Mechanistic modeling of empty‐full separation in recombinant adeno‐associated virus production using anion‐exchange membrane chromatography

Recombinant adeno‐associated viral vectors (rAAVs) have become an industry‐standard technology in the field of gene therapy, but there are still challenges to be addressed in their biomanufacturing. One of the biggest challenges is the removal of capsid species other than that which contains the gene of interest. In this work, we develop a mechanistic model for the removal of empty capsids—those that contain no genetic material—and enrichment of full rAAV using anion‐exchange membrane chromatography. The mechanistic model was calibrated using linear gradient experiments, resulting in good agreement with the experimental data. The model was then applied to optimize the purification process through maximization of yield studying the impact of mobile phase salt concentration and pH, isocratic wash and elution length, flow rate, percent full (purity) requirement, loading density (challenge), and the use of single‐step or two‐step elution modes. A solution from the optimization with purity of 90% and recovery yield of 84% was selected and successfully validated, as the model could predict the recovery yield with remarkable fidelity and was able to find process conditions that led to significant enrichment. This is, to the best of our knowledge, the first case study of the application of de novo mechanistic modeling for the enrichment of full capsids in rAAV manufacturing, and it serves as demonstration of the potential of mechanistic modeling in rAAV process development.

2. Targeted tissue and cell-specific tropism based on a diversity of naturally occurring serotypes, an ever-expanding array of novel engineered capsids, and increasingly sophisticated application of transcriptional regulation.
3. A favorable safety profile including minimal propensity for random integration events and immunogenicity that is considered low relative to other viral vectors.
4. A fairly simple and well-studied genome enabling relatively facile modification for recombinant applications.
To date, four AAV gene therapies have successfully reached commercial licensure, and more than 200 clinical trials have been conducted with a tidal wave of INDs on the horizon (Bulcha et al., 2021).
Despite the popularity and growing body of successful outcomes, significant challenges remain.In the case of in vivo treatments entering the clinic-especially those pushing higher doses and systemic administration-ensuring a robust safety profile while maintaining efficacy is a top priority.Recently, in trials utilizing high-dose systemic delivery, there have been several instances of treatment-emergent serious adverse events (TESAEs), including patient deaths (Kuzmin et al., 2021).
Such events prompted the FDA Cellular, Tissue, and Gene Therapies Advisory Committee to host a meeting to discuss the toxicity risks of rAAV in gene therapy (U. S. Food and Drug Administration, 2021).While no single mechanism can account for all TESAEs, a number of potential sources of risk were called out; most notably, the heterogenous population of capsid species often present in the drug product.These range from totally empty (non-genome containing) capsids to partially-filled and over-filled capsids containing all manner of undesired DNA (plasmid, helpervirus, host-cell, truncated, concatenated, or elongated transgene, heterocomplexes and epigenetically diverse variants thereof) (Fuentes et al., 2023).According to the FDA, "although rAAV vectors are generally not considered to be pro-inflammatory, AAV vectors can engage all arms of the immune system, [and] immune recognition of AAV vectors can blunt therapeutic effect of a product and/or raise safety concerns" (U. S. Food and Drug Administration, 2021).While some studies implicate empty capsids (EC), correlate total capsid dosed to immunogenic response, and/or attribute deleterious mechanisms to the range of encapsulated impurities, the FDA acknowledged, "however, the effects of such impurities on the safety of AAV vectors are not well understood" (U. S. Food and Drug Administration, 2021).
In addition to safety, the impact of non-GOI capsids to efficacy is also a concern.Though not fully understood, there is growing consensus that the presence of ECs might reduce target cell transduction due to competitive binding (Parker et al., 2003).
The result of these discussions is the added emphasis on the removal of capsid impurities from rAAV products.While significant advances have been made in molecular engineering and upstream process development to decrease heterogeneity during production (e.g., increasing the percentage of full, genome-containing vectors straight out of the host cell), the burden of full-particle enrichment typically falls on downstream process developers.
Although rAAV manufacturing processes have matured significantly in recent years, there is still not a consensus platform process, and this is especially true of full particle enrichment.Many processes leverage gradient ultracentrifugation (e.g., Sucrose, Iodixanol, or Cesium-Chloride) to separate species based on density.However, owing to greater scalability and more readily tunable selectivity, chromatographic methods are becoming much more common.A review of available literature suggests a diversity of chromatographic approaches, including variations in: 1. Stationary phase format (e.g., diffusive vs. convective).
The diversity of approaches is equally matched by the variety of performance outcomes in terms of product yield and enrichment.In addition to approach, the literature also suggests that inherent molecular variability can impact performance, including serotype, transgene size and sequence, and overall milieu of product and impurity populations to be separated (Dickerson et al., 2021;Joshi et al., 2021;Rieser et al., 2021;Schofield, 2021).
When considering the emerging emphasis on full-capsid enrichment, the range of variables impacting performance, and the backdrop of historically tight development timelines, downstream developers are often expected to generate deep insight and robust manufacturing processes with potentially parsimonious data sets.We believe that this is a problem ideally suited to the application of mechanistic modeling.
Mechanistic models are based on the detailed description of the physical and biochemical phenomena behind the processes with the use of mass balances.This description gives information that allows us to reduce the amount of experimental data considerably.Mechanistic models are a powerful tool for the design and optimization of processes as a broader range of important process parameters can be explored to find the optimal conditions (Abt et al., 2018;Borg et al., 2014;Karlsson et al., 2004;Kroll et al., 2017;Ng et al., 2012).In addition, these models are also recommended by ICH Q8(2) as a key tool in pharmaceutical Quality-by-Design (U. S. Food and Drug Administration, 2009).
There are many examples of employing mechanistic modeling to complex chromatographic operations, with a large number of applications successfully addressing subtle separations in charge and aggregate variants in the field of monoclonal antibody production-a challenge perhaps similar in complexity to rAAV full enrichment (Borg et al., 2014;Kumar et al., 2015;Saleh et al., 2020).Models can help to define and optimize processes, improve performance robustness, aid in the prediction of failure modes and selection of characterization design space, mitigate deviation risk, or even bolster the assessment of deviation events.
Herein, we describe the first documented approach to the calibration, generation, and testing of a mechanistic model for the enrichment of full capsids (FCs) in rAAV manufacturing.This work presents a case study in the successful application of a basic mechanistic model in rAAV production and serves as a readily expandable foundation for further development.

