Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N30/00—Investigating or analysing materials by separation into components using adsorption, absorption or similar phenomena or using ion-exchange, e.g. chromatography or field flow fractionation
  • G01N30/02—Column chromatography
  • G01N30/86—Signal analysis
  • G01N30/8693—Models, e.g. prediction of retention times, method development and validation
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
  • B01D—SEPARATION
  • B01D15/00—Separating processes involving the treatment of liquids with solid sorbents; Apparatus therefor
  • B01D15/08—Selective adsorption, e.g. chromatography
  • B01D15/26—Selective adsorption, e.g. chromatography characterised by the separation mechanism
  • B01D15/36—Selective adsorption, e.g. chromatography characterised by the separation mechanism involving ionic interaction, e.g. ion-exchange, ion-pair, ion-suppression or ion-exclusion
  • B01D15/361—Ion-exchange
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N27/00—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means
  • G01N27/26—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating electrochemical variables; by using electrolysis or electrophoresis
  • G01N27/416—Systems
  • G01N27/447—Systems using electrophoresis
  • G01N27/44704—Details; Accessories
  • G01N27/44743—Introducing samples
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N30/00—Investigating or analysing materials by separation into components using adsorption, absorption or similar phenomena or using ion-exchange, e.g. chromatography or field flow fractionation
  • G01N30/02—Column chromatography
  • G01N30/86—Signal analysis
  • G01N30/8624—Detection of slopes or peaks; baseline correction
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N30/00—Investigating or analysing materials by separation into components using adsorption, absorption or similar phenomena or using ion-exchange, e.g. chromatography or field flow fractionation
  • G01N30/02—Column chromatography
  • G01N30/88—Integrated analysis systems specially adapted therefor, not covered by a single one of the groups G01N30/04 - G01N30/86
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N30/00—Investigating or analysing materials by separation into components using adsorption, absorption or similar phenomena or using ion-exchange, e.g. chromatography or field flow fractionation
  • G01N30/02—Column chromatography
  • G01N30/88—Integrated analysis systems specially adapted therefor, not covered by a single one of the groups G01N30/04 - G01N30/86
  • G01N2030/8809—Integrated analysis systems specially adapted therefor, not covered by a single one of the groups G01N30/04 - G01N30/86 analysis specially adapted for the sample
  • G01N2030/8813—Integrated analysis systems specially adapted therefor, not covered by a single one of the groups G01N30/04 - G01N30/86 analysis specially adapted for the sample biological materials
  • G01N2030/8827—Integrated analysis systems specially adapted therefor, not covered by a single one of the groups G01N30/04 - G01N30/86 analysis specially adapted for the sample biological materials involving nucleic acids
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N30/00—Investigating or analysing materials by separation into components using adsorption, absorption or similar phenomena or using ion-exchange, e.g. chromatography or field flow fractionation
  • G01N30/02—Column chromatography
  • G01N30/88—Integrated analysis systems specially adapted therefor, not covered by a single one of the groups G01N30/04 - G01N30/86
  • G01N2030/8809—Integrated analysis systems specially adapted therefor, not covered by a single one of the groups G01N30/04 - G01N30/86 analysis specially adapted for the sample
  • G01N2030/8813—Integrated analysis systems specially adapted therefor, not covered by a single one of the groups G01N30/04 - G01N30/86 analysis specially adapted for the sample biological materials
  • G01N2030/8831—Integrated analysis systems specially adapted therefor, not covered by a single one of the groups G01N30/04 - G01N30/86 analysis specially adapted for the sample biological materials involving peptides or proteins
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N30/00—Investigating or analysing materials by separation into components using adsorption, absorption or similar phenomena or using ion-exchange, e.g. chromatography or field flow fractionation
  • G01N30/02—Column chromatography
  • G01N30/04—Preparation or injection of sample to be analysed
  • G01N30/16—Injection

Definitions

• the present disclosure generally relates to calibration of a mechanistic ion-exchange chromatography model for a chromatography machine.
• Chromatography is a method used for molecule separation and purification during the downstream processing of biomolecules, and is an important step in the purification of biopharmaceuticals.
• solutions of biomolecules can be purified and concentrated using porous packed beds that separate different molecules based on their differences in mass, size, or charge.
• Ion-exchange (IEX) chromatography is a purification step based on ionic interactions between chromatographic material and molecules, and involves using charged sites on the surface of the packing material to adsorb biomolecules based on charged sites on their 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 their surface. Adsorbed biomolecules can be eluted by decreasing the molecules’ surface affinity through the usage of a buffer solution of increased ionic strength.
• Mechanistic models are a tool used for knowledge-based process development, process optimization, predictive process control, and gain of process understanding of chromatographic separation processes. Mechanistic models provide predictions of important process outputs and process performance indicators over a large process range.
• mechanistic CEX chromatography modeling is a useful tool based on first principles to describe the transport and elution behavior of molecules and predict the behavior of a chromatography step.
• the application of a CEX chromatography model in process development to explore the design space of process parameters, such as loading factors or elution gradients, can reduce the effort of iterative experimentation.
• mechanistic modeling provides the opportunity to gain insight on the mechanisms affecting the separations of a protein therapeutic and its impurities.
• mechanistic modeling provides a useful, science-based tool for process design and optimization.
• mechanistic CEX chromatography modeling can be utilized to make decisions on CEX step parameters such as gradient slope, collection criteria, and load factor.
• mechanistic models require prior knowledge and a thorough calibration process in order to provide enough predictivity in small- and large-scale separation processes.
• a mechanistic model requires a well-defined mathematical description of each process step.
• studies using and suggesting workflows for mechanistic models for process optimization, process investigation and performance assessment or model-based control There are a number of models available that can describe chromatographic steps of biopharmaceuticals.
• GRM general rate model
• the adsorption of biomolecules to the adsorbent can be described by adsorption models.
• vast numbers of models are available that have proven to be applicable to chromatography.
• An early adsorption model is the Langmuir model that allows for concentration-dependent adsorption to surfaces with finite capacity
• a further milestone in modeling adsorption behavior 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 material caused by ionic interactions on adsorption behavior of molecule mixtures. In a number of studies the successful application of the SMA model to ion-exchange chromatography has been shown.
