Calibration of a mechanical ion exchange chromatography model

Abstract

A method is provided that includes obtaining geometric measurements associated with a second DPFR in a chromatography machine including a first dispersed plug flow reactor (DPFR) and a continuous stirred tank reactor (CSTR) prior to the column and a second DPFR after the column; generating, by a processor, transport model parameters of a transport model associated with the second DPFR based on the geometric measurements; supplying tracer molecules to the chromatography machine; capturing one or more tracer molecule measurements based on the tracer molecules moving through the chromatography machine; and estimating, by a processor, one or more transport model parameters of a transport model associated with the first DPFR and the CSTR based on the transport model associated with the second DPFR and the one or more tracer molecule measurements based on the tracer molecules moving through the chromatography machine.

Description

Technical Field

[0001] Cross - Reference to Related Applications This application claims priority to U.S. Provisional Patent Application No. 63 / 123,170, entitled "Mechanistic Ion - Exchange Chromatography Model Calibration," filed on December 9, 2020, the entire disclosure of which is hereby incorporated by reference herein.

[0002] This disclosure generally relates to the calibration of mechanistic ion - exchange chromatography models of chromatographs.

Background Art

[0003] The biopharmaceutical industry has made significant progress in the field of digital biomanufacturing over the past few decades with the introduction of powerful processors and large - capacity hard drives capable of storing and interpreting large amounts of data. Digital tools for process development and analysis have evolved rapidly, improving process performance and efficiency. The application of predictive models enables in silico exploration of the design space during process development and improvement of real - time control strategies in the manufacturing environment.

[0004] Chromatography is a method used for the separation and purification of molecules during the downstream processing of biomolecules and is an important step in the purification of biopharmaceuticals. Using chromatography, a biomolecule solution can be purified and concentrated using a porous packed bed that separates different molecules based on differences in the mass, size, or charge of the biomolecules. Ion exchange (IEX) chromatography is a purification process based on the ionic interaction between the chromatographic material and the molecules and involves using charged sites on the surface of the packing material to adsorb biomolecules based on the charged sites on the surface. Cation exchange (CEX) chromatography is an ion exchange chromatography mode that uses negatively charged sites on the surface of the adsorbent to adsorb biomolecules based on positively charged sites on the surface of the biomolecules. The adsorbed biomolecules can be eluted by reducing the surface affinity of the molecules through the use of a buffer solution with increased ionic strength.

[0005] The Quality by Design (QbD) approach described by the US Food and Drug Administration (FDA) in 2004 introduced the concept of building product quality requirements into the production process. In the following years, the International Council for Harmonization of Technical Requirements for Pharmaceuticals for Human Use (ICH) approved the QbD approach and introduced guidelines that define a systematic approach and scientific principles for the drug development process.

[0006] Apart from the regulatory monitoring requirements for the development of biopharmaceutical processes in the CEX step, technical issues also arise, and scale-up, process improvement, and process characterization to a larger scale become resource-intensive tasks.

[0007] With an accelerated and stringent timeline, there is little room to meticulously explore the process design space to find process parameters that enable maximum yield and purity while meeting the stringent constraints for process robustness and maximum molecule recovery. A process developed under such conditions in the early stages of a First-in-Human (FIH) study meets all the constraints required at that time but may lack scalability if the quality, quantity, or cost requirements change later.

[0008] As a result, iterative experiments requiring high resource levels are necessary to identify critical process parameters that reduce material consumption and improve process performance, such as yield and molecular purity. Methods that can be integrated into the early process development phase, enabling targeted experiments around the most promising process parameter range, can help guide processes to a more optimal state in terms of performance and scalability under accelerated timeline conditions.

[0009] Mechanistic models are tools used for knowledge-based process development, process optimization, predictive process control, and gaining process understanding in chromatographic separation processes. Mechanistic models provide predictions of key process outputs and performance indicators across a wide range of processes. In particular, mechanistic CEX chromatography modeling is a useful first-principles tool for describing molecular transport and elution behavior and predicting the behavior of chromatographic processes. Applying CEX chromatography models in process development to explore the design space for process parameters such as charging factors or elution gradients can reduce the effort required for iterative experiments. Furthermore, mechanistic modeling provides an opportunity to gain insights into the mechanisms influencing the separation of therapeutic proteins and their impurities. This knowledge can be used to inform decision-making during development and to optimize production quality and process performance. Essentially, mechanistic modeling provides a science-based tool useful for process design and optimization. For example, mechanistic CEX chromatography modeling can be used to make decisions about CEX process parameters such as gradient slope, collection criteria, and charging factors. However, mechanical models require prior knowledge and meticulous calibration processes to provide sufficient predictive power in small-scale and large-scale isolation processes. In particular, mechanical models require a well-defined mathematical description of each process step. Several studies exist that use mechanical models for process optimization, process investigation, and performance assessment or model-based control, suggesting workflows for mechanical models.

[0010] Several models are available that can describe the chromatography process of biopharmaceuticals. One of the first mathematical descriptions of the chromatography process described the adsorption of CO2 onto coal and silica gel using empirical formulas. Since then, chromatography models have further developed to include many possible contributions to mass transfer dynamics based on first principles. A key development is the General Factor Model (GRM). The GRM describes a combination of dynamic transport phenomena such as forced convection (by pressure), molecular diffusion, and molecular adsorption in a liquid chromatography system. This makes it possible to describe transport phenomena within the chromatography column in more detail than previous simplified versions (e.g., the ideal model and the Thomas model). For molecules smaller than the pore size of the chromatography material, the lumped pore model (POR) can be a suitable simplification of the GRM.

[0011] The adsorption of biomolecules onto adsorbents can be described by adsorption models. Here again, a vast number of models have proven applicable to chromatography are available. An initial adsorption model is the Langmuir model, which allows for concentration-dependent adsorption onto a surface with finite capacity. A further milestone in adsorption behavior modeling is the steric-mass action (SMA) model. Its equations allow for the influence of ionic strength, steric shielding of binding sites, and the affinity of biomolecules to the chromatographic material resulting from ionic interactions on the adsorption behavior of molecular mixtures. Several studies have demonstrated the successful application of the SMA model to ion-exchange chromatography. Detailed models are available that can describe non-intuitive adsorption behavior even under non-ideal process conditions such as high column loading. Model development activities for industrial chromatography processes can rely on existing transport and adsorption models. However, before application, the mechanistic model needs to be calibrated; that is, suitable model parameters must be identified so that the model describes the desired process.

[0012] However, the calibration process—namely, model development and estimation of model parameters—is still a very time-consuming process.

[0013] In other words, model parameters can generally be obtained by measuring them using methods such as optical microscopy and identifying pore transport coefficients. However, direct measurement of model parameters is often not possible or is extremely laborious; therefore, recursive parameter estimation is a method often used in chromatographic modeling.

[0014] In addition to the effects of competitive adsorption and ionic strength, mass transfer in the additional column volume affects the absolute elution time and peak shape in chromatogram simulations. Furthermore, the configuration of the tube, valve, or mixing chamber also affects the residence time of each component. During adsorption, parameter estimation involves using a recursive method from the start of elution until each eluted component is reflected in the adsorption parameters. Therefore, parameters estimated without considering the additional column volume are scale-dependent and may not be suitable when the system size or system configuration changes. This effect on the chromatogram can be particularly large when the column size is small compared to the additional column volume. However, in many cases, this effect has not been considered when estimating adsorption model parameters.

[0015] Scaling up the investigation involves applying conventional ion exchange chromatography models. One drawback of this discovery in this field is that the mass transfer coefficient depends on the flow velocity, and therefore, adaptation to the flow velocity is necessary.

[0016] In this study, multiple model calibration methods were compared for parameter identification in an SMA adsorption model, and the reverse fitting method was found to be more suitable for the purpose. For example, adsorption model parameters can be identified using a neural network, which accelerates parameter identification after a training period compared to chromatogram reverse fitting. A robust model calibration workflow, including a set of 14 experiments, is suggested for calibrating a multi-component SMA model of a bispecific antibody. These 14 experiments are used to calibrate the adsorption model and are added to the experiments to characterize the columns, requiring additional column characterization. Based on this workflow, the value of the mechanical model for investigation can be demonstrated in a process robustness study.

[0017] However, there is no explanation of how transport behavior in the additional column volume inherent to chromatographic instruments is considered in the calibration workflow. Many physical processes affect the chromatographic behavior of molecules. Apart from the effects of competitive adsorption and ionic intensity, mass transfer in the additional column volume affects absolute elution time and peak shape in chromatogram simulations. The configuration of tubes, valves, or mixing chambers affects the absolute residence time of each component. Consequently, during adsorption parameter estimation using recursive methods, the time elapsed from the start of elution to the elution of each component will affect the estimated adsorption model parameters. Therefore, parameters estimated without considering the additional column volume are scale-dependent and may not be suitable for larger or smaller system sizes or changing system configurations. This effect can have a significant impact on the chromatogram, especially when the column size is small compared to the additional column volume. The importance of proper representation of the additional column volume has not been demonstrated in previous publications. However, in many contributions, how this effect can be considered in the model calibration workflow has not been addressed. [Overview of the Initiative] [Problems that the invention aims to solve]

[0018] For the sake of time and effort in industrial process development, it is preferable to reduce the number of additional experiments required for model calibration to as few as possible. [Means for solving the problem]

[0019] This disclosure provides a workflow for CEX model calibration using a minimal set of experiments. The models provided by this disclosure include a model sequence that takes into account mass transfer in additional column volume and involves a combination of a fitted dead-volume model before the chromatographic column and a model set up solely from the geometric values ​​of the tube after the chromatographic column. Furthermore, in the models provided by this disclosure, model input parameters that reflect mass transfer and model input parameters that reflect molecular-specific adsorption behavior are identified separately. This disclosure demonstrates that the adsorption parameters are scalable across process size and provides sufficient predictive quality for scale-up process runs. Advantageously, this disclosure provides a chromatographic model calibration method with increased model accuracy and agility.

[0020] Calibration is structured into three parts of sequential parameter estimation, separating the transport model and the adsorption model from their differences. First, the unit operation representation of the chromatographic kit and its u-parameters are identified. Next, the transport model of the packed bed is identified. Finally, the adsorption model parameters are estimated.

[0021] Figure 1A shows an example of a channel representation commonly used in chromatography kits and machines such as AKTA® Avant. As shown in Figure 1A, various dead volumes exist before the column. Since these dead volumes affect the peak position relative to the start of elution, it is necessary to describe the dead volumes as precisely as possible in the model in order to isolate this effect from the adsorption behavior, which also affects the peak position.