| AKTA FPLC
The experimental work for the model calibration and validation was carried out in the chromatography system ÄKTA™ Avant 150 with standard configuration using a 0.6 mL mixer.The chromatography matrix was the membrane Mustang Q XT from Pall Corporation (New York, USA), with volume of 0.86 mL.The run method used during the model calibration is described in Supporting Information: Table S1.
The run method used for the validation experiment was also as described in Supporting Information: Table S1, except for the elution conditions, given by the optimization.

| rAAV6 test article
Experiments were conducted using partially purified recombinant AAV6 vector containing a ~4.2 kB transgene encoding for an engineered T-cell receptor.
Briefly, the vector was produced by triple-transient transfection of suspension HEK293 cells in a 200-L single-use bioreactor.The cells were then lysed with a non-ionic detergent in the presence of endonuclease, clarified by depth and membrane filtration, concentrated and buffer exchanged by tangential-flow ultrafiltration, and captured by AAVX affinity chromatography (Thermo Fisher Scientific).Neutralized AAVX elution pool was sub-aliquoted and frozen at −80°C.Before each anion-exchange chromatography (AEX) run, AAVX-purified material was thawed at room temperature, diluted with buffer to a conductivity enabling binding to the AEX membrane while maintaining capsid stability, and 0.2 µm filtered.The load material was determined to be comprised of 15% FC (purity of 15%).

| Calculation of the hold-up volumes
The total hold-up volume between the pumps and the conductivity sensor was calculated by the time delay between the time at which the gradient started and the conductivity signal, using the average value of all the experiments.This time delay was multiplied by the elution flow rate to get the total hold-up volume.This volume included the hold-up volume in the system and in the column (Equation 1), and it was used to calculate the hold-up volume in the column.The system hold-up volume was calculated by summing the theoretical volumes of the components and tubing between the pumps and the conductivity sensors (obtained from the Äkta Avant manual), and the hold-up volume in the column was calculated by subtracting the system hold-up volume to the total hold-up volume.
The chromatography data was corrected to account for the system hold-up volume.
The calculated hold-up volume in the column was higher than the column volume provided by the manufacturers, meaning that the column hold-up volume was made up of a hold-up volume in the inlet and outlet areas that are not part of the chromatographic material itself, and the void volume in the chromatographic material (Equation 2).It is important to accurately account for the hold-up volumes in the inlet and outlet areas as they affect resolution, and for that reason, they must be calculated and modeled separately from the chromatography column.The exact void in the chromatographic material was unknown.Empirical determination of void volume could aid in model building, but for simplicity it was assumed to be 34%.
Then, knowing the column volume (provided by the manufacturer), the void volume in the chromatographic material could be calculated, and the hold-up volume in the inlet and outlet areas of the column were obtained by subtracting the void volume in the chromatographic material from the total hold-up volume in the column, calculated with Equation (1). (2)