• model parameters generally can be obtained by measuring, such as using optical microscopy to determine pore transport coefficients.
• measuring such as using optical microscopy to determine pore transport coefficients.
• recursive parameter estimation is a method often used in chromatography modeling.
• adsorption model parameters may be identified using neural networks, which, after a training period for the neural network, accelerates the parameter identification in comparison to the reverse chromatogram fitting.
• a robust model calibration workflow involves a set of 1 experiments is suggested to calibrate a multi-component SMA model for a bispecific antibody. Those 14 experiments are used for the calibration of the adsorption model and added to that experiments for characterizing the column and extra column characteristics are required. Based on this workflow, the value of the mechanistic model for the investigation of process robustness investigation may be demonstrated.
• the present disclosure provides a workflow for CEX model calibration using a minimal set of experiments.
• the model provided by the present disclosure takes the mass transfer in the extra column volume into account, and involves a model sequence that entails a combination of fitted dead volume models prior to a chromatography column and models that are set-up only from geometric values of tubing after a chromatography column.
• the model input parameters reflecting the mass transfer and those reflecting molecule-specific adsorption behavior are determined in a decoupled manner.
• the present disclosure demonstrates that the adsorption parameter can be scaled across process size, and demonstrates a sufficient predictive quality for scale-up process runs.
• the present disclosure provides a chromatography model calibration approach with increased model accuracy and agility.
• the calibration is structured in three parts for a sequential parameter estimation that decouples parts of the transport model and adsorption model from each other. First, a unit-operation representation of a chromatography skid) and its transport parameters is identified. Next, a transport model for the packed bed is identified. Finally, adsorption model parameters are estimated.
• FIG. 1A illustrates an example flow path representation generally used in chromatographic skids and machines, such as the AKTATM Avant.
• FIG. 1A there are varying dead volumes prior to the column. Since this dead volume influences the peak position relative to the elution start point, the dead volume needs to be accounted for in the model as precisely as possible to decouple this effect from the adsorption behavior that also impacts the peak position.
• Possible representations range from simple time shifts to mechanistic representations of the build-in tubing and valve volume.
• a BiTE® (bispecific T-cell engager) antibody construct a combination of a DPFR model and a CSTR model is used to represent the dead volume prior to the column.
• the dead volume residing from column outlet to UV and conductivity sensor is represented by DPFR models as well.
• a combination of tubing models and valve models is used to represent the flow path from each sample pump to UV sensor and from inlet pump to conductivity sensor. Both flow pathways are a combination of a fitted DPFR model and a CSTR model prior to the column and a DPFR model set-up from geometric specifications provided by the vendor.
• the specific sequence of steps involves first obtaining geometric values of the tubing after the column (tubing diameter, length), e.g., by measurement or based on vendor specifications, and then running experiments that feed a tracer molecule into the system from the desired location.
• a sequence of DPFR - CSTR - DPFR model is set up, with the DPFR model after the column specified according to the geometric values of the specific tubing. That is, while the geometric specifics of this DPFR after the column are fixed, the parameter specifying the dispersion properties of the DPFR is not fixed, and is estimated together with the properties of the DPFR and CSTR before the column.
• the estimation includes estimating geometric parameters of DPFR and CSTR before column, and transport coefficients, such as dispersion, of DPFR before and after column.
• the parameters that are not included in the estimation are the geometric parameters of DPFR after the column. This step is performed for both the sample path flow (blue in FIG. 1 A) and inlet flow path (green in FIG. 1A).
• binding parameters can be estimated. As many components in the model as peaks should be simulated by the model may be included. Then, parameters for each of the modeled components may be estimated. The range of the estimated parameters may be used for including more components that form one or more of the chromatogram peaks, and the binding parameters may be estimated again using tight boundaries for the parameters.
• the first innovation in this sequence lies in specifying the DPFR model after the column according to the geometric values of the specific tubing. This entails that a combination of fitted models and models that are set up based on geometric specifications are used to identify the level of transport effects that hit the column at its beginning. Accordingly, the time that the point sample and the elution buffer hit the column may be identified more accurately than lumping together both flow pathways prior to the column and subsequent to the column without running more complex bypass experiments that separate the paths. Additionally, using the methods provided herein, it is possible separate the transport behavior of the buffer from the transport behavior of the molecule solution.
• a 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 concluded, more components are added to the model. This is necessary for BiTEs® and often antibodies as there are several molecule species that elute in such close proximity that their UV sum signal appears as one peak. Now, this more complex model needs to be re-calibrated with a higher number of components, which results in a much larger number of estimated adsorption parameters. However, due to the previously roughly estimated adsorption parameters from the less complex model, a smaller parameter space can be applied to the parameter estimation this time, which speeds up the estimation procedure.
• the method provided herein is more flexible and more accurate than prior methods for modeling dead volumes in chromatography skids and machines, such as shifting the point of elution start according to the dead volume, or determining the dead volume based on bypass experiments. Both prior methods include the dead volume after the column outlet as dead volume accounted for prior to the column.
• the method provided herein allows estimation of adsorption parameters with less influence from transport effects. This approach decouples transport and adsorption effects on the chromatogram more effectively than previous methods. This is beneficial when process specifications are changed that influence the transport of the molecules. This is the case in scale-up applications. In such a case the impact of scaled-up 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 have to be calibrated again under the changed process conditions.
• a method comprising: obtaining, for a chromatography machine including a first dispersed plug flow reactor (DPFR) and a continuous stirred tank reactor (CSTR) prior to a column, and a second DPFR after the column, geometric measurements associated with the second DPFR; generating, by a processor, transport model parameters for a transport model associated with the second DPFR based on the geometric measurements; feeding a tracer molecule into the chromatography machine; capturing one or more tracer molecule measurements based on the tracer molecule traveling through the chromatography machine; and estimating, by the processor, based on the transport model associated with the second DPFR and the one or more tracer molecule measurements based on the tracer molecule traveling through the chromatography machine, one or more transport model parameters for a transport model associated with the first DPFR and the CSTR.
