Mechanistic ion-exchange chromatography model calibration

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 pending U.S. Provisional Patent Application No. 63 / 123,170, entitled “Mechanistic Ion-Exchange Chromatography Model Calibration,” filed December 9, 2020, the entire disclosure of which is incorporated herein by reference.

[0002] The present disclosure relates generally to the calibration of mechanistic ion exchange chromatography models of chromatography machines. [Background technology]

[0003] The biopharmaceutical industry has made great strides in the field of digital biomanufacturing over the last few decades with the introduction of powerful processors and large capacity hard drives capable of storing and interpreting large amounts of data. Digital tools to assist in process development and analysis have rapidly evolved to improve process performance and efficiency. The application of predictive models allows in silico exploration of the design space during process development as well as improving control strategies in real time in the manufacturing environment.

[0004] Chromatography is a method used for the separation and purification of molecules during downstream processing of biomolecules and is a key step in the purification of biopharmaceuticals. Chromatography can be used to purify and concentrate biomolecule solutions using porous packed beds that separate different molecules based on differences in the mass, size, or charge of the biomolecules. Ion exchange (IEX) chromatography is a purification process based on ionic interactions 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 biomolecule surface. The adsorbed biomolecules can be eluted by reducing the surface affinity of the molecules through the use of buffer solutions with increased ionic strength.

[0005] The Quality by Design (QbD) approach, described by the US Food and Drug Administration (FDA) in 2004, introduces the concept of building product quality requirements into the manufacturing process. In the following years, the International Conference on Harmonization (ICH) endorsed the QbD approach and introduced guidelines that define the systematic approach and scientific principles of the drug discovery process.

[0006] Apart from the regulatory oversight requirements of biopharmaceutical process development of CEX steps, technical challenges also arise, making the technology transfer to larger scale, process improvement and process characterization a resource intensive task.

[0007] The accelerated and strict timeline leaves little room for thorough exploration of the process design space to find process parameters that allow maximum yield and purity while meeting strict constraints for process robustness and maximum molecule recovery. A process developed under such conditions in the early stages of first-in-human (FIH) research may meet all the constraints required at the time, but may lack scalability if quality, quantity, or cost demands change later.

[0008] As a result, iterative experiments requiring high resource levels are required to identify critical process parameters that reduce material consumption while increasing process performance such as yield and molecular purity. Methods that can be integrated into the early process development stages that allow targeted experiments around the most promising process parameter ranges can help lead to more optimal processes 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 of chromatographic separation processes. Mechanistic models provide predictions of key process outputs and process performance indicators over a wide process range. In particular, mechanistic CEX chromatography modeling is a useful tool based on first principles that describes the transport and elution behavior of molecules and predicts the behavior of chromatographic processes. The application of CEX chromatography models in process development to explore the design space of process parameters such as loading factors or elution gradients can reduce the effort of iterative experiments. Furthermore, mechanistic modeling provides an opportunity to gain insight into the mechanisms that affect the separation of therapeutic proteins and their impurities. This knowledge can be used to inform decision-making during development and optimize production quality and process performance. Essentially, mechanistic modeling provides a science-based tool useful for process design and optimization. In one example, mechanistic CEX chromatography modeling can be utilized to make decisions about CEX process parameters such as gradient slope, collection criteria, and loading factors. However, mechanistic models require prior knowledge and a thorough calibration process to provide sufficient predictability for small- and large-scale separation processes. In particular, mechanistic models require a well-defined mathematical description of each process step. There have been several studies that use mechanistic models for process optimization, process investigation, and performance assessment or model-based control, and suggest workflows for mechanistic models.

[0010] Several models are available that can describe the biopharmaceutical chromatography process. One of the first mathematical descriptions of the chromatography process described the adsorption of CO2 on coal and silica gel using empirical equations. Since then, chromatography models have been further developed to include many possible contributions to mass transfer kinetics based on first principles. An important step is the development of the general rate model (GRM). The GRM describes the combination of kinetic transport phenomena such as forced convection (by pumping), molecular diffusion, and molecular adsorption in liquid chromatography systems. It allows a more detailed description of the transport phenomena in the chromatography column than previous simplifications (e.g. the ideal model and the Thomas model). For molecules smaller than the pore size of the chromatographic 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. Again, a huge number of models are available that have proven applicable to chromatography. The initial adsorption model is the Langmuir model, which allows for concentration-dependent adsorption onto surfaces with finite volume. 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 affinity of biomolecules to chromatographic materials caused by ionic interactions on the adsorption behavior of molecular mixtures. Several studies have shown the successful application of SMA models 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 already existing transport and adsorption models. However, before application, the mechanistic models need to be calibrated; that is, suitable model parameters need to be identified such that the model describes the desired process.

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

[0013] That is, the model parameters can generally be obtained by measuring, such as using optical microscopy, to determine the pore transport coefficients, however, direct measurement of the model parameters is often not possible or is very laborious, and therefore recursive parameter estimation is the method often used in chromatography 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 the chromatogram simulation. Furthermore, the configuration of the tubing, valves, or mixing chamber also affects the residence time of each component. During adsorption, parameter estimation involves using a recursive method over the time 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 for larger or smaller scale systems or when the system configuration changes. This effect on the chromatogram can be large, especially when the column size is small compared to the additional column volume. However, in many cases, this effect has not been considered when estimating the adsorption model parameters.

[0015] The scale-up of the study is the application of previously investigated ion exchange chromatography models. One drawback of this finding in this field is that the mass transfer coefficients are flow rate dependent and therefore require adaptation to the flow rate.

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

[0017] However, there is no description of how the transport behavior in the additional column volume inherent to the chromatographic instrument is taken into account in the calibration workflow. Many physical processes affect the chromatographic behavior of molecules. Apart from competitive adsorption and ionic strength effects, mass transfer in the additional column volume affects the absolute elution time and the peak shape in the chromatogram simulation. The configuration of the tubing, valves, or mixing chamber affects the absolute residence time of each component. As a result, during adsorption parameter estimation using the recursive method, the time that passes from the start of elution until each component elutes will affect the estimate of the 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 scales or changing system configurations. This effect can have a large impact on the chromatogram, especially when the column size is small compared to the additional column volume. The importance of an appropriate additional column volume representation has not been shown in previous publications. However, in many contributions, how this effect can be taken into account in the model calibration workflow has not been addressed. Summary of the Invention [Problem to be solved by the invention]

[0018] In the interest of industrial process development time and effort, 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] The present disclosure provides a workflow for CEX model calibration using a minimal set of experiments. The model provided by the present disclosure takes into account mass transfer in additional column volumes and includes a model sequence with a combination of a fitted dead volume model before the chromatography column and a model set up only from the geometry of the tubing after the chromatography column. Furthermore, in the model provided by the present disclosure, model input parameters reflecting mass transfer and model input parameters reflecting molecule-specific adsorption behavior are specified separately. The present disclosure shows that the adsorption parameters are scalable across process sizes and exhibit sufficient predictive quality for scale-up process runs. Advantageously, the present disclosure provides a chromatography model calibration approach with increased model accuracy and agility.

[0020] The calibration is structured in three parts of sequential parameter estimation that separates the transport model part and the adsorption model part. First, the unit operation representation of the chromatography skid and its kinetic 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 flow path representation commonly used in chromatography skids and machines such as the AKTA™ Avant. As shown in Figure 1A, there is a variable dead volume before the column. This dead volume affects the peak position relative to the start of elution, and therefore the dead volume needs to be accounted for as accurately as possible in the model in order to separate this effect from the adsorption behavior, which also affects the peak position.

[0022] Possible representations range from simple time shifts to mechanistic representations of the volumes of tubing and valves involved. In the case of the BiTE® (Bispecific T Cell Engager) antibody construct, a combination of the DPFR and CSTR models is used to represent the dead volume before the column. The dead volume present from the column outlet to the UV and the conductivity sensor are represented by the DPFR model as well.