| Estimation of the extinction coefficients
The experimental data is a UV absorbance signal, while the simulated data is in concentration units.Therefore, a conversion is needed to be able to compare both.Beer-Lambert law can be used to relate concentration with absorbance (Equation 3).
where A is the absorbance, ε is the extinction coefficient in L/g cm, c is the concentration in g/L, and l is the path length of the UV sensor.
A potential approach for the comparison of experimental and simulated chromatograms is to convert the experimental absorbance signal to a concentration signal.However, this approach requires a deconvolution of the absorbance signal to obtain two separate absorbance peaks, which would then be converted to concentration by applying Beer-Lamber law.This is very challenging in this case since the elution peaks in the experimental data are overlapped.
Instead, the approach taken in this case was to convert the simulated concentrations to absorbances by using Beer-Lambert law.The simulated absorbances for EC and FC were summed to obtain a curve that could be comparable with the experimental absorbance curve.
The extinction coefficients are needed for the conversion of simulated concentrations to absorbances.EC and FC have different extinction coefficients and their determination is not trivial.Generalized extinction coefficients obtained from the literature were tried (Sommer et al., 2002), but the size of the obtained simulated EC and FC peaks did not fit the experimental data.Therefore, the extinction coefficients were adjusted so that the simulated absorbance curve fitted the experimental one.
A mass balance was used to obtain the same area under the peak as in the experiment.The loaded amount of EC and FC converted to absorbance (using Beer-Lambert law) should be equal to the total area under the peak in the elution phase, which can be calculated experimentally.This simple mass balance together with Beer-Lambert law leads to Equation (4).
where AUP exp is the experimental area under the peak in AU•min, F elu is the elution flow rate in mL/min, V load is the loaded volume in mL, p is the pathlength of the UV sensor (0.2 cm), c in EC , and c in FC , are the inlet concentrations of EC and FC, respectively, in capsids per mL, and ε EC and ε FC are the extinction coefficients of EC and FC, respectively, in AU•mL per cm and capsid.
There are two unknowns in Equation (4) (the extinction coefficients) and one equation, so it is not possible to obtain both coefficients from this equation.This means that, if this equation is satisfied, the area under the peaks will be the same as in the experimental data, but there is still a degree of freedom, which is the relative sizes between EC and FC.Therefore, one of the extinction coefficients, in this case, the one for EC (ε EC ), was included in the calibration problem as one more parameter together with the model parameters, and the other one (ε FC ) was calculated using Equation 4. ε EC was expressed as r ε the ratio between the extinction coefficient of FC and EC.
Then, it was r EC FC / , the parameter that was included in the calibration.A higher r EC FC / gives a higher EC peak and lower FC peak and vice versa.Equation ( 4) was applied for two wavelengths (280 and 260 nm), and two r EC FC / were therefore used (one for each wavelength) in the calibration to have a good fit of the experimental data in both wavelengths.
While this method demonstrates how one can overcome ill-defined extinction coefficients during model calibration, in practice, this mass-balance approach has since become unnecessary in most use cases utilizing naturally occurring serotypes.This is due to significant progress of late in the use of UV and light scattering methods to quantitate rAAV, and it is highly likely that a range of vendors can provide accurate extinction coefficients given only serotype and transgene length or sequence.

