access the ACDC database The Analytical Column Database (ACDC) contains information on all HPLC and GC columns in the PTDC database. Using the ACDC REST API, I downloaded information such as column ID, manufacturer, stationary phase type, diameter, particle size, product number, USP code, pore size, and surface area, and saved it locally as a CSV file.

[0074] Access to the USP Database Parameters for over 750 stationary phase hydrophobic subtraction models were downloaded from the United States Pharmacopeia (USP) webpage using a web scraper because the REST API was unavailable. Manual data download was not an option due to the constantly updating data. Using Google Chrome's developer tools, XMLHttpRequest (XHR) requests sent by the browser while loading the requested webpage data were intercepted. These XHR requests were simulated using a Python script. The responses sent by the webpage were stored locally in a CSV file.

[0075] A combination of analytical column information from the ACDC database and the PQRI database. Information extracted from ACDC and USP web pages was merged to obtain a dataset containing stationary phase information for columns used in SAM methods, including column dimensions, particle size, pore size, PQRI parameters, and features such as numbers describing the frequency of use of specific columns in SAM. Fuzzy string matching was used to merge the data sources based on stationary phase names.

[0076] chemical structure To predict retention times, molecular descriptors and molecular fingerprints were evaluated to represent the chemical structure of the molecules. The Integrated Roche Chemistry Information (IRCI) database is a web application that maintains the molecular structures of all registered molecules in Roche. Other databases for molecular structures, such as ChEMBL (https: / / www.ebi.ac.uk / chembl), may also be used. Using the IRCI REST API, mol files for each peak of the purified Empower dataset (approximately 600 molecules) were downloaded. Using RDKit, the mol files were converted to specific RDKit mol files, and molecular descriptors were computed using the Mordred package (Moriwaki et al., 2018). Fingerprints were generated using RDKit.

[0077] Combining individual data sources As the final step after collecting and preprocessing individual raw data sources, all the data was integrated to obtain two distinct datasets that could be immediately used to train ML models. One dataset holds molecular descriptors, and the other holds molecular fingerprints. Figure 4 shows a star schema representing the final datasets.

[0078] Retention time prediction We evaluated different ML algorithms using molecular descriptor datasets. The general procedure involved using the GridSearchCV method provided by Scikit-learn for hyperparameter tuning and a random 75 / 25 train-test split before performing 10-fold cross-validation on the training set. After determining ideal hyperparameter values, a new model was trained across the entire training set, and its performance was evaluated using the test set. The use of molecular fingerprints for RT prediction was evaluated only using XGB (purely due to time constraints; other methods are expected to be more appropriate).

[0079] Model Evaluation The performance of the model is measured by the correlation coefficient (R 2 ), mean absolute error (MAE), and mean absolute rate of error (MAPE) were used for evaluation. R is the most common metric for regression problems. 2 In addition to (Muller & Guido, 2016), we calculated MAE to give a sense of how good the prediction is in just a few minutes. We used MAPE to account for the magnitude of RT. 2 We used this method to select the best hyperparameters during grid exploration.

[0080] Random training-test split and unified training-test split Before training an ML model, the dataset needs to be split into a training set and a test set. The scikit-learn train_test_split method was used to perform a random split. The results of the model using a random train-test split showed a decrease in predictive performance at longer retention times, indicating that the random state defined by this method affects the predictive score. Therefore, a unified train-test split using an 80 / 20 split was implemented. To do this, the dataset was first sorted by retention time, and then observations every 5th time were added to the test set. Furthermore, since there were too few observations with RT > 30 minutes to achieve a 5:1 train-test ratio, it was decided to limit the retention time to 30 minutes.

[0081] Feature scaling For linear models and SVMs, it is important to scale features before training the model. If scaling is not applied, features with larger values ​​have a greater impact than features with smaller values ​​(Muller & Guido, 2016). To scale the input features, we used MinMaxScaler provided by Scikit-learn. Normally, each feature is scaled individually, but since the time-point and output features are related to each other (time points 1-3 and output points 1-3), we applied a special procedure. For both time points and output points, we created a NumPy array (Harris et al., 2020) that holds all values ​​from each time point to fit the scaler. In this way, all features have the same minimum and maximum values. After fitting the scaler, each feature was transformed individually. Compared to linear models and SVMs, tree-based models do not require scaling of the input data because each feature is processed individually (Muller & Guido, 2016).

[0082] Dummy model The dummy model serves as a baseline for evaluating the results of other models. If a model achieves a higher score than the dummy regressor, its predictions are considered better than those predicting random values ​​(Muller & Guido, 2016). The dummy regressor predicts the same output for each observation. In this case, it predicted the mean retention time from observations in the test set (11.6 minutes).

[0083] Feature Selection XGB When feature importance is calculated in XGB, models with different numbers of features can be evaluated. Reducing the number of features helps prevent overfitting of the model and thus improves predictive accuracy through better generalization (Muller & Guido, 2016). Furthermore, less complex models speed up both training and prediction. The following number of features were evaluated: [5, 10, 20, 50, 75, 100, 125, 150, 175, 200, 225, 250, 500, 640]. The “weight” importance scale from the XGB model was applied to select the nth most important feature.

