Methods and devices for chromatographic separation
The method addresses the challenge of determining molecule-specific isotherm parameters by using a series of chromatograms and computational grids to minimize an aggregated distance measure, resulting in rapid and efficient chromatography model calibration.
Patent Information
- Application Number
- JP2024564961
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2022-05-05
- Filing Date
- 2023-04-27
- Publication Date
- 2025-05-27
AI Technical Summary
Current methods for chromatographic separation, particularly those supported by mechanistic modeling, face challenges in efficiently determining molecule-specific isotherm parameters, which are necessary for accurate chromatographic process optimization and calibration.
A method involving a series of chromatograms performed under non-identical operating modes, where retention behavior data is recorded, and a computational grid is generated to calculate partition coefficient values and minimize an aggregated distance measure, allowing for the rapid derivation of adsorption model parameters.
This approach enables quick derivation of model parameters from a small number of experiments at low loading densities, reducing the complexity and time required for chromatography model calibration and settings determination.
Smart Images
Figure 2025516317000001_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a method for performing chromatography. In particular, it relates to the chromatographic separation of at least one target molecule using specific chromatographic settings.
Background Art
[0002] In order to perform chromatographic separation efficiently, it is necessary to perform process development and / or process characterization and / or process optimization of chromatography. This involves cumbersome and time-consuming experimental work.
[0003] To improve the situation, mechanistic modeling of chromatography is increasingly being used to solve the practical problems of chromatographic process development, process optimization, and process characterization through fast and cost-effective computer simulations and optimizations.
[0004] However, before a mechanistic model can be applied, it is first necessary to calibrate the current chromatographic process. The latest models of chromatography include a concentration transport equation that describes the movement of solutes through the interstitial volume of the chromatographic column. For example, when using a packed bed of porous particles, when the micropore volume filled with fluid is also involved, the transport of solutes into and within the pores can also be simulated. The adsorption and desorption of solutes are described by so-called isotherms and are necessary for all types of chromatography except size exclusion chromatography (SEC). For example, ion exchange, hydrophobic interaction, or affinity chromatography.
[0005] The biggest challenge in mechanistic modeling is to determine the molecule-specific parameters of the isotherm. The isotherm describes the equilibrium state between the adsorbed solute concentration and the solute concentration in the solution.
[0006] The equilibrium state is defined by how much solute can be bound to the adsorbent when the solute concentration in the mobile phase and the surrounding conditions (such as pH, ionic strength / charge, etc.) are given. The equilibrium isotherm usually has a "linear range" at low loadings, where the adsorbed molecule concentration is proportional to the molecule concentration in the solute. As the solute concentration in the mobile phase increases, the curve flattens as it approaches the capacity of the adsorbent. The isotherm describes the binding of the solute as a function of the mobile phase conditions (ionic strength, pH, etc.) and is molecule-specific. As a result, the isotherm contains several parameters, the values of which need to be determined, for example, by calibration experiments conducted in the laboratory.
[0007] Among the conventional methods for model calibration, there are those that use the so-called Yamamoto method. This method is preferably used in a simple ion exchange chromatography (IEC) model that separates the determination of parameters affecting the linear region of the isotherm from the determination of parameters affecting the non-linear region. This reduces the dimensionality of the parameter determination problem, and as an additional advantage, only a small amount of sample is required for experiments in the linear region of the isotherm. Unfortunately, the parameter values identified by the Yamamoto method can only be used when the elution behavior under high loading conditions can actually be described by a variant of a simple stoichiometric displacement model (SDM) based on the law of mass action (LMA). If the binding behavior of a molecule does not follow the LMA / SDM mechanism, the identified parameters will lead to misunderstandings and become unusable. However, even for a slightly extended LMA-type SDM model such as Mollerup's IEC model, https: / / doi.org / 10.1016 / j.jbiotec.2007.05.036, no closed-form equation may be generated when solving the integration with the Yamamoto approach. In addition, new colloidal models for chromatography are formulated in such a complex way that they cannot be easily integrated. Therefore, the state-of-the-art for non-LMA-type models is to use curve fitting that requires the complete solution of all model equations to calculate the chromatogram. This not only takes time but also the parameter determination problem can become high-dimensional, resulting in relatively more time being spent.
[0008] Therefore, there is a need for an improved method for performing chromatographic separation. In particular, there is a need for an improved method for performing chromatographic separation supported by mechanistic modeling.
Prior Art Documents
Non-Patent Documents
[0009]
Non-Patent Document 1
Non-Patent Document 2
Non-Patent Document 3
Non-Patent Document 4
Non-Patent Document 5
Summary of the Invention
Problems to be Solved by the Invention
[0010] An object of embodiments of the present invention is to provide a solution that alleviates or solves the above-mentioned drawbacks and problems.
Means for Solving the Problems
[0011] The above and further objects are achieved by the subject matter described herein. Further advantageous implementations of the invention are further defined herein.
[0012] According to a first aspect of the invention, the above and other objects are achieved by a method, the method comprising the steps of performing an experiment as a series of chromatograms, the series of chromatograms including at least two chromatograms using non-identical operating modes; for each of the chromatograms, recording retention behavior data of at least one target molecule, the retention behavior data indicating at least the measured elution point and the characteristics of the measured elution point; generating at least one computational grid in at least one dimension, the range of the grid indicating the maximum range between the start point and the end point of the experiment; selecting an adsorption model from a predefined set of adsorption models, the adsorption model having initial candidate values for the adsorption model parameters; using the selected adsorption model to calculate partition coefficient values for all points within the computational grid; calculating the integral of a function of the calculated partition coefficient values over at least two paths within the computational grid to obtain the characteristics of the calculated elution point; calculating an aggregated distance measure from the characteristics of the calculated elution point to the characteristics of each measured elution point; selecting new candidate values for the adsorption model parameters; repeating the steps of calculating the partition coefficient values, calculating the integral, calculating the aggregated distance measure, and selecting new candidate values until the aggregated distance measure is minimized; and determining the parameters of the adsorption model using the selected values of the adsorption model parameters that minimize the aggregated distance measure.
[0013] In one embodiment according to the first aspect, the measured elution points include selection of time points and / or selection of volumes and / or selection of mobile phase modifier concentrations at elution and / or characteristics of the chromatographic column.