• DPFR dispersed plug flow reactor
• CSTR continuous stirred tank reactor
• the method may include feeding an experimental sample into the chromatography machine; capturing one or more experimental measurements based on the experimental sample traveling through the chromatography machine; and estimating, by the processor, based on the one or more experimental measurements based on the experimental sample traveling through the chromatography machine, the estimated one or more transport model parameters for the transport model associated with the first DPFR and the CSTR, and the transport parameters for the transport model associated with the second DPFR, one or more adsorption model parameters for an adsorption model associated with the experimental sample.
• the geometric measurements may include tubing diameter measurements and tubing length measurements associated with the second DPFR.
• the one or more tracer molecule measurements are captured based on a chromatogram associated with the tracer molecule traveling through the chromatography machine.
• the one or more experimental measurements are captured based on a chromatogram associated with the experimental sample traveling through the chromatography machine.
• the method may include identifying, by the processor, the experimental sample based on the adsorption model associated with the experimental sample.
• the estimating the one or more adsorption model parameters for the adsorption model associated with the experimental sample may be a first estimating of a first one or more adsorption parameters for a first adsorption model associated with the experimental sample, and the method may further include a second estimating, by the processor, of a second one or more adsorption parameters for a second adsorption model associated with the experimental sample based on a range associated with the first one or more binding parameters for the first adsorption model associated with the experimental sample. Additionally, 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.
• the first DPFR and a CSTR prior to the column, and the second DPFR after the column are part of an inlet flow path of the chromatography machine, and wherein the chromatography machine further includes a sample flow path having a first DPFR and a CSTR prior to a sample flow path column, and a second DPFR after the sample flow path column, and the steps of the method are further performed for the first DPFR and the CSTR prior to the sample flow path column, and the second DPFR after the sample flow path column.
• the experimental sample is a first experimental sample
• the method may further include feeding a second experimental sample into the chromatography machine; capturing one or more second experimental measurements based on the second experimental sample traveling through the chromatography machine; and estimating, by the processor, based on the one or more second experimental measurements based on the second experimental sample traveling through the chromatography machine, the estimated one or more transport model parameters for the transport model associated with the first DPFR and the CSTR, and the transport parameters for the transport model associated with the second DPFR, one or more adsorption model parameters for an adsorption model associated with the second experimental sample.
• the second experimental sample is distinct from the first experimental sample.
• the transport model parameters include one or more of: dispersion coefficient in DPFR, volume of DPFR, cross-section area of DPFR, and volume of CSTR.
• the adsorption model parameters include one or more of: adsorption coefficient, desorption coefficient, characteristic charge, and shielding factor.
• the method further includes estimating, by the processor, 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 molecule traveling through the chromatography machine, one or more column-specific transport model parameters for a column-specific transport model associated with the column of the chromatography machine.
• the column-specific transport model parameters include one or more of: column porosity and column dispersion.
• the method further includes estimating, by the processor, based on the columnspecific 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 molecule traveling through the chromatography machine, one or more resin transport parameters for a resin transport model associated with resin particles of the chromatography machine.
• the resin transport parameters include one or more of: film transport coefficient for each component and pore porosity.
• estimating one or more adsorption model parameters for 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.
• the tracer molecule is dextran. In some examples, the tracer molecule is NaCI. Furthermore, in some examples, the tracer molecule is a DNA molecule. Moreover, in some examples, the tracer molecule is a nanoparticle.
• FIG. 1A illustrates a flow path representation of a chromatography machine (e.g., such as the AKTATM Avant). As shown in FIG. 1A, flow paths from different locations depending on line priming procedures indicate varying time points for when sample or elution buffer enters the column.
• a chromatography machine e.g., such as the AKTATM Avant.
• FIG. 1B illustrates an example of how the mobile phase travels through a packed bed column.
• FIG. 1C illustrates a visualization of the steric mass action model, including parameter meaning.
• FIG. 2 illustrates a graph of a sum of square difference (SSD) alignment issue using synthetic data, in accordance with some examples.
• FIG. 3 illustrates a graph of a comparison of standard position penalty and initially reduced position penalty metrics, in accordance with some examples.
• FIG. 4 illustrates an exemplary stage-wise approach for model development.
• FIG. 5 illustrates a diagram of flow paths used for gradient elution, in accordance with some examples.
• FIG. 6 illustrates a chromatography machine system representation for a CEX model.
• Unit operation sequence of a general model construction Dispersed plug flow reactor (DPFR) and continuous stirred tank reactor (CSTR) represent peak delay and peak broadening that is caused in the system not including the column (valves, sensors, mixing chamber). Salt and molecules might experience different tubing or valve systems, so the parameters associated with those unit operations might vary between proteins and salt species.
• DPFR Dispersed plug flow reactor
• CSTR continuous stirred tank reactor
• FIGS. 7 A and 7B illustrate calibration of pre-column models for transport within the chromatography skid.
• FIG. 7A illustrates dextran tracer breakthrough from the sample pump
• FIG. 7B illustrates NaCI tracer from the inlet pump.
• FIGS. 8A, 8B, and 80 illustrate calibration of column transport model parameters.
• FIG. 8A illustrates dextran breakthrough tracer (non-pore penetrating)
• FIG. 8B illustrates dextran pulse tracer (non-pore penetrating)
• FIG. 8C illustrates FVIP for a BITE® (bispecific T-cell engager) antibody construct breakthrough (pore-penetrating).
• FIGS. 9A and 9B illustrate a comparison of experimental and simulated chromatograms and fractionation data sets under elution conditions.
• FIG. 9A illustrates a best fit for a 5mM/CV gradient run
• FIG. 9B illustrates a best fit for a 11 mM/CV gradient run.
• FIGS. 10A, 10B, 10C, and 10D illustrate model validation on process scale experiments with varying load factor, gradient, and stop collect criteria.
• FIG. 10A illustrates model validation for 8mM/CV gradient and 25g/L load factor on a bench top scale column.
• FIG. 10B illustrates model validation for 8mM/CV gradient and 25g/L load factor on process scale with 30% stop collect criteria.
• FIG. 10C illustrates model validation for 8mM/CV gradient and 15 g/L load factor on process scale with 45% stop collect criteria.
• FIG. 10D illustrates model validation for 8mM/CV gradient and 5g/L load factor on process scale with 30% stop collect criteria.
• FIG. 11 illustrates a flow diagram of an exemplary method, in accordance with some examples provided herein.
• chromatography refers to a method for molecule separation and purification in a downstream process.