[0084] Clustering of analytical columns Since different vendors sell columns with similar properties, we evaluated clustering that groups columns with similar properties based on a hydrophobic subtraction model. The goal of this approach was to reduce the number of column types in the laboratory. This can be achieved by an optimizer that predicts groups (clusters) of columns where all columns share similar properties. For clustering, we evaluated KMeans and DBSCAN. Since ion exchange capacity (c in the hydrophobic subtraction model) is pH-dependent, it was necessary to perform two clustering methods.

[0085] Principal component analysis Before applying the clustering algorithm, we evaluated principal component analysis (PCA) to reduce the number of features from five to two. By rotating the dataset, PCA transforms the dataset to yield uncorrelated features. After rotating the dataset, in many cases only a subset of features is selected based on their importance in explaining the data (Muller & Guido, 2016). Using two features makes it possible to plot the clustering results. Before applying PCA, we scaled all features using MinMaxScaler.

[0086] KMeans Using KMeans, the number of clusters must be defined by the user. This was done iteratively by changing the number of clusters, performing PCA on the dataset, and then plotting the results. Finding the ideal number of clusters is crucial. Too many clusters will not achieve column reduction, while too few clusters will include columns that do not produce similar output. Clustering was also applied to datasets without prior PCA using the defined number of clusters.

[0087] DBSCAN Compared to KMeans, the number of clusters is defined by the hyperparameters eps and min_samples. eps determines the maximum distance between data points that should be considered "neighbors" to each other. min_samples is the number of observations that must be in the same neighborhood to form a cluster. If the number of observations in the same neighborhood is less than min_samples, these observations are declared as noise (Muller & Guido, 2016). Since all columns should be represented by clusters, min_samples was fixed at 0. The following eps values ​​were tested: [0.04, 0.06, 0.08, 0.1].

[0088] Recommended Tools The objective of the recommended tool is to find the appropriate HPLC instrument parameters for separating a given set of molecules. To achieve this, the tool uses an ML model for predicting retention times to find the combination of method parameters that maximizes the separation between the analytes. In total, there are 18 method parameters to be determined. These parameters are all features in the ML model: flow rate, temperature, pH, timepoint_1, timepoint_2, timepoint_3, elution_power_1, elution_power_2, elution_power_3, column_length, column_inner_diameter, column_particle_size, column_pore_size, H (hydrophobicity), S (steric interaction), A (hydrogen bond acidity), B (hydrogen bond basicity), c (ion exchange capacity) (https: / / www.usp.org / resources / pqri-approach-column-equiv-tool). All other features, which are molecular descriptors used by the ML model, are based on the selected analytes.

[0089] Optimization method We evaluated two different optimization methods: brute force and evolutionary algorithms.

[0090] Using brute force, all possible combinations of method parameters must be tested to find the combination that yields the best separation of the test substance. Using 18 parameters, some of which have over 40 distinct values, results in a massive dataset that is impossible to process by computer. We evaluated whether the dataset size could be reduced by limiting the possible values ​​of each parameter, but there are still millions of combinations to test. Therefore, we considered two evolutionary algorithms: differential evolution (DE) and genetic algorithms (GA). Evolutionary algorithms are metaheuristics (algorithmic frameworks) and are often inspired by nature. The goal of metaheuristics is to solve complex optimization problems (Bianchi et al., 2008). In this study, the optimization problem is to find the 18 method parameters that maximize separation. The strength of metaheuristics lies in their ability to efficiently explore search spaces that are too large for other methods such as brute force (Blum & Roli, 2003). Both DE and GA are population-based methods, meaning that multiple candidate solutions are maintained and improved over time by the algorithm (Teghem, 2010). The search space can be constrained by defining its boundary using DE and GA. In contrast to DE, GA allows defining the search space using distinct values. Since distinct values ​​are a requirement for this work, we decided to continue developing the recommendation tool using GA.

[0091] Genetic algorithms for method parameter selection Using PyGAD, a genetic algorithm (GA) can be implemented by providing a goodness-of-fit function for evaluating candidate solutions, defining a gene space (search space), and setting parameters to guide the optimization process. The defined parameters include, among others, the number of generations, the number of parental crosses, the number of solutions per generation, as well as the mutation rate and crossover behavior. Figure 5 illustrates the key elements of the genetic algorithm. A solution, also called a chromosome, consists of genes. One gene represents one feature, such as flow rate or temperature. Thus, one solution holds all the information necessary to generate an instrumental method. In every generation, genes from solutions (parents) that have reached a high goodness-of-fit value are exchanged through crossover to produce the next generation (offspring). These offspring are then evaluated again using the goodness-of-fit function. In addition to crossover, mutations occur in randomly selected genes. In the mutation process, the current value is exchanged for a new value from the gene space of that particular gene.