[0014] In one embodiment according to the first aspect, the grid range represents a range of mobile phase modifier concentrations, the function of the calculated partition coefficient values is an inverse function, and the step of calculating the aggregated distance measure calculates the characteristics of the calculated elution points by using the inverse function of the calculated partition coefficient values to calculate the integral over at least two paths within the calculation grid, and includes the step of calculating the characteristics of the calculated elution points, and the step of calculating the aggregated distance measure between the characteristics of the calculated elution points and the characteristics of each measured elution point.
[0015] In one embodiment according to the first aspect, the method further includes the step of selecting a chromatographic column model from a set of predefined chromatographic column models, and the step of determining candidate values for additional adsorption model parameters by fitting the retention behavior data to the simulated chromatogram.
[0016] In one embodiment according to the first aspect, the range of the calculation grid indicates the temporal duration of a series of chromatographic runs and the axial column dimensions of a series of chromatographic runs, and the step of calculating an aggregated distance measure includes selecting a chromatographic column model from a predefined set of chromatographic column models, and using the selected chromatographic column model and the partition coefficient values calculated on the calculation grid to calculate a propagation velocity value for at least one target molecule from the inlet of the column to the outlet of the column, and calculating the characteristics of the calculated elution points by calculating the integral of the propagation velocity values to obtain at least one trajectory through the calculation grid, and simulating the retention behavior data of at least one target molecule, and calculating an aggregated distance measure (D) between the characteristics of the calculated elution points and the characteristics of each measured elution point.
[0017] In one embodiment according to the first aspect, the method further includes selecting candidate values for additional adsorption model parameters by fitting the simulated retention behavior data to the simulated chromatogram.
[0018] In one embodiment according to the first aspect, the method further includes calibrating a mechanistic model using the determined values of the adsorption model parameters, the selected candidate values of the additional adsorption model parameters, and the chromatographic column model parameters, and simulating a chromatographic run using the calibrated mechanistic model to obtain a chromatographic setting selected from a set of settings including a loading solution and elution conditions.
[0019] In one embodiment according to the first aspect, the method further includes applying the obtained chromatographic setting to a chromatographic separation process to separate at least one target molecule.
[0020] In one embodiment according to the first aspect, the step of selecting an adsorption model includes selecting a plurality of adsorption models from a predefined set of adsorption models, the step of calculating a distribution coefficient value includes calculating a distribution coefficient value for each of the plurality of adsorption models, the step of calculating an integral includes calculating an integral for each of the plurality of adsorption models, for each of the plurality of adsorption models, a step of calculating an aggregated distance measure, for each of the plurality of adsorption models, a step of selecting a new candidate value for an adsorption model parameter, for each of the plurality of adsorption models, a step of calculating a distribution coefficient value, a step of calculating an integral, a step of calculating an aggregated distance measure, and a step of selecting are repeated until the aggregated distance measure is minimized, and using the selected value of the adsorption model parameter related to the adsorption model among the plurality of adsorption models that minimizes the aggregated distance measure to determine the parameters of the adsorption model (595).
[0021] At least one advantage of the present disclosure according to the first aspect is that model parameters can be quickly derived from a relatively small number of experiments conducted at a low loading density.
[0022] According to a second aspect of the present invention, the above and other objects are achieved by a device, the device being a control unit comprising a circuit, the circuit comprising a processing circuit and a memory, the memory comprising instructions executable by the processing circuit, the control unit being communicatively coupled to a controllable unit of a fluid network, whereby the device is configured to execute the method according to the first aspect when the instructions are executed by the processing circuit, the control unit comprising.
[0023] According to a third aspect of the present invention, the above and other objects are achieved by a computer program comprising computer-executable instructions, the computer-executable instructions being for causing a control unit to execute any of the method steps according to the first aspect when executed on a processing circuit comprised in the control unit.
[0024] According to a fourth aspect of the present invention, the above-described object and other objects are achieved by a computer program product including a computer-readable storage medium in which the computer program described in the third aspect is embodied.
[0025] The advantages of the present disclosure according to the second to fourth aspects are that the model parameters can be quickly derived from a relatively small number of experiments carried out at a low load density. A more complete understanding of the embodiments of the present invention will be provided to those skilled in the art by considering the following detailed description of one or more embodiments, and the realization of the additional advantages will also be provided. It should be understood that like reference numerals are used to identify like elements shown in one or more of the figures.
Brief Description of the Drawings
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Best Mode for Carrying Out the Invention
[0027] A more complete understanding of the embodiments of the present invention will be provided to those skilled in the art by considering the following detailed description of one or more embodiments, and the achievement of its additional advantages will also be provided. It should be understood that like reference numerals are used to identify like elements shown in one or more figures.
[0028] To predict or simulate any kind of chromatographic process, it is necessary to describe the dominant natural principles by mathematical model equations. In fact, column chromatography models usually include three separate but combined models: a hydrodynamic model that describes the general flow and transport patterns in the column, a model that describes the concentration transport in the pores of the beads if applicable, and an adsorption isotherm that models the adsorption process thermodynamically. A wide variety of such models are known in the literature that describe different chromatographic and interaction modes. Given the model and the corresponding model parameters, the resulting chromatogram can be predicted by computer simulation.
[0029] Mechanistic models consider physical and biochemical effects by natural laws. For example, outside the adsorbent beads in a chromatographic system, the injected components are usually transported by convective effects induced by the connected pump. Dispersion effects include, among others, molecular diffusion and non-ideal flow. Inside the pores of the adsorption particles / beads, diffusion dominates the movement of the fluid. Finally, the components are adsorbed on the inner surface of the particles / beads.
[0030] Examples of mechanistic models can be found at https: / / www.cytivalifesciences.com / en / us / solutions / bioprocessing / knowledge-center / what-are-mechanistic-chromatography-models.
[0031] Examples of isothermal models can be found at https: / / www.cytivalifesciences.com / en / us / solutions / bioprocessing / knowledge-center / adsorption-isotherm-models.
[0032] Examples of other models can be found at https: / / doi.org / 10.1016 / j.jbiotec.2007.05.036 and https: / / doi.org / 10.1016 / j.chroma.2021.462397.