• IEX ion-exchange chromatography
• CEX cation-exchange
• AEX anion-exchange
• AKTATM refers to the product name of CytivaTM chromatography machines.
• DPFR dispersed plug-flow reactor
• CSTR continuous stirred tank reactor
• mixing chamber refers to a small tank (-1-10 mL) for mixing buffer solutions in a chromatography machine, such as the AKTATM .
• valve refers to a valve that couples all parts in a chromatography machine such as the AKTATM. These valves can switch between numerous inputs and outputs and have a small volume (-1-1000 L).
• model calibration refers to a procedure to estimate unknown model parameters.
• adsorption refers to the process by which a solid holds molecule of a gas or liquid or solute as a thin film.
• dead volume refers to voids within the chromatography machine that are filled with liquid.
• line priming refers to filling tubing/valves prior to the process start with necessary fluid (e.g., buffers).
• fitting refers to the procedure of recursively estimating unknown model parameters by comparing the simulation to measured values.
• elution refers to the process of removing adsorbed molecules from chromatographic material.
• the column model provided herein describes important transport and adsorption effects of counter-ions and molecules present in the column in solute and adsorbed state.
• a variety of adsorption models can be selected, but the most important adsorption model describes how salt-ions as mobile phase modulators are influencing the adsorption kinetics of molecules. Such processes are described on a seconds time scale, and on micro meter and meter length scales.
• a simplified general rate model (GRM) and the steric mass-action model are used to simulate the transport and elution behavior of acidic, main, and basic charge variants of target molecule and high molecular weight (HMW) impurity species.
• the mobile phase travels 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 ratio between the packed beads).
• This movement is forced convection and is described by a convection term along the column length z.
• effects in the interstitial volume / void between beads in liquid mobile phase
• Fickian diffusion, wall effects, or molecules traveling different paths through the bed that lead to broadening of peaks, which are lumped together and described in the model by a dispersion term.
• the flux of molecules from the interstitial volume into the porous particle volume p of the bed can be hindered which is considered by the model by a film mass transfer model.
• the diffusive transport is assumed to be much faster than the mass transfer into the pores and thus assumed to be instantaneous.
• GMM general rate model
• POR lumped pore diffusion
• the GRM is used to describe transport of biomolecules through a porous packed bed due to convection, dispersion, and diffusion.
• Convection is the movement of a species through a system due to the motion of the bulk fluid surrounding it.
• Dispersion describes peak broadening due to viscosity of a mixture, collisions with tubing walls or particles, and travel through a packed bed.
• Further mass transfer Transport from bulk liquid into the pore and diffusion inside of the pore is described by the GRM.
• the diffusion into the pore from the bulk liquid can be a rate limiting step due to spatial confinement depending on the proportion of molecule size and pore size. The rate at which this transport occurs is described proportional to the film mass transfer coefficient.
• the second component is the diffusion through the pore, which is described with the diffusion coefficient of the respective species. This usually occurs more quickly than the film mass transport. Due to this assumption the equations of the GRM are simplified such that a radial concentration gradient in the pores is neglected, which leads to the lumped pore model.
• the simplified GRM for any species concentration is denoting the number of components, t denoting time in s, z denoting the axial coordinate along the column length L, and r denoting radial bead coordinate along bead radius r p .
• l, p, s denote the reference volumes of interstitial volume (void between beads), pore volume (void inside beads), and solid volume (solid part including adsorbed molecules).
• the interstitial flow velocity is denoted by u in m/s
• the axial dispersion coefficient is denoted by D ax in m 2 /s
• the column porosity volume ratio of interstitial void and total bed volume
• the bead porosity volume ratio of liquid pore volume and total bead volume
• E P the film mass transfer coefficient
• k fi in m/s.
• a model of a dispersed plug-flow reactor was used to describe molecule transport in tubing.
• the equations of a DPFR describe convective laminar flow in a cylindrical tube, neglecting a flow profile.
• the model equations are described by:
• a continuous stirred tank reactor (CSTR) model was used to describe mixing effects within the chromatography system of valves and mixing chambers. That is, a tank model with inlets and outlets and constant volume is used to describe how the concentrations of multiple components change when mixing them together.
• the model equations are described by:
• V m in m 3 denotes the tank volume
• the steric mass action (SMA) model describes adsorption, desorption, and steric interactions of a protein with a resin. These interactions with the resin are characterized with four parameters: adsorption coefficient, desorption coefficient, a steric factor, and a characteristic charge. These parameters are specific to each modeled species. Unlike the transport parameters, the binding parameters translate between different scales and systems so long as the resin and molecule stay the same.
• Adsorption and desorption coefficients describe the rate at which the molecules adsorb (bind) and desorb (elute) from the resin. They describe the binding kinetics of the modeled species and are affected by salt concentration.
• the steric factor and characteristic charge parameters describe the influence of a molecule’s size and surface charge on the binding kinetics, respectively.
• the steric factor describes the number of spaces a molecule “shields” from binding on the resin.
• the characteristic charge describes the number of charge-based interactions a molecule has with a resin. The sum of the steric factor and characteristic charge quantify the total number of binding sites occupied by the molecule on the resin. A visualization of these four factors is shown in FIG. 1C.
• the ionic capacity of the resin is required in order to determine the binding capacity of the protein to the resin.
• the SMA model is based around a neutral charge balance on the resin, so all charged sites are occupied with either counter ions or oppositely charged protein.
• the ionic capacity can be determined from a titration experiment which is detailed in the methods section.
• a in mol/m 3 denotes the total column capacity
• v t denotes the characteristic charge
• ⁇ i denotes the steric factor
• concentration of counter ions available for molecule adsorption (not shielded) is the total amount of counter ions adsorbed to the resin.
• a key limitation of the SMA isotherm is that binding parameter values are applicable only at the pH they were determined at. This limits the robustness of a predictive mechanistic model since pH is an important process parameter in the CEX step. In order to expand on the current SMA model and improve robustness, a function that can address pH dependence is required.
• the special discretization of the chromatography models can be achieved by using a finite volume method.
• the mass balance equations are set-up for a number of uniform finite volume elements along the column length z and the bead radius r.
• the concentrations in each cell volume are averaged, which results in a new set of state variables that are associated to each cell volume.