[0092] Figure 5 shows the general procedure for the optimization process using GA. The first step of the process is to define the molecules to be separated by providing Roche numbers. Using the Roche numbers, mol files are downloaded from IRCI and molecular descriptors are calculated for each molecule. Next, GA generates first-generation solutions by randomly selecting values ​​from the gene space for each gene to create the solution. The generated descriptors and method parameters are merged to obtain a solution and the retention time for each test substance is predicted. The goodness of fit value of the current solution is evaluated using the predicted retention times and Equation 1. The goodness of fit function takes into account the mean retention time difference (Δi) and gradient duration (t) between adjacent peaks (n). A higher goodness of fit indicates better expected separation between all test substances. The gradient duration in the goodness of fit function is added as a penalty term to limit the execution time. Based on the results of the first generation, GA creates new candidate solutions through crossover and random mutation among the best solutions of the first generation. The process of calculating the goodness of fit for all solutions of the second generation is repeated. If one of the new solutions achieves a higher degree of fit than the first-generation best solution, this solution is stored as the best solution. This process is repeated until a predetermined number of generations are reached. Then, the best_solution is used to configure the device method.

number

[0093] Implementation of genetic algorithms The optimizer was configured to run 100 generations using 20 solutions each. To create a new generation, 10 low-fit solutions from the previous generation were replaced with 10 new solutions created by crossover and mutation of 10 high-fit solutions. This behavior was achieved by using stationary-state selection as the parental selection type for the parameters (M. Mitchell, 1996). The mutation type was set to random, and the number of mutation genes was set to 1. The number of genes was set to 14, even though 18 method parameters had to be selected. This is because only specific combinations of parameters H, S, A, B, and c, i.e., cluster centers, are allowed. Without this constraint, the optimizer might select parameters that lead to columns that do not exist. The gene space of the column was set between 0 and 42, corresponding to the number of unique stationary phases available in the dataset. This method allowed for evaluation of the optimizer by comparing predicted retention times with measured retention times, as every number in the gene space corresponds to exactly one stationary phase. For future use, the tool can also suggest other columns within the same cluster as the predicted column. Therefore, the analyst can select a column already available in their laboratory. Based on the selected cluster number, parameters H, S, A, B, and c were added to the solution. c values ​​(c_28, c_70) were selected according to the pH of the solution (e.g., c_28 means a pH less than 7, e.g., 2.8, and c_70 means pH 7.0; see https: / / www.usp.org / resources / pqri-approach-column-equiv-tool). It was decided not to apply PCA before clustering so that the predicted parameters corresponded to exactly one column. The gene space for column dimensions was fixed at 150 mm × 4.6 mm. The particle size was set to 3.0, between the common 2.7 μm and 3.5 μm particles. To avoid overpressure of the HPLC system in combination with the specified column dimensions, the gene space of the flow rate was set to [0.75, 1.0, 1.25].Two options (time point and elution power) were defined to define the gene space of the gradient. The gradient may be fixed. This gradient progresses from 5%B to 95%B in 30 minutes. If the gradient is not fixed, there are no restrictions, and GA recommends a gradient.

[0094] Optimization constraints Constraints were introduced to prevent the optimizer from proposing impossible values. The following constraints were defined: • If time point 1 ≤ time point 2 ≤ time point 3, the execution time can only increase with time. • Welding force 1 ≤ Welding force 2 ≤ Welding force 3: The welding force must remain constant or increase along the gradient. • RT final elution peak ≤ time point 3: The peak should elute during the gradient, not during the column washing process. • If time point 2 = time point 3, then elution force 2 = elution force 3: If time point does not increase (i.e., only one step in the gradient), then elution force cannot increase either.

[0095] Each time a constraint was violated, the goodness-of-fit value was multiplied by 0.1.

[0096] Testing recommended tools To evaluate the optimizer, two instrumental methods and their corresponding standards conformity tests (SSTs) were randomly selected. For evaluation, a new XGB model was trained using all data except for the Roche number / method_id combinations from the selected instrumental methods. Parameters were proposed by the optimizer using both gradient options. If columns were not available in standard dimensions, the optimizer was rerun with adjusted parameters from existing columns to obtain correct retention time predictions. The lab was measured using the optimized parameters with LC-MS (Agilent 1290 LC and Agilent 6150 MSD). Results were evaluated by comparing the predicted retention time with the measured retention time. In addition, retention times were predicted for all labs using the parameters described in the original methods.

[0097] Web application A web application was implemented using Ploty Dash ("Plotly Technologies Inc. Collaborative data science", 2015). This allows the analyst to input multiple test substances by providing information that enables the identification of compounds, such as Roche numbers. Furthermore, the analyst can make a choice between two gradient options. Because the results of GA (and other metaheuristics) can vary, the tool runs the optimization process multiple times (e.g., five times). This variation is caused by the random generation of the first generation, as well as the crossover and mutation behavior of the algorithm. A trained analyst selects the run with the highest overall goodness-of-fit value, or selects a run based on available columns or predicted RT (e.g., a shorter RT).

[0098] result Data acquisition and preprocessing Chromatography data A total of 523,038 injections from BS10 (1,760,386 peaks) and 152,330 injections from BS12 (424,164 peaks) were downloaded (accessed on 08.06.2022). After preprocessing the chromatographic data, a total of 1,122,540 peaks with known SAM documents remained. Roche numbers could be assigned to 513,877 of these peaks. Because the dataset retains the same information multiple times (same molecule and same method_id), the data was grouped by Roche number and method_id, and the mean retention time and standard deviation were calculated. This resulted in 1,800 unique Roche number / method_id combinations and a total of 600 unique Roche numbers.

[0099] HPLC equipment method We processed 240 different SAM documents, including manual extraction of mobile phase compositions and gradient programs.