| Mechanistic model
The reactive-dispersive model (Andersson et al., 2014;Seidel-Morgenstern, Schmidt-Traub, et al., 2012) was used for the description of the column (Equations 5 and 6).In this model, it is assumed that the rate-limiting step is the adsorption.Danckwerts boundary conditions for the rAAV species (Equations 5a and 5b) and the modifier (Equations 6a and 6b) were used.Multiple-component Langmuir isotherm with salt and pH dependance was used for the description of the adsorption (Equations 7 and 8), adapted from the pH-dependent adsorption kinetics described by Saleh et al. (2020).
where c and c S are the mobile phase concentration of the rAAV species and the modifier (Cl − in this case), c in and c in S , are the inlet concentration of the rAAV species and the modifier, q is the concentration in the stationary phase, D ax is the axial dispersion coefficient, v is the superficial fluid velocity, ε is the column void, L is the column length, q max is the maximum adsorption capacity, H is Henry's constant, K pH1 and K pH2 are the pH dependence constants, pH 0 is the reference pH, H 0 is Henry's constant at the reference pH, k kin is the adsorption rate constant, β is the equilibrium modifier- dependence parameter, and the subindexes i and j refers to the two rAAV species: EC and FC.
The dispersion coefficient was estimated using Equation ( 9) (Rastegar & Gu, 2017;Seidel-Morgenstern, Schmidt-Traub, et al., 2012), where D is the column diameter, and Pe is the diameter-based Peclet number: The inlet and outlet of the columns, whose volumes were calculated according to the procedures explained in the previous section, were modeled as ideally stirred tanks (Equation 10), with one before and another one after the column.Both tanks were modeled with equal volume, being the sum of volumes equal to the previously The spatial derivatives were discretized using the Finite Volume Method, as shown elsewhere (Nilsson & Andersson, 2017), with 20 axial grid points.The low number of grid points led to certain numerical dispersion.However, the total dispersion in the column was higher than the numerical dispersion, so the axial dispersion in the model could be adjusted in the model calibration to provide the same total dispersion as in the experimental data.The advantage of choosing a low number of grid points is the higher computation speed.The system of differential equations was solved with a function called solve_ivp (built in the Python package scipy, in the module integrate), with the Backward Differentiation Formula integration method (Shampine & Reichelt, 1997).

| Model calibration
There were in total 14 model parameters to be found in the model calibration (Supporting Information: Table S2).

The model calibration was performed in different iterations
where different parameters were obtained in each iteration.This way, the complexity of the problem was reduced and the time for the parameter estimation was also decreased.In all the iterations, the parameters were obtained by minimizing the sum of the squared difference between the simulated and the experimental absorbance curves (least square method), using the calibration function curve_fit (built in the Python package scipy, in the module optimize), with the Trust Region Reflective algorithm (Branch et al., 1999).Experimental absorbances at wavelengths of 260 and 280 nm were used for the model calibration.
Initial model calibration was performed using data from linear gradient experiments with three different flow rates (2, 5, and 10 CV/min).These experiments were performed at pH 9.0, which was set to be the reference pH (pH 0 ).For this reason, the pH dependence constants (K pH1, EC , K pH1, FC , K pH2, EC , and K pH2, FC ) were not included in this calibration as all the experiments were done at the same pH.The loading density in these experiments was low and the column was far from being saturated, meaning that the maximum adsorption capacity (q max ) could not be obtained in this calibration.It was set to a very high number for the initial model calibration.The ratios of extinction coefficients (r EC/FC,280nm and r EC/FC,260nm ) obtained in the initial calibration were set constant in the subsequent calibrations.
A second model calibration was performed using data from linear gradient experiments with three different gradient lengths (20, 40, and 80 CV).The parameters obtained in the initial calibration were used as a starting point for the second calibration, thus leading to a quicker and more effective parameter estimation.The second calibration was used to obtain the following parameters: H 0, EC , H 0, FC , β EC , β FC , k kin, EC , k kin, FC , and Pe.
A third model calibration was performed using data from linear gradient experiments with four different pH values (8.0, 8.5, 9.0, and 9.5), and the pH dependence constants were obtained.For each of the four experiments, Henry's constants (H H and EC FC ) were obtained to achieve the best fit with the experiments, resulting in four sets of Henry's constants.Then, they were fitted to Equation ( 8) to obtain the pH dependence parameters.
A fourth model calibration was performed using data from linear gradient experiments with three different loading densities (challenges) (5•10 12 , 1•10 13 , and 1•10 14 vector genome (vg) per mL column).They were used to obtain the maximum adsorption capacity (q max ).
Finally, it was checked that the obtained model parameters provided good fitting-no statistically significant differences in peak shape, area, retention time, or other assessment of chromatographic performance-for all the experiments.A final calibration was performed for fine-tuning of the parameters using all the experimental data at the same time.