[0023] A combination of tubing 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 paths are a combination of fitted DPFR and CSTR models before the column and a DPFR model setup from the geometric specifications provided by the vendor. After identifying the separate model parts of the column model, the two representations of the dead volumes of the inlet and sample flow paths are combined into a more complex model. The two DPFR models following the column are specified by the tubing diameter and length specified by the vendor. Only the dispersion coefficients of the two DPFR models are set to the estimated value of the DPFR before the column.

[0024] The specific sequence of steps includes first obtaining the post-column tubing geometric values ​​(tubing diameter, length), e.g., by measurement or based on vendor specifications, and then performing an experiment to feed tracer molecules into the system from a desired location. Next, a series of DPFR-CSTR-DPFR models are set up, where the post-column DPFR model is specified according to the specific tubing geometric values. That is, the geometric specifications of this DPFR after the column are fixed, but the parameters specifying the dispersion properties of the DPFR are not fixed and are estimated together with the properties of the pre-column DPFR and CSTR. In total, the estimation includes 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 DPFR. The parameters not included in the estimation are the geometric parameters of the post-column DPFR. This step is performed in both the sample path flow (blue in FIG. 1A) and the inlet flow path (green in FIG. 1A). Once all the transport parameters are estimated, the binding parameters can be estimated. As many components as there are peaks to be simulated by the model can be included in the model. Then, the parameters of each component to be modeled can be estimated. The range of the estimated parameter may be used to encompass more components that form one or more of the chromatographic peaks, and the binding parameters may again be estimated using tighter bounds on the parameter.

[0025] The first innovation in this sequence is to specify the post-column DPFR model according to the specific tube geometry values. This is accompanied by the fact that a combination of the fitted model and the model set up based on the geometry specification is used to identify the level of transport effect that hits the column at the start. Thus, the time when the point sample and elution buffer hit the column can be identified more accurately than by lumping both pre-column and post-column flow paths together, without performing more complex bypass experiments to separate the paths. Furthermore, using the methods provided herein, it is possible to separate the transport behavior of the buffer from that of the molecular solution.

[0026] In the prior art, 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 focusing on model calibration, most prior art includes new methods to estimate adsorption parameters, but does not include new methods to estimate pre-column dead volumes.

[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. When this step is over, more components are added to the model. This is necessary for BiTEs and often antibodies, since there are several molecular species eluting in such close proximity that the UV sum signal appears as one peak. Now 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 previously roughly estimated adsorption parameters from a less complex model, a smaller parameter space can now be applied for parameter estimation, which accelerates the estimation procedure.

[0028] Decoupling transport and adsorption effects in the chromatogram allows for more accurate chromatographic models. Furthermore, the models are more flexible with respect to the field of application. It means that as long as the resin is the same, the adsorption model parameters can remain the same while other process specifications change. This is an insight that is often not implemented. However, it allows for shorter model calibration procedures, i.e. shorter model calibration procedures compared to performing a new model calibration every time the process is changed. Model-based process development can benefit from this speed improvement. Furthermore, the models are more accurate compared to those where it is difficult to distinguish transport effects from the adsorption parameters.

[0029] The method provided herein is more flexible and accurate than conventional methods of modeling dead volumes in chromatography skids and machines, such as shifting the start of elution according to the dead volume or identifying the dead volume based on a bypass experiment, both of which include the dead volume after the column outlet as the dead volume described before the column.

[0030] Finally, the method provided herein can estimate adsorption parameters with a low degree of influence from transport effects. This approach separates transport and adsorption effects in a chromatogram more efficiently than conventional methods. This is beneficial when process specifications that affect the transport of molecules change. This is the case for scale-up applications. In such cases, the scale-up effects of tubing, flow rates, etc. can be accounted for in a separate part 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 aspect, 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; providing 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.

[0032] In some examples, the method may include providing an experimental sample to a chromatography machine; capturing one or more experimental measurements based on the experimental sample moving through the chromatography machine; and estimating, by a processor, one or more adsorption model parameters of an adsorption model associated with the experimental sample based on the one or more experimental measurements based on the experimental sample moving through the chromatography machine, the estimated one or more 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.

[0033] Additionally, in some instances, the geometric measurements may include vessel diameter and vessel length measurements associated with the second DPFR.

[0034] Additionally, in some instances, the one or more tracer molecule measurements are captured based on a chromatogram associated with the tracer molecule traveling through the chromatography machine. Similarly, in some instances, the one or more experimental measurements are captured based on a chromatogram associated with an experimental sample traveling through the chromatography machine.

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

[0036] Further, in some examples, estimating one or more adsorption model parameters of an adsorption model associated with the experimental sample may include first estimating a first one or more adsorption parameters of a first adsorption model associated with the experimental sample, and the method may further include second estimating, by the processor, a second one or more adsorption parameters of a second adsorption model associated with the experimental sample based on a range associated with the first one or more binding parameters of the first adsorption model associated with the experimental sample. Further, in some examples, the method may include identifying, by the processor, the experimental sample based on the second adsorption model associated with the experimental sample.

[0037] Furthermore, in some examples, the first DPFR and CSTR before the column and the second DPFR after the column are part of an inlet path of a chromatography machine, and the chromatography machine 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, and the process described in claim 1 is further performed in the first DPFR and CSTR before the sample flow path column and the second DPFR after the sample flow path column.

[0038] Further, in some examples, the experimental sample is a first experimental sample, and the method may further include providing a second experimental sample to the chromatography machine, capturing one or more second experimental measurements based on the second experimental sample moving through the chromatography machine, and estimating, by the processor, estimated one or more 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 the one or more second experimental measurements based on the second experimental sample moving through the chromatography machine. For example, in some examples, the second experimental sample is separate from the first experimental sample.

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

[0040] Further, in some examples, the method further includes estimating, by the processor, one or more column-specific transport model parameters of a column-specific transport model associated with a column of the chromatography machine based on the transport model associated with the first DPFR and 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 chromatography machine. Further, in some examples, the column-specific transport model parameters include one or more of column porosity and column dispersion.

[0041] Further, in some examples, the method further includes estimating, by the processor, one or more resin transport parameters of a resin transport model associated with resin particles of the chromatography machine based on the column-specific transport model, the transport model associated with the first DPFR and 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 chromatography machine. Further, in some examples, the resin transport parameters include one or more of a film transport coefficient and a pore porosity of each component.

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

[0043] Further, in some embodiments, the tracer molecule is dextran. In some embodiments, the tracer molecule is NaCl. Further, in some embodiments, the tracer molecule is a DNA molecule. Further, in some embodiments, the tracer molecule is a nanoparticle. [Brief description of the drawings]