[0100] HPLC column information A total of 1993 unique columns (based on product numbers) were downloaded from ACDC. These columns were manually linked to SAM documents. Of these 1993 columns, 107 were used in one of the SAMs. 757 different column types were available on the USP webpage (accessed May 2022). The downloaded parameters of the hydrophobic subtraction model were linked to the columns used in the SAM document. After linking, 94 different columns (based on product numbers), including dimensions and hydrophobic subtraction model parameters, remained in the dataset.

[0101] chemical structure We computed all 1613 available 2D molecular descriptors from the Mordred package. All descriptors that could not be computed for all molecules were later removed from the dataset. This resulted in a dataset with 622 different descriptors. Using RDKit, we computed a 1024-bit morgan fingerprint for each mol file.

[0102] Retention time prediction using molecular descriptors Evaluation of various machine learning models The linear Lasso model, using the following hyperparameters, namely alpha: 0.001, tolerance: 1e-06, and max_iterations: 500, produced a prediction score of 0.663 (R 2 ) was achieved. SVR was 0.743 R using C:1000 and gamma:0.01. 2 And it achieved an MAE of 2.4 minutes. The tree-based model with the lowest predictive performance, using bootstrap: True, max_depth: 16, min_samples leaf: 1, num_estimators: 175, achieved an R&D score of 0.770. 2 It was a random forest. GB and XGB were R 2These models showed similar results of 0.802 and 0.811, respectively. For GB, a learning rate of 0.1 was used, along with a max_depth of 5, a min_samples leaf of 100, and an estimator of 1500. To train the XGB model, a learning rate of 0.05, a max_depth of 4, a max_leaves of 0, a min_child weight of 4, and an estimator of 750 were used. The dummy regressor used to determine the baseline score achieved an MAE of 5.9 minutes by consistently predicting the mean retention time of the training data. All evaluated models surpassed this baseline score. The results of the evaluated models are summarized in Table 4, and the prediction error plots are shown in Figure 7. XGB and GB showed good fit across the entire RT range, while RF and Lasso overestimated RT in the lower range and underestimated RT for observations with RT > 20 minutes. SVR achieved similar performance across the entire RT range, but was generally lower than XGB and GB. The results show that the two gradient boosting models have the highest predictive performance. Since training the XGB model is significantly faster compared to GB, we decided to further optimize the XGB model. [Table 4]

[0103] XGB model tuning We further improved the performance of the XGB model by evaluating "unified training-test splitting" and applying feature selection.

[0104] Unified training-test splitting Figure 8 shows histograms of both sampling methods before limiting the retention time. Using this sampling method, R 2We increased the value from 0.811 to 0.830, while decreasing the MAE from 1.9 minutes to 1.6 minutes. We used the same hyperparameter settings as described in subsection 3.3.1. Figure 9 shows the 20 most important features of the XGB model when using a unified train-test split. Apart from instrumentation method features, the most important features are as follows: • SLogP: Octanol-water partition coefficient (Wildman & Crippen, 1999). • ATSC: Autocorrelation of topological structures, also known as central Moreau-Broto autocorrelation. ATSC measures the distribution of atomic properties on a molecular graph (DR. Todeschini & Consonni, 2020). • ABC: An atomic bond affinity index that shows excellent correlation with the heat of formation of alkanes (Estrada, 2008). • VSA_EState: Hybridization of van der Waals surface area and electrical topological state (Guha & Willighagen, 2012).

[0105] Feature Selection Table 5 shows the model performance using various numbers of features. The best score was achieved using 65 of the most important features. The required features particle_size and inner_diameter were not among the top 65, so these two features were added manually. Feature selection was used to reduce the number of features from 640 to 67 while increasing the prediction score. The following hyperparameters were used for evaluation: gamma: 0, learning_rate: 0.05, max_depth: 4, max_leavs: 0, min_child_weight: 4, n_estimators: 750. [Table 5]

[0106] Hyperparameter tuning after feature selection After significantly reducing the number of features in the model, the hyperparameters of XGB were re-evaluated using the parameter grid shown in the following code list. param_grid_feature_selection={ 'n_estimators':[1,10,20,50,100,200,500,750,1000,1250,1500], 'learning_rate':[0.01,0.05,0.1], 'max_depth':[3,4,5], 'max_leaves':[0], 'min_child_weight':[4], 'gamma':[0]}

[0107] Figure 10 shows the results of varying the values of n_estimators, max_depth, and learning_rate. The best R2 was achieved using the following parameters: n_estimators: 750, learning_rate: 0.05, max_depth: 4,'max_leavs: 0, min_child_weight: 4, and gamma: 0. All other parameters used their default values. The unified training-test split and feature selection, followed by hyperparameter tuning, increased R 2 from 0.811 to 0.827, decreased MAE from 1.9 minutes to 1.6 minutes, and decreased MAPE from 26.5% to 21.5%. Table 6 shows the average test scores of 10-fold CV as a function of the number of estimators. Using more than 750 estimators results in a slight decrease in the prediction score, indicating overfitting. Figure 11 shows the prediction error and residual plots of the final model.

Table 6

[0108] Retention Time Prediction Using Molecular Fingerprints The results using molecular fingerprinting and random training-test splitting for RT prediction are shown in Figure 12. This model has an R of 0.810. 2 It achieved a MAE of 1.9 min and a MAPE of 26.4%. These values ​​are comparable to models using molecular descriptors. The best parameters evaluated using GridSearchCV were a learning_rate of 0.05, 3000 estimators, a max_depth of 4, a max_leaves of 0, a min_child_weight of 4, and a gamma of 0.