[0022] Possible representations range from simple time shifts to mechanical representations of the volumes of the internal tubes and valves. In the case of BiTE® (bispecific T cell engager) antibody constructs, a combination of the DPFR model and the CSTR model is used to represent the dead volume before the column. The dead volume and conductivity sensors present from the column outlet to UV are similarly represented by the DPFR model.

[0023] The combination of tube and valve models is used to represent the flow paths from each sample pump to the UV sensor and from the inlet pump to the conductivity sensor. Both flow paths are combinations of pre-column fitted DPFR and CSTR models and DPFR model setups from geometric specifications provided by the vendor. After identifying the separate model parts of the column model, the two representations of the dead volume of the inlet and sample flow paths are combined to form a more complex model. The two DPFR models following the column are specified by the tube diameter and length specified by the vendor. Only the variance coefficients of these two DPFR models are set as the estimate of the pre-column DPFR.

[0024] The specific sequence of steps involves first obtaining the geometric values ​​(tube diameter, length) of the post-column tube, for example, by measurement or based on vendor specifications, and then conducting experiments to supply tracer molecules to the system from a desired location. Next, a series of DPFR-CSTR-DPFR models are set up, with the post-column DPFR model specified according to the geometric values ​​of a particular tube. That is, the geometric specifications of this post-column DPFR are fixed, but the parameters specifying the dispersion characteristics of the DPFR are not fixed and are estimated together with the characteristics of the pre-column DPFR and CSTR. Overall, the estimation involves estimating the geometric parameters of the pre-column DPFR and CSTR, as well as the transport coefficients, such as dispersion, of the pre-column and post-column DPFRs. Parameters not included in the estimation are the geometric parameters of the post-column DPFR. This step is performed for both the sample pathway flow (blue in Figure 1A) and the inlet pathway (green in Figure 1A). Once all transport parameters are estimated, the binding parameters can be estimated. The model can include as many components as the peaks to be simulated. Then, the parameters of each component being modeled can be estimated. The estimated parameter range can be used to include more components that form one or more chromatogram peaks, and the combined parameter can again be estimated using a dense boundary between the parameters.

[0025] The first innovation in this sequence lies in specifying the post-column DPFR model according to the geometric values ​​of a particular tube. This is accompanied by the fact that a combination of a fitted model and a model set up based on the geometric specifications is used to identify the level of transport effect impacting the column at the start. Thus, the time that the point sample and elution buffer impact the column can be identified more accurately than combining both the pre-column and post-column channels together, without performing more complex bypass experiments that separate the paths. Furthermore, it is possible to separate the transport behavior of the buffer from the transport behavior of the molecular solution using the method provided herein.

[0026] In conventional techniques, the focus of model-based process development is on how the model supports process design and optimization. Model calibration procedures are often not described. When the focus is on model calibration, most conventional techniques include new methods for estimating adsorption parameters, but do not include new methods for estimating the dead volume before the column.

[0027] The second innovation in this sequence is that the adsorption model parameters are roughly estimated using a model with a reduced number of components. As this step is complete, more components are added to the model. This is necessary for BiTE® and often for antibodies, as there are several molecular species that elute in the vicinity such that the UV sum signal appears as a single peak. Here, this more complex model needs to be recalibrated with a larger number of components, resulting in a much larger number of estimated adsorption parameters. However, due to the adsorption parameters that were roughly estimated earlier from a less complex model, a smaller parameter space can now be applied to the parameter estimation, thereby accelerating the estimation procedure.

[0028] Separating transport and adsorption effects in the chromatogram allows for a more accurate chromatographic model. Furthermore, the model is more flexible in terms of application domains. This means that, as long as the resin remains the same, the adsorption model parameters can remain the same even if other process specifications change. This is an insight that is often overlooked. However, it enables shorter model calibration procedures, compared to performing a new model calibration every time the process changes. Model-based process development can benefit from this speed improvement. Moreover, the model is more accurate compared to those where it is difficult to distinguish transport effects from adsorption parameters.

[0029] The method provided herein is more flexible and accurate than conventional methods for modeling dead volume in chromatography kits and machines, such as shifting the elution start time according to the dead volume or identifying the dead volume based on bypass experiments. Both conventional methods include the dead volume after the column exit as the dead volume described before the column.

[0030] Ultimately, the method provided herein allows for the estimation of adsorption parameters with reduced influence from transport effects. This technique more efficiently separates transport and adsorption effects in the chromatogram than conventional methods. This is beneficial when process specifications affecting molecular transport change. This applies to scale-up applications. In such cases, the effects of scale-up, such as tubing and flow rates, can be explained by separate parts of the model, and the adsorption model remains the same and does not need to be recalibrated under the changed process conditions.

[0031] In one embodiment, a method is provided comprising: acquiring geometric measurements associated with a second DPFR in a chromatograph including a first dispersed plug flow reactor (DPFR) and a continuous stirred tank reactor (CSTR) before the column and a second DPFR after the column; generating transport model parameters of a transport model associated with the second DPFR based on the geometric measurements using a processor; supplying tracer molecules to the chromatograph; capturing one or more tracer molecule measurements based on the tracer molecules moving through the chromatograph; and estimating one or more transport model parameters of a transport model associated with the first DPFR and CSTR based on a transport model associated with the second DPFR and one or more tracer molecule measurements based on the tracer molecules moving through the chromatograph using a processor.

[0032] In some examples, the method may include feeding an experimental sample into a chromatograph, capturing one or more experimental measurements based on the experimental sample moving through the chromatograph, and using a processor to estimate one or more adsorption model parameters of an adsorption model associated with the experimental sample based on one or more experimental measurements based on the experimental sample moving through the chromatograph, one or more estimated transport model parameters of a transport model associated with a first DPFR and CSTR, and transport parameters of a transport model associated with a second DPFR.

[0033] Furthermore, in some examples, geometric measurements may include pipe diameter and pipe length measurements associated with the second DPFR.

[0034] Furthermore, in some cases, one or more tracer molecule measurements are captured based on chromatograms associated with the tracer molecules as they move through the chromatograph. Similarly, in some cases, one or more experimental measurements are captured based on chromatograms associated with the experimental samples as they move through the chromatograph.

[0035] Furthermore, in some examples, the method may include the processor identifying the experimental sample based on the adsorption model associated with the experimental sample.

[0036] Furthermore, in some cases, estimating one or more adsorption model parameters of an adsorption model associated with an experimental sample may begin with estimating one or more first adsorption parameters of a first adsorption model associated with the experimental sample, and this method uses a processor to estimate one or more second adsorption parameters of a second adsorption model associated with the experimental sample, based on the range associated with the first one or more binding parameters of the first adsorption model associated with the experimental sample. next This may further include estimation. Furthermore, in some examples, the method may include the processor identifying the experimental sample based on a second adsorption model associated with the experimental sample.

[0037] Furthermore, in some examples, a first DPFR and CSTR before the column and a second DPFR after the column are part of the inflow path of the chromatograph, and the chromatograph further includes a sample channel having a first DPFR and CSTR before the sample channel column and a second DPFR after the sample channel column, and the step according to claim 1 is further performed with the first DPFR and CSTR before the sample channel column and the second DPFR after the sample channel column.

[0038] Furthermore, in some examples, the experimental sample is the first experimental sample, and the method may further include feeding the second experimental sample into a chromatograph, capturing one or more second experimental measurements based on the second experimental sample moving through the chromatograph, and using a processor to estimate one or more estimated transport model parameters of the transport model associated with the first DPFR and CSTR, transport parameters of the transport model associated with the second DPFR, and one or more adsorption model parameters of the adsorption model associated with the second experimental sample, based on one or more second experimental measurements based on the second experimental sample moving through the chromatograph. For example, in some examples, the second experimental sample is separate from the first experimental sample.

[0039] Furthermore, in some examples, the transport model parameters include one or more of the dispersion coefficient in the DPFR, the volume of the DPFR, the cross-sectional area of ​​the DPFR, and the volume of the CSTR. Furthermore, in some examples, the adsorption model parameters include one or more of the adsorption coefficient, desorption coefficient, characteristic charge, and shielding factor.

[0040] Furthermore, in some examples, the method further includes the processor estimating one or more column-specific transport model parameters of a column-specific transport model associated with the chromatograph column, based on a first transport model associated with DPFR and CSTR, a second transport model associated with DPFR, and one or more tracer molecule measurements based on tracer molecules moving through the chromatograph. Furthermore, in some examples, the column-specific transport model parameters include one or more of the column porosity and column dispersion rate.

[0041] Furthermore, in some examples, the method further includes the processor estimating one or more resin transport parameters of a resin transport model associated with resin particles in a chromatograph, based on a column-specific transport model, a transport model associated with a first DPFR and CSTR, a transport model associated with a second DPFR, and one or more tracer molecule measurements based on tracer molecules moving through the chromatograph. Furthermore, in some examples, the resin transport parameters include one or more film transport coefficients and pore porosity of each component.

[0042] Furthermore, in some cases, estimating one or more adsorption model parameters associated with the experimental sample is based on one or more column-specific transport models or resin transport models.