• the numerical integration is solving 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 equation at the first and last finite volume.
• the weighted essentially non-oscil latory (WENO) scheme is used for approximating the concentrations at the finite volume boundaries.
• the time-stepping solver or ODE solver used here is part of the CADET framework and is using a backward-differential formula (BFD) method for time integration.
• the CADET implementation is using the implicit differential-algebraic (IDA) solver contained in the SUNDIALS package.
• the solver tolerances were set with Abstol at 10 -6 , Algtol at 10 -6 , Reltol at 10 -8 , and initial step size as 10 -4 .
• goal means a set of shape-sensitive metrics.
• Each metric is a single scalar value such as the time difference between simulation and measurement at peak max, the height difference at peak max, etc.
• Metrics are defined on the basis of specific knowledge of the modeled process and of typical errors in the measurement data.
• the metrics in a goal can be passed to a multi-objective search algorithm or they can be combined into one objective and passed to a single-objective search algorithm.
• Multiple metrics can guide (multi-objective) search strategies much better to the desired optimum than the commonly applied sum of squared differences (SSD) can guide (single objective) search strategies.
• the metrics are grouped into scores to organize the specification of goals for different parameter estimation procedures in CADET-Match.
• a suitable goal 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.
• a goal that does not have this property can guide search algorithms in the wrong direction. This might appear trivial but is critically important and at the core of why new goals had to be created. Due to competitive binding and other complex mechanisms, many model parameters influence the simulated chromatograms in non-linearly coupled ways. Therefore, some customarily applied metrics such as SSD can increase while the model parameters move closer to their correct values.
• 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 cause of the delay which is often not possible in practice.
• a good goal needs to account for this, since otherwise the simulated peaks end up in the correct location but with the wrong shape. Wrong shapes generally indicate errors in the underlying physics of the model. Hence, good metrics should prefer peaks with nearly fitting shape but small offsets rather than peaks without offset but with wrong shapes.
• the SSD requires a sufficient overlap between the simulated and measured chromatograms to be sensitive to parameter changes and guide the search algorithm towards the optimum. This can complicate the choice of suitable starting points, in particular for sharp and/ or small peaks.
• a further disadvantage of the SSD is illustrated in FIG. 2 using a synthetic example with parameters shown in Table 1 The parameters of scenario 2 are much closer to the ground truth, with only a relatively small deviation in the characteristic charge, v, even though Scenario 1 has a smaller SSD and would hence normally be considered a better fit.
• the peak shape of Scenario 2 is more similar to the ground truth but out of alignment.
• the shape and position of a chromatogram are determined by mass transport through the entire system, including the column and external volumes, and binding to the functionalized resin.
• the disadvantages of the SSD are avoided by separately measuring the shape, position, and height of individual peaks without requiring base line separation. Metrics for peak position are sensitive to changes of the respective model parameters, independent of peak overlaps between simulation and measured data. This provides flexibility and robustness with respect to the choice of starting points for the search algorithms, which is critically important for automation in industrial applications. Focusing on individual peaks allows to reduce the impact of process variations and further components that are not fully included in the model. For example, pump washes or pressure alarms can cause spurious peaks, and industrial feeds usually contain large numbers of more or less uncharacterized impurities.
• separate metrics can be assigned to distinct but partially separated peaks of target components and impurities of high and low molecular weight. Separate metrics also help to provide (multi-objective) search algorithms with more precise information on which component impacts which peak. All metrics yield zero for a perfect match between simulation and experiment.
• the shape metric is the most innovative of the new metrics and a core component of nearly all scores. It is the difference between one and the maximum of the Pearson correlation between measured and simulated chromatograms over a continuous range of time offsets (see equation 18, below). For evaluating this metric, the simulated chromatogram is shifted in time, . The maximum in equation (18) is determined by an initial grid search followed by Powell’s method. While it is advisable for the SSD to simulate the chromatogram on the same grid as the measurement data, continuous offsets require interpolating the simulated data. This is implemented in CADET-Match using the 5 th order spline. The interpolation can be improved by simulating the chromatogram on a denser grid than required for the SSD.
• Allowing for continuous time offsets that are independent of the discrete measurement grid is crucial for creating a smooth metric. However, it complicates the analytical tracking of parameter sensitivities.
• the shape metric is typically applied to individual peaks that are sliced out of the chromatogram. As required, it is zero for a perfect match between simulation and experiment and increases for worse agreement. By design, this metric only accounts for shape similarity and requires two other metrics to measure the time offset and height difference between simulation and measurement data.
• the position metric can be more complex than it might first appear. It is based on the time offset, t s , obtained from maximizing equation (19), below.
• the standard position metric gives an immediate penalty for a time offset with a linear ascent to one when out of alignment by t r (see equation 20, below).
• t r is the length of the measurement time interval. It can be replaced by the retention time of a non-binding tracer if sufficient starting points are provided to the search algorithm.
• this metric it a good choice for estimating column and particle porosity. However, it requires great care in running experiments to ensure there are as few delays as possible and alarms are immediately cancelled. Such delays affect the chromatogram almost exactly like changes in the column and particle porosities.
• FIG. 3 illustrates the difference between the standard and initially reduced position penalty metrics.
• the initial reduction, 1/2 , and range, 1 /10, are chosen by experience and can be changed by the user.
• the peak height metric relates the maximal concentration of the simulated chromatogram to that of the measured data, (see equation (18)). This metric ascends to one when the difference in either direction is larger than 100%.
• Scores are defined for individual components and can target the full chromatogram, individual peaks, or parts thereof, such as only the front of a peak.
• Each score is a set of metrics that depend on the index of the component, i, and on the set of considered time points, J. Goals will be composed of one or several scores that can then be combined into one objective or passed to a multi-objective search algorithm.
• the SSD score is the set of differences between simulated and measured chromatogram data, see equation (23) below. For technical reasons, each difference is interpreted as separate metric. In section 8, a goal will be defined as sum of squares of these metrics.
• the peak front score is designed to extract as much usable information as possible from the chromatogram. Unsupervised application of this score requires to automatically determine the usable time interval while robustly removing the non-ideal parts with high precision on the cut points.