[0033] As used in this specification and the corresponding claims, "or" shall be understood as the mathematical OR, including "and" and "or", and not as the exclusive OR (XOR). The indefinite article "a" in this disclosure and the claims shall not be limited to "one", but can also be understood as "one or more", i.e., plural.
[0034] In this disclosure, the processing circuit and the processing means are referred to interchangeably.
[0035] In this disclosure, the term "target molecule" refers to the desired molecule, typically the molecule separated in a liquid chromatography process.
[0036] In the present disclosure, the term "chromatography" or "liquid chromatography" refers to a process for separating the components of a mixture. The mixture is dissolved in a first substance called the mobile phase. The mixture and the first substance are fed into the inlet of a chromatography column filled with a second substance called the stationary phase. Different components of the mixture pass through the stationary phase at different rates, thereby separating from each other at the outlet of the chromatography column. Depending on the characteristics of the specific mobile phase and stationary phase, which substances move fast or slow and how well they are separated are determined. These different retention times are called retention times and are recorded as retention data.
[0037] In the present disclosure, the term "chromatogram run" refers to the cycle in which the mixture and the first substance move from the inlet to the outlet of the chromatography column.
[0038] In the present disclosure, the term "operating mode" defines the characteristics of a chromatogram run. For example, characteristics of the chromatography column, characteristics of the bead / micropore volume, characteristics of the mobile phase, characteristics of the stationary phase, and characteristics of the mixture. This may include mobile phase modifiers such as pH, salt concentration, and ionic strength, which may vary during the chromatogram run.
[0039] In the present disclosure, the terms "retention behavior" and "retention behavior data" refer to the behavior of the mixture and the first substance moving through the chromatography column, as well as the data recording that behavior. The retention behavior data may further include the characteristics of the chromatogram run defined above. The retention behavior data may further include data processed or aggregated based on the above data categories. In one example, the retention behavior data includes the retention times of the components of the mixture from the inlet to the outlet of the chromatography column. In a further example, the retention behavior data includes the execution volume, or the total volume of the mixture and the mobile phase.
[0040] In the present disclosure, the term "elution point" refers to the peak at which the components of a mixture reach the outlet of a chromatography column and are detected. In one example, the "elution point" represents the peak of a chromatogram from a chromatography run. Detection of the arriving components can be performed using a spectrophotometer, a mass spectrometer, an ultraviolet (UV) detector, or fractionation analysis. In relation to the recorded signal, the "elution point" can be defined, for example, as the highest point of the signal value, the last maximum value of the signal, or the center of mass.
[0041] In the present disclosure, the terms "measured elution point characteristics" or "calculated elution point characteristics" refer to retention behavior data that define the measured elution point, such as the migration time from injection at the inlet to detection at the outlet of the column, the total volume of the mixture, and the mobile phase composition at elution, including the current ionic strength, salt concentration, current pH, slope of the current elution gradient, etc.
[0042] The injection point or start point indicates a chromatography characteristic, such as the time point, when the components of the mixture reach the inlet of the chromatography column. In one example, the "injection point" or POI represents the first point of a chromatogram from a chromatography run. In another example, the POI is defined as the time point at which half of the sample volume is injected.
[0043] In the present disclosure, the term "adsorption model" refers to a model that at least models adsorption equilibrium. Usually, an adsorption model describes the change in concentration of the adsorbed mixture as a function of the mixture concentration in the mobile phase and the concentration bound to the adsorbent / beads, taking into account the characteristics of the material and the mobile phase. Examples of adsorption models include the Langmuir model or the colloidal particle adsorption (CPA) model. See also https: / / www.cytivalifesciences.com / en / us / solutions / bioprocessing / knowledge-center / adsorption-isotherm-models.
[0044] In the present disclosure, the term "distribution coefficient value" refers to the ratio of the concentration of a substance in one phase to the concentration of the substance in a second phase when the two concentrations are in equilibrium.
[0045] In the present disclosure, the term "computational grid" refers to the discretization of a computational domain composed of elements, faces, and nodes. An example of a computational grid is a Cartesian grid. In a Cartesian grid, the faces of the elements are arranged along the axes of a Cartesian frame or reference coordinate system. The nodes defined as the intersections of the faces can be arranged either evenly (equidistantly) or unevenly. Accordingly, the elements (or cells) can be, for example, line segments (1D), rectangles (2D), or cubes (3D). An example of a computational grid can be found in "Notes on computational Thermo-Fluid Dynamics", DOI: 10.13140 / RG.2.1.5174.3124. The computational grid has a range that effectively defines the maximum / minimum starting and ending points of the experiments or chromatographic runs used in the present disclosure.
[0046] In the present disclosure, the term "point within the computational grid" refers to the discrete points of the computational grid. Usually, each point within the computational grid contains the same number of (coordinate) values as the dimension of the computational grid. That is, in a 1D computational grid each point contains a single value, in a 2D computational grid each point contains two values, and in an N-dimensional computational grid each point contains N values.
[0047] In the present disclosure, the term "path" or "path within the computational grid" refers to a set of values from the computational grid from a starting point (SP) to an ending point (EP), for example, points indicating changes in pH and salt concentration.
[0048] In the present disclosure, the term "integrate" or "compute the integral" refers to computing a definite integral over an interval. An example of a method for computing the definite integral of a function defined on a computational grid over a given interval is the composite trapezoidal rule.
[0049] In the present disclosure, the term "aggregated distance metric" refers to a distance metric calculated using at least two partial distance metrics, for example, the partial distance between a measured elution point characteristic and a calculated elution point characteristic. An example of an aggregated distance metric is the metric used in the least squares method, where the distance metric is the sum of squared residuals minimized by varying the parameter candidate values. The residuals are typically calculated between one or more characteristics of the measured elution point and the calculated elution point.
[0050] In the present disclosure, the term "fluid network" refers to a fluidly connected device component configured to hold, direct, and control the flow of a fluid. Examples of device components included in a fluid network are conduits / pipes, fluid containers / receptacles, sensors, valves, fluid columns, etc. Some device components may be controllable, communicatively coupled to a control unit, responsive to control signals received from the control unit, and / or transmit data, such as device component characteristics and / or measurement data, to the control unit as control signals. Examples of such controllable device components are sensors and controllable valves. Briefly, the present disclosure eliminates the need for slow, high-dimensional curve fitting for model calibration, particularly for calibrating isotherm models. The present disclosure further determines isotherm parameters in the linear range using only the observed elution points and does not require knowledge of the complete chromatogram. An advantage of the present disclosure is the ability to rapidly derive model parameters from a relatively small number of experiments conducted at low loading densities.