[0043] Furthermore, in some examples, the tracer molecule is dextran. In some examples, the tracer molecule is NaCl. Furthermore, in some examples, the tracer molecule is a DNA molecule. Furthermore, in some examples, the tracer molecule is a nanoparticle. [Brief explanation of the drawing]

[0044] [Figure 1A] The diagram shows the flow path of a chromatography machine (e.g., AKTA® Avant, etc.). As shown in Figure 1A, the flow paths from different locations depending on the line priming procedure represent the various points in time when the sample or elution buffer enters the column. [Figure 1B] This shows an example of how the mobile phase moves through a packed bed column. [Figure 1C] This section shows a visualization of the stereomass action model, including the meaning of the parameters. [Figure 2] The graphs of the squared difference sum (SSD) alignment problem using synthetic data are shown in several examples. [Figure 3] The following graphs compare the standard position penalty metric with the initial drop position penalty metric using several examples. [Figure 4] This section illustrates the methods used at each stage of model development. [Figure 5] The diagrams of the flow paths used for gradient elution in several examples are shown. [Figure 6] The CEX model represents the chromatograph system, and the general model construction, the unit operation of dispersed plug flow reactors (DPFRs), and continuous stirred tank reactors (CSTRs) represent peak delay and peak broadening that occur in systems without columns (valves, sensors, mixing chambers). Salts and molecules may experience different tubular or valve systems, and therefore their unit operation and associated parameters may differ between proteins and salt species. [Figure 7A] The calibration of the column pre-model of transport within the chromatography kit is shown, with Figure 7A showing the dextran tracer breakthrough from the sample pump, and Figure 7B showing the NaCl tracer from the inlet pump tail. [Figure 7B] The calibration of the column pre-model of transport within the chromatography kit is shown, with Figure 7A showing the dextran tracer breakthrough from the sample pump, and Figure 7B showing the NaCl tracer from the inlet pump tail. [Figure 8A] The calibration of column transport model parameters is shown in Figure 8A, which shows the text run breakthrough tracer (no pore penetration); Figure 8B, which shows the dextran pulse tracer (no pore penetration); and Figure 8C, which shows the FVIP of the BiTE® (bispecific T cell engager) antibody construct breakthrough (with pore penetration). [Figure 8B]The calibration of column transport model parameters is shown in Figure 8A, which shows the text run breakthrough tracer (no pore penetration); Figure 8B, which shows the dextran pulse tracer (no pore penetration); and Figure 8C, which shows the FVIP of the BiTE® (bispecific T cell engager) antibody construct breakthrough (with pore penetration). [Figure 8C] The calibration of column transport model parameters is shown in Figure 8A, which shows the text run breakthrough tracer (no pore penetration); Figure 8B, which shows the dextran pulse tracer (no pore penetration); and Figure 8C, which shows the FVIP of the BiTE® (bispecific T cell engager) antibody construct breakthrough (with pore penetration). [Figure 9A] Figure 9A shows a comparison of chromatograms and fractionated datasets between experiments and simulations under elution conditions, with Figure 9A showing the best fit under a 5 mM / CV gradient run, and Figure 9B showing the best fit under an 11 mM / CV gradient run. [Figure 9B] Figure 9A shows a comparison of chromatograms and fractionated datasets between experiments and simulations under elution conditions, with Figure 9A showing the best fit under a 5 mM / CV gradient run, and Figure 9B showing the best fit under an 11 mM / CV gradient run. [Figure 10A] The model validation in process-scale experiments with various charging factors, gradients, and stop collection criteria is shown. Figure 10A shows the model validation with an 8 mM / CV gradient and a 25 g / L charging factor on a benchtop-scale column. Figure 10B shows the model validation with an 8 mM / CV gradient and a 25 g / L charging factor on a process scale with a 30% stop collection criterion. Figure 10C shows the model validation with an 8 mM / CV gradient and a 15 g / L charging factor on a process scale with a 45% stop collection criterion. Figure 10D shows the model validation with an 8 mM / CV gradient and a 5 g / L charging factor on a process scale with a 30% stop collection criterion. [Figure 10B]The model validation in process-scale experiments with various charging factors, gradients, and stop collection criteria is shown. Figure 10A shows the model validation with an 8 mM / CV gradient and a 25 g / L charging factor on a benchtop-scale column. Figure 10B shows the model validation with an 8 mM / CV gradient and a 25 g / L charging factor on a process scale with a 30% stop collection criterion. Figure 10C shows the model validation with an 8 mM / CV gradient and a 15 g / L charging factor on a process scale with a 45% stop collection criterion. Figure 10D shows the model validation with an 8 mM / CV gradient and a 5 g / L charging factor on a process scale with a 30% stop collection criterion. [Figure 10C] The model validation in process-scale experiments with various charging factors, gradients, and stop collection criteria is shown. Figure 10A shows the model validation with an 8 mM / CV gradient and a 25 g / L charging factor on a benchtop-scale column. Figure 10B shows the model validation with an 8 mM / CV gradient and a 25 g / L charging factor on a process scale with a 30% stop collection criterion. Figure 10C shows the model validation with an 8 mM / CV gradient and a 15 g / L charging factor on a process scale with a 45% stop collection criterion. Figure 10D shows the model validation with an 8 mM / CV gradient and a 5 g / L charging factor on a process scale with a 30% stop collection criterion. [Figure 10D] The model validation in process-scale experiments with various charging factors, gradients, and stop collection criteria is shown. Figure 10A shows the model validation with an 8 mM / CV gradient and a 25 g / L charging factor on a benchtop-scale column. Figure 10B shows the model validation with an 8 mM / CV gradient and a 25 g / L charging factor on a process scale with a 30% stop collection criterion. Figure 10C shows the model validation with an 8 mM / CV gradient and a 15 g / L charging factor on a process scale with a 45% stop collection criterion. Figure 10D shows the model validation with an 8 mM / CV gradient and a 5 g / L charging factor on a process scale with a 30% stop collection criterion. [Figure 11] A flowchart illustrating an exemplary method, based on several examples provided herein, is shown. [Modes for carrying out the invention]

[0045] definition As used herein, "chromatography" refers to a method of separating and purifying molecules in a downstream process.

[0046] As used herein, “ion exchange chromatography” (“IEX”) refers to a chromatography process based on ionic interactions between molecules and chromatographic materials.

[0047] As used herein, “cation exchange” (“CEX”) refers to a chromatography process based on the interaction of cations between molecules and chromatographic materials.

[0048] As used herein, “anion exchange” (“AEX”) refers to a chromatography process based on anion interactions between molecules and chromatographic materials.

[0049] As used herein, "AKTA®" refers to the product name of a Cytiva® chromatography machine.

[0050] As used herein, “Dispersed Plug Flow Reactor” (“DPFR”) refers to a cylindrical tube having a convective laminar flow with a plug flow profile rather than a flow profile with a gentle slope.

[0051] As used herein, “continuous stirring tank reactor” (“CSTR”) refers to a tank reactor filled with a fluid to be completely mixed.

[0052] As used herein, "mixing chamber" refers to a small tank (approximately 1-10 mL) used for mixing buffer solutions within a chromatography machine such as an AKTA®.

[0053] As used herein, "valve" refers to a valve that connects all components within a chromatography machine such as an AKTA®. These valves can be switched between many inputs and outputs and may have small capacities (approximately 1 to 1000 μL).

[0054] As used herein, "model calibration" refers to the procedure for estimating unknown model parameters.

[0055] As used herein, “adsorption” refers to the process by which a solid holds molecules of a gas, liquid, or solute as a thin film.

[0056] As used herein, "dead volume" refers to the voids within a chromatography machine that are filled with liquid.

[0057] As used herein, "line priming" refers to filling a pipe / valve with the necessary fluid (e.g., buffer) before the start of the process.

[0058] As used herein, “fitting” refers to the procedure of iteratively estimating unknown model parameters by comparing simulations with measured values.

[0059] As used herein, "elution" refers to the process of removing adsorbed molecules from a chromatographic material.

[0060] theory Generally, the column models provided herein describe the important transport and adsorption effects of counterions and molecules present in an adsorbed state within the solute in the column. While a variety of adsorption models can be selected, the most important adsorption models describe how salt ions, as mobile phase modulators, influence the adsorption kinetics of molecules. Such processes are described on a second-time scale as well as on micrometer and meter-length scales. Simplified general fraction models (GRMs) and steric mass action models are used to simulate the transport and elution behavior of acidic, major, and basic charge variants of target molecules and high molecular weight (HMW) impurity species.

[0061] Transportation model As shown in Figure 1B, the mobile phase moves through a packed bed column having length L. The movement can be described by the volumetric flow rate, column cross-sectional area, and column porosity (porosity between packed beads). This movement is forced convection and is described by a convection term along the column length z. The pore volume l (the voids between beads in the liquid mobile phase) has effects on molecules moving through the bed via different pathways, such as diffusion of Fick, wall effects, or peak broadening; these are combined and described by a dispersion term in the model. Molecular flow from the pore volume to the porous particle volume p of the bed may be obstructed, which is considered by the film mass transfer model. Within the bead pores, diffusive transport is assumed to be much faster than mass transfer to the pores and is therefore assumed to be instantaneous. Consequently, there is no concentration gradient along the bead radius, which leads to the Simplified Generalized Factor Model (GRM) equations with a concentrated pore diffusion (POR) model. The model describing transport is independent of the adsorption capacity or the model describing molecular adsorption to the solid phase. It is assumed that the column packing and bead size are highly homogeneous, which leads to the assumption, firstly, that the concentration gradient in the radial direction of the column is negligible, and secondly, that the porosity of the packed bed and the porosity of the beads do not change along the column axis and bead radius.

[0062] GRM is used to describe the transport of biomolecules through porous packed beds due to convection, dispersion, and diffusion. Convection is the movement of species through a system due to the motion of the bulk fluid surrounding the system. Dispersion describes peak broadening due to the viscosity of the mixture, collisions with tube walls or particles, and movement through the packed bed. Further mass transport: transport from bulk liquid to pores and diffusion within pores are described by GRM. Diffusion from bulk liquid to pores can be a rate-limiting process due to spatial confinement depending on the ratio of molecular size to pore size. The rate at which this transport occurs is described in proportion to the film mass transport coefficient. The second component is diffusion through pores, which is described using various diffusion coefficients. This usually occurs faster than film mass transport. Due to this assumption, the GRM equations are simplified so that radial concentration gradients within the pores are ignored, thereby leading to a concentrated pore model.

[0063] The simplified GRM for any species concentration is ci∈[0,N c ] and N c 'x' indicates the number of components, 't' indicates the time in seconds, 'z' indicates the axial coordinate along the column length L, and 'r' is the bead radius r p The radial bead coordinates are shown along the axis.

number

[0064] Danckwerts boundary conditions apply:

number

[0065] The initial conditions are

number

[0066] l, p, and s represent the interstitial volume (voids between beads), pore volume (voids within beads), and solid volume (the solid portion including adsorbed molecules). The interstitial flow velocity is denoted by u in units of m / s, and the axial dispersion coefficient is D in units of m 2 / s ax The column porosity (the volume ratio of interstitial voids to the total bed volume) is denoted by ε c The bead porosity (the ratio of liquid pore volume to the total bead volume) is denoted by ε p The film mass transfer coefficient is denoted by k in units of m / s f,i and is denoted by.

[0067] The model of a dispersion plug flow reactor (DPFR) was used to describe the molecular transport in the tube. The equations of the DPFR describe the convective laminar flow in a cylindrical tube, ignoring the flow profile. The model equations are

Number

[0068] Here

Number

Number

[0069] The continuous diffusion layer reactor (CSTR) model was used to describe the mixing effect inside the chromatographic system of the valve and mixing chamber. That is, it describes how the concentrations of multiple components change when they are mixed together using an inlet, an outlet, and a tank model with a constant volume. The model equations are

Number

[0070] The initial conditions are

Number

[0071] Here,

number

[0072] Three-dimensional mass action model The steric-mass interaction (SMA) model describes the adsorption, desorption, and steric interactions between proteins and resins. These interactions with resins are characterized by four parameters: adsorption coefficient, desorption coefficient, steric factor, and characteristic charge. These parameters are specific to the particular model being studied. Unlike transport parameters, binding parameters can move between different scales and systems, as long as the resin and molecules remain the same.