[0044] [Figure 1A] A representation of the flow path of a chromatography machine (e.g., AKTA™ Avant, etc.) is shown, and as shown in Figure 1A, the flow path from different locations depending on the line priming procedure indicates various points at which sample or elution buffer enters the column. [Figure 1B] 1 shows an example of how the mobile phase moves through a packed bed column. [Figure 1C] A visualization of the solid mass action model is shown, including the meaning of the parameters. [Diagram 2] 1 shows a graph of the Sum of Squared Differences (SSD) alignment problem using synthetic data, with some examples. [Diagram 3] 13 illustrates a graph comparing a standard position penalty metric to an initial degraded position penalty metric, with several examples. [Figure 4] 1 illustrates an exemplary stage-by-stage approach to model development. [Diagram 5] FIG. 1 shows a diagram of a flow path used for gradient elution, according to some examples. [Figure 6] A chromatograph system representation of the CEX model is shown, with the general model construction, dispersive plug flow reactor (DPFR), and continuous stirred tank reactor (CSTR) unit operations representing the peak delays and peak broadening that occur in systems that do not include columns (valves, sensors, mixing chambers); salts and molecules may experience different tubing or valve systems, and therefore parameters associated with those unit operations may differ between protein and salt species. [Figure 7A] Calibration of the pre-column model of transport within the chromatography skid is shown: FIG. 7A shows the dextran tracer breakthrough from the sample pump, while FIG. 7B shows the NaCl tracer from the inlet pump tail. [Figure 7B] Calibration of the pre-column model of transport within the chromatography skid is shown: FIG. 7A shows the dextran tracer breakthrough from the sample pump, while FIG. 7B shows the NaCl tracer from the inlet pump tail. [Figure 8A] Calibration of column transport model parameters is shown, FIG. 8A shows textran breakthrough tracer (no pore penetration), FIG. 8B shows dextran pulse tracer (no pore penetration), and FIG. 8C shows FVIP of BiTE® (Bispecific T Cell Engager) antibody construct breakthrough (with pore penetration). [Figure 8B]Calibration of column transport model parameters is shown, FIG. 8A shows textran breakthrough tracer (no pore penetration), FIG. 8B shows dextran pulse tracer (no pore penetration), and FIG. 8C shows FVIP of BiTE® (Bispecific T Cell Engager) antibody construct breakthrough (with pore penetration). [Figure 8C] Calibration of column transport model parameters is shown, FIG. 8A shows textran breakthrough tracer (no pore penetration), FIG. 8B shows dextran pulse tracer (no pore penetration), and FIG. 8C shows FVIP of BiTE® (Bispecific T Cell Engager) antibody construct breakthrough (with pore penetration). [Figure 9A] A comparison of chromatogram and fractionation data sets between experimental and simulated elution conditions is shown, with FIG. 9A showing the best fit with a 5 mM / CV gradient run, while FIG. 9B shows the best fit with an 11 mM / CV gradient run. [Figure 9B] A comparison of chromatogram and fractionation data sets between experimental and simulated elution conditions is shown, with FIG. 9A showing the best fit with a 5 mM / CV gradient run, while FIG. 9B shows the best fit with an 11 mM / CV gradient run. [Figure 10A] Model validation with process scale experiments with various loading factors, gradients, and stop collection criteria are shown, where FIG. 10A shows model validation with an 8 mM / CV gradient and 25 g / L loading factor with a benchtop scale column, FIG. 10B shows model validation with an 8 mM / CV gradient and 25 g / L loading factor with a process scale with 30% stop collection criteria, FIG. 10C shows model validation with an 8 mM / CV gradient and 15 g / L loading factor with a process scale with 45% stop collection criteria, and FIG. 10D shows model validation with an 8 mM / CV gradient and 5 g / L loading factor with a process scale with 30% stop collection criteria. [Figure 10B]Model validation with process scale experiments with various loading factors, gradients, and stop collection criteria are shown, where FIG. 10A shows model validation with an 8 mM / CV gradient and 25 g / L loading factor with a benchtop scale column, FIG. 10B shows model validation with an 8 mM / CV gradient and 25 g / L loading factor with a process scale with 30% stop collection criteria, FIG. 10C shows model validation with an 8 mM / CV gradient and 15 g / L loading factor with a process scale with 45% stop collection criteria, and FIG. 10D shows model validation with an 8 mM / CV gradient and 5 g / L loading factor with a process scale with 30% stop collection criteria. [Figure 10C] Model validation with process scale experiments with various loading factors, gradients, and stop collection criteria are shown, where FIG. 10A shows model validation with an 8 mM / CV gradient and 25 g / L loading factor with a benchtop scale column, FIG. 10B shows model validation with an 8 mM / CV gradient and 25 g / L loading factor with a process scale with 30% stop collection criteria, FIG. 10C shows model validation with an 8 mM / CV gradient and 15 g / L loading factor with a process scale with 45% stop collection criteria, and FIG. 10D shows model validation with an 8 mM / CV gradient and 5 g / L loading factor with a process scale with 30% stop collection criteria. [Figure 10D] Model validation with process scale experiments with various loading factors, gradients, and stop collection criteria are shown, where FIG. 10A shows model validation with an 8 mM / CV gradient and 25 g / L loading factor with a benchtop scale column, FIG. 10B shows model validation with an 8 mM / CV gradient and 25 g / L loading factor with a process scale with 30% stop collection criteria, FIG. 10C shows model validation with an 8 mM / CV gradient and 15 g / L loading factor with a process scale with 45% stop collection criteria, and FIG. 10D shows model validation with an 8 mM / CV gradient and 5 g / L loading factor with a process scale with 30% stop collection criteria. [Figure 11] 1 illustrates a flow diagram of an exemplary method according to some examples provided herein. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

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

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

[0047] As used herein, "cation exchange" ("CEX") refers to a chromatographic process based on cationic interactions between molecules and a chromatographic material.

[0048] As used herein, "anion exchange" ("AEX") refers to a chromatographic process based on anionic interactions between molecules and a chromatographic material.

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

[0050] As used herein, a "dispersed plug flow reactor" ("DPFR") refers to a cylindrical tube with convective laminar flow having a plug flow profile rather than a gently sloping flow profile.

[0051] As used herein, "continuous stirred tank reactor" ("CSTR") refers to a tank reactor filled with intimately mixed fluids.

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

[0053] As used herein, "valve" refers to the valves that connect all the components in a chromatography machine, such as the AKTA™. These valves can switch between many inputs and outputs and can have small volumes (approximately 1-1000 μL).

[0054] As used herein, "model calibration" refers to a 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 void space within a chromatography machine that is filled with liquid.

[0057] As used herein, "line priming" refers to filling tubing / valves with required fluids (e.g., buffers) before the process begins.

[0058] As used herein, "fitting" refers to the procedure of iteratively estimating unknown model parameters by comparing simulations to measurements.

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

[0060] theory In general, the column models provided herein describe the important transport and adsorption effects of counterions and molecules present in an adsorbed state in the solute within the column. Although a variety of adsorption models can be selected, the most important adsorption models describe how salt ions, as mobile phase modulators, affect the adsorption kinetics of molecules. Such processes are described on second time scales and micrometer and meter length scales. A simplified general rate model (GRM) and steric mass action model are used to simulate the transport and elution behavior of acidic, major, and elementary charge variants of the target molecule and high molecular weight (HMW) impurity species.

[0061] Transportation Model As shown in FIG. 1B, the mobile phase moves through a packed bed column with length L. The movement can be described by the volumetric flow rate, the column cross-sectional area, and the column porosity (void fraction between packed beads). This movement is forced convection and is described by a convection term along the column length z. In the interstitial volume l (voids between beads in the liquid mobile phase) there are molecules moving different paths through the bed that lead to effects, e.g., Fickian diffusion, wall effects, or peak broadening, which are lumped together and described by a dispersion term in the model. Molecular flow from the interstitial volume to the porous particle volume p of the bed can be hindered, which is taken into account by the model, by the film mass transfer model. Inside the bead pores, diffusion transport is assumed to be much faster than mass transfer into the pores, and is therefore assumed to be instantaneous. As a result, there is no concentration gradient along the bead radius leading to a simplified general rate model (GRM) equation with lumped pores, the lumped pore diffusion (POR) model. The model describing the transport is independent of the models describing the adsorption capacity or molecular adsorption to the solid phase. The column packing and bead size are assumed to be highly homogeneous, which leads, firstly, to the neglect of concentration gradients in the column radial direction and, secondly, to the assumption that the packed bed porosity and bead porosity do not vary along the column axis and bead radius.

[0062] GRM is used to describe the transport of biomolecules through a porous packed bed due to convection, dispersion, and diffusion. Convection is the movement of species through the 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 the tube walls or particles, and movement through the packed bed. Further mass transport: transport from the bulk liquid to the pores and diffusion inside the pores are described by GRM. Diffusion from the bulk liquid into the pores can be the rate limiting step due to spatial confinement depending on the ratio of the molecular size and the pore size. The rate at which this transport occurs is described in proportion to the film mass transfer coefficient. The second component is diffusion through the pores, which is described using various diffusion coefficients. This usually occurs at a faster rate than the film mass transport. Due to this assumption, the GRM equations are simplified to ignore the radial concentration gradient in the pores, leading to the lumped pore model.