[0051] The present disclosure identifies isotherm parameters active in the linear range by applying a generalized method triggered by the Yamamoto method, but can be used for any given model equation, thereby enabling rapid identification of model parameters beyond LMA-type models. Further, calculations of elution point approximations are performed for any given model equation, also supporting the use of multiple mobile phase modifiers and non-linear gradient elution experiments, which are known drawbacks of the conventional Yamamoto method.
[0052] At least one advantage of the present disclosure is that it can significantly reduce the complexity and time of calculations required to arrive at a calibrated chromatography model and, by extension, the settings for liquid chromatography.
[0053] FIG. 1 shows the characteristics of the measured elution points M-POE in different operating modes in two or more chromatography runs. As can be seen from FIG. 1, different combinations of chromatographic run characteristics / operating modes result in different elution points. For example, characteristics of the chromatography column, characteristics of the beads / pore volume, characteristics of the mobile phase, characteristics of the stationary phase, and characteristics of the mixture, etc. The characteristics of M-POE can be represented from the perspective of mobile phase modifiers 101, 102 such as pH, salt concentration, and ionic strength at the time when the peak is detected.
[0054] In the example, a three-dimensional figure is shown. It should be understood that any number of dimensions can be applied without departing from the present disclosure. pH is shown on the Y-axis, salt concentration on the X-axis, and parameter GH on the Z-axis. Parameter GH103 can represent the normalized gradient slope, which is a characteristic of the runs used in the conventional Yamamoto method.
[0055] FIG. 2 shows a calculation grid MTX, a surface S, and measured elution points (M-POE) according to one or more embodiments of the present disclosure. The calculation grid is shown as two-dimensional calculation grids 101, 102 in FIG. 2. However, it is understood that without departing from the present disclosure, a calculation grid of any dimension can be selected according to the application.
[0056] In one example, the calculation grid MTX is arranged in one dimension, the pH changes according to a specific gradient in the chromatography run, and the elution point is characterized by the "normalized gradient slope" GH103 and pH102 at the time of peak detection.
[0057] In yet another example, the computational grid is arranged in one dimension, the salt concentration C varies according to a specific gradient in the chromatographic run, and the elution point is characterized by the "normalized gradient slope" GH at peak detection and the salt concentration.
[0058] In yet another example, the computational grid is arranged in two dimensions, and the pH and the salt concentration C vary together in the chromatographic run. The example shown in FIG. 2 corresponds to this. The elution point of the target molecule is indicated by three characteristic properties.
[0059] Since the adsorption model predicts the results of chromatographic experiments, it can be used to generate predicted elution points that should naturally exist on the hypersurface within the grid.
[0060] The surface S is generated by applying candidate values of the parameters to the adsorption model and then simulating / calculating the characteristics of the elution points over the range of the computational grid. In other words, when the pH and the salt concentration C at elution are used as inputs to the model, the model can be used to calculate the normalized gradient slope leading to the given elution point characteristics that form the surface. Different candidate values are used to minimize the distance between the measured characteristics of the elution point M-POE and the surface S calculated with the model / distribution coefficient values. Since multiple distances between the measured characteristics of the elution point M-POE and the surface are considered, this will substantially minimize the aggregated distance D.
[0061] In one example, the computational grid is arranged in three dimensions, and the pH varies according to a specific gradient together with a first salt concentration C1 and together with a second salt concentration C2.
[0062] This solution has the advantage that non-linear surfaces can also be considered.
[0063] FIG. 3 shows the aggregated distance measure D according to one or more embodiments of the present disclosure. The distance between the surface S and the characteristics M-POE_i of each measured elution point is calculated.
[0064] In one embodiment, the aggregated distance metric D is the metric used in the least squares method, and the distance metric is the sum of squared residuals that is minimized by varying the parameter candidate values. The residuals are then formed by the distances from the surface S to the characteristics of each measured elution point M-POE.
[0065] Exemplary specifications of the measured elution point M-POE include the migration time from the inlet to the outlet of the column, the total volume of the mixture and the mobile phase, the current salt concentration, the current pH, the current gradient slope, and the like.
[0066] Depending on the application, other curve fitting methods known in the art can also be used. Examples of other curve fitting methods include Bayesian linear curve fitting or ridge regression.
[0067] FIG. 4 shows paths T1, T2 within the computational grid MTX according to one or more embodiments of the present disclosure. The paths show how the operating mode changes through a series of chromatographic runs.
[0068] In one example, the retention behavior of molecules in the first chromatographic run is described using a first path T1 where pH 102 is constant and the salt concentration C103 changes according to a first gradient defined by the extent of the computational grid MTX. In other words, the salt concentration continuously increases from the starting point SP1 to elution at the ending point EP1.
[0069] In a further example, the retention behavior of molecules in the second chromatographic run is described using a second path T2, where the salt concentration C is constant and the pH changes according to a second gradient defined by the extent of the computational grid MTX. In other words, the pH continuously increases from the starting point SP2 to elution at the ending point EP2.
[0070] FIG. 5 shows a flowchart of a method 500 according to one or more embodiments of the present disclosure. In one or more embodiments, the method 500 is executed by a computer. The method includes the following.
[0071] Step 510: Perform an experiment as a series of chromatograms. The series of chromatograms includes at least two chromatograms using non-identical operating modes.
[0072] The operating mode will be further explained in the first part of the description.
[0073] In one example, in each chromatogram of the series of chromatograms, the pH changes according to a specific gradient. In a further example, in each chromatogram of the series of chromatograms, the pH and the salt concentration C change according to a specific gradient.
[0074] Step 520: For each of the chromatograms, record the retention behavior data of at least one target molecule, where the retention behavior data indicates at least the measured elution point M-POE. The measured elution point M-POE has the previously defined characteristic M-POE_i.
[0075] The retention behavior data may include any characteristic or feature of the chromatogram. Examples of retention behavior data to be recorded include the retention time or the time it takes for the target molecule to move from the inlet of the column to the outlet of the column, and the operating volume or the volume of the mixture used in the chromatogram.