• the back end of this interval is chosen at the first inflection point of the measured chromatogram, i.e. the upper cut point is at the first maximum of the time derivative. By experience, this is a good choice as non-ideal interactions mainly impact on the height and tailing of the peak.
• 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. By experience, 0.1 % is a robust choice for this threshold.
• the exact positions of these cut points are determined using Powell’s method on the continuous spline approximation from section 5. The nearest time points of the discrete measurement data are then used as boundaries of the time interval specified by J.
• Optical detectors that are typically applied for measuring chromatograms can usually not distinguish between different chemical components. Instead, they deliver a single sum signal where the contributions of the individual components are weighted by their extinction coefficients. Such signals alone cannot be used for parameter estimation unless the peaks of the relevant components are sufficiently separated. For instance, the acidic, main, and basic components of a monoclonal antibody often completely overlap in a single peak. This situation is normally addressed by fractionation, i.e. pooling the efflux of the column into a series of vials. Each of these vials is then analyzed offline to quantify the components of interest, which provides additional information for setting up a dedicated parameter estimation score.
• the previously introduced metrics can generally be applied to the concentrations in each vial using the centers of the corresponding collection intervals as time points. For precise comparison, the corresponding per component simulations are averaged over the same collection intervals when a metric is applied to fractionation data.
• the resulting information is often sparse, with 5 to 10 fractions per peak, and can be afflicted with additional errors in the fractionation times and volumes. Small shifts in the collection intervals can cause major changes in the distribution of components between the analyzed fractions, particularly for sharp peaks.
• the smoothing procedure from section 5 is not suitable for such sparse measurements.
• the spline approximation must be applied to the original simulated data before it is shifted and virtually fractionated to determine the time offset, t s , in order to maintain sub-grid accuracy.
• the scores S(- auss and Sp eak as well as their immediately penalized versions can be computed.
• the SSD score can be applied to fractionation data by averaging the simulations over the collection intervals.
• CADET-Match uses two alternative search strategies, gradient descent, and a multi-objective genetic algorithm. For gradient descent, all metrics need to be combined into a single scalar value, while the genetic algorithm can operate on multiple metrics.
• GA Genetic algorithms
• CADET-Match provides functionality to monitor the progress of specific indicators such as peak height, shape, mass, etc. This allows to observe if the starting points yield reasonable results and if the search algorithm continuously improves the goal. Online monitoring enables early aborting if progress is poor or if results are already good enough. This is essential for rapid testing of models, goals, starting points and stopping criteria. Since suitable starting points can be hard to determine, a GA with rather large population size is generally a good choice for initial testing. Multi-start gradient search is not a good alternative, as parallel iterative processes are more difficult to monitor.
• CADET-Match provides several transformation rules, i.e. biunique maps between model parameters, p, that are passed to the chromatography simulator and estimated parameters, p’, that are passed to the search algorithm. These transformations are based on upper bounds, p, and lower bounds, p, of the model parameters.
• the sensitivity of a system with respect to an input at a working point is defined as the derivative of the systems solution.
• Such an input can be model parameters or feed concentrations.
• the sensitivity measures how much a change of a certain model input influences the model output.
• the sensitivity of any model input can be calculated by the CADET library and written to the ,h5 output.
• CADET is using algorithmic differentiation.
• Numeric approximations of the analytic derivative can be obtained by finite differences method, which is available in the MoChA tool as well.
• Model parameters generally can be obtained by measuring, such as using optical microscopy to determine pore transport coefficients.
• taking direct measurements of model parameters is often not possible or very laborious, hence recursive parameter estimation is a method often used in chromatography modeling.
• Parameter identifiability describes the ability to find model parameters that are unique for a known given input and model equation.
• chromatography model parameters have poor identifiability when various parameter sets give rise to the same simulated chromatogram or chromatograms with only small deviation. This fact makes parameter estimation a challenge.
• the parameter identifiability can be visualized by outlining the objective value calculated for the evaluation of fit quality for a specific parameter value.
• BiTE® bispecific T-cell engager
• the molecule is a half-life extended BiTE® as a member of a class of bispecific antibodies that is subject to high expectations in cancer treatment and other severe diseases.
• the BiTE® molecule was produced by using Chinese hamster ovary cell lines that were 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 resulting in Filtered Virus Inactivated Pool (FVIP). [0123] Sequentially, virus inactivation was applied by adding 1 M formic acid.
• nVIP Non-Filtered Virus Inactivated Pool
• FVIP Filtered Virus inactivated Pool
• Capto SP ImpRes resin (CytivaTM) was packed into a Millipore vantage column (i.d. 1.15 cm and ht 20.7 cm) with a compression ratio of 1.11, which results in a column volume of 21.5 mL.
• the asymmetry factor of the column was 0.91 and the HETP was 0.0203 cm.
• Dextran Blue 2000 solution (CytivaTM) was used as a tracer molecule for dead volume and dispersion experiments.
• the ionic capacity of the Capto SP ImpReS resin used was obtained by a titration method introduced by Thiemo Huuk 2016.
• a small column with a 1 ,7mL CV packed with the same lot of CaptoSP ImpRes was exposed to 0.5mM Hydrochloric Acid (HCI) for -500CV.
• HCI Hydrochloric Acid
• the column was then flushed with water to remove remaining acid.
• the column was exposed to 0.01 M Sodium Hydroxide (NaOH).
• NaOH Sodium Hydroxide
• the volume of NaOH required to fully exchange counter ions was used to determine the ionic capacity of the column according to Thiemo Huuk 2016.
• FVIP Filtered viral inactivated pool
• a Dextran breakthrough and pulse tracer experiment was run including the column. Dextran solution was loaded from the sample line. Initially, 3 CV of 18% ethanol were flowed to establish a baseline UV and conductivity reading. 10mL Dextran was loaded for the pulse experiment, while loading continued until a stable UV signal was achieved for the breakthrough experiment.
• a protein breakthrough experiment was run using an equilibration buffer at a conductivity of 44 mS/cm and the conductivity adjusted FVIP pool so that the column was equilibrated and loaded under non-binding conditions.
• the column was first equilibrated with the high conductivity equilibration buffer for 3 CV and then run with 40mL of the conductivity adjusted FVIP pool. Regeneration was performed after the loading to confirm no protein bound to the column.
• Chromatography buffers are listed below in Table 3.