[0063] The simplified GRM for any species concentration is ci ∈ [0,N c ] and N c denotes the number of components, t denotes time in seconds, z denotes the axial coordinate along the column length L, and r denotes the bead radius r p 4 shows the radial bead coordinates along

number

[0064] Danckwerts boundary conditions are applied:

number

[0065] The initial condition is

number

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

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

number

[0068] Where:

number

number

[0069] A continuous diffusion bed reactor (CSTR) model was used to describe the mixing effects inside the chromatography system of valves and mixing chambers. That is, a tank model with an inlet and outlet and a constant volume is used to describe how the concentrations of multiple components change when they are mixed together. The model equation is

number

[0070] The initial condition is

number

[0071] Where:

number

[0072] Stereoscopic mass action model The Steric Mass Action (SMA) model describes the adsorption, desorption, and steric interactions of proteins with the resin. These interactions with the resin are characterized using four parameters: adsorption coefficient, desorption coefficient, steric factor, and characteristic charge. These parameters are specific to each species being modeled. Unlike transport parameters, binding parameters are transferable 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) from the resin. They describe the binding kinetics of the species being modeled and are affected by salt concentration. The steric factor and characteristic charge parameters describe the effect of molecular size and surface charge, respectively, on the binding kinetics. The steric factor describes the number of spaces a molecule is "shielded" from binding on the resin. The characteristic charge describes the number of charge-based interactions a molecule has with the resin. The sum of the steric factor and the characteristic charge gives 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 required to determine the binding capacity of a protein to the resin. The SMA model is based on a neutral charge balance on the resin, and therefore all charged sites are occupied by counterions or oppositely charged proteins. The ionic capacity can be determined from titration experiments detailed in the Methods section.

[0075] The equation system for the SMA model is described below.

number

[0076] where Λ is mol / m 3 indicates the total column volume in units of ν i denotes the characteristic charge, and σ i denotes the steric factor, and k a,i teeth

number

number

number

[0077] The main limitation of SMA isotherms is that the binding parameter values ​​are only applicable at the pH for which they were specified. Since pH is a critical process parameter in CEX steps, this limits the robustness of the predictive mechanistic models. To extend the current SMA models and improve their robustness, functions that can address the pH dependence are required.

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

[0079] Numerical Solvers Since analytical solutions are not available, a numerical solution of all the above systems of equations is computed. The general approach is to discretize the partial differential equations (PDEs) along special variables, which results in a number of ordinary differential equations (ODEs). The ODE system can then be solved using a time-stepping algorithm.

[0080] A special discretization of the chromatography model can be achieved by using the finite volume method. Here, mass balance equations of 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, which generates a new set of state variables associated with each cell volume. Numerical integration solves the discretized equations for those averaged volume concentrations. The boundary conditions at the column inlet and outlet (equations (3) and (4)) are integrated into the discretized equations at 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 Formula (BFD) method for time integration. The CADET implementation uses an 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 was set with an initial step size as

[0082] Parameter Estimation Algorithm Goal System This disclosure introduces a new objective system to estimate chromatographic model parameters, where objective means a set of metrics that are influenced by shape. Each metric is a single scalar value, such as the time difference between the simulation and the actual measurement at the peak maximum, the height difference at the peak maximum, etc. The metrics are defined based on specific knowledge of the process being modeled and typical errors in the actual measurement data. The metrics in the objectives can be passed to a multi-objective search algorithm or can be combined into one objective and passed to a single-objective search algorithm.

[0083] Multiple metrics can guide the search strategy towards the desired optimum much better (multi-objective) than the commonly applied sum of double differences (SSD) can guide the search strategy (single-objective). Metrics are grouped into scores to organize the specification of objectives for the different parameter estimation procedures in CADET-Match. A suitable objective must have the property that as the fit quality improves, the value of at least one metric must decrease, and as the fit quality worsens, the value of at least one metric must increase. An objective that does not have this property may mislead the search algorithm. This may seem trivial, but it is crucial and is the core of why new objectives must be created. Due to competitive binding and other complex mechanisms, many model parameters affect the simulated chromatogram in a nonlinear manner. Thus, while the model parameters are approaching the correct values, some customarily applied metrics such as SSD will increase.

[0084] In addition, measured chromatograms from industrial large-scale applications are often affected by systematic errors such as pump delays that can cause a time offset between the measured and simulated signals unless the model captures the source of the delay, which is often not possible in practice. A good target is needed to account for this, because otherwise the simulated peaks will be in the right place but with the wrong shape. The wrong shape generally indicates an error in the physics underlying the model. Therefore, a good metric should favor peaks with a roughly matching shape but a small offset over peaks with no offset but the wrong shape.

[0085] Sum of Squared Differences For SSD, the squared difference between the simulated and measured chromatograms is summed over the time points (see Section 16 below). For normalized root mean square difference (NRMSD), the SSD is divided by the number of time points and 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 calculated over the entire chromatogram J={1;…;N d} or a subset of the data J ⊂ {1;…;N d}. SSD is most commonly applied using a gradient descent search algorithm; therefore, it is included here for comparison. The theory is well defined in a maximum likelihood estimation framework with independent uniformly distributed random measurement errors. However, these assumptions are generally not valid for modeling large-scale preparative chromatography, where systematic errors such as feed fluctuations, pump delays, and flow rate fluctuations typically dominate detector noise. For interpreting the results, NRMSD is more suitable than SSD because the numerator has the same units as the data and is related to the maximum concentration by the denominator.

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[0086] SSD is sensitive to parameter changes and requires sufficient overlap between simulated and measured chromatograms to guide the search algorithm towards the optimum. This can complicate the selection of a suitable starting point, especially for sharp and / or small peaks. A further shortcoming of SSD is shown in Figure 2 using a synthetic example with the parameters shown in Table 1. Although the parameters of scenario 2 are much closer to the ground truth, with only a relatively small deviation in the characteristic charge ν, scenario 1 nevertheless has a smaller SSD and is therefore usually considered a better fit. In addition, the peak shape of scenario 2 is more similar to the ground truth, but with a misalignment.

[0087] In real experiments, such time offsets are often caused by pump delays that cannot be explained by the mechanistic model. In this case, SSD favors peaks that are in the right position, even if it is obvious to the human eye that the peak shape is completely wrong. The model can also reproduce the correct peak shape, but not the right position, with a much larger SSD. As the peak shape is mainly determined by the binding model parameters, SSD leads to unphysical parameter values. Therefore, we introduce here an alternative metric that favors peak shape over position and has a lower demand on the selection of a suitable starting point.

[0088] [Table 1]

[0089] Alternative Metrics The shape and position of the chromatogram are determined by the mass transport through the entire system, including the column and external volumes, and the binding to the functionalized resin. The drawbacks of SSD are avoided by measuring the shape, position, and height of each individual peak separately without the need for baseline separation. The peak position metrics are sensitive to changes in each model parameter and are independent of peak overlap between simulation and actual data. This provides flexibility and robustness with respect to the selection of the starting point of the search algorithm, which is crucial for automation in industrial applications. By focusing on individual peaks, the influence of process variations and further components not fully included in the model can be reduced. For example, pump washes or pressure alarms can give rise to false peaks, and industrial supplies usually contain a large number of more or less unknown impurities. In such cases, separate metrics can be assigned to the distinct but partially separated peaks of the target component and the high and low molecular weight impurities. The separate metrics also help to provide the (multi-objective) search algorithm with more precise information about which components affect which peaks. All metrics yield zero in the case of perfect agreement between simulation and experiment.