[0076] Step 530: Generate at least one calculation grid MTX in at least one dimension, where the range of the grid indicates the maximum range between the starting point / injection point SP and the end point / elution point EP.
[0077] The calculation grid will be further explained in the first part of the description. In one example, the calculation grid has two dimensions, where the pH is shown in one dimension and the salt concentration C is shown in the second dimension. In this example, the grid can be viewed as a mesh, and each intersection of the mesh is represented by a pair of values of pH and C.
[0078] In other words, the two-dimensional computational grid MTX is generated for a first range of pH and a second range of salt concentration C. The grid can then be formed using appropriate step sizes along the first and second ranges.
[0079] Step 540: Select one adsorption model from a predefined set of adsorption models. The adsorption model has initial candidate values for the adsorption model parameters.
[0080] For adsorption models, see the first part of the description and further explanation at https: / / www.cytivalifesciences.com / en / us / solutions / bioprocessing / knowledge-center / adsorption-isotherm-models.
[0081] Step 550: Using the selected adsorption model, calculate the partition coefficient values for all points within the computational grid.
[0082] In one example, the partition coefficient value K is calculated according to the following relationship.
[0083]
Equation
[0084] where k eq , k eq,1 , v, v 1 are molecule-specific parameters of the model and Λ is a constant.
[0085] Step 560: Calculate the integral of the function of the calculated partition coefficient values over at least two paths within the computational grid MTX to obtain the characteristics C-POE_i of the calculated elution points.
[0086] Paths and the computational grid are further explained in the first part of the description.
[0087] Step 570: Calculate an aggregated distance measure D from the characteristic C-POE_i of the calculated elution points to the respective experimental reference characteristic value M-POE_i of the measured elution points.
[0088] The aggregated distance measure is further described in connection with FIG. 3.
[0089] Step 580: Select new candidate values for the adsorption model parameters.
[0090] In one example, the new candidate values for the adsorption model parameters are selected from a predefined set of candidate values. Examples of the parameters of the adsorption model are k eq , k eq,1 , v, v 1 as above.
[0091] Step 590: Repeat step 550 for calculating the partition coefficient values, step 560 for calculating the integral, step 570 for calculating the aggregated distance measure, and step 580 for selecting new candidate values until the aggregated distance measure D is minimized.
[0092] Step 595: Determine the parameters of the adsorption model using the selected values of the adsorption model parameters that minimize the aggregated distance measure.
[0093] In one example, the parameters of the adsorption model are determined using the latest parameters of the adsorption model selected in step 580.
[0094] In one embodiment, the measured elution points M-POE include the selection of a time point and / or a volume and / or a mobile phase modifier concentration at elution.
[0095] Figure 6 shows a first embodiment of the method described in relation to Figure 5. In this embodiment, the grid range indicates the range of mobile phase modifier concentrations 101, 102 achieved in the chromatography medium. The path can be defined by any subset within the range of the computational grid MTX, i.e., from the starting point / injection point SP to the ending point / elution point EP in one or more dimensions. This function includes an inverse function. Calculating the aggregated distance measure (D) includes the following.
[0096] Step 5701: Calculate the characteristics C-POE_i of the elution point using the grid MTX by calculating the integral over two or more paths within the computational grid MTX using the inverse function of the calculated partition coefficient values to obtain the characteristics C-POE_i of the elution point.
[0097] Step 5702: Calculate the aggregated distance measure D between the calculated characteristics C-POE_i of the elution point and the measured characteristics M-POE_i of the elution point.
[0098] Alternatively, or additionally, the method further includes the following.
[0099] Step 5703: Select one chromatographic column model from a predefined set of chromatographic column models.
[0100] Step 5704: Determine candidate values for additional adsorption model parameters by fitting the retention behavior data to the simulated chromatogram. Examples of additional adsorption model parameters include parameters that describe binding kinetics or parameters that are distinguishable only in the non-linear isotherm range, such as those that describe steric effects or intermolecular interactions.
[0101] Figure 7 shows a second embodiment of the method described in connection with Figure 5. In this embodiment, the extent of the computational grid MTX indicates the temporal duration of a series of chromatographic runs and the axial column dimensions of a series of chromatographic runs. Calculating the aggregated distance measure D involves the following.
[0102] Step 5706: Select one chromatographic column model from a predefined set of chromatographic column models.
[0103] Alternatively, or additionally, the method further includes the following.
[0104] Step 5707: Using the partition coefficient values calculated using the selected chromatographic column model and the computational grid, calculate the propagation speed value of at least one target molecule from the inlet of the column to the outlet of the column.
[0105] Alternatively, or additionally, the method further includes the following.
[0106] Step 5708: Simulate the retention behavior data of at least one target molecule by calculating the integral of the propagation speed value to obtain at least one trajectory through the computational grid MTX and by calculating the characteristics C-POE_i of the elution point.
[0107] Alternatively, or additionally, the method further includes the following.
[0108] Step 5709: Select candidate values for additional adsorption model parameters by fitting the retention behavior data to the simulated chromatogram.
[0109] Figure 8 shows an embodiment of the method described in connection with Figure 6 and / or Figure 7. The method further includes the following.
[0110] Step 810: Calibrate the mechanistic model using the determined values of the adsorption model, the selected candidate values of the additional adsorption model parameters, and the chromatographic column model parameters.
[0111] Alternatively, or in addition, the method further includes the following.
[0112] Step 820: Simulate a chromatographic run using the calibrated mechanistic model to obtain chromatographic settings selected from a set of settings including a loading solution and elution conditions.
[0113] Alternatively, or in addition, the method further includes the following.
[0114] Step 830: Apply the obtained chromatographic settings to a chromatographic separation process to separate at least one target molecule.
[0115] Additionally, or alternatively, the method further includes performing model discrimination.
[0116] Step 540 of selecting an adsorption model includes the step of selecting a plurality of adsorption models from a predefined set of adsorption models.
[0117] Step 550 of calculating partition coefficient values includes the step of calculating partition coefficient values for each of the plurality of adsorption models.
[0118] Step 560 of calculating an integral includes the step of calculating an integral for each of the plurality of adsorption models.