| Model-based optimization
Model-based optimization was performed with two objectives: to demonstrate the potential of modeling by obtaining the optimal process conditions, and to validate the developed model by showing agreement between the experiment and the simulation.
The purification process was optimized using the calibrated model to maximize recovery yield while keeping a specific desired product purity (a desired percent FC).The product purity depends on the pooling cutoff points; therefore, an optimization algorithm was developed to calculate the optimal cutoff point to ensure the desired pre-defined purity.This algorithm used an optimization function built in the scipy package in python called minimize, using the minimization method Sequential Least Squares Programming (Kraft, 1988), which is appropriate for constrained problems.Purity was introduced as a constraint, the cutoff points were the decision variables and yield was set as objective.
A second optimization algorithm on top of that mentioned above was developed to find the optimal conditions in the elution phase.
Two different cases were studied: Case A, with a single-step isocratic elution, and Case B, with a two-step elution where two different salt concentrations were used.In Case A, one decision variable was considered: the salt concentration in the elution step; in Case B, three decision variables were considered: the salt concentration in the two steps, and the relative length of these two steps.The objective in both cases was to maximize yield.Loading density and flow rate were set to constant values (1•10 13 vg/mL and 2.0 CV/min and pH 9.0, respectively) to narrow down the scope of the optimization problem, but an optimization of these parameters could also be performed.In the base scenario, elution length and pH were set to 40 CV and 9.0, respectively.However, the effect of these parameters on the optimal solutions was studied.Elution lengths from 10 to 40 CV and pH values from 8.0 to 9.5 were considered.The second optimization algorithm-also run in python-was identical to the first except that it used the Nelder-Mead minimization method (Nelder & Mead, 1965).

| Analytical methods
Full-capsid titer, or vector-genomes titer, was determined by a qualified quantitative polymerase chain reaction (qPCR) assay.
Briefly, the qPCR method utilized forward and reverse primers and probes specific to a promoter present in the transgene sequence.

| Calibration
The model parameters were estimated according to the procedures described in the previous section, and the obtained values are presented in Supporting Information: Table S2.FCs, as expected, have longer retention time than ECs.The primary explanation is that empty and FCs have slightly different surface charge and hydrophobicity characteristics (Heldt et al., 2023).In the case of AAV6 on anion exchange resins, FCs behave as having slightly more negative charge than ECs.This difference is often described and measured in terms of isoelectric point (Li et al., 2021).Wang et al. (2019) reported isoelectric points of empty and full AAV6.2-asimilar serotype to AAV6-as 6.3 and 5.9, respectively.Although pI is likely to vary by capsid serotype, transgene, and even production process, these values are demonstrative of the modest surface charge differences one can expect to see between full and empty species.Often-and likely incorrectly-the surface charge difference is attributed to charge penetration of the DNA content (or lack thereof); this does not account for the likely presence of counterions, nor the physical limitations of charge penetration.On the contrary, evidence suggests that surface charge differences result from conformational changes associated with nucleic acid content, driven for example by interactions between capsid amino acid residue side chains and encapsidated DNA, or lack thereof (Heldt et al., 2023;Mietzsch et al., 2021).This implies that the conformational change of FCs happens after DNA is packaged, rather than a capsid with that specific composition or conformation is somehow favored for packaging; however, such has not been concretely proven.There are still some open questions on the connection between capsid structure and packaging.While some research has shown 'divergent and stochastic' capsid assembly, a finding compatible with the hypothesis that only a certain subset of capsids are suited for packaging, other work describes no significant differences between EC and FC viral protein composition, only their conformation (Mietzch et al., 2021;Wörner et al., 2021).Clearly, deeper characterization of different species of AAV (e.g., empties, partials, fulls, heavies, etc.), including at the single-particle level, will ultimately prove invaluable in clarifying the fundamental differences between AAV species and serve as guideposts for molecular optimizations and processing decisions (Du et al., 2023).Despite lack of total clarity on root cause, the effect of different process parameters on the chromatograms-including the retention behavior of the different capsid species, and the impact on separation and enrichment-is discussed in the subsequent sections.

| Effect of flow rate
In Figure 1, the simulated and experimental chromatograms for 2.0, 5.0, and 10 CV/min are presented, at the wavelengths of 280 and 260 nm.As can be seen, simulated (dotted blue) and experimental (solid red) curves are nearly identical at both wavelengths and for the three flow rates.Differences in shape are trivial with key features such as shoulders, peak heights, widths, and retentions virtually indistinguishable.
The effect of flow rate in the separation of EC and FC with the membrane is negligible, as observed in Figure 1.This was expected as membrane chromatography is a convective-based technology, meaning that diffusion is negligible (Charcosset, 2012).Unlike chromatography resins where the molecules must diffuse through the internal porous channels of the particles, membranes have open, straightthrough pores with convective-based mass transport, which allows the use of much higher flow rates without negatively affecting the separation (Boi, 2019;Charcosset, 2012;Lalli et al., 2019).