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

number

number

[0091] Peak Position The location metric may be more complicated than it first appears. The location metric is a time offset t obtained from maximizing s Based on.

number

[0092] The standard position metric imposes an immediate penalty on time offsets (see Equation 20 below), and when out of alignment, t r It rises linearly to 1 by 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 to estimate the column and particle porosity. However, care must be taken in the execution of the experiment to ensure that delays are as small as possible and that alarms are cancelled immediately. Such delays affect the chromatogram in much the same way as column and particle porosity changes. As discussed above, in the presence of such delays, it can be advantageous for the parameter estimation procedure to compromise the alignment of the simulated and actual peaks while still achieving a match in shape and height between the simulated and actual peaks. Thus, first, 1 / 10t r If the alignment is less than t, the penalty is reduced by 1 / 2, and then the alignment is deviated. r An alternative position penalty metric is introduced that ramps linearly to 1 by . 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 1 / 2 and range 1 / 10 were chosen experimentally and can be changed by the user.

number

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

number

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

[0095] Sum of Squared Differences The SSD score is a set of differences between the simulated and measured chromatogram data, see equation (23) below. For technical reasons, each difference is interpreted as a separate metric. In section 8, the goal 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 scores is a combination of peak shape, position, and height, S ガウス This score is typically applied to the time interval specified by the index set J that contains a single peak with an approximately Gaussian shape. This time interval is not automatically detected, but must be specified by the user. A more detailed score S ピーク further accounts for the shape of the time derivative, minimum, and maximum, making it more suitable for fitting non-Gaussian peaks. By combining the peak shape with the shape of its derivative, this score is highly sensitive to the curvature of the chromatogram. The time offsets in the peak and the slope are not technically constrained to be equal. In practice, they will rarely differ except in the very first iteration of the search algorithm with a bad starting point. The score

number

number

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[0097] Peak Front In some cases, only the front of the peak can be used for parameter estimation, while the other parts of the peak are degraded due to non-specific interactions of the tracer molecule with the column or tubing. Dextran is a prominent example of such non-ideal behavior leading to strong tailing and reduction in peak height. On the other hand, dextran is commonly applied as a tracer that does not penetrate the particle pores. Errors in the experimental run can also make the rear of the peak unusable for parameter estimation. These situations are addressed by the score S, which takes into account the peak shape and position but not the peak height. 前部 This score is typically used 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 front score is designed to extract as much usable information as possible from the chromatogram. Unsupervised application of this score requires that the cut points be highly accurate while still robustly removing non-ideal parts to automatically determine the usable time interval. For the dextran data, the tail 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. Experimentation has shown that this is a good choice since non-ideal interactions mainly affect peak height and tailing. The lower cut point is chosen where the measured chromatogram starts to differ from the baseline by more than 0.1% of the concentration at the upper cut point. Experimentation has shown that 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 time points of the discrete measured data are then used as the boundaries of the time interval specified by J.

[0099] Fractionation Data Optical detectors, typically applied to measure chromatograms, usually cannot distinguish between different chemical components. Instead, they deliver a single sum signal, with the contributions of the individual components weighted by their extinction coefficients. Such a signal cannot be used alone for parameter estimation, 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 components of interest and provide additional information to set up dedicated parameter estimation scores.

[0100] The metrics introduced above can generally be applied to the concentrations in each vial using the center of the corresponding collection interval as the time point. For precise comparison, the corresponding simulations for each component are averaged over the same collection interval when the metrics are applied to fraction data. The resulting information is often sparse, with 5-10 fractions per peak, and may have additional errors in fraction times and volumes. Even small shifts in the collection interval can lead to large changes in the distribution of components among the analyzed fractions, especially for sharp peaks. The smoothing procedure from section 5 is not suitable for such sparse measurements. Nevertheless, to maintain subgrid accuracy, the time offset t s To determine the offset, 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 mentioned above are defined per component, but can also be applied to the sum signal. Scores of several components can be merged to create the goal of the applied search strategy. By including the score on the sum signal, it is wise to use all available information. CADET-Match uses two alternative search strategies: gradient descent and a multi-objective genetic algorithm. In the case of gradient descent, all metrics need to be combined into one scalar value, while the genetic algorithm can operate on several metrics.

[0102] Gradient descent The gradient descent algorithm searches for a local optimum in the objective function using derivative information on the parameters sought. Gradient descent has long been used for parameter estimation in chromatography. Gradient descent is very efficient near the optimum sought, but can fail if the objective function is not smooth or the Jacobian becomes singular. Furthermore, the algorithm is prone to getting trapped in a local optimum that may be far from the starting point. This can be avoided by basin hopping or a multi-start strategy. The latter is often applied to improve the results of population-based search strategies.

[0103] Genetic Algorithm (GA) Genetic algorithms (GAs) are an example of biomimicry. At their core, genetic algorithms work like a colony of bacteria adapting to an external environment and share many of the same characteristics. GAs are embarrassingly similar. An initial population is created, often using quasi-random methods such as Latin hypercube sampling or Sobol sequences. Each member of the population is then evaluated based on one or more objectives. At the end of each generation, the best members survive and reproduce to form the next generation. The next generation is created by a combination of reproduction and mutation of the surviving members. There are variations on this procedure that maintain the diversity of the population, select which members to include in the next generation, and change how reproduction and mutation are performed. 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 properly process experimental data and determine suitable starting points can be a difficult and arduous task. Based on experiments, it is unlikely that a new model or concept will be implemented correctly from scratch. However, such problems can only be tested by attempting to fit a model to the data. Since errors can often be identified early in the parameter estimation process, CADET-Match provides the ability to monitor the progress of certain indicators such as peak height, shape, mass, etc. This allows observing whether starting points give reasonable results and whether the search algorithm improves on the objectives all the time. Online monitoring allows early stopping if the progress is poor or the results are already good enough. This is crucial for rapid testing of models, objectives, starting points, and stopping criteria. Since suitable starting points can be difficult to determine, 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 iterative processes are more difficult to monitor.

[0105] Parameter Conversion Most search strategies struggle when the sought parameters are spread over several orders of magnitude or are correlated with each other. Parameter transformations can help to mitigate such problems. CADET-Match provides several transformation rules, i.e., one-to-one maps, between the model parameters p passed to the chromatography simulator and the estimated parameters P' passed to the search algorithm. These transformations are based on the upper bounds of the model parameters

number

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[0106] The linear transformation (see Equation 27 below)

number

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[0107] Nonlinear parameter correlations need to be addressed in particular because they are difficult to detect. For example, the adsorption and equilibrium constants k a and k eq is usually the adsorption and desorption constant k a and k d The correlation is much lower than that of the relationship k eq =k a / k d is the search algorithm k a and k eq While operating on k a and k d to the simulator. The corresponding transformation (see Eqs. 29 and 30 below) also accounts for the large parameter range. This decouples the binding rate from the concentration equilibrium.

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

[0109] Sensitivities for any model input can be calculated by the CADET library and written to the .h5 output. CADET uses algorithmic differentiation. Numerical approximations of the analytical derivatives can be obtained by finite difference methods, which are also available in the MoChA tool.

[0110] Parameter Identifiability Model parameters can generally be obtained by measuring, for example using optical microscopy, to determine pore transport coefficients. However, taking direct measurements of model parameters is often not possible or very laborious, and therefore recursive parameter estimation is the method often used in chromatography modeling. Parameter identifiability describes the ability to find model parameters specific to a given known input and model equation. In the case of chromatography, model parameters have poor identifiability when different parameter sets produce the same simulated chromatogram or chromatograms with negligible deviations. This makes parameter estimation difficult. Parameter identifiability can be visualized by plotting an objective value that is calculated to assess the fit quality of a particular parameter value.

[0111] Materials and Methods A new modality BiTE® (bispecific T cell engager) antibody construct is used as an example to present the systematic approach herein. The molecule is a half-life extended BiTE® as a member of a class of bispecific antibodies that holds high promise in cancer therapy and other serious diseases. The BiTE® molecule was produced by using a Chinese Hamster Ovary cell line developed by Amgen, and then captured by a Protein A affinity step. The BiTE® was captured by a Protein A affinity step, followed by viral inactivation and depth filtration to generate a filtered viral inactivated pool (FVIP).

[0112] Subsequently, viral inactivation was applied by adding 1 M formic acid. The pool was neutralized to pH 5.0 using 2 M Tris system to generate the non-filtered viral inactivated pool (nVIP). The nVIP was filtered through a Millistak+® HC pod depth filter to generate the filtered viral inactivated pool (FVIP).

[0113] The experiments were carried out using an AKTA™ Avant 150 chromatograph with Unicorn 7.3 software. In-line pH, UV, and conductivity measurements were performed using standard UV, pH, and conductivity probes installed on the chromatograph. Off-line 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 confirm the readings.