[0119] For each of the plurality of adsorption models, a step (570) of calculating an aggregated distance metric D is performed.
[0120] For each of the plurality of adsorption models, a step 580 of selecting new candidate values of the adsorption model parameters is performed.
[0121] Step 595 of determining the parameters of the adsorption model is executed using the selected values of the adsorption model parameters related to the adsorption model among a plurality of adsorption models that minimize the aggregated distance metric.
[0122] FIG. 9 shows a device 900 according to one or more embodiments of the present disclosure.
[0123] The device 900 includes a control unit 960 that includes circuitry, such as a processor and a memory. The memory can include instructions executable by the processor, whereby the device is operable to perform any of the steps or methods described herein.
[0124] Additionally or alternatively, the device 900 may further include a controllable fluid network that includes, for example, fluidly coupled pipes, fluidly coupled and controllable valves, and fluidly coupled and controllable pumps.
[0125] Additionally or alternatively, the device may further include a chromatography column 930 that includes at least one fluid inlet 931 and one fluid outlet 932. The fluid inlet 931 and the one fluid outlet 932 are typically fluidly coupled to the controllable fluid network.
[0126] The device 900 may optionally further include a fraction collection unit 950. The fraction collection unit 950 is typically fluidly coupled to the controllable fluid network.
[0127] Additionally or alternatively, the device may further include a display 980.
[0128] Additionally or alternatively, the device may further include an input device 970.
[0129] In one embodiment, the device further comprises one or more sensors configured to measure characteristics of the fluid within the device and / or the fluid network. The control unit 960 is further communicatively coupled to each sensor. The sensor may be configured to measure the pressure and / or pH and / or conductivity of the fluid within the device. Any sensor suitable for measuring the fluid can be used.
[0130] Device 900 may be in the form of, for example, a chromatography device, an electronic control unit, a server, an on-board computer, a fixed computing device, a laptop computer, a tablet computer, a handheld computer, a wrist-worn computer, a smartwatch, a smartphone, or a smart TV. Device 900 may include a processing circuit communicatively coupled to a transceiver configured for wired or wireless communication. Device 900 may further include at least one optional antenna (not shown). The antenna can be coupled to the transceiver and is configured to transmit and / or emit and / or receive wired or wireless signals in communication networks such as WiFi, Bluetooth, 3G, 4G, 5G, etc. In one example, the processing circuit can be any of a processing circuit and / or a central processing unit and / or a processor module and / or a plurality of processors configured to cooperate with each other. Further, device 900 may further include a memory. The memory may include, for example, hard RAM, a disk drive, a floppy disk drive, a flash drive, or other removable or fixed media drive, or any other suitable memory selection known in the art. The memory can include instructions executable by the processing circuit for performing any of the steps or methods described herein. The processing circuit can optionally be communicatively coupled to any of one or more sensors such as a transceiver, a memory, a pH sensor, a conductivity sensor, and a pressure sensor, or any suitable type of sensor capable of measuring characteristics of the fluid processed by the device and / or the device. Device 900 may be configured to transmit / receive control signals directly to / from any of the above-described units or an external node, or to transmit / receive control signals via a wired and / or wireless communication network.
[0131] A wired / wireless transceiver and / or a wired / wireless communication network adapter can be configured to transmit and / or receive data values or parameters as signals to / from a processing circuit and to / from other external nodes. For example, it can be a measured pH or conductivity, or the amount of buffer solution produced, etc.
[0132] In one embodiment, the transceiver communicates directly with an external node or communicates via a wireless communication network.
[0133] In one or more embodiments, the input device 970 is configured to receive an input or instruction from a user and transmit a user input signal indicating the user input or instruction to the processing circuit.
[0134] In one or more embodiments, the display 980 is configured to receive a display signal from the processing circuit indicating a rendered object such as a text or graphical user input object, and display the received signal as an object such as a text or graphical user input object.
[0135] In one embodiment, the display 980 is integrated with the user input device 970, configured to receive a display signal from the processing circuit indicating a rendered object such as a text or graphical user input object, and display the received signal as an object such as a text or graphical user input object, and / or configured to receive an input or instruction from a user and transmit a user input signal indicating the user input or instruction to the processing circuit.
[0136] In a further embodiment, device 900 may further include and / or be coupled to one or more additional sensors (not shown) configured to receive and / or acquire and / or measure physical properties related to the device and / or the atmosphere surrounding the device and to transmit one or more sensor signals indicative of the physical properties of the device to a processing circuit. For example, a temperature sensor that measures the ambient air temperature, etc.
[0137] In embodiments, the communication network uses a wired or wireless communication technique that can include at least one of, but is not limited to, a local area network (LAN), a metropolitan area network (MAN), a global system for mobile networks (GSM), an enhanced data GSM environment (EDGE), a universal mobile telecommunications system, a long term evolution, a high speed downlink packet access (HSDPA), a wideband code division multiple access (W-CDMA), a code division multiple access (CDMA), a time division multiple access (TDMA), Bluetooth®, Zigbee®, Wi-Fi, a voice over internet protocol (VoIP), LTE Advanced, IEEE 802.16m, Wireless MAN-Advanced, an evolved high speed packet access (HSPA+), 3GPP® long term evolution (LTE), Mobile WiMAX (IEEE 802.16e), an ultra mobile broadband (UMB) (former evolution data optimized (EV-DO) Rev.C), a high speed low latency access by seamless handoff orthogonal frequency division multiplexing (Flash-OFDM), a large capacity space division multiple access (iBurst®), and a mobile broadband wireless access (MBWA) (IEEE 802.20) system, a high performance radio metropolitan area network (HIPERMAN), a beam division multiple access (BDMA), a worldwide interoperability for microwave access (Wi-MAX), as well as ultrasonic communication, etc. to communicate.
[0138] Furthermore, those skilled in the art should understand that the device 900 may include the necessary communication capabilities in the form of, for example, functions, means, units, elements, etc. to implement this solution. Examples of other such means, units, elements, and functions include processors, memories, buffers, control logic, encoders, decoders, rate matchers, dereate matchers, mapping units, multipliers, decision units, selection units, switches, interleavers, deinterleavers, modulators, demodulators, inputs, outputs, antennas, amplifiers, receiver units, transmitter units, DSPs, MSDs, TCM encoders, TCM decoders, power supply units, feed lines, communication interfaces, communication protocols, etc., and these are appropriately configured together to implement this solution.