[0109] Clustering of analytical columns Clustering using PCA The reduction from five features to two features (first and second principal components) can explain approximately 85% of the dataset's variance. Figure 13 shows the results of KMeans clustering after applying PCA. The pH dependence of the ion exchange parameter "c" can be seen by comparing the cluster distributions in both plots. As explained, when using DBSCAN, all columns should form clusters, so min_samples was fixed to 0. Figure 14 shows the clusters formed using DBSCAN in combination with PCA using different values ​​for eps. We decided to use the KMeans algorithm as the optimizer because KMeans can also predict clusters for new observations (Pedregosa et al., 2011).

[0110] optimizer We decided to omit the PCA process and use 43 clusters instead of 30 to test the optimizer. Using 43 clusters (i.e., the number of different stationary phases in the dataset), the optimizer evaluates the parameters of one particular column. In this way, the actual column parameters, rather than cluster-centric parameters, were used for prediction, allowing us to compare the predicted retention time with the measured retention time. For the optimizer evaluation, we randomly selected two SAM methods, namely SAM-0114188 and SAM-0113392.

[0111] Comparison of measured RT and predicted RT using SAM method parameters The initial test involved predicting the elution time (RT) for all molecules described in one of two SAM literatures. The optimizer model was trained independently of the test set, except that all Roche number / method_id combinations from the SAMs were omitted before training the model. Figure 15 shows the measured RT (from Empower data) and predicted RT for each molecule using the specified method, with the same method parameters. The overall accuracy of the predictions was good, with MAEs of 0.10 min (SAM-0114188) and 1.09 min (SAM-0113392). For SAM-0114188, the elution order of the predicted RT matched the measured result. For SAM-0113392, changes in the elution order were observed for peak numbers 2 and 3 (Figure 15b).

[0112] Comparison of predicted RT and measured RT using optimizer output SAM-0114188 Table 7 shows the optimizer output for the molecules used in SAM-0114188 when a fixed gradient was not used. The optimizer was run five times, and each solution had the same goodness of fit. Method parameters differed slightly between each solution but were within the same range (e.g., the suggested pH was acidic in all solutions). 5 回目The proposed method parameters (index 4) for the execution were evaluated in the laboratory. Cluster 6 corresponded to Waters' Symmetry C18 column. Mobile phase A consisted of water + 0.1% TFA, and mobile phase B consisted of acetonitrile + 0.1% TFA. [Table 7]

[0113] Table 8 shows the optimizer output for SAM-0114188 using a fixed gradient. Cluster 6 corresponded to Waters' Symmetry C18 column. Mobile phase A was water + 0.1% TFA, and mobile phase B was acetonitrile + 0.1% TFA. [Table 8]

[0114] A comparison of predicted and measured RTs is shown in Figure 16. The proposed method parameters without a fixed gradient (Figure 16a) resulted in good separation between all peaks and peaks eluted in the correct order. The difference between predicted and measured RTs was not within the MAE range for any peak. Peak 2 eluted when %B reached 95 during the gradient column washing step. Another test was performed by increasing B by 5% at each time point of the predicted gradient. The difference in RT between predicted and measured decreased for all peaks, however, the RT difference for peak 2 was still over 5 minutes (see Figure 16b). Using the “fixed” gradient condition, the measured peaks showed good separation and the correct elution order. In contrast to the results without a fixed gradient, the elution of the test substance was too early, as shown in Figure 16c.

[0115] SAM-0113392 Table 9 shows the optimizer output for SAM-0113392 without gradient limiting. The solutions shown are those tested in the laboratory. Cluster 1 corresponds to a Phenomenex Kinetex Biphenyl column. The following mobile phases were used to achieve a pH of 3: A: Water + 0.01% TFA, B: Acetonitrile + 0.01% TFA. Figure 17a shows a comparison of the predicted RT and measured RT by the optimizer. Peak 0 eluted excessively early compared to the predicted RT, while peaks 2, 3, and 4 eluted too late and did not show good separation from each other. [Table 9]

[0116] Table 10 shows the optimizer output for SAM-0113392 using a fixed gradient. The solutions shown are those tested in the laboratory. Cluster 11 corresponded to Waters' Acquity UPLC CSH C18. Mobile phase A consisted of a 10 mM ammonium acetate aqueous solution in water adjusted to pH 6 with acetic acid. Mobile phase B consisted of acetonitrile + 0.01% acetic acid. Figure 17b shows a comparison of the predicted RT and measured RT by the optimizer. Peak 1 eluted much earlier than predicted, while the elution order of peaks 3 and 4 changed. Compared to results without gradient constraints, the measured RT was more accurate, and good separation between all peaks was observed. [Table 10]

[0117] Web application Figure 18 shows the graphical user interface of the web application prototype. The web app was created using Plotly Dash ("Plotly Technologies Inc. Collaborative data science", 2015) and allows the user to define up to five molecules, which are listed as Roche numbers. The application allows the user to choose between a fixed gradient, where only flow rate, temperature, pH, and column are optimized, and an unrestricted option, where all parameters except column dimensions are optimized. The optimization process can be started by clicking the start button. Once the optimization is performed, the solution appears on the results card. From the generated solutions, a trained analyst selects the one with the best goodness of fit. If the proposed gradient seems unreasonable, for example, if it is too flat, the analyst may select a different solution. Often, multiple solutions have the same goodness of fit value. In this case, the solution can also be selected based on the available columns.