[0114] Benchtop Experiments For benchtop scale runs, Capto SP ImpRes resin (Cytiva™) was packed into a Millipore vantage column (1.15 cm internal diameter and 20.7 cm height) with a compression ratio of 1.11, resulting in a column volume of 21.5 mL. The column had an asymmetry factor of 0.91 and a HETP of 0.0203 cm.

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

[0116] The ionic capacity of the used Capto SP ImpReS resin was obtained by the titration method introduced by Thiemo Huuk 2016. A small column of 1.7 mL CV packed with the same lot of Capto SP ImpReS was exposed to 0.5 mM hydrochloric acid (HCL) for about 500 CV. The column was then washed with water to remove any residual acid. The column was exposed to 0.01 M sodium hydroxide (NaOH). Finally, the ionic capacity of the column was determined by Thiemo Huuk 2016 using the volume of NaOH required to completely exchange the counterions.

[0117] The filtered viral inactivation pool (FVIP) material was used for benchtop scale chromatography runs. The feed materials were from the same manufacturing lot and the feed characteristics are shown in Table 2 below.

[0118] [Table 2]

[0119] The conductivity of the unbound pulsed feed material was adjusted to 180 mS / cm using 4 M 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. The dextran solution 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 1 M NaCl solution to determine the holdup from the sample pump to the conductivity meter.

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

[0122] Protein breakthrough experiments were performed using equilibration buffer with a conductivity of 44 mS / cm and conductivity-adjusted FVIP pool so that the column was equilibrated and loaded under non-binding conditions. The column was first equilibrated with high conductivity equilibration buffer for 3 CV, and then 40 mL of conductivity-adjusted FVIP pool was run through the column. Regeneration was performed after loading to ensure that no protein was bound to the column.

[0123] A gradient elution run was performed by first equilibrating over 5 CV and loading FVIP material at 25 g / L of resin. A wash step with equilibration buffer was performed over 3 CV. Elution was performed with a gradient of 5, 8, and 11 mM / CV to perform a one-step elution.

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

[0125] [Table 3]

[0126] Process robustness experiment For the process robustness runs, Non-Filtered Viral Inactivated Pool (NVIP) material was used. The same lot of material at a concentration of 4.80 g / L was injected at various loads and gradients.

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

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

[0129] [Table 4]

[0130] algorithm The model equations were solved by the Chromatography Analysis and Design Toolkit (CADET), an open source simulator. The software allows combining various transport and adsorption models of the chromatographic process as well as CSTR and DPFR type transport models to describe the set of unit operations. Furthermore, the software provides model-based analysis tools, such as providing sensitivity with respect to the model input parameters. The software package is available at https: / / github.com / modsim / CADET. CADET was accessed through a Python interface. The parameter search was performed by CADET-Match, an open source software package based on the CADET engine, available at https: / / github.com / modsim / CADET-Match. The estimation algorithm used in this tool uses a multi-objective maximization that measures the similarity between the simulated and the measured chromatograms. The result where the product of these objective values ​​is the highest was used to identify the best fit.

[0131] Results and Discussion For the model development, the step-by-step approach was as follows. Using this approach, transport effects such as peak delay or peak broadening caused by the transport of molecules in tubing and valves are separated from adsorption effects in the model. This is particularly important because the mentioned transport effects can be collapsed into adsorption coefficients through recursive model calibration, which reduces the model applicability at various column scales. The step-by-step approach is shown in Figure 4.

[0132] Phase 1: Process Systems Capture Figure 1A shows a flowpath representation of commonly used chromatography skids and machines such as the AKTA™. Figure 1A shows various dead volumes before the column. This dead volume affects the shift of the peak during elution with respect to the start of elution, so the dead volume needs to be accounted for in the model. Possible representations range from a simple time shift at the start of elution to a mechanistic representation of the volumes of the built-in tubing and valves.

[0133] The simplest representation of the path a molecule undergoes in a chromatographic machine is outlined in Figure 5. This combination of unit operations was used to create a representation of the process required for gradient elution.

[0134] The resulting unit operation model system is set up by combining the DPFR and CSTR models with the column model. A model sequence with multiple unit operations is shown in Figure 4.

[0135] A pipe model and a tank model are used to simulate the effects of the pipes, mixers and valves. The column model equations given in equations (1)-(7) are used.

[0136] Identification of additional column transport parameters A combination of the tubing model equations and the valve model equations given in Equations (11) and (12) are used to represent the flow path from the sample pump to the UV sensor and 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 (the inlet pump (buffer) path and the sample pump (molecule) path) and the DPFR model setup from only the geometric specifications (length and diameter) provided by the vendor. As described herein, the pre-column tubing model and the mixer / valve model are fitted individually for the dextran breakthrough bypass and salt bypass runs. In addition, the models of tube 6 and tube 7 are set up according to the AKTA™ Avant150 manual with 1 mm diameter and 17 cm and 10 cm, respectively. The dispersion coefficients of those two models are set to the dispersion coefficients estimated in the bypass experiment.

[0137] Step 2: Capturing transport and column transport properties Identification of bypass transport parameters The parameters describing the transport behavior from the column can be separated from the effects resulting from adsorption by performing dextran and salt tracer experiments that bypass the column. The inlet and outlet tubing of the column are connected by a zero-volume connector so that the column is excluded from the flow path of the bypass experiment. The flow path important for the gradient elution run is shown in Figure 6. A list of the parameters estimated in this step is given.

[0138] Table 5 provides a list of the names, descriptions, and ranges of the parameters estimated for each pathway the molecule undergoes. 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 with dextran. Possible causes are pressure deviations caused by interactions with the tube walls or strong high density gradients. Such non-ideal behavior can be observed at different inflection points during the rise of the breakthrough (see FIG. 7A). Due to this behavior, the parameter estimation algorithm fits the simulation to the beginning of the breakthrough or the front of the peak, ignoring previous points in the chromatogram. In CADET-Match, this approach is fully automated. The results of this model calibration step are shown in FIG. 7A and FIG. 7B.

[0141] The final parameters are given in Tables 6A-6C. In Figures 7A and 7B, the effect of tracer molecules such as dextran is clear, showing that fitting the first rise of the dextran breakthrough leads to different parameters compared to fitting the entire dextran breakthrough, as shown in Figure 7A. The small pre-peak at the dextran breakthrough rise was assumed to be an artifact and was largely ignored by the estimation algorithm. The fit in Figure 7A provides the model parameters of the unit operations of the sample path (see Figure 6). The calibration result in Figure 7B shows the model representation of the inlet path (see Figure 6). Only negligible deviations between the fitted model and the conductivity signal are observed, due to the close to ideal behavior of the salt tracer.

[0142] [Table 6]

[0143] [Table 7]

[0144] [Table 8]

[0145] Identification of column transport parameters Dextran breakthrough and pulse experiments performed with the column in line were used to identify column specific transport parameters. Knowledge of the hold-up volume and dispersion caused by the pre- and post-column tubing allows for more accurate parameterization of column specific transport effects. Blue Dextran 2000 acts as a non-pore penetrating tracer molecule for Capto SP ImpReS, therefore in this first step the interstitial phase column transport is calibrated. The transport parameters estimated using the 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] Again, the CADET-Match tool was used for this estimation step, and the resulting fits are shown in Figures 8A and 8B.

[0148] The simulated trace breakthrough and pulse at the front of the chromatogram were fitted to the experimental dextran and showed a very good fit, with the resulting model parameters given in Tables 6A-6C. As a next step, the transport parameters related to the resin particles are estimated. These parameters refer to mass transport from the void volume into the particle and particle porosity. In Table 7, the parameters and parameter ranges used in the estimation procedure are given. The results of the particle transport calibration step are shown in Figure 8C. The resulting model parameter values ​​are given in Tables 6A-C.

[0149] [Table 10]

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

[0151] The non-idealities at the top of the chromatogram in Figure 8C are caused by a pressure alarm due to loading the column to full capacity and are ignored in the parameter estimation. Again, only the first part of the breakthrough front is used by the estimation engine. In this step of the model calibration, FVIP material containing the target molecule and impurities is used. Therefore, the parameters obtained by this step describe the pore transport of the actual molecule used and not the tracer molecule.