[0139] In particular, the processing circuit and / or processing means of the present disclosure may include a processing circuit, a processor module, and one or more instances of a plurality of processors configured to cooperate with each other, a central processing unit (CPU), a processing unit, a processing circuit, a processor, an application-specific integrated circuit (ASIC), a microprocessor, a field-programmable gate array (FPGA), or other processing logic capable of interpreting and executing instructions. Thus, the expressions "processing circuit" and / or "processing means" may represent a processing circuit including a plurality of processing circuits, such as any, some, or all of those described above. The processing means can further execute data processing functions for input, output, and processing of data, including data buffering and device control functions such as user interface control.
[0140] Exemplary embodiments In an exemplary embodiment, it is assumed that there is a unique mapping between the elution time and the elution volume / retention volume of the target molecule. Using the mapping, it is possible to determine the elution volume from the elution time and vice versa. The elution volume will not be considered further. The unique mapping is not possible only when the flow stops, but in this case, there is no need to predict the elution either.
[0141] Calculation of the Characteristics of the Elution Point in the Case of Linear Gradient Elution In the case of a linear gradient, there is also a unique mapping of the retention time to the concentration of the mobile phase modifier that changes over a predefined gradient. If the modifier concentration at elution is known, the retention time can be inferred from that modifier concentration.
[0142] Next, the remaining problem to be solved is how to determine the modifier concentration at elution for a given mode of operation characterized here by a specific gradient slope.
[0143] The mathematical derivation of the Yamamoto method is based on the following equation,
[0144]
Equation
[0145] It states that the integral of the product of the distribution coefficient of the target molecule from the concentration CB at the start of the gradient to the concentration CR at elution and the distribution coefficient Kp(C) is equal to the normalized gradient slope GH. Note that in some texts, the distribution coefficient K' of the modifier species is explicitly included and the denominator is written as (Kp(C) - K'), while in others it is assumed to be included in Kp(C). Here, the latter notation is used.
[0146] Assuming a general case where the above integral cannot be easily solved, for example, it is numerically evaluated along a discretized set of points {C0, C1,..., Cn}. Here, C0 = CB and Cn corresponds at least to the modifier concentration at the end of the gradient.
[0147]
Equation
[0148] When determining the modifier concentration at elution for a given GH, continue the integration and summation of segments until the subtotal is equal to or greater than GH. In the former case, the passing point Ci provides the value to be determined, and in the latter case, a more accurate value between C(i - 1) and Ci can be determined by interpolation.
[0149] When determining the normalized gradient slope GH related to a given modifier concentration at elution, continue the integration and summation of segments until the subtotal Ci is equal to or greater than CR. In the former case, the current total provides the value to be determined, and in the latter case, a more accurate value between the last subtotal and the total can be determined by interpolation.
[0150] Calculation of the characteristics of elution points in a general case In the case of isocratic elution, step elution, or more complex operating modes, it is not possible to assume the existence of a one-to-one mapping between the retention time and the mobile phase modifier concentration. As a result, since the modifier concentration is not suitable for sensitive error measurements for possible distance functions, only the calculation of the retention time is considered below.
[0151] First, a grid is created that is spatially the length of the column and temporally at least over the experimental period. The modifier concentration is determined on the space / time grid. Although not all grid points are relevant below, for simplicity, the method of efficiency optimization will not be described further.
[0152] Next, determine the relevant mobile phase modifier concentration at the grid points. This can be done, for example, with a stencil-based finite difference implementation of the convective diffusion model. These values serve as the basis for calculating the Kp value at each point of the space / time grid.
[0153] An exemplary equation for the propagation velocity value of a low-concentration solute that can be adsorbed is u prop (t) = u(t) / (ε tot +(1 - ε tot )K p ) and in the equation, u(t) is the linear flow rate, ε totis the total porosity, and Kp is the partition coefficient of the target molecule, which is a function of the mobile phase modifier concentration (such as ionic strength, pH, etc.).
[0154] To obtain the trajectory of the target molecule moving towards the outlet of the column through the space / time grid, the distance traveled per time interval is calculated by integrating the propagation speed value at the current position of the space / time grid. This integration continues until the travel distance becomes equal to or greater than the column length. In the former case, the current time point provides the required value, and in the latter case, a more accurate value between the last time point and the current time point can be determined by interpolation.
[0155] If the last point of the time grid is reached before the distance traveled in space becomes equal to or greater than the column length, elution has not occurred. As long as the current propagation speed value is positive, the remaining time until reaching the outlet can be estimated.
[0156] Exemplary application examples The above
[0157]
Number
[0158] Assuming that an exemplary model from the above is calibrated with a linear gradient experiment, as schematically shown in Figure 2, for example, three experiments with different salt gradients at two constant pH values each, and seven experiments at the center point with a medium pH and a medium gradient slope can be used.
[0159] In the conventional Yamamoto approach, proceed as follows. For each of the three results at a constant pH, apply the conventional Yamamoto method to obtain the values of the terms k eq ·exp(k eq,1 ·pH) and v + v 1 ·pH. Then, by solving a system of simultaneous equations, the individual parameters k eq , k eq,1 , v, v 1 are determined.
[0160] Consider the following experimental results at a capacity Λ = 0.5M.
[0161]
Table 1
[0162] In the above classical procedure, k eq = 7.8e-4, k eq,1 = -11.7, v = 7.2, v 1 = -4.5. However, the predicted salt concentration at the holding time at the center point is 0.129M, which is unacceptably far from the measured value of 0.135M.
[0163] Using a new method based on the integration of the function of the distribution coefficient on the grid, the overall fitness of all points is significantly improved, and the predicted salt concentration at the holding time is 0.133M, obtaining different values k eq = 3.9e-3, k eq,1 = -3.9, v = 6.2, v 1 = -0.63.
[0164] Finally, it should be understood that the present invention is not limited to the above-described embodiments and relates to all embodiments within the scope of the appended independent claims and incorporates them.