[0118] conclusion In summary, we trained an ML model using a dataset of available HPLC data and then used it to optimize the development of analytical methods using GA. Using the developed tools, we can propose a set of predefined HPLC method parameter settings for a test substance that can serve as a starting point for analytical chemists. To evaluate the different solutions proposed by GA, we predicted the RT of the test substance using an XGB model. The XGB model was trained using n=1191 observations, each consisting of 49 molecular descriptors and 18 method parameters. This model was then trained using R 2We achieved a time interval of 0.827 and a MAE of 1.6 minutes. A web application prototype was implemented to provide access to the tool. Based on predicted RT using optimized parameters, the tool was able to find appropriate settings for all evaluated cases. To our knowledge, a method for predicting RT considering method parameters has not yet been developed in other studies. We expect that adding more data to the training dataset will improve the RT prediction accuracy of the ML model. Once deployed, the tool could potentially increase efficiency in the development process of new HPLC methods by reducing the need for costly and time-consuming step-by-step methods.

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[0120] Embodiment Further specific embodiments of the present invention are listed below. The specific embodiments described herein are provided as examples, not as limitations. Any subtitles in this specification are included for convenience only and should not be construed as limiting this disclosure.

[0121] 1. In one embodiment, a computer implementation method for predicting the HPLC retention time of one or more compounds is disclosed, and this method is (a) Obtaining values ​​for one or more structural and / or physicochemical properties of the compound and one or more HPLC method parameters, (b) Using a machine learning model to predict the retention time of each of the compounds when subjected to HPLC using one or more HPLC method parameters. Includes, The machine learning model is trained using a training dataset, which includes the molecular structural and / or physicochemical properties of one or more compounds, and for each compound, includes one or more sets of chromatographic data, including retention times for each compound and associated HPLC method parameters.

[0122] 2. In one embodiment, the method of Embodiment 1 is disclosed, wherein a machine learning model further predicts a metric representing peak width, and one or more sets of chromatographic data in the training dataset further include a metric representing the peak width of each compound.

[0123] 3. In one embodiment, the method of Embodiment 1 or 2 is disclosed, in which one or more compounds are individually selected from pharmaceutically active agents and their degradable organisms.

[0124] 4. In one embodiment, any of the methods described in Embodiments 1 to 3 is disclosed, wherein the HPLC method parameters are selected from the group consisting of HPLC type, flow rate, temperature, pH, column length, column inner diameter, column particle size, column pore size, column steric interaction, column hydrogen bond acidity, column hydrogen bond basicity, column ion exchange capacity (c_28), column ion exchange capacity (c_70), and one or more metrics that define the elution phase gradient.

[0125] 5. In one embodiment, any of the methods in Embodiments 1 to 4 is disclosed, wherein the HPLC method parameters include one or more parameters selected from the group consisting of column length, column inner diameter, column particle size, column pore size, column steric interaction, column hydrogen bond acidity, column hydrogen bond basicity, column ion exchange capacity (c_28), column ion exchange capacity (c_70), and one or more metrics that define the elution phase gradient, and optionally include one or more parameters selected from the group consisting of HPLC type, flow rate, temperature, and pH.

[0126] 6. In one embodiment, a method according to any of Embodiments 1 to 5 is disclosed, wherein the HPLC method parameters include one or more parameters selected from the group consisting of column length, column inner diameter, column particle size, column pore size, column stereointeraction, column hydrogen bond acidity, column hydrogen bond basicity, column ion exchange capacity (c_28), column ion exchange capacity (c_70), and one or more metrics that define the elution phase gradient.

[0127] 7. In one embodiment, one or more metrics that define the elution phase gradient are (i) the elution power of each of the multiple mobile phases, and / or (ii) a metric that defines the time-dependent change in the proportions of multiple mobile phases during elution (optionally, one or more metrics that define the time-dependent change in the proportions of multiple mobile phases during elution include one or more time point values ​​corresponding to the change in the rate of change of the mobile phase proportions, and / or values ​​for the rate of change of the mobile phase proportions at one or more time points during elution), and / or a metric that describes a function representing the change in the proportion of mobile phases in one or more regions (e.g., each of) of the gradient, and / or (iii) The elution power of the mobile phase at two or more (e.g., three) different time points (optionally, the mobile phase may include multiple mobile phases, and the elution power at a given time point is determined by summing the elution power of each of the multiple mobile phases, weighted according to their respective proportions). One of the methods of Embodiments 1 to 6, including the above, is disclosed.

[0128] 8. In one embodiment, any of the methods of Embodiments 1 to 7 is disclosed, wherein one or more physicochemical properties include one or more molecular descriptors, and further / or one or more molecular structural properties include a molecular fingerprint and / or one or more structural molecular descriptors.

[0129] 9. In one embodiment, the method of Embodiment 8 is disclosed, wherein the structural molecular descriptor and / or molecular fingerprint is a 2D molecular descriptor or molecular fingerprint.