[0073] The adsorption and desorption coefficients describe the rates of molecular adsorption (binding) and desorption (elution) of molecules from the resin. They describe the binding dynamics of the species being modeled and are influenced by the salt concentration. The steric factor and characteristic charge parameter describe the effects of molecular size and surface charge on binding dynamics, respectively. The steric factor describes the number of spaces in which the molecule is "shielded" from binding on the resin. The characteristic charge describes the number of charge-based interactions that the molecule has with the resin. The sum of the steric factor and characteristic charge indicates the total number of binding sites occupied by the molecule on the resin. A visualization of these four factors is shown in Figure 1C.

[0074] In addition to steric factors and characteristic charges, the ionic capacity of the resin is also necessary to determine the protein binding capacity to the resin. The SMA model is based on the neutral charge balance on the resin, and therefore all charged sites are occupied by counterions or reverse-charged proteins. The ionic capacity can be determined from titration experiments, which are detailed in the methods section.

[0075] The equations of the SMA model are explained below.

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[0076] In the formula, Λ is mol / m 3 The unit indicates the total column volume, ν i σ represents the characteristic charge, i k indicates the stereofactor, a,i teeth

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[0077] The main limitation of SMA isotherms is that the coupled parameter values ​​are only applicable at the specified pH. Since pH is a critical process parameter in the CEX process, this limits the robustness of the predictive mechanistic model. To extend the current SMA model and improve its robustness, a function capable of addressing pH dependence is needed.

[0078] Model calibration experiments were performed according to a standard process, with the only difference being the pH of the buffer and charged materials.

[0079] Numerical solver Since analytical solutions are unavailable, numerical solutions to all of the above equation systems are calculated. A common method is to discretize the partial differential equations (PDEs) along special variables, which yields several ordinary differential equations (ODEs). The ODE system can then be solved using a time-step algorithm.

[0080] Special discretization of the chromatographic model can be achieved by using the finite volume method. Here, mass equilibrium equations for several uniform finite volume elements along the column length z and bead radius r are set up. The concentrations in each cell volume are averaged, thereby generating a new set of state variables associated with each cell volume. Numerical integration solves the discretization equations for these averaged volume concentrations. Boundary conditions at the column inlet and outlet (equations (3) and (4)) are integrated into the discretization equations for the first and last finite volumes. A weighted essentially non-oscillatory (WENO) scheme is used to approximate the concentrations at the finite volume boundaries.

[0081] The time-step solver or ODE solver used here is part of the CADET framework and uses the backward difference (BFD) method for time integration. The CADET implementation uses the implicit differential algebra (IDA) solver included in the SUNDIALS package. The solver tolerance is 10 -6 Abstol, 10 -6 Algtol, 10 -8 Reltol, and 10 -4 It was set using the initial step size.

[0082] Parameter estimation algorithm Target system This disclosure introduces a novel target system for estimating chromatographic model parameters, where a target means a set of geometry-influenced metrics. Each metric is a single scalar value, such as the time difference between simulation and measurement at peak maximum, or the height difference at peak maximum. Metrics are defined based on specific knowledge of the process being modeled and typical errors in the measurement data. The metrics within a target can be passed to a multi-objective search algorithm, or combined into a single objective and passed to a single-objective search algorithm.

[0083] Multiple metrics can guide a search strategy much better toward a desired optimal state (multi-objective) than the commonly applied double difference sum (SSD) can guide the search strategy (single-objective). Metrics are grouped into scores to organize the target specification toward different parameter estimation procedures in CADET-Match. A suitable target must have the property that as fit quality improves, the value of at least one metric must decrease, and as fit quality deteriorates, the value of at least one metric must increase. A target that does not have this property risks leading the search algorithm in the wrong direction. This may seem trivial, but it is extremely important and is the core of why new targets must be created. Due to competitive coupling and other complex mechanisms, many model parameters have a non-linear coupling effect on the simulated chromatogram. Therefore, while model parameters are approaching their correct values, some will increase depending on conventionally applied metrics such as SSD.

[0084] In addition, chromatograms measured from large-scale industrial applications are often affected by systematic errors, such as pump delays, which can cause a time offset between the measured and simulated signals, unless the model captures the causes of delays that are often not actually possible. A good metric is needed to account for this, because otherwise the simulated peaks will be in the correct location but have an incorrect shape. An incorrect shape generally indicates an error in the physics underlying the model. Therefore, a good metric should prefer a peak with a nearly correct shape but a small offset over a peak with no offset but an incorrect shape.

[0085] Sum of squared differences For SSD, the squared difference between the simulated chromatogram and the measured chromatogram is summed over time points (see Section 16 below). For normalized root mean square difference (NRMSD), the SSD is divided by the number of time points, then the square root is taken, and the result is divided by the maximum of the measured data (see Section 17 below). Due to the monotonicity of this transformation, SSD and NRMSD have the same minimum. These metrics are applied to the entire chromatogram J = {1;…;N} d} or a subset of data J⊂{1;…;N d It can be applied to}. SSD is most commonly applied using the gradient descent search algorithm. Therefore, it is included here for comparison. The theory is well defined as a maximum likelihood estimation framework with independent, uniformly distributed random measurement errors. However, these assumptions are generally not valid for modeling large-scale preparatory chromatography where systematic errors such as supply fluctuations, pump delays, and flow rate fluctuations typically prevail due to detector noise. To interpret the results, NRMSD is more suitable than SSD because the numerator has the same units as the data and the denominator is more related to the maximum concentration.

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[0086] SSDs are sensitive to parameter changes and require sufficient overlap between simulated and experimental chromatograms to guide the search algorithm toward optimization. This can complicate the selection of a suitable starting point, especially with sharp and / or small peaks. Further disadvantages of SSDs are shown in Figure 2 using a composite example with the parameters shown in Table 1. Although the parameters in Scenario 2 are much closer to ground truth and there is only a relatively small deviation in the characteristic charge ν, Scenario 1 nevertheless has a smaller SSD and is therefore generally considered a better fit. In addition, the peak shape of Scenario 2 is more similar to ground truth, but the alignment is off.

[0087] In actual experiments, such time offsets are often caused by pump delays that cannot be explained by the mechanistic model. In this case, SSD prefers a peak located to the right, even if the peak shape is clearly incorrect to the human eye. The model can also reproduce the correct peak shape, but not to the right, and the SSD is much larger. Since the peak shape is determined primarily by the coupled model parameters, SSD leads to non-physical parameter values. Therefore, we introduce here an alternative metric that favors peak shape over position and has a lower demand for selecting a suitable starting point.

[0088] [Table 1]

[0089] Alternative metrics The shape and position of the chromatogram are determined by mass transport and binding to the functionalized resin throughout the entire system, including the column and external volume. The drawbacks of SSD are avoided by separately measuring the shape, position, and height of individual peaks without requiring baseline separation. The peak position metrics are susceptible to changes in each model parameter and independent of peak overlap between simulation and experimental data. This provides flexibility and robustness in selecting starting points for search algorithms, which are crucial for automation in industrial applications. Focusing on individual peaks reduces the influence of process variations and additional components not fully included in the model. For example, pump cleaning or pressure alarms can produce false peaks, and industrial supplies typically contain numerous impurities of more or less unknown nature. In such cases, separate metrics can be assigned to distinguishable but partially separated peaks representing the target component as well as high and low molecular weight impurities. Separate metrics also help provide more precise information to (multipurpose) search algorithms about which components affect which peaks. All metrics yield zero when the simulation and experiment perfectly match.

[0090] Peak shape The shape metric is the most innovative of the new metrics and is a core component of almost all scores. It is the difference between one of the Pearson correlations between the measured and simulated chromatograms over a continuous range of time offsets and the maximum (see Equation 18 below). To evaluate this metric, the simulated chromatogram is shifted over time.

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[0091] Peak position The positional metric can be more complex than when it first appeared. The positional metric is obtained by maximizing the time offset t of equation (19) below. s Based on.

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[0092] The standard position metric imposes an immediate penalty for time offset (see Equation 20 below), and if it deviates from the alignment, t r It increases linearly to 1. Here, t ris the length of the measurement time interval. If a sufficient starting point is provided to the search algorithm, this can be replaced by the residence time of the unbound tracer. As shown in the results section, this metric is a good choice for estimating the porosity of the column and particles. However, care must be taken in running the experiment to ensure that delays are as small as possible and that alarms are canceled immediately. Such delays affect the chromatogram in almost the same way as changes in the porosity of the column and particles. As discussed earlier, if such delays are present, it may be advantageous for the parameter estimation procedure to compromise the alignment between the simulated and measured peaks while matching the shape and height between the simulated and measured peaks. Therefore, firstly, 1 / 10t r If the range is less than half, the penalty is reduced by half, and then if it deviates from the alignment, t r An alternative position metric is introduced that increases linearly up to 1. See equation (21) below. Figure 3 shows the difference between the standard position penalty metric and the initial drop position penalty metric. The initial drop of 1 / 2 and the range of 1 / 10 are experimentally selected and can be modified by the user.

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[0093] Peak height The peak height metric correlates the maximum concentration in the simulated chromatogram to that in the measured data (see Equation (18)). This metric increases to 1 if the difference in either direction is greater than 100%.

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[0094] Joint score The previously introduced metrics serve as building blocks for creating scores that quantify the difference between simulated chromatograms and measured data. Scores are defined for individual components and can target the full chromatogram, individual peaks, or parts of peaks, such as only the leading edge of a peak. Each score is a set of metrics that depend on the component's index i and a set of considered time points J. The goal will consist of one or more scores, which may be combined into a single goal or passed to a multi-objective search algorithm.

[0095] Sum of squared differences The SSD score is a set of differences between simulated chromatogram data and measured chromatogram data. See equation (23) below. For technical reasons, each difference is interpreted as a separate metric. In Section 8, the target is defined as the sum of the squares of these metrics. S SSD ={X i,j -Y i,j |j∈J} (23)

[0096] Full Peak The simplest of the new scoring methods is the combination of peak shape, position, and height S. ガウス This score is typically applied to a time interval specified by an index set J containing a single, roughly Gaussian peak. This time interval is not automatically detected but must be specified by the user. A more detailed score S is available. ピーク This further describes the shape, minimum, and maximum of the time derivative and is better suited to fitting non-Gaussian peaks. By combining the peak shape with the shape of its derivative, this score has high sensitivity to the curvature of the chromatogram. The time offsets in the peak and slope are not technically constrained to be equal. In practice, they are hardly different except in the very first iteration of the search algorithm with a poor starting point.