• non-filtered viral inactivated pool (NVIP) material was used. The same lot material with a concentration of 4.80 g/L was injected for varying loads and gradients.
• the model equations were solved by the Chromatography Analysis and Design Toolkit (CADET), an open source simulator.
• CADET Chromatography Analysis and Design Toolkit
• the software allows for combining varying transport and adsorption models for chromatographic steps, as well as CSTR and DPFR type transport models, to describe sequences of unit operations.
• the software provides tools for model-based analysis, such as providing sensitivities with respect to model input parameters.
• the software package is available on https://github.com/modsim/CADET.
• CADET was accessed by a Python interface.
• the parameter search was performed by the open source software package CADET-Match that is based on the CADET engine, available on https://github.com/modsim/CADET-Match.
• the estimation algorithm that is used in this tool uses the maximization of multiple objectives that measure the similarity between simulated and measured chromatograms. The best fit was identified by using the result with the highest product of these objective values.
• stage-wise approach For model development a stage-wise approach was followed. This approach is used to separate transport effects, such as peak delay or peak broadening caused by transport of molecules in tubing and valves, from adsorption effects in the model. This is especially important as mentioned transport effects could be lumped into adsorption coefficient by recursive model calibration which decreases model applicability on varying column scales.
• the stage-wise approach is indicated in FIG. 4.
• FIG. 1A illustrates a flow path representation of generally used chromatographic skids and machines, such as AKTATM.
• FIG. 1A illustrates varying dead volumes prior to the column. Since this dead volume influences a peak shift during elution with respect of the elution start, the dead volume needs to be accounted for in the model. Possible representations range from simple time shifts of when elution starts to mechanistic representations of the build-in tubing and valve volume.
• FIG. 5 A simplified representation of pathways the molecules experience in the chromatography machine is outlined in FIG. 5. This combination of unit operations was used to develop a representation of the process required for gradient elution. [0141] The resulting system of unit operation models is set-up combining DPFR and CSTR models and a column model. The model sequence entailing multiple unit operations is indicated in FIG. 4.
• tubing model and tank are used to simulate effects of tubing and mixer and valves.
• column model equations given in equations (1) to (7) are used.
• a combination of tubing models and valve models equations given in equations (11) and (12) are used to represent the flow path from sample pump to UV sensor and from inlet pump to conductivity sensor. All pathways are set up as a combination of a fitted DPFR and CSTR model prior to the column (inlet pump (buffer) pathway, and sample pump (molecule) pathway) and DPFR models set up only from geometric specifications (length and diameter) provided by the vendor. As described herein, tubing model and mixer/valve models prior to the column are fitted to Dextran breakthrough bypass and salt bypass runs individually. Furthermore, the tubing 6 and tubing 7 models are set up according to the AKTATM Avant 150 manual with 1 mm diameter and 17 cm and 10 cm, respectively. Dispersion coefficients for those two models are set to the dispersion coefficient estimated for the bypass experiments.
• Table 5 provides a list of parameter names, descriptions and ranges that are estimated for each pathway molecules are experiencing. The ranges correspond to the bounds used for the estimator algorithm.
• FIG. 7B the effect of a tracer molecule such as Dextran are evident and show that a fit to the first rising part of the Dextran breakthrough, as shown in FIG. 7A, leads to different parameters in comparison to fitting the whole Dextran breakthrough.
• the small pre-peak at the rise of the Dextran breakthrough is assumed to be an artifact and has been predominantly ignored by the estimation algorithm.
• the fit in FIG. 7A provides the model parameter for the sample pathway unit operations (refer to FIG. 6).
• the calibration result in FIG. 7B indicates the model representation of the inlet pathway (refer to FIG. 6). Due to the close to ideal behavior of the salt tracer only negligible deviations between fitted model and conductivity signal are observed.
• the transport parameters related to the resin particles are estimated. Those parameters refer to the mass transport from the interstitial volume into the particles and to the particle porosity.
• Table 7 the parameters and their ranges used for the estimation procedure are given.
• the result of the particle transport calibration step is indicated in FIG. 80.
• Table 7 provides a list of parameter names and ranges subject to particle transport.
• Fractionation data were used to determine the modeled species.
• the targeted chromatogram area of interest is the main peak and the following peak with impurities.
• the main peak is represented in the model by lumping all charge variants of the target molecule into three charge variant species: the acidic, main, and basic charge variant.
• the molecular weight is considered equal for all three variants.
• all species contained in the peak of impurities are described in the model as one single component.
• a five-component model is obtained, one salt species describing sodium as counter ions and four protein components that describe the acidic, main, and basic charge variants and high molecular weight (HMW) component.
• HMW high molecular weight
• the model uses the concentration of each modeled species in the FVIP material as input parameter, which means that for an accurate representation of molecule species that enter the column, analytical experiments need to be conducted to determine the feed load protein concentrations for each modeled species.
• the load protein concentrations were identified by using the experimental fractionation pools along with the UV chromatograms instead of analytical profiles of the feed solution. The ratios between the peak areas in the fractionation pool and the ratios between the peaks in the UV chromatogram are calculated. Then by considering the total protein concentration present in FVIP material, the concentration of each species in the feed material is calculated.
• Table 9 provides a list of adsorption parameter names and ranges subject to estimation. Each parameter is estimated for each modeled species.
• the ionic capacity A was set to 1339 mM according to the procedure described above in the “Bench Top Experiments” section. The best fits obtained are indicated in FIGS. 9A and 9B. The final adsorption model parameter values are listed in Tables 6A-6C .
• model validation activities contain comparing model prediction on process scale at varying load factor, gradient slopes, and stop collect criteria. The results of model validation are compared in 12 and 13.
• a model development approach was introduced for a pharmaceutical therapeutic molecule that suggests a stage wise method calibrating parts of the model in three steps to build the final model. This approach can be used to decouple transport model descriptions from the adsorption model.
• a model representation was developed for a chromatographic system that contains multiple unit operations.
• the system describes the pathways either the sample molecules or the buffer molecules experience during a salt elution step, both of which contain valves and tubing apart from the column.
• the model parameters are estimated that describe the interstitial column transport.
• the next step taken estimates the parameters describing mass transfer into the pores.