[0130] 10. In one embodiment, any of the methods of Embodiments 1 to 9 is disclosed, wherein one or more structural and / or physicochemical properties include a molecular descriptor selected from the group consisting of SLogP, ATSC5v, ATSC8d, ATSC3Z, ABC, VSA_EState4, ATSC5dv, and ATSC6i.

[0131] 11. In one embodiment, any of the methods in embodiments 6 to 10 is disclosed, wherein the elution phase gradient is a fixed gradient.

[0132] 12. In one embodiment, any of embodiments 1 to 11 is disclosed, in which the HPLC method parameters for which retention times are predicted in step (b) are constrained to be within a predetermined range and / or selected from a predetermined set of values, and further / or the training dataset includes a set of chromatographic data obtained using the HPLC method parameters within the range and / or the respective sets of values, and the HPLC method parameters for which retention times are predicted in step (b) are within the range and / or selected from the set of values.

[0133] 13. In one embodiment, any of the methods in Embodiments 6 to 10 is disclosed, wherein the elution phase gradient is a non-fixed gradient.

[0134] 14. In one embodiment, any of the methods of Embodiments 1 to 13 is disclosed, in which the machine learning model is an extreme gradient boosted model (e.g., an extreme gradient boosted tree), a gradient boosted model (e.g., a gradient boosted tree), a random forest model, a Lasso regression model, or a support vector machine, preferably an extreme gradient boosted model.

[0135] 15. In one embodiment, any of the methods of Embodiments 1 to 14 is disclosed, in which a machine learning model is trained to minimize the difference between the predicted retention time and the corresponding retention time in the training data.

[0136] 16. One embodiment is disclosed in which a machine learning model is trained using a dataset containing data for at least 100, at least 200, at least 300, at least 400, at least 500, or at least 600 compounds, according to any of embodiments 1 to 15.

[0137] 17. In one embodiment, the method of Embodiment 16 is disclosed, wherein the dataset includes at least two, three, four, or five sets of chromatographic data, each containing the retention time of the compound and associated HPLC method parameters.

[0138] 18. In one embodiment, any of the methods of Embodiments 1 to 17 is disclosed, wherein HPLC is reversed-phase chromatography, normal-phase chromatography, size exclusion chromatography, ion exchange chromatography, or hydrophilic interaction liquid chromatography, and optionally HPLC is reversed-phase chromatography or normal-phase chromatography.

[0139] 19. In one embodiment, a machine learning model is trained using a set of predictive features selected from a larger set through a feature selection process, the larger set of predictive features being selected from molecular structural or physicochemical properties (e.g., molecular descriptors or molecular fingerprints) as well as HPLC method parameters, as disclosed in any of Embodiments 1 to 18.

[0140] 20. In one embodiment, a computer implementation method is disclosed for identifying a set of HPLC method parameters suitable for separating a compound in a composition comprising two or more compounds, wherein the method is (a) Performing one of the methods from Embodiments 1 to 19 for multiple sets of HPLC method parameters, (b) Using the results of step (a), calculate one or more isolation performance metrics, (c) Identifying one or more sets of HPLC method parameters by applying one or more criteria to the separation performance metric. Includes.

[0141] 21. In one embodiment, the method of Embodiment 20 is disclosed, in which the separation performance metric includes one or more of the following: i) the mean retention time difference between adjacent peaks corresponding to the predicted retention times of two or more compounds, ii) the gradient duration, and iii) a prediction metric representing the peak width, and optionally includes both i) and ii).

[0142] 22. In one embodiment, a method of Embodiment 20 or 21 is disclosed in which the separation performance metric includes i) the mean retention time difference between adjacent peaks corresponding to the predicted retention times of two or more compounds (where the criterion is to maximize this mean retention time difference), ii) the gradient duration (where the criterion is to minimize this gradient duration), and / or iii) the predicted peak width (where the criterion is to minimize this peak width).

[0143] 23. In one embodiment, one or more sets of HPLC method parameters in step (a) are generated by an optimization algorithm and optionally by a genetic algorithm, as disclosed in any of embodiments 20 to 22.

[0144] 24. In one embodiment, a method of Embodiment 23 is disclosed, in which step (a) comprises running a genetic algorithm until one or more termination criteria are met, optionally selected from i) a predetermined number of generations being reached, and ii) the difference between a separation performance metric for one or more sets of HPLC method parameters of the current iteration and a separation performance metric for one or more sets of HPLC method parameters of the immediately preceding iteration being less than a threshold.

[0145] 25. In one embodiment, a method of Embodiment 23 or 24 is disclosed in which the genetic algorithm is initialized with a randomly selected set of HPLC method parameters, the genetic algorithm is initialized with a set of HPLC method parameters selected from a predetermined set or range of each HPLC method parameter, and / or the genetic algorithm is initialized with a set of HPLC method parameters provided by the user.

[0146] 26. In one embodiment, a method of any of Embodiments 1 to 25 is disclosed, in which one or more sets of HPLC method parameters are selected from each predetermined set and / or range (e.g., by a genetic algorithm).

[0147] 27. In one embodiment, any of the methods disclosed in embodiments 20 to 26 is disclosed, which includes presenting the user with one or more sets (e.g., five) of HPLC method parameters that satisfy one or more criteria to be used as the separation performance metric.

[0148] 28. In one embodiment, a computer program product is disclosed which includes computer-readable instructions that cause one or more processors to perform any of the methods of Embodiments 1 to 27 when executed by one or more processors.