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[0097] Peak front In some cases, only the leading edge of the peak can be used for parameter estimation, as the rest of the peak is degraded by unspecified interactions of the tracer molecule with the column or tube. Dextran is a prominent example of such non-ideal behavior, leading to strong tailing and a decrease in peak height. On the other hand, dextran is commonly used as a tracer that does not penetrate particle pores. Errors in experimental execution may also prevent the trailing edge of the peak from being used for parameter estimation. These situations are considered when scoring S, which takes into account the shape and position of the peak but not the peak height. 前部 This is addressed by [method / method]. This score is typically used in conjunction with fairly short time intervals and a small number of data points. S 前部 ={shape(X i ,Y i )J ;Position(X i ,Y i ) J (26)

[0098] The peak leading score is designed to extract as much usable information as possible from the chromatogram. In the unsupervised application of this score, the usable time intervals must be automatically determined while robustly removing non-ideal portions with high accuracy. For dextran data, the trailing end of this interval is chosen at the first inflection point of the measured chromatogram; i.e., the upper cut point is at the first maximum of the time derivative. Experimentally, this is a good choice, as non-ideal interactions primarily affect peak height and tailing. The lower cut point is chosen where the measured chromatogram begins to deviate from the baseline by more than 0.1% of the concentration at the upper cut point. Experimentally, 0.1% is a robust choice for this threshold. The exact locations of these cut points are determined using Powell's method for continuous spline approximations from Section 5. The nearest neighbor time points of the discrete measurement data are then used as boundaries for the time intervals specified by J.

[0099] Fractionated data Optical detectors typically used in chromatogram measurements are usually unable to distinguish between different chemical components. Instead, the optical detector delivers a single sum signal, with the contributions of individual components weighted by extinction coefficients. Such a signal cannot be used for parameter estimation on its own unless the peaks of the relevant components are well separated. For example, the acidic, major, and basic components of a monoclonal antibody often completely overlap in a single peak. This situation is usually addressed by fractionation, i.e., by pooling the column effluent into a series of vials. Each of these vials is then analyzed offline to quantify the component of interest and provide additional information for setting up dedicated parameter estimation scores.

[0100] The previously introduced metric can generally be applied to the concentration in each vial, using the center of the corresponding acquisition interval as the time point. For precise comparison, simulations for each corresponding component are averaged over the same acquisition interval when the metric is applied to fractional data. The resulting information is often sparse, with 5-10 fractions per peak, and may have additional errors in fractionation time and volume. Even small shifts in the acquisition interval can lead to significant changes in the distribution of components between the fractions being analyzed, especially in the case of sharp peaks. The smoothing procedure from Section 5 is not suitable for such sparse measurements. Nevertheless, to maintain subgrid accuracy, a time offset t is used. s To identify this, a spline approximation must be applied to the original simulation data before it is shifted and effectively fractionated. Based on this offset, the score

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[0101] Search Strategy The scores described above are defined for each component, but they can also be applied to the sum signal. The scores of multiple components can be merged to create the target of the applied search strategy. It is wise to use all available information by including the scores on the sum signal. CADET-Match uses two alternative search strategies: gradient descent and a multi-objective genetic algorithm. Gradient descent requires combining all metrics into a single scalar value, while the genetic algorithm can operate on multiple metrics.

[0102] Gradient descent The gradient descent algorithm uses derivative information about the parameters being sought to find local optima of the target function. Gradient descent has long been used for parameter estimation in chromatography. While gradient descent is highly efficient near the desired optimal, it can fail if the target function is not smooth or if the Jacobian is singular. Furthermore, this algorithm is prone to getting stuck in local optima that may be far from the starting point. This can be avoided by basin hopping or multi-start strategies. The latter is often applied when improving the results of population-based search strategies.

[0103] Genetic Algorithms (GA) Genetic algorithms (GAs) are an example of biomimicry. Fundamentally, genetic algorithms function like bacterial colonies adapting to their external environment and share many of the same characteristics. GAs are remarkably similar. An initial population is created, often using quasi-random methods such as Latin hypersquare sampling or Sobol sequencing. Each member of the population is then evaluated based on one or more objectives. At the end of each generation, the optimal members survive and regenerate to form the next generation. The next generation is created by a combination of breeding and mutation of the surviving members. This procedure has variations that maintain population diversity, select members to include in the next generation, and change how breeding and mutation are carried out. These variations give rise to different algorithms such as NSGA2, NSGA3, and SPEA2. In light of the no-free-lunch theorem, different GA variants were tested and optimized on a variety of problems before settling on NSGA2 for single-objective problems and NSGA3 for multi-objective problems.

[0104] Online monitoring Building complex models that correctly and appropriately process experimental data and determine suitable starting points can be a difficult and laborious task. It is unlikely that a new model or concept will be correctly implemented from scratch based on experiments. However, such problems can only be tested by attempting to fit the model to the data. Since errors can often be identified in the early stages of the parameter estimation process, CADET-Match provides the ability to monitor the progress of specific indicators such as peak height, shape, and mass. This allows observation of whether the starting point yields reasonable results and whether the search algorithm is constantly improving the target. Online monitoring allows for early termination if progress is poor or if the results are already sufficiently good. This is crucial for rapid testing of models, targets, starting points, and termination criteria. Because determining suitable starting points can be difficult, GAs with fairly large population sizes are generally a good choice for initial testing. Multi-start gradient search is not a good alternative because parallel iteration processes are more difficult to monitor.

[0105] Parameter conversion Most search strategies struggle when the parameters being sought are spread across several orders of magnitude or correlated with each other. Parameter transformations can help soften such problems. CADET-Match provides several transformation rules, or one-to-one maps, between model parameters p passed to a chromatography simulator and estimated parameters P' passed to a search algorithm. These transformations provide an upper bound on the model parameters.

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[0106] The linear transformation (see Equation 27 below) is applied to the original range

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[0107] Nonlinear parameter correlations are difficult to detect and therefore require special attention. For example, the adsorption and equilibrium constant k a and k eq Typically, the adsorption and desorption constant k a and k d The degree of correlation is much lower. Relationship k eq =k a / k d The search algorithm is k a and k eq While operating against k a and k d This allows the data to be passed to the simulator. The corresponding transformations (see equations 29 and 30 below) also explain the large parameter range. This decouples the binding ratio from concentration equilibrium.

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[0108] Sensitivity analysis The system's sensitivity to inputs at a working point is defined as the derivative of the system solution. Such inputs can be model parameters or supply concentrations. Sensitivity measures how much a change in a particular model input affects the model output.

[0109] The sensitivity of any model input can be calculated using the CADET library and written to the .h5 output. CADET uses algorithmic differentiation. Numerical approximation of the analytical derivative can be obtained using the finite difference method, which is similarly available in the MoChA tool.

[0110] Parameter identifiability Model parameters can generally be obtained by measuring them using methods such as optical microscopy to identify pore transport coefficients. However, obtaining direct measurements of model parameters is often impossible or extremely cumbersome; therefore, recursive parameter estimation is a common method used in chromatographic modeling. Parameter identifiability describes the ability to find model parameters that are specific to a given set of known inputs and model equations. In the case of chromatography, model parameters have poor identifiability when various parameter sets produce the same simulation chromatogram or chromatograms with only slight deviations. This makes parameter estimation difficult. Parameter identifiability can be visualized by plotting target values ​​calculated to evaluate the fit quality of specific parameter values.

[0111] Materials and methods A novel modality, BiTE® (bispecific T-cell engager) antibody structure, is used as an example to demonstrate the systematic approach described herein. The molecule is BiTE®, a half-life extension antibody, which is a member of a class of bispecific antibodies that are highly promising for cancer treatment and other serious diseases. The BiTE® molecule was prepared using a Chinese hamster ovary cell line developed by Amgen and subsequently captured by a protein A affinity step. BiTE® was captured by a protein A affinity step, followed by viral inactivation and deep filtration to produce a filtered viral inactivation pool (FVIP).

[0112] Next, virus inactivation was applied by adding 1M formic acid. The pool was neutralized to pH 5.0 using a 2M Tris system to produce an unfiltered virus-inactivated pool (nVIP). The nVIP was filtered using a Millistak+(registered trademark) HC pod depth filter to produce a filtered virus-inactivated pool (FVIP).

[0113] The experiment was performed using an AKTA® Avant150 chromatography system with Unicorn 7.3 software. pH, UV, and conductivity measurements were performed in-line using standard UV, pH, and conductivity probes installed on the chromatography system. Offline measurements of UV, pH, and conductivity were performed using SoloVPE (C Technologies, Inc.), a pH probe (ThermoFisher Scientific), and a conductivity probe (ThermoFisher Scientific), respectively, to verify the readings.

[0114] Benchtop experiment For a benchtop scale run, Capto SP ImpRes resin (Cytiva®) was packed into a Millipore vantage column (1.15 cm inner diameter and 20.7 cm height) at a compression ratio of 1.11, resulting in a column volume of 21.5 mL. The column asymmetry factor was 0.91, and the HETP was 0.0203 cm³.

[0115] Dextran Blue 2000 solution (Cytiva®) was used as a tracer molecule for dead volume and dispersion experiments. For dextran breakthrough and pulse experiments, a 2L solution was prepared with a dextran concentration of 0.1g / L in Milli-Q water.

[0116] The ion capacity of the Capto SP ImpReS resin used was obtained by the titration method described by Thiemo Huuk 2016. A 1.7 mL CV miniature column packed with Capto SP ImpReS from the same lot was exposed to 0.5 mM hydrochloric acid (HCl) at approximately 500 CV. The column was then washed with water to remove any residual acid. The column was then exposed to 0.01 M sodium hydroxide (NaOH). Finally, the ion capacity of the column was determined by Thiemo Huuk 2016 using the volume of NaOH necessary to completely replace the counterions.

[0117] Filtered virus-inactivated pool (FVIP) material was used for chromatographilan on a benchtop scale. The supplied materials were from the same manufacturing lot, and their supply characteristics are shown in Table 2 below.

[0118] [Table 2]

[0119] The conductivity of the unbonded pulse supply material was adjusted to 180 mS / cm using 4M sodium chloride.

[0120] All benchtop experiments were performed at a flow rate of 2.60 ml / min. Benchtop bypass experiments were performed by connecting the column inlet and outlet tubes of the chromatograph to zero-volume connectors. Dextran solution was flowed from the sample pump at a flow rate of 2.60 ml / min until the UV signal stabilized. The same procedure was used with a 1 M NaCl solution to identify holdup from the sample pump to the conductivity meter.