| Effect of gradient slope
The gradient slope affects the separation of EC and FC, as expected.The lower the slope (longer gradient length), the better the resolution, as shown in Figure 2, although the product comes out less concentrated.Overall, the model can predict the chromatograms for the three gradient lengths in good agreement with the experimental data.Curiously, there are some deviations in the retention time when changing the gradient slope.However, most importantly, peak shape (height, width, shoulders, etc.)-that is what ultimately encompasses selectivity between EC and FC-of the simulated peaks closely resembles that of the experimental F I G U R E 1 Experimental and simulated chromatograms at flow rates 2.0 (panels a and b), 5.0 (c and d), and 10.0 CV/min (e and f).280 nm (panels on the left) and 260 nm (panels on the right) absorbances are shown.The dotted blue curve is the experimental peak and the red curve is the simulated peak, which is the sum of the EC peak (dark gray) and the FC peak (light gray).The time axis starts with the elution phase.EC, empty capsid; FC, full capsid.
ones.It is notable that there seems to be a third component eluting after the FC in the experiment with gradient length of 80.0 CV.This tail could be due to aggregates, overpackaged species (heavy capsids), heterocomplexes of protein and DNA, or other related impurities, which are not accounted for in the model.This model is to be used to predict and optimize the separation of FC and EC, and the removal of other impurities is considered out of scope.
While understanding the composition of the third component warrants further investigation-and could be responsible for minor discrepancies between simulated and experimental data at extremes of the model-this deviation is ultimately not considered to be a significant problem for the validity of the model.
Specifically, exclusion of the third peak-beginning to resolve only at the end of the elution phase during a highly extended gradientdoes not appear to dramatically affect the separation between EC and FC.

| Effect of pH
Henry's constant is an indication of the adsorption affinity of compounds with the stationary phase and helps define their retention time.The greater the difference in Henry's constant between two species, the greater the likelihood of being able to resolve them.Usefully, the effect of pH in the model can be introduced through pH-dependent Henry's constants.Henry's constant increases with pH for both EC and FC, which means that their retention times both become longer with increasing pH (see Supporting Information: Figure S1).However, the change is nonuniform, and in fact the difference in Henry's constant between EC and FC increases with increasing pH.This ultimately suggests that EC and FC peak resolution is better at higher pH values.
The obtained values for Henry's constants H 0,EC and H 0,FC were fitted to a second-degree polynomial expression (Equation 8), with good agreement as shown in Supporting Information: Figure S1.
This allowed to obtain the model parameters for the pH dependence included in Equation ( 8): H 0,EC , H 0,FC , K pH1, EC , K pH1, EC , K pH2, EC and K pH2, FC .
By qualitative assessment, the fitting of the chromatograms at the different pH is satisfactory, as shown in Figure 3.Some deviation in the retention time can be seen for pH 8.5, which was also expected, as the estimation of Henry's constant for that pH differs slightly from the experimental point (see Supporting Information: Figure S1), but the shape of the simulated chromatographic peaks is almost identical to that of the experimental ones, which suggests the model is capable of incorporating pH dependence.There is a clear trend-both simulated and experimental-of an increasing pronounced front shoulder as pH is increased, suggesting resolution improving with increasing pH.