• the adsorption model parameters are estimated in the last stage of model calibration. For each parameter estimation step a separate set of experiments is used.
• the accuracy of the model is assessed by using experiments performed at different column scales.
• the model predicts the elution behavior for process robustness experiments with acceptable quality and can be used to explore the ranges of process parameters, such as gradient slope, load factor, and stop collect criteria.
• the model predicts the process at higher scale with acceptable quality but reveals general limitations.
• One of those limitations is that often the feed concentration of each modeled species is not known, which requires additional analytical experiments.
• an alternative way is suggested to identify the feed concentrations from UV chromatogram and fractionation data. No previous study has revealed this drawback of mechanistic models before or described how this issue was approached.
• the present disclosure provides an approach to identify the feed concentrations from fractionation data and UV chromatogram is suggested that does not require additional experiments.
• a minimal set was used for model calibration and validation.
• a set of 12 experiments are used for the complete workflow, including determination of extra column transport model parameters to model validation.
• the methods provided herein can be used and reproduced by other modelers as the solvers and algorithms are publicly available. Furthermore, the model includes a set of unit operations that are available to be used in HDF5 format and the simulations are ready to be reproduced. The results described herein can be used to further investigate and enhance model and workflow capabilities, which is a major contribution to the progressing chromatography community.
• FIG. 11 illustrates a flow diagram 100 of an example method as described herein.
• a chromatography machine including a first dispersed plug flow reactor (DPFR) and a continuous stirred tank reactor (CSTR) prior to a column, and a second DPFR after the column
• geometric measurements associated with the second DPFR may be obtained (block 102).
• the geometric measurements associated with the second DPFR may include tubing diameter measurements and tubing length measurements associated with the second DPFR. These measurements may be obtained, e.g., based on measuring the tubing diameter and tubing length, and/or based on known manufacturer specifications for the chromatography machine.
• Transport model parameters for a transport model associated with the second DPFR may be generated (block 104), e.g., by a processor, based on the geometric measurements.
• the transport model parameters may include dispersion coefficient in DPFR, volume of DPFR, cross-section area of DPFR, etc.
• a tracer molecule (e.g., dextran, NaCI, or another suitable tracer molecule) may be fed (block 106) into the chromatography machine.
• One or more tracer molecule measurements may be captured (block 108) based on the tracer molecule traveling through the chromatography machine. For instance, the one or more tracer molecule measurements may be captured based on a chromatogram associated with the tracer molecule traveling through the chromatography machine.
• one or more transport model parameters for a transport model associated with the first (and second) DPFR and the CSTR may be estimated (block 110).
• the transport model parameters may include dispersion coefficient in DPFR, volume of DPFR, cross-section area of DPFR, volume of CSTR, etc.
• one or more column-specific transport model parameters for a column-specific transport model associated with the column of the chromatography machine may be estimated 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 molecule traveling through the chromatography machine.
• the column-specific transport model parameters may include column porosity, column dispersion, etc.
• one or more resin transport parameters for a resin transport model associated with resin particles of the chromatography machine may be estimated 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 molecule traveling through the chromatography machine.
• an experimental sample may be fed (block 112) into the chromatography machine.
• One or more experimental measurements based on the experimental sample traveling through the chromatography machine may be captured (block 114).
• the one or more experimental measurements may be captured based on a chromatogram associated with the experimental sample traveling through the chromatography machine.
• one or more adsorption model parameters for an adsorption model associated with the experimental sample may be estimated (block 116), e.g., by a processor.
• the column-specific transport model and/or the resin transport model may also be factors used in estimating the adsorption model parameters for the adsorption model.
• the adsorption model parameters may include one or more of: adsorption coefficient, desorption coefficient, characteristic charge, shielding factor, etc.
• a second set of adsorption parameters for a second adsorption model associated with the experimental sample may be estimated based on ranges associated with the initially-estimated adsorption parameters.
• the experimental sample may be identified based on the adsorption model associated with the experimental sample (and/or based on the second adsorption model associated with the experimental sample).
• the chromatography machine may include an inlet flow path including a first DPFR and a CSTR prior to an inlet flow path column, and a second DPFR after the inlet flow path column as well as a sample flow path including a first DPFR and a CSTR prior to a sample flow path column, and a second DPFR after the sample flow path column, and the method 100 may be performed for both the inlet flow path and the sample flow path.
• blocks 112, 114, and 116 may be performed again, using a second experimental sample (e.g., distinct from the first experimental sample), but using the same estimated transport model parameters. That is, once a transport model for the chromatography machine is developed, the transport model may be used to determine adsorption model parameters for multiple experimental samples.
• a method comprising: obtaining, for a chromatography machine including a first dispersed plug flow reactor (DPFR) and a continuous stirred tank reactor (CSTR) prior to a column, and a second DPFR after the column, geometric measurements associated with the second DPFR; generating, by a processor, transport model parameters for a transport model associated with the second DPFR based on the geometric measurements; feeding a tracer molecule into the chromatography machine; capturing one or more tracer molecule measurements based on the tracer molecule traveling through the chromatography machine; and estimating, by the processor, based on the transport model associated with the second DPFR and the one or more tracer molecule measurements based on the tracer molecule traveling through the chromatography machine, one or more transport model parameters for a transport model associated with the first DPFR and the CSTR.
• DPFR dispersed plug flow reactor
• CSTR continuous stirred tank reactor
• the estimating the one or more adsorption model parameters for the adsorption model associated with the experimental sample is a first estimating of a first one or more adsorption parameters for a first adsorption model associated with the experimental sample, and further comprising: a second estimating, by the processor, of a second one or more adsorption parameters for a second adsorption model associated with the experimental sample based on a range associated with the first one or more binding parameters for the first adsorption model associated with the experimental sample.
• transport model parameters include one or more of: dispersion coefficient in DPFR, volume of DPFR, cross-section area of DPFR, and volume of CSTR.
• adsorption model parameters include one or more of: adsorption coefficient, desorption coefficient, characteristic charge, and shielding factor.
• column-specific transport model parameters include one or more of: column porosity and column dispersion.
• 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 of any of aspects 1-22.
• a non-transitory computer-readable storage medium storing instructions that, when executed by a processor, cause the processor to perform the steps of the method of any of aspects 1-22.

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