[0121] Dextran breakthrough and pulse tracer experiments were performed, including those involving a column. The dextran solution was loaded from the sample line. First, 3 CV of 18% ethanol was run to establish baseline UV and conductivity readings. In the pulse experiment, 10 mL of dextran was loaded, while in the breakthrough experiment, loading continued until a stable UV signal was achieved.

[0122] Protein breakthrough experiments were performed using a conductivity-44 mS / cm equilibrium buffer and a conductivity-adjusted FVIP pool to ensure the column was equilibrium and loaded under non-binding conditions. First, the column was equilibriumized over 3 CVs using a high-conductivity equilibrium buffer, and then 40 mL of the conductivity-adjusted FVIP pool was flowed through the column. After loading, regeneration was performed to confirm that no proteins were bound to the column.

[0123] First, equilibration was performed over 5 CV, and a gradient elution run was carried out by adding FVIP material at a rate of 25 g per liter of resin. A washing step using equilibrium buffer was performed over 3 CV. Elution was performed at gradients of 5, 8, and 11 mM / CV, and a single-step elution was performed.

[0124] The chromatography buffers are listed in Table 3 below.

[0125] [Table 3]

[0126] Process Robustness Experiment For process-robust runs, non-filterable virus-inactivated pool (NVIP) material was used. The same lot of material at a concentration of 4.80 g / L was injected with various charge levels and gradients.

[0127] All process robustness experiments were performed at a flow rate of 4.33 mL / min. These experiments included a 44 mL column (1.6 cm inner diameter, 22 cm length). Unless otherwise specified, a 30% collection stop criterion (in percentage of the maximum major peak value) was applied by stopping the collection mode and immediately switching to 100% elution buffer upon detection of this event. This technique is part of the Unicorn automated chromatography control system.

[0128] Protein experiments were performed using different elution gradients, loading factors, and collection criteria. Table 4 shows the combinations of parameters used in the process robustness experiments.

[0129] [Table 4]

[0130] algorithm The model equations were solved using the open-source simulator Chromatography Analysis and Design Toolkit (CADET). The software allows for the description of a series of unit actions by combining various transport and adsorption models for the chromatography process, as well as CSTR and DPFR type transport models. Furthermore, the software provides model-based analysis tools, including sensitivity to model input parameters. The software package is available at https: / / github.com / modsim / CADET. CADET was accessed via a Python interface. Parameter lookup was performed using CADET-Match, an open-source software package based on the CADET engine, which is available at https: / / github.com / modsim / CADET-Match. The estimation algorithm used in this tool employs multi-objective maximization to measure the similarity between simulated and measured chromatograms. The best fit was identified by using the result with the highest product of these objective values.

[0131] Results and Discussion In model development, the steps involved were as follows. This method was used to separate transport effects, such as peak delay or peak broadening caused by molecular transport within the tubes and valves, from adsorption effects in the model. This is particularly important because the transport effects described can be combined into adsorption coefficients by recurrent model calibration, which reduces the applicability of the model across various column scales. The steps involved are shown in Figure 4.

[0132] Stage 1: Capture of the process system Figure 1A shows a flow path representation of commonly used chromatography kits and machines, such as those from AKTA®. Figure 1A shows various dead volumes before the column. This dead volume needs to be modeled because it affects the peak shift during elution with respect to the start of elution. Possible representations range from a simple time shift at the start of elution to a mechanical representation of the volume of the built-in tubes and valves.

[0133] Figure 5 outlines the simplest representation of the pathway a molecule experiences in a chromatograph. This combination of unit actions was used to create a representation of the process required for gradient elution.

[0134] The resulting unit-action model system is set up by combining the DPFR and CSTR models with the column model. Figure 4 shows the model sequence with multiple unit actions.

[0135] The effects of pipes, mixers, and valves are simulated using pipe and tank models. The column model equations given in equations (1) to (7) are used.

[0136] Identifying additional column transport parameters The combination of the tube model equations and valve model equations given in equations (11) and (12) is used to represent the flow path from the sample pump to the UV sensor and the flow path from the inlet pump to the conductivity sensor. All paths are set up as a combination of the fitted pre-column DPFR and CSTR models (inlet pump (buffer) path and sample pump (molecular) path) and the DPFR model setup from only the geometric specifications (length and diameter) provided by the vendor. As described herein, the pre-column tube model and mixer / valve model are fitted individually to the dextran breakthrough bypass and salt bypass runs. Furthermore, the tube 6 and tube 7 models are set up according to the AKTA® Avant150 manual with a diameter of 1 mm and lengths of 17 cm and 10 cm, respectively. The coefficients of variance of these two models are set to the coefficients of variance estimated in the bypass experiment.

[0137] Stage 2: Capture of transport and column transport characteristics Identification of bypass transport parameters Parameters describing the transport behavior from the column can be separated from effects arising from adsorption by performing dextran and salt tracer experiments that bypass the column. The column inlet and outlet are connected by zero-volume connectors so that the column is excluded from the flow path in the bypass experiments. The important flow path for the gradient elution run is shown in Figure 6. A list of parameters to be estimated in this process is given.

[0138] Table 5 provides a list of the names, descriptions, and ranges of the parameters estimated for each pathway the molecule experiences. The ranges correspond to the limits used in the estimator algorithm.

[0139] [Table 5]

[0140] It is important to note that non-ideal behavior was observed in dextran. Possible causes include interaction with the pipe wall or pressure deviations resulting from strong high-density gradients. Such non-ideal behavior can be observed at various inflection points during the rise of the breakthrough (see Figure 7A). Due to this behavior, the parameter estimation algorithm fits the simulation to the beginning of the breakthrough or peak, ignoring the preceding points in the chromatogram. In CADET-Match, this method is fully automated. The results of this model calibration process are shown in Figures 7A and 7B.

[0141] The final parameters are given in Tables 6A to 6C. In Figures 7A and 7B, the effect of tracer molecules such as dextran is clear, and as shown in Figure 7A, the fit to the initial rise of the dextran breakthrough leads to different parameters compared to the fit to the entire dextran breakthrough. Small pre-peaks during the dextran breakthrough rise were assumed to be artifacts and were largely ignored by the estimation algorithm. The fit in Figure 7A provides model parameters for the unit operation of the sample pathway (see Figure 6). The calibration results in Figure 7B show the model representation of the inlet pathway (see Figure 6). Due to the near-ideal behavior of the salt tracer, only negligible discrepancies are observed between the fitted model and the conductivity signal.

[0142] [Table 6]

[0143] [Table 7]

[0144] [Table 8]

[0145] Identifying column transport parameters Column-specific transport parameters were identified using dextran breakthrough and pulse experiments performed on columns in the line. Knowing the hold-up volume and dispersion generated by the pre- and post-column tubes allows for more precise parameter identification of column-specific transport effects. Blue Dextran 2000 acts as a non-porous transporous tracer molecule for Capto SP ImpReS; therefore, in this initial step, interstitial phase column transport is calibrated. The transport parameters estimated using dextran experiments are given in the table. Table 7 provides a list of parameters that underwent interstitial phase column transport calibration.

[0146] [Table 9]

[0147] Here too, the CADET-Match tool was used in this estimation process. The fitted results are shown in Figures 8A and 8B.

[0148] The simulated trace breakthroughs and pulses are fitted to the dextran experiment in the front of the chromatogram and show an even better fit. The resulting model parameters are given in Tables 6A to 6C. The next step involves estimating transport parameters related to the resin particles. These parameters refer to mass transport from the void volume into the particles and particle porosity. Table 7 shows the parameters and parameter ranges used in the estimation procedure. The results of the particle transport calibration step are shown in Figure 8C. The resulting model parameter values ​​are given in Tables 6A to 6C.

[0149] [Table 10]

[0150] Table 7 provides a list of the names and ranges of the parameters that underwent particle transport.

[0151] The non-idealism at the top of the chromatogram in Figure 8C is caused by a pressure alarm resulting from loading the column to its full capacity and is ignored in the parameter estimation. Here again, only the first part of the breakthrough pre-process is used by the estimation engine. In this step of model calibration, the FVIP material containing the target molecule and impurities is used. Therefore, the parameters obtained in this step describe the pore transport of the molecule actually used, not the tracer molecule.

[0152] Stage 3: Capture of quantitative adsorption behavior Here, the adsorption behavior of the target molecule can be identified by using a model description of the chromatograph's unit operation system in step 3. Complete experimental chromatography was performed using different gradient slopes (5 mM / CV, 8 mM / CV, 11 mM / CV, and "step" elution). Elution volumes were fractionated at 0.5 CV intervals, and the fractions were analyzed by analysis size exclusion (SEC-HPLC) and cation exchange (CEX-HPLC) chromatography to obtain the content of the molecule of interest.

[0153] The species being modeled The species to be modeled was determined using fractionated data. The target chromatogram area of ​​interest is the primary peak and the subsequent peak containing impurities.

[0154] Based on the analyzed fractions, the major peak is modeled by grouping all charge variants of the target molecule into three charge variant species: acidic variant, major variant, and basic variant. The molecular weight is assumed to be equal for all three variants. Based on the SEC analysis of the fractions, all species included in the impurity peaks are explained in the model as a single component. Finally, a five-component model is obtained, namely one salt species describing sodium as the counterion, four protein components describing the acidic, major, and basic charge variants, and a high molecular weight (HMW) component.

[0155] The model uses the various concentrations to be modeled in the FVIP material as input parameters, which means that analytical experiments must be performed to identify the various feed protein concentrations to be modeled in order to accurately represent the molecular species entering the column. For efficiency and time-series reasons, the feed protein concentrations were identified by using an experimental fraction pool along with a UV chromatogram instead of an analytical profile of the feed solution. The ratios between peak areas in the fraction pool and the ratios between peaks in the UV chromatogram are calculated. The various concentrations in the feed material are then calculated by considering the total protein concentration present in the FVIP material.

[0156] Calibration results 5mM / CV and 11mM / CV gradient runs were used in parallel for coupled parameter estimation. UV signals and fractional data were used for estimation. The estimated parameters and parameter ranges are listed in the table.

[0157] Table 9 provides a list of the names and ranges of the estimated parameters. Each of the various modeled parameters is estimated.

[0158] [Table 11]

[0159] The ion capacity Λ was set to 1339 mM following the procedure described above in the "Benchtop Experiment" section. The best fit obtained is shown in Figures 9A and 9B. The final adsorption model parameter values ​​are listed in Tables 6A to 6C.