| Effect of loading density
The model appears to predict the chromatogram both at low and high loading densities (Figure 4) with reasonable fidelity.There are some minor deviations, predominantly in the low loading density.
Case A more rigorous assessment of predictive resolution capacitythat is model performance-could be derived by Gaussian peak fitting and moment analysis to mathematically describe retention  c).The dotted blue curve is the experimental peak and the red curve is the simulated peak, which is the sum of the EC peak (dark gray) and the FC peak (light gray).The time axis starts with the elution phase.EC, empty capsid; FC, full capsid.
time differences and peak-area differences of the EC and FC peaks if desired, likely necessary to further optimize the model against the loading density parameter.However, for the present purposes, general qualitative agreement was deemed sufficient.In the experiments with low and medium loading densities (5•10 12 and 1•10 13 vg/mL), the column is far from being saturated, and likely for F I G U R E 3 Experimental and simulated chromatograms at pH 8.0, 8.5, 9.0, and 9.5 (panels a-d).The dotted blue curve is the experimental peak and the red curve is the simulated peak, which is the sum of the EC peak (dark gray) and the FC peak (light gray).
The dotted blue curve is the experimental peak and the red curve is the simulated peak, which is the sum of the EC peak (dark gray) and the FC peak (light gray).The time axis starts with the elution phase.EC, empty capsid; FC, full capsid.
that reason, the chromatograms both have similar resolution (pronounced shoulders).At a loading density of 1•10 14 vg/mL, the number of available binding sites is likely scarce, which affects the chromatogram, leading to left-shifted peaks and lower resolution (Seidel-Morgenstern, Schulte, et al., 2012).

| Case A: Single-step elution
As a first pass, an analysis of the effect of the salt concentration in the elution phase on the yield using a single-step 40 CV isocratic wash and a model-defined optimum pooling strategy for two different purity requirements was performed: 80% and 90% (Figure 5).In some manufacturing processes, rAAV enrichment is carried out via a single linear gradient elution with differential peak collection/pooling.Case A in comparison-being isocratic (not gradient) but still single step-most represents a version of displacement chromatography with the model thus defining a salt concentration that elutes both EC and FC but at the point of maximal selectivity and resolution.Baseline separation is not achieved and thus pooling strategies are required.This is conceptually interesting but rarely seen in manufacturing settings.
As expected, the higher the purity requirement, the lower the yield that can be obtained.This is because FC and EC elute so close together that their peaks are overlapping even at the most optimal resolution (Supporting Information: Figure S2) and thus to capture a pool with fewer total EC invariably requires that pool also have fewer total FC.Note that the yield is 0 when the purity requirement cannot be fulfilled at a specific salt concentration.
As can be seen in Figure 5, there is an optimal salt concentration, which is the same regardless of the purity requirement.The optimal salt concentration is 0.128 M NaCl, and the yield obtained is 84.6%.
The chromatogram corresponding to the optimal point with pooling cutoff points to get a purity of 90% is presented in Supporting Information: Figure S2.
The elution length is 40 CV, and shorter lengths were tested (10, 15, and 20 CV), but the purity requirements were not fulfilled for any salt concentration at any of the tested elution lengths.For that reason, further study of the optimization problem was needed, and in that direction, a two-step elution was considered (Case B).