[0149] 29. In one embodiment, a non-temporary computer-readable medium is disclosed that stores computer-readable instructions causing one or more processors to perform any of the methods of Embodiments 1 to 27 when executed by one or more processors.

[0150] 30. In one embodiment, a system is disclosed, and this system is At least one processor, A non-temporary computer-readable medium containing instructions that cause at least one processor to perform any of the methods of Embodiments 1 to 27 when executed by at least one processor, and It is equipped with.

Claims

1. A computer implementation method for predicting the HPLC retention time of one or more compounds, (a) Obtaining values ​​for one or more structural and / or physicochemical properties of the compound and one or more HPLC method parameters, (b) Using a machine learning model and one or more HPLC method parameters, predict the retention time of each of the compounds when subjected to HPLC. Includes, A computer implementation method wherein the machine learning model is trained using a training dataset, the training dataset comprises the molecular structural properties and / or physicochemical properties of one or more compounds, and for each compound, comprises one or more sets of chromatographic data including retention times for each compound and associated HPLC method parameters.

2. The method according to claim 1, wherein the machine learning model further predicts a metric representing peak width, and one or more sets of chromatographic data in the training dataset further include a metric representing the peak width of each of the compounds.

3. The method according to claim 1 or 2, wherein the HPLC method parameters are selected from the group consisting of HPLC type, flow rate, temperature, pH, column length, column inner diameter, column particle size, column pore size, column steric interaction, column hydrogen bond acidity, column hydrogen bond basicity, column ion exchange capacity (c_28), column ion exchange capacity (c_70), and one or more metrics that define the elution phase gradient, for example, the HPLC method parameters include one or more parameters selected from the group consisting of column length, column inner diameter, column particle size, column pore size, column steric interaction, column hydrogen bond acidity, column hydrogen bond basicity, column ion exchange capacity (c_28), column ion exchange capacity (c_70), and one or more metrics that define the elution phase gradient.

4. The method according to any one of claims 1 to 3, wherein the one or more physicochemical properties include one or more molecular descriptors, and further / or the one or more molecular structural properties include a molecular fingerprint and / or one or more structural molecular descriptors, and optionally the one or more structural and / or physicochemical properties include a molecular descriptor selected from the group consisting of SLogP, ATSC5v, ATSC8d, ATSC3Z, ABC, VSA_ESTate4, ATSC5dv, and ATSC6i.

5. The method according to any one of claims 1 to 4, wherein the HPLC is reversed-phase chromatography, normal-phase chromatography, size exclusion chromatography, ion exchange chromatography, or hydrophilic interaction liquid chromatography, and optionally the HPLC is reversed-phase chromatography or normal-phase chromatography.

6. The method according to any one of claims 1 to 5, wherein the machine learning model is trained using a set of predictive features selected from a larger set through a feature selection process, the larger set of predictive features being selected from molecular structural properties or physicochemical properties (e.g., molecular descriptors or molecular fingerprints) and HPLC method parameters, respectively.

7. A computer implementation method for identifying a set of HPLC method parameters suitable for separating a compound in a composition containing two or more compounds, (a) Performing the method according to any one of claims 1 to 6 for a plurality of sets of HPLC method parameters, (b) Using the results of step (a), calculate one or more isolation performance metrics, (c) Identifying one or more sets of HPLC method parameters by applying one or more criteria to the separation performance metric. A method that includes this.

8. The method according to claim 7, wherein the separation performance metric includes one or more of the following: i) the average retention time difference between adjacent peaks corresponding to the predicted retention times of the two or more compounds, ii) the gradient duration, and iii) a prediction metric representing the peak width, and optionally includes both i) and ii).

9. The method according to claim 7 or 8, wherein the separation performance metric includes i) the mean retention time difference between adjacent peaks corresponding to the predicted retention times of the two or more compounds (where the criterion includes maximizing the mean retention time difference), ii) the gradient duration (where the criterion includes minimizing the gradient duration), and / or iii) the predicted peak width (where the criterion includes minimizing the peak width).

10. The method according to any one of claims 7 to 9, wherein one or more sets of HPLC method parameters in step (a) are generated by an optimization algorithm and optionally by a genetic algorithm.

11. The method according to claim 10, wherein step (a) comprises running the genetic algorithm until one or more stopping criteria are met, the stopping criteria being optionally selected from i) a predetermined number of generations being reached, and ii) the difference between a separation performance metric for one or more sets of HPLC method parameters of the current iteration and a separation performance metric for one or more sets of HPLC method parameters of the immediately preceding iteration being less than a threshold.

12. The method according to any one of claims 7 to 11, comprising presenting to the user one or more sets (e.g., five) of HPLC method parameters that satisfy one or more criteria with respect to the separation performance metric.

13. A computer program product comprising computer-readable instructions that cause one or more processors to perform the method according to any one of claims 1 to 12 when executed by one or more processors.

14. A non-temporary computer-readable medium storing computer-readable instructions that cause one or more processors to perform the method according to any one of claims 1 to 12 when executed by one or more processors.

15. At least one processor, A non-transient computer-readable medium containing an instruction that, when executed by the at least one processor, causes the at least one processor to perform the method according to any one of claims 1 to 14. A system equipped with these features.

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