[0160] Model Appraisal To measure model predictability for model validation, process performance indicators (PPIs) such as pool volume, yield, and pool concentration are used. Further gradient experimental runs at various process scales (44 mL column) and benchtop scale (21.5 mL column) with varying loading and gradients are used for model validation. Model scale-up was performed by setting the column diameter and column length to the specified values ​​for process scale columns. Furthermore, the volumetric flow rate was changed from 2.60 mL / min to 4.33 mL / min. All model parameters were maintained to be the same as those estimated by model calibration. The PPI thresholds for model acceptance are listed in Table 9. Visualizations of model predictions and experimental data for process scales are presented in Figures 10A, 10B, 10C, and 10D.

[0161] [Table 12]

[0162] Benchtop and process-scale gradient runs are used for model validation. First, the PPIs of runs with a 25g / L loading factor are compared, and the results are shown in Table 10.

[0163] [Table 13]

[0164] As shown in Table 11, the model is observed to predict the PPI of benchtop-scale processes within a 5% deviation range. Model predictions for runs at process scale are within a 13% deviation range. Both 5% and 13% are well within the predefined acceptable ranges given in Table 10.

[0165] Further model validation activities include comparing model predictions for process scales under various charging factors, gradient slopes, and data collection stop criteria. The results of model validation are compared in Tables 12 and 13.

[0166] [Table 14]

[0167] [Table 15]

[0168] From Tables 12 and 13, it is observed that the model predictions remain well within the defined PPI range while changing the loading factors. However, the model appears to lose predictivity with respect to yield when the gradient slope is changed, even when the gradient slope is close to the value at which model calibration was performed. In those runs, a tendency towards overall overestimation of yield and pool capacity can be observed. The reason for the yield overestimation can be found in overall overestimation of the peak area, which is linked to a single model limitation, a general problem in mechanical chromatography modeling. This indicates that the mass loaded into the simulated column was higher than that measured by the UV detector in the chromatogram, leading to a peak area shift of approximately 10%. The model appears to have very high sensitivity to protein loading. More accurate loading concentrations to determine the mass supplied are not available in this dataset.

[0169] In Table 12, the portion of charge variants in the collected pool of primary, basic, and acidic charge variants is compared between predicted and measured values. All simulated portions deviate from experimentally obtained values ​​by 0–16.2%. The values ​​demonstrate sufficient model accuracy to predict charge variant profiles with various charging factors and gradient slopes. This suggests that the model calibration workflow is suitable for model calibration activities in industrial CEX process development.

[0170] It is worth noting that in order to convert UV signals from AU units to SI units, it is necessary to assign molecular weights to the various types being modeled. SI units are convenient for simulation activities. The molecular weight of HMW species is not precisely known. Therefore, the amount of HMW species in supply is also not precisely determined. In the process of improving model accuracy, the molecular weight of HMW can be considered more precisely.

[0171] Further improvements in model accuracy can be achieved by combining the UV280 and UV300 measurement signals in a more integrated manner. It is observed that the maximum values ​​of the major peaks in some of the presented chromatograms are very close to the upper end of the linear range of the UV280 signal. This may contribute to the deviations observed in the chromatogram peak area and the simulated peaks. Here, flexible data integration in combining the UV280 and UV300 data signals would be valuable for improving model accuracy.

[0172] Summary and Conclusion To construct the final model, we introduced a model development method for pharmaceutical therapeutic molecules that suggests a three-step method calibration process for each stage of the model. This method can be used to separate the description of the transport model from the adsorption model.

[0173] A model representation of the chromatography system, including multiple unit operations, was created. The system describes the pathways experienced by either sample molecules or buffer molecules during the salt elution step, both of which include valves and tubes, apart from the column. In the next step, model parameters describing interstitial column transport are estimated. The following step estimates parameters describing mass transfer to the pores. Finally, in the final stage of model calibration, adsorption model parameters are estimated. A separate experimental set is used in each parameter estimation step.

[0174] The accuracy of the model is assessed by using experiments run at various column scales. The model can be used to predict elution behavior in process robustness experiments with acceptable quality and to explore various process parameters such as gradient slope, loading factor, and collection stop criteria.

[0175] Using it, one can conclude that the suggested workflow is accompanied by steps necessary to construct model parts for additional column capacity, intra-column transport, and adsorption behavior. Beneficial features of the method provided herein are: · few experiments are required for calibration, · additional column capacity is characterized and each model part can be reused for other molecules, · by the relative decoupling of calibration of the transport model and calibration of the adsorption model, the model can reflect equipment changes and can further be used across various scales.

[0176] The model predicts the process on a larger scale with acceptable quality, but reveals general limitations. One of those limitations is that, often, the various feed concentrations being modeled are not known and additional analytical experiments are required. Due to time and labor, an alternative method for identifying feed concentrations from UV chromatograms and fractionation data is suggested. In previous studies, this shortcoming of mechanistic models has not been revealed or how to address this problem has not been explained. The present disclosure provides a method for identifying feed concentrations from split data and UV chromatograms, suggesting that no additional experiments are needed. Due to time and labor, a minimum set was used for model calibration and verification. A set of 12 experiments was used for a complete workflow including the identification of additional column transport model parameters to model verification. A set of 9 experiments was used for model calibration under binding conditions at a certain pH value, and an additional set of 4 experiments was necessary to estimate transport model parameters for the case of transport inside and outside the column. Further, model validation experiments were used. It is generally known that model acceptability and predictability increase with the amount of knowledge and experiments useful for model calibration. However, as the experimental effort increases, the acceptability of integrating model-based methods into platform process development. Thus, identifying the minimum set of experiments for model calibration supports integrating chromatographic modeling into industrial process development activities.

[0177] Furthermore, it was revealed that the model has a higher sensitivity to the amount of protein loaded than suggested by the experiment. Thus, PPI is often overestimated rather than estimated. Here, two approaches can help improve model accuracy. First, increase the analytical effort to improve the properties of the feed material. Second, include parameter uncertainty estimation in model assessment. Here, the estimated parameters can be investigated with respect to the variation of the feed material concentration. Such insights are valuable for guiding process optimization and process robustness experiments.

[0178] The methods provided herein, with their solvers and algorithms publicly available, can be used and reproduced by other modelers. Furthermore, the models include a set of unit behaviors available for use in the HDF5 format, and the simulations are reproducible. The results described herein can be used for further investigation and enhancement of the model and workflow capabilities, which represents a significant contribution to the evolving chromatography community.

[0179] Exemplary Method Figure 11 shows a flowchart 100 of an example of the method described herein. In a chromatograph including a first dispersed plug flow reactor (DPFR) and a continuous stirred tank reactor (CSTR) before the column and a second DPFR after the column, geometric measurements associated with the second DPFR can be obtained (block 102). For example, geometric measurements associated with the second DPFR may include tube diameter measurements and tube length measurements associated with the second DPFR. These measurements can be obtained, for example, based on measuring tube diameter and tube length and / or based on known manufacturing specifications of the chromatograph.

[0180] For example, the processor may generate transport parameters for a transport model associated with a second DPFR based on geometric measurements (block 104). For example, the transport model parameters may include the dispersion coefficient at the DPFR, the capacity of the DPFR, the cross-sectional area of ​​the DPFR, and so on.

[0181] A tracer molecule (e.g., dextran, NaCl, or another suitable tracer molecule) can be supplied to the chromatograph (block 106). One or more tracer molecule measurements can be captured based on the tracer molecule moving through the chromatograph (block 108). For example, one or more tracer molecule measurements can be captured based on the tracer molecule moving through the chromatograph and the associated chromatogram.

[0182] Based on a second transport model associated with the DPFR and one or more tracer molecule measurements based on tracer molecules moving through a chromatograph, one or more transport model parameters of the first (and second) DPFR and the transport model associated with the CSTR can be estimated (block 110). For example, the transport model parameters may include the coefficient of dispersion at the DPFR, the volume of the DPFR, the cross-sectional area of ​​the DPFR, the volume of the CSTR, etc.

[0183] Furthermore, in some cases, one or more column-specific transport model parameters associated with the chromatograph column can be estimated based on a first transport model associated with DPFR and CSTR, a second transport model associated with DPFR, and one or more tracer molecule measurements based on tracer molecules moving through the chromatograph. For example, column-specific transport model parameters may include column porosity, column dispersion, etc.

[0184] Furthermore, in some cases, one or more resin transport parameters of a resin transport model associated with resin particles in a chromatograph can be estimated based on a column-specific transport model, a transport model associated with a first DPFR and CSTR, a transport model associated with a second DPFR, and one or more tracer molecule measurements based on tracer molecules moving through the chromatograph.

[0185] The experimental sample may be optionally fed into the chromatograph (block 112). One or more experimental measurements may be captured based on the experimental sample as it moves through the chromatograph (block 114). For example, one or more experimental measurements may be captured based on the chromatogram associated with the experimental sample as it moves through the chromatograph.

[0186] Based on one or more experimental measurements based on the experimental sample moving through the chromatograph, one or more estimated transport model parameters of the transport model associated with the first DPFR and CSTR, and the transport parameters of the transport model associated with the second DPFR, one or more adsorption model parameters of the adsorption model associated with the experimental sample can be estimated, for example, by a processor (block 116). In some examples, the column-specific transport model and / or resin transport model may also be factors used in estimating the adsorption model parameters of the adsorption model. For example, the adsorption model parameters may include one or more such as the adsorption coefficient, desorption coefficient, characteristic charge, and shielding factor. In some examples, the adsorption parameters of the second set of the second adsorption model associated with the experimental sample may be estimated based on the range associated with the initially estimated adsorption parameters.

[0187] In some cases, experimental samples can be identified based on an adsorption model associated with the experimental sample (and / or a second adsorption model associated with the experimental sample).

[0188] Furthermore, in some examples, the chromatograph may include an inlet channel containing a first DPFR and CSTR before the inlet channel column and a second DPFR after the inlet channel column, and a sample channel containing a first DPFR and CSTR before the sample channel column and a second DPFR after the sample channel column, and method 100 may be performed on both the inlet channel and the sample channel.

[0189] Furthermore, in some cases, blocks 112, 114, and 116 can be repeated using a second experimental sample (e.g., separate from the first experimental sample) but with the same estimated transport model parameters. That is, once a transport model for a chromatograph is developed, it can be used to determine the adsorption model parameters for multiple experimental samples.

[0190] manner 1. A method comprising: acquiring geometric measurements associated with a second DPFR in a chromatograph including a first dispersed plug flow reactor (DPFR) and a continuous stirred tank reactor (CSTR) before the column and a second DPFR after the column; generating transport model parameters of a transport model associated with the second DPFR based on the geometric measurements using a processor; supplying tracer molecules to the chromatograph; capturing one or more tracer molecule measurements based on the tracer molecules moving through the chromatograph; and estimating one or more transport model parameters of a transport model associated with the first DPFR and CSTR based on a transport model associated with the second DPFR and one or more tracer molecule measurements based on the tracer molecules moving through the chromatograph using a processor.