[0152] Step 3: Capturing quantitative adsorption behavior Here, a model description of the system of unit operations of the chromatographic machine can be used in step 3 to identify the adsorption behavior of the target molecule. Full experimental chromatographic runs with different gradient slopes (5 mM / CV, 8 mM / CV, 11 mM / CV, and "step" elution) were performed. The elution volume was fractionated at intervals of 0.5 CV and the fractions were analyzed by analytical size exclusion (SEC-HPLC) and cation exchange (CEX-HPLC) chromatography to obtain the content of the molecule of interest.

[0153] Modeled species The fractionation data was used to determine the species to be modeled. The target chromatogram areas of interest are the main peak and the trailing peak with impurities.

[0154] Based on the analyzed fractions, the main peak is represented in the model by collapsing all charge variants of the target molecule into three charge variant species: acidic, major, and base variants. The molecular weight is considered equal for all three variants. Based on the SEC analysis of the fractions, all species contained in the impurity peak are accounted for in the model as single components. Finally, a five-component model is obtained: one salt species describing sodium as counterion, four protein components describing the acidic, major, and base charge variants, and a high molecular weight (HMW) component.

[0155] The model uses the concentration of each species being modeled in the FVIP material as an input parameter, which means that for an accurate representation of the molecular species entering the column, analytical experiments need to be performed to identify the feed load protein concentration of each species being modeled. For the sake of effort and time series, the load protein concentration was identified by using the experimental fraction pools together with the UV chromatogram instead of the analytical profile of the feed solution. The ratio between the peak areas in the fraction pools and the ratio between the peaks in the UV chromatogram are calculated. The concentration of each species in the feed is then calculated by considering the total protein concentration present in the FVIP material.

[0156] Calibration Results 5 mM / CV and 11 mM / CV gradient runs were used in parallel for binding parameter estimation. UV signal and fractionation data were used for estimation. The parameters and parameter ranges that underwent estimation are listed in the table.

[0157] Table 9 provides a list of the names and ranges of the parameters that were estimated. Each parameter of the modeled species is estimated.

[0158] [Table 11]

[0159] The ionic capacity Λ was set to 1339 mM according to the procedure described above in the "Benchtop Experiments" section. The best fits obtained are shown in Figures 9A and 9B. The final adsorption model parameter values ​​are listed in Tables 6A-C.

[0160] Model Valuation Process performance indicators (PPIs) pool volume, yield, and pool concentration are used to measure model predictiveness for model validation. Further gradient experimental runs at process scale (44 mL column) and benchtop scale (21.5 mL column) with varying loading and gradient are used for model validation. Model scale-up was performed by setting the column diameter and column length to the specified values ​​of the process scale column. Additionally, the volumetric flow rate was changed from 2.60 mL / min to 4.33 mL / min. All model parameters were kept the same as those estimated by model calibration. The PPI thresholds for model acceptability are listed in Table 9. Visualization of the model predictions and experimental data for process scale are presented in Figure 10A, Figure 10B, Figure 10C, and Figure 10D.

[0161] [Table 12]

[0162] Gradient runs at benchtop and process scale are used for model validation. First, the PPI of the run at 25 g / L loading factor is compared, and the results are shown in Table 10.

[0163] [Table 13]

[0164] As shown in Table 11, it is observed that the model predicts the PPI of the bench-top scale process within 5% deviation. The model prediction of the process scale run is within 13% deviation. Both 5% and 13% are well within the predefined acceptable range given in Table 10.

[0165] Further model validation activities include comparing process-scale model predictions at various charging factors, gradient slopes, and collection stop criteria. The results of the 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 are well within the defined PPI range while changing the loading factor. However, the model appears to become less predictive in terms of yield when the gradient slope is changed, even when the gradient slope is close to the value at which the model calibration was performed. A trend can be observed in those runs showing a general overestimation of yield and pool volume. The reason for the overestimation of yield can be found in the general overestimation of peak areas, which is linked to one model limitation that is a general problem in mechanistic chromatography modeling. This shows that the mass loaded on the simulated column was higher than that measured by the UV detector in the chromatogram, leading to a peak area deviation of about 10%. The model appears to have a very high sensitivity to protein loading. A more accurate feed concentration to determine the mass fed to is not available in this dataset.

[0169] In Table 12, the fraction of charge variants in the collected pool of major, basic, and acidic charge variants is compared between predicted and measured values. All simulated fractions deviate from the experimentally obtained values ​​by 0-16.2%. The values ​​indicate sufficient model accuracy to predict the charge variant profiles at various loading 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 transfer the UV signal from AU units to SI units, it is necessary to assign molecular weights to each species being modeled. SI units are convenient for simulation activities. The molecular weights of the HMW species are not precisely known. Thus, the amounts of HMW species in the feed are likewise not precisely specified. In the process of improving the model accuracy, the molecular weights of the HMWs can be taken into account more precisely.

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

[0172] Summary and Conclusion We present a model development methodology for pharmaceutical therapeutic molecules that suggests a step-by-step method calibration part of the model in three steps to build the final model. This methodology can be used to separate the transport model description from the adsorption model.

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

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

[0175] With that, it can be concluded that the suggested workflow is accompanied by the steps required to configure the model portion for additional column volume, intracolumn transport, and adsorption behavior. Beneficial features of the method provided herein include: Fewer experiments are required for calibration Additional column capacity is characterized and each model portion can be reused for other molecules; The relative decoupling of transport model calibration from adsorption model calibration allows the models to reflect instrument changes and to be used across a range of scales.

[0176] The model predicts the process at larger scales with acceptable quality, but reveals general limitations. One of those limitations is that in many cases the feed concentrations of the various species being modeled are not known, and additional analytical experiments are required. Due to time and effort, alternative methods of identifying the feed concentrations from UV chromatograms and fractionation data are suggested. Previous studies have not previously revealed this shortcoming of mechanistic models or described how to address this issue. The present disclosure provides an approach to identifying the feed concentrations from fractionation data and UV chromatograms, and suggests that no additional experiments are required. Due to time and effort, a minimal set was used for model calibration and validation. A set of 12 experiments is used for the complete workflow, including identification of additional column transport model parameters to model validation. A set of 9 experiments was used for model calibration under binding conditions at a certain pH value, and a set of 4 additional experiments was required to estimate the transport model parameters in the case of on-column and off-column transport. In addition, model validation experiments were used. It is generally known that model acceptability and predictability increase with the amount of knowledge and experiments available for model calibration. However, as the experimental effort increases, so does the acceptability of integrating model-based methods into platform process development. Therefore, identifying a minimal set of experiments for model calibration supports the integration of chromatographic modeling into industrial process development activities.

[0177] Furthermore, it was found that the model has a higher sensitivity to the amount of protein fed than experiments suggest. Thus, PPI is often overestimated compared to the estimate. Two approaches can now help improve model accuracy. First, increase analytical efforts to improve feed characteristics. Second, include parameter uncertainty estimation in the model assessment. Here, estimated parameters can be examined with respect to variations in feed concentration. Such kind of insights are valuable to guide process optimization and process robustness experiments.

[0178] The methods provided herein can be used and reproduced by other modelers because the solvers and algorithms are publicly available. Furthermore, the models include a set of unit operations available for use in HDF5 format, making the simulations reproducible. The results described herein can be used to further explore and enhance the models and workflow capabilities, which is a major contribution to the evolving chromatography community.

[0179] Exemplary Methods 11 shows a flow diagram 100 of one example of a method described herein. In a chromatography machine 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 may be obtained (block 102). For example, the geometric measurements associated with the second DPFR may include tube diameter measurements and tube length measurements associated with the second DPFR. These measurements may be obtained, for example, based on measuring tube diameters and tube lengths and / or based on known manufacturing specifications of the chromatography machine.

[0180] For example, the processor may generate transport parameters of a transport model associated with the second DPFR based on the geometric measurements (block 104). For example, the transport model parameters may include a diffusion coefficient in the DPFR, a volume of the DPFR, a cross-sectional area of ​​the DPFR, etc.