Explanation of Signs
[0165] 101 Mobile phase modifier, two-dimensional calculation grid, mobile phase modifier concentration 102 Mobile phase modifier, two-dimensional calculation grid, pH, mobile phase modifier concentration 103 Parameter GH, salt concentration C 900 Device 930 Chromatographic column 931 Fluid inlet 932 Fluid outlet 950 Fraction collection unit 960 Control unit 970 Input device, user input device 980 Display
Claims
1. A step (510) of performing an experiment as a series of chromatograms, wherein the series of chromatograms includes at least two chromatograms using non-identical operating modes, step (510); For each of the chromatograms, a step (520) of recording retention behavior data of at least one target molecule, wherein the retention behavior data indicates at least a measured elution point (M-POE) and characteristics (M-POE_i) of the measured elution point, step (520); A step (530) of generating at least one computational grid (MTX) in at least one dimension, wherein the range of the computational grid (MTX) indicates the maximum range between the start point and the end point of the experiment, step (530); A step (540) of selecting an adsorption model from a predefined set of adsorption models, wherein the adsorption model has initial candidate values for adsorption model parameters, step (540); Using the selected adsorption model, a step (550) of calculating partition coefficient values for all points within the computational grid; A step (560) of calculating the integral of a function of the calculated partition coefficient values over at least two paths within the computational grid (MTX) to obtain characteristics (C-POE_i) of the calculated elution points; A step (570) of calculating an aggregated distance measure (D) from the calculated characteristics (C-POE_i) of the elution points to the characteristics (M-POE_i) of each of the measured elution points; A step (580) of selecting new candidate values for the adsorption model parameters; Repeating the step (550) of calculating the partition coefficient values, the step (560) of calculating the integral, the step (570) of calculating the aggregated distance measure, and the step (580) of selecting new candidate values until the aggregated distance measure (D) is minimized, step (590); A step (595) of determining the parameters of the adsorption model using the selected values of the adsorption model parameters that minimize the aggregated distance measure (D); A method (500) comprising the above steps.
2. The method (500) according to claim 1, wherein the measured elution point (M-POE) includes selection of a time point and / or selection of a volume and / or selection of a mobile phase modifier concentration at elution and / or characteristics of a chromatographic filler.
3. The range of the calculation grid (MTX) indicates a range of mobile phase modifier concentrations (101, 102), the function of the calculated partition coefficient values is an inverse function, and the step of calculating the aggregated distance measure (D) is calculating an integral over at least two paths within the calculation grid (MTX) using the inverse function of the calculated partition coefficient values to obtain the characteristics (C-POE_i) of the calculated elution point thereby calculating the characteristics (C-POE_i) of the calculated elution point (step 5701); and calculating the aggregated distance measure (D) between the characteristics (C-POE_i) of the calculated elution point and the characteristics (M-POE_i) of each of the measured elution points (step 5702). The method (500) according to claim 1 or 2, comprising:
4. selecting a chromatographic column model from a set of predefined chromatographic column models (step 5703); determining candidate values of additional adsorption model parameters by fitting the retention behavior data to a simulated chromatogram (step 5704). The method (500) according to claim 3, further comprising:
5. The range of the calculation grid (MTX) indicates the temporal duration of the series of chromatographic fillers and the axial column dimensions of the series of chromatographic fillers, and the step of calculating the aggregated distance measure (D) is selecting a chromatographic column model from a set of predefined chromatographic column models (step 5706); calculating a propagation speed value of at least one target molecule from an inlet of the column to an outlet of the column using the selected chromatographic column model and the partition coefficient values calculated on the calculation grid (MTX) (step 5707). Calculating the characteristics (C-POE_i) of the calculated elution points by calculating the integral of the propagation speed values to obtain at least one trajectory through the calculation grid (MTX), and simulating the retention behavior data of the at least one target molecule (step 5708); including the step of calculating the characteristics (C-POE_i) of the calculated elution points; the aggregated distance measure (D) between the characteristics (C-POE_i) of the calculated elution points and the characteristics (M-POE_i) of each of the measured elution points is calculated; The method (500) according to any one of claims 1 to 4.
6. Selecting candidate values for additional adsorption model parameters by fitting the retention behavior data to a simulated chromatogram (step 5709); The method (500) according to claim 5, further comprising.
7. Calibrating a mechanistic model using the determined values of the adsorption model parameters, the selected candidate values of the additional adsorption model parameters, and the chromatographic column model parameters (step 810); Simulating a chromatographic run using the calibrated mechanistic model to obtain a chromatographic setting selected from a set of settings including a loading solution and elution conditions (step 820); The method (500) according to any one of claims 1 to 6, further comprising.
8. Applying the obtained chromatographic setting to a chromatographic separation process to separate the at least one target molecule (step 830); The method (500) according to claim 7, further comprising.
9. The step of selecting an adsorption model (540) includes selecting a plurality of adsorption models from the set of predefined adsorption models; The step of calculating the partition coefficient value (550) includes calculating the partition coefficient value for each of the plurality of adsorption models; The step of calculating the integral (560) includes calculating the integral for each of the plurality of adsorption models; For each of the plurality of adsorption models, calculating an aggregated distance measure (D) (step 570); For each of the plurality of adsorption models, a step (580) of selecting a new candidate value for the adsorption model parameter; For each of the plurality of adsorption models, a step (550) of calculating the distribution coefficient value, a step (560) of calculating the integral, a step (570) of calculating the aggregated distance measure, and a step (580) of selecting, and repeating (590) until the aggregated distance measure (D) is minimized; Determining (595) the parameters of the adsorption model using the selected values of the adsorption model parameters associated with the adsorption model among the plurality of adsorption models that minimize the aggregated distance measure (D); The method (500) according to any one of claims 1 to 8, further comprising.
10. A device (900) comprising a control unit (960) having a circuit, wherein the circuit A processing circuit; And a memory The memory includes instructions executable by the processing circuit, and the control unit is communicatively coupled to a controllable unit of a fluid network, whereby the device, when the instructions are executed by the processing circuit, is configured to perform the method (500) according to any one of claims 1 to 9. A control unit (960) Comprising a device (900).
11. A computer program including computer-executable instructions, the computer-executable instructions being for causing the control unit to execute any of the method steps of the method (500) according to any one of claims 1 to 9 when executed on a processing circuit included in the control unit. A computer program.
12. A computer program product including a computer-readable storage medium embodying the computer program according to claim 11.