[0191] 2. The method according to embodiment 1, further comprising: supplying an experimental sample to a chromatograph; capturing one or more experimental measurements based on the experimental sample moving through the chromatograph; and using a processor to estimate one or more adsorption model parameters of an adsorption model associated with the experimental sample based on one or more experimental measurements based on the experimental sample moving through the chromatograph, one or more estimated transport model parameters of a transport model associated with a first DPFR and CSTR, and transport parameters of a transport model associated with a second DPFR.

[0192] 3. The method according to embodiment 1 or 2, wherein the geometric measurements include the second DPFR and associated pipe diameter and pipe length measurements.

[0193] 4. The method according to any one of embodiments 1 to 3, wherein one or more tracer molecule measurements are captured based on the chromatogram associated with the tracer molecule as it moves through the chromatograph.

[0194] 5. One or more experimental measurement values are captured based on a chromatogram associated with an experimental sample moving through a chromatograph, according to any one of aspects 2 to 4.

[0195] 6. The method according to any one of aspects 2 to 5, further comprising identifying an experimental sample by a processor based on an adsorption model associated with the experimental sample.

[0196] 7. Estimating one or more adsorption model parameters of an adsorption model associated with an experimental sample first involves estimating first one or more adsorption parameters of a first adsorption model associated with the experimental sample. The method is that the processor, based on a range associated with first one or more binding parameters of a first adsorption model associated with the experimental sample, next estimates second one or more adsorption parameters of a second adsorption model associated with the experimental sample The method according to any one of aspects 2 to 6, further comprising this.

[0197] 8. The method according to aspect ⑦, further comprising identifying an experimental sample by a processor based on a second adsorption model associated with the experimental sample.

[0198] 9. The first DPFR and CSTR before the column and the second DPFR after the column are part of the inflow path of the chromatograph. The chromatograph further includes a sample flow path having the first DPFR and CSTR before the sample flow path column and the second DPFR after the sample flow path column. The steps according to claim 1 are further executed by the first DPFR and CSTR before the sample flow path column and the second DPFR after the sample flow path column. The method according to any one of aspects 1 to 8.

[0199] 10. The method according to any one of embodiments 2 to 9, wherein the experimental sample is a first experimental sample, and the method further comprises feeding a second experimental sample into a chromatograph, capturing one or more second experimental measurements based on the second experimental sample moving through the chromatograph, and using a processor to estimate one or more estimated transport model parameters of a transport model associated with the first DPFR and CSTR, transport parameters of a transport model associated with the second DPFR, and one or more adsorption model parameters of an adsorption model associated with the second experimental sample, based on one or more second experimental measurements based on the second experimental sample moving through the chromatograph.

[0200] 11. The method according to embodiment 10, wherein the second experimental sample is separate from the first experimental sample.

[0201] 12. The method according to any one of embodiments 1 to 11, wherein the transport model parameters include one or more of the dispersion coefficient in the DPFR, the volume of the DPFR, the cross-sectional area of ​​the DPFR, and the volume of the CSTR.

[0202] 13. The method according to any one of embodiments 2 to 12, wherein the adsorption model parameters include one or more of the adsorption coefficient, desorption coefficient, characteristic charge, and shielding factor.

[0203] 14. The method according to any one of embodiments 1 to 13, further comprising using a processor to estimate one or more column-specific transport model parameters of a column-specific transport model associated with a chromatograph column, based on a transport model associated with a first DPFR and CSTR, a transport model associated with a second DPFR, and one or more tracer molecule measurements based on tracer molecules moving through the chromatograph.

[0204] 15. The method according to embodiment 14, wherein the column-specific transport model parameters include one or more of the column porosity and the column dispersion rate.

[0205] 16. The method according to embodiment 14 or 15, further comprising the processor estimating one or more resin transport parameters of a resin transport model associated with resin particles in a chromatograph, based on a column-specific transport model, a transport model associated with a first DPFR and CSTR, a transport model associated with a second DPFR, and one or more tracer molecule measurements based on tracer molecules moving through the chromatograph.

[0206] 17. The method according to embodiment 16, wherein the resin transport parameters include one or more of the film transport coefficient and pore porosity of each component.

[0207] 18. Estimating one or more adsorption model parameters of an adsorption model associated with an experimental sample, further based on one or more column-specific transport models or resin transport models, according to any one of embodiments 2 to 17.

[0208] 19. The method according to any one of embodiments 1 to 18, wherein the tracer molecule is dextran.

[0209] 20. The method according to any one of embodiments 1 to 19, wherein the tracer molecule is NaCl.

[0210] 21. The method according to any one of embodiments 1 to 19, wherein the tracer molecule is a DNA molecule.

[0211] 22. The method according to any one of embodiments 1 to 19, wherein the tracer molecule is a nanoparticle.

[0212] 23. A computer system including a processor and one or more memories storing instructions that, when executed by the processor, cause the computer system to perform a step of the method according to any one of embodiments 1 to 22.

[0213] 24. A non-temporary computer-readable storage medium that stores instructions, when executed by a processor, causing the processor to perform a step of the method described in any one of embodiments 1 to 22.

Claims

1. It is a method, A chromatograph, represented by a model including a first dispersion plug flow reactor (DPFR) and a continuous stirred tank reactor (CSTR) before the column, and a second DPFR after the column, is used to obtain geometric measurements associated with the second DPFR, The processor generates transport model parameters for the transport model associated with the second DPFR based on the geometric measurements, The process involves supplying tracer molecules to the aforementioned chromatograph, Based on the tracer molecules moving through the chromatograph, one or more tracer molecule measurements are captured. The processor estimates one or more transport model parameters of the first DPFR and the transport model associated with the CSTR based on the transport model associated with the second DPFR and the one or more tracer molecule measurements based on the tracer molecules moving through the chromatograph, A method that includes this.

2. The experimental sample is supplied to the chromatograph, To capture one or more experimental measurements based on the experimental sample moving through the chromatograph, The processor estimates one or more adsorption model parameters of an adsorption model associated with the experimental sample based on one or more experimental measurements based on the experimental sample moving through the chromatograph, one or more estimated transport model parameters of the transport model associated with the first DPFR and the CSTR, and the transport parameters of the transport model associated with the second DPFR. The method according to claim 1, further comprising:

3. The method according to claim 1, wherein the geometric measurement includes a pipe diameter measurement and a pipe length measurement associated with the second DPFR.

4. The method according to claim 1, wherein the one or more tracer molecule measurements are captured based on a chromatogram associated with the tracer molecule as it moves through the chromatograph.

5. The method according to claim 2, wherein the one or more experimental measurements are captured based on a chromatogram associated with the experimental sample as it moves through the chromatograph.

6. The method according to claim 2, further comprising the processor identifying the experimental sample based on the adsorption model associated with the experimental sample.

7. Estimating one or more adsorption model parameters of the adsorption model associated with the experimental sample involves first estimating one or more first adsorption model parameters of the first adsorption model associated with the experimental sample, and the method is as follows: The processor further includes estimating a second one or more adsorption model parameters of a second adsorption model associated with the experimental sample, based on the range associated with the first one or more binding parameters of the first adsorption model associated with the experimental sample, The method according to claim 2, wherein the first one or more bonding parameters relate to bonding between the molecules of the experimental sample and the resin.

8. The method according to claim 7, further comprising the processor identifying the experimental sample based on the second adsorption model associated with the experimental sample.

9. The method according to claim 1, wherein the model including the first DPFR and CSTR before the column and the second DPFR after the column is part of a model representing the inflow path of the chromatograph, and the chromatograph further includes a sample flow path represented by a model having the first DPFR and CSTR before the sample flow path column and the second DPFR after the sample flow path column, and the step according to claim 1 is further performed with the first DPFR and CSTR before the sample flow path column and the second DPFR after the sample flow path column.

10. The aforementioned experimental sample is the first experimental sample, and the method is as follows: The second experimental sample is supplied to the chromatograph, To capture one or more second experimental measurements based on the second experimental sample moving through the chromatograph, The processor estimates, based on the one or more second experimental measurements based on the second experimental sample moving through the chromatograph, one or more estimated transport model parameters of the transport model associated with the first DPFR and the CSTR, the transport parameters of the transport model associated with the second DPFR, and one or more adsorption model parameters of the adsorption model associated with the second experimental sample. The method according to claim 2, further comprising:

11. The method according to claim 10, wherein the second experimental sample is separate from the first experimental sample.

12. The method according to claim 1, wherein the transport model parameters include one or more of the dispersion coefficient in the DPFR, the volume of the DPFR, the cross-sectional area of ​​the DPFR, and the volume of the CSTR.

13. The method according to claim 2, wherein the adsorption model parameters include one or more of an adsorption coefficient, a desorption coefficient, a characteristic charge, and a shielding factor.

14. The method according to claim 1, further comprising the processor estimating one or more column-specific transport model parameters of a column-specific transport model associated with the column of the chromatograph, based on the transport model associated with the first DPFR and the CSTR, the transport model associated with the second DPFR, and the one or more tracer molecule measurements based on the tracer molecules moving through the chromatograph.

15. The method according to claim 14, wherein the column-specific transport model parameters include one or more of column porosity and column dispersion rate.

16. The method according to claim 14, further comprising using the processor to estimate one or more resin transport parameters of a resin transport model associated with resin particles in the chromatograph, based on the column-specific transport model, the transport model associated with the first DPFR and the CSTR, the transport model associated with the second DPFR, and the one or more tracer molecule measurements based on the tracer molecules moving through the chromatograph.

17. The method according to claim 16, wherein the resin transport parameters include one or more of the film transport coefficient and pore porosity of each component.

18. The method according to claim 2, wherein the estimation of one or more adsorption model parameters of the adsorption model associated with the experimental sample is further based on one or more column-specific transport models or resin transport models.

19. The method according to claim 1, wherein the tracer molecule is dextran.

20. The method according to claim 1, wherein the tracer molecule is NaCl.

21. The method according to claim 1, wherein the tracer molecule is a DNA molecule.

22. The method according to claim 1, wherein the tracer molecule is a nanoparticle.

23. A computer system comprising a processor and one or more memories storing instructions that, when executed by the processor, cause a computer system to perform the steps of the method according to any one of claims 1 to 22.

24. A non-temporary computer-readable storage medium that stores instructions, when executed by a processor, causing the processor to perform the steps of the method according to any one of claims 1 to 22.

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