[0181] A tracer molecule (e.g., dextran, NaCl, or another suitable tracer molecule) may be provided to the chromatography machine (block 106). One or more tracer molecule measurements may be captured based on the tracer molecule traveling through the chromatography machine (block 108). For example, one or more tracer molecule measurements may be captured based on a chromatogram associated with the tracer molecule traveling through the chromatography machine.

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

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

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

[0185] Optionally, an experimental sample may be provided to a chromatography machine (block 112). One or more experimental measurements may be captured based on the experimental sample moving through the chromatography machine (block 114). For example, one or more experimental measurements may be captured based on a chromatogram associated with the experimental sample moving through the chromatography machine.

[0186] Based on one or more experimental measurements based on the experimental sample moving through the chromatographic machine, the estimated one or more 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 may be estimated (block 116), for example by a processor. In some examples, the column-specific transport model and / or the 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 of an adsorption coefficient, a desorption coefficient, a characteristic charge, a shielding factor, etc. In some examples, a second set of adsorption parameters of the second adsorption model associated with the experimental sample may be estimated based on ranges associated with the initial estimated adsorption parameters.

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

[0188] Further, in some examples, a chromatography machine may include an inlet flow path including a first DPFR and a CSTR before the inlet flow path column and a second DPFR after the inlet flow path column, and a sample flow path including a first DPFR and a CSTR before the sample flow path column and a second DPFR after the sample flow path column, and method 100 may be performed on both the inlet flow path and the sample flow path.

[0189] Additionally, in some instances, blocks 112, 114, and 116 may be executed again using a second experimental sample (e.g., separate from the first experimental sample), but using the same estimated transport model parameters. That is, once a transport model for a chromatography machine is developed, the transport model may be used to identify adsorption model parameters for multiple experimental samples.

[0190] Aspects 1. A method comprising: acquiring 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.

[0191] 2. The method of embodiment 1, further comprising: providing an experimental sample to a chromatography machine; capturing one or more experimental measurements based on the experimental sample moving through the chromatography machine; and estimating, by a processor, one or more adsorption model parameters of an adsorption model associated with the experimental sample based on the one or more experimental measurements based on the experimental sample moving through the chromatography machine, the estimated one or more 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.

[0192] 3. The method of embodiment 1 or 2, wherein the geometric measurements include vessel diameter measurements and vessel length measurements associated with the second DPFR.

[0193] 4. The method of any one of aspects 1 to 3, wherein the one or more tracer molecule measurements are captured based on a chromatogram associated with the tracer molecule traveling through a chromatography machine.

[0194] 5. The method of any one of aspects 2-4, wherein the one or more experimental measurements are captured based on a chromatogram associated with an experimental sample traveling through a chromatography machine.

[0195] 6. The method of any one of aspects 2-5, further comprising: identifying, by the processor, the experimental sample 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 the experimental sample may include first estimating a first one or more adsorption parameters of a first adsorption model associated with the experimental sample, and the method may include second estimating, by the processor, a second one or more adsorption parameters of a second adsorption model associated with the experimental sample based on ranges associated with the first one or more binding parameters of the first adsorption model associated with the experimental sample. The method of any one of aspects 2 to 6, further comprising:

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

[0198] 9. The method of any one of aspects 1 to 8, wherein the first DPFR and CSTR before the column and the second DPFR after the column are part of an inlet path of a chromatography machine, the chromatography machine further comprising 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, and the process of claim 1 is further carried out with the first DPFR and CSTR before the sample flow path column and the second DPFR after the sample flow path column.

[0199] 10. The method of any one of aspects 2-9, wherein the experimental sample is a first experimental sample, and the method further includes providing a second experimental sample to a chromatography machine; capturing one or more second experimental measurements based on the second experimental sample moving through the chromatography machine; and estimating, by the processor, estimated one or more transport model parameters of a transport model associated with the first DPFR and CSTR, a transport parameter 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 the one or more second experimental measurements based on the second experimental sample moving through the chromatography machine.

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

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

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

[0203] 14. The method of any one of aspects 1-13, further comprising estimating, by the processor, one or more column-specific transport model parameters of a column-specific transport model associated with a column of the chromatography machine based on a transport model associated with the first DPFR and CSTR, a transport model associated with the second DPFR, and one or more tracer molecule measurements based on the tracer molecules moving through the chromatography machine.

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

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

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

[0207] 18. The method of any one of aspects 2 to 17, wherein estimating one or more adsorption model parameters of the adsorption model associated with the experimental sample is further based on one or more of a column-specific transport model or a resin transport model.

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

[0209] 20. The method of any one of aspects 1-19, wherein the tracer molecule is NaCl.

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

[0211] 22. The method of any one of aspects 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 the steps of the method described in any one of aspects 1 to 22.

[0213] 24. A non-transitory computer-readable storage medium having stored thereon instructions that, when executed by a processor, cause the processor to perform the steps of the method according to any one of aspects 1 to 22.

Claims

1. 1. A method comprising: 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 following the column; generating, with a processor, transport model parameters for a transport model associated with the second DPFR based on the geometric measurements; providing a tracer molecule to the chromatography machine; capturing one or more tracer molecule measurements based on the tracer molecules traveling through the chromatography machine; estimating, by the 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; The method includes:

2. providing an experimental sample to the chromatography machine; capturing one or more experimental measurements based on the experimental sample moving through the chromatography machine; estimating, by the processor, one or more adsorption model parameters of an adsorption model associated with the experimental sample based on the one or more experimental measurements based on the experimental sample moving through the chromatography machine, the estimated one or more 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 of claim 1 further comprising:

3. The method of claim 1 , wherein the geometric measurements include pipe diameter and pipe length measurements associated with the second DPFR.

4. The method of claim 1 , wherein the one or more tracer molecule measurements are captured based on a chromatogram associated with the tracer molecule traveling through the chromatography machine.

5. The method of claim 2 , wherein the one or more experimental measurements are captured based on a chromatogram associated with the experimental sample traveling through the chromatography machine.

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

7. Estimating the one or more adsorption model parameters of the adsorption model associated with the experimental sample includes first estimating a first one or more adsorption parameters of a first adsorption model associated with the experimental sample, the method comprising:

3. The method of claim 2, further comprising: second estimating, by the processor, a second one or more adsorption parameters of a second adsorption model associated with the experimental sample based on ranges associated with the first one or more binding parameters of the first adsorption model associated with the experimental sample.

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

9. 2. The method of claim 1, wherein the first DPFR and CSTR before the column and the second DPFR after the column are part of an inlet path of the chromatography machine, the chromatography machine further comprising a sample flow path having a first DPFR and CSTR before a sample flow column and a second DPFR after the sample flow column, and the steps of claim 1 are further performed with the first DPFR and CSTR before the sample flow column and the second DPFR after the sample flow column.

10. The experimental sample is a first experimental sample, and the method comprises: providing a second experimental sample to the chromatography machine; capturing one or more second experimental measurements based on the second experimental sample moving through the chromatography machine; estimating, by the processor, the estimated one or more 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 an adsorption model associated with the second experimental sample based on the one or more second experimental measurements based on the second experimental sample moving through the chromatography machine; The method of claim 2 further comprising:

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

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

13. The method of 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. 2. The method of claim 1, further comprising estimating, by the processor, one or more column-specific transport model parameters of a column-specific transport model associated with the column of the chromatography machine 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 chromatography machine.

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

16. 15. The method of claim 14, further comprising estimating, by the processor, one or more resin transport parameters of a resin transport model associated with resin particles of the chromatography machine 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 chromatography machine.

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

18. 3. The method of claim 2, wherein estimating one or more adsorption model parameters of an adsorption model associated with the experimental sample is further based on one or more of a column-specific transport model or a resin transport model.

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

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

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

22. The method of claim 1 , wherein the tracer molecules are nanoparticles.

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

24. A non-transitory computer readable storage medium storing instructions which, when executed by a processor, cause the processor to perform the steps of the method according to any one of claims 1 to 22.

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