| Case B: Two-step elution
In a two-step elution, the elution is divided into two steps: Step 1 (aka wash), with lower salt concentration to elute the EC but not the FC; and Step 2 (aka elution), with higher salt concentration to elute the FC.That way, both components can be effectively separated, and the elution length can be reduced significantly by using a higher salt concentration in the step.
The optimal yield for different purity requirements was obtained (Figure 6).The exact value of the salt concentration in the second step was not relevant in this model as long as it was high enough to quickly elute the FC.For that reason, the same optimization problem but with only two decision variables (salt concentration in the first elution step, and the relative length of the two steps) was also solved, setting the salt concentration in the second step to 0.30 M NaCl.In Figure 6a, it is shown that the results from both optimizations (with two and three decision variables) are identical.For that reason, further optimization analysis was performed using only the mentioned two decision variables, thus saving computation time.It is also confirmed in this figure that two-step elution gives better results than a single-step elution.
The effect of pH on the optimal solution was studied.Figure 6b shows that the higher the pH, the higher the yield as a result of the better resolution, although there is an optimum at pH 9.0, as the yield at pH 9.0 is slightly higher than at pH 9.5.For that reason, the pH was set constant to 9.0 in the remaining part of the optimization study.
The yield at pH 8.0 is much lower than for the rest of pH values, and this is due to the low resolution at that pH.Ultimately, as the purity requirement gets higher, the impact of pH on yield becomes more and more significant.Thus, when designing a process, it's important to consider that lower purity requirements will likely be more tolerant to wider pH ranges, whereas when very high levels of percent full are required pH might be a potent lever necessitating tight control.
A three-dimensional response plot where the effect of both decision variables on the yield was obtained (Figure 7).In this case, elution length was constrained at 40 CV, pH was 9.0, and the purity requirement was 90%.There is an optimal value for the salt concentration in the first step (around 0.12 M), at which yield is 88.5%, and the chromatogram corresponding to that point is shown in Supporting Information: Figure S3.This can be thought of as the salt concentration of Step 1 that elutes/removes the optimal amount of EC to maximize the yield of FC during Step 2 while still achieving 90% purity (90% FC) during Step 2. Below that value, the yield is 0, F I G U R E 5 Yield obtained at different salt concentrations in Case A, for purities 80% and 90% (for an elution length of 40 CV and a pH of 9.0).
meaning that the purity requirement simply cannot be fulfilled within the constraints defined.Beyond that value, the purity requirement can still be readily satisfied, but the yield decreases with the salt concentration since the resolution between the two peaks gets lower.In other words, a "stronger" Step 1 will ultimately elute more FC while eluting EC in an effort to meet the purity requirement.
To evaluate the effect of the total elution length, the process was optimized for four different elution lengths: 10, 15, 20, and 40 CV for different purity levels (Figure 8).The elution can be shortened significantly without having a big effect on the yield and purity.For the very low elution lengths, it is not possible to reach certain purity levels, as expected.However, it is possible to find solutions with very high yields and purities with an elution length of 20 CV, thus reducing the elution length (and therefore the buffer consumption) twice compared to the original optimization problem with a 40 CV elution, as well as reducing the dilution of product and maintaining comfortable working process volumes.
In the context of a two-step isocratic wash-and-elution, the model provides interesting insights regarding the effect of the length of Step 1 (EC wash)-and the interaction of Step 1 length and Step 1 salt concentration-on yield and purity during Step 2 (FC elution).
Generally, a longer elution at a lower salt concentration leads to a higher yield as long as the salt is high enough to achieve an elution that satisfies the purity requirement-otherwise, yield defaults to 0.
In practical terms, this is sometimes referred to as a gentle or weak elution.In practice, there is a limit to how long an elution can and should be, taking into account process time, buffer usage, and product dilution.In contrast, generally, a shorter elution requires a higher salt concentration to satisfy the purity requirement-in this case, remove sufficient EC-in the decreased volume.However, a higher salt concentration leads to a poorer resolution and thus lower yields, as more FC are lost while removing EC.Ultimately, there is thus an optimum salt concentration and elution length-somewhere between "low" and "high," "short" and "long"-that is able to satisfy purity requirements while providing acceptable yields from a process that is amenable to manufacturing.
Whereas salt concentration and pH are near-universally considered critical parameters in chromatographic full-capsid enrichment, wash length is less commonly studied and leveraged.However, it is clear that for such a fine separation as EC from FC, Step 1 length is a valuable tool.While isocratic chromatography is often preferable over gradient chromatography from a scale-up and transfer perspective, many rAAV manufacturers utilize some version of gradient chromatography to achieve optimal separation of EC and FC because the common isocratic levers of salt and pH-even with tight controlmay still be limited in terms of purity and yield.This model suggests wash length is a potent additional lever, key to expanding purity and yield capabilities, likely to be tunable for things like variable load challenge and/or load purity-potentially an opportunity for online process control, and ultimately ripe for optimization.

| Validation
The optimization results must be validated, and to do so, an optimal point must be selected and tested experimentally.The optimal solution was selected from the set of solutions shown in Figure 8 with a total elution length of 20 CV and purity of 90%.The process conditions for the selected solution are summarized in Supporting Information: Table S3. Figure 9 shows the simulated chromatogram corresponding to the selected solution, where the obtained recovery yield was 84.1% with a purity of 90%.
The selected solution was run experimentally, and the obtained chromatogram is shown in Supporting Information: Figure S4.The purity was 64.5% and the recovery yield was 88.2%.Therefore, the model was accurate at predicting the recovery yield and it was able to identify a process operation with a significant enrichment-from 15% FC to 64.5% FC-even though final purity was overpredicted.This was possibly due to the fact that the quality of the input data determined the quality of the output results; purity data were generated by comparing two methods-qPCR titer to Capsid ELISA titer-and consequently, they were subject to greater variability.
Regarding the productivity, it was defined as amount of FC purified divided by the purification time and the column volume.The purification time was the same in the simulation and the experiment, as the phase times were fixed.Then, the difference in productivity depended only on the difference in yield, which resulted in slightly higher experimental productivity (4.24•10 11 vg/min/mL) compared to the one predicted by the model (4.04•10 11 vg/min/mL) (Table 1).

| CONCLUSIONS AND DISCUSSION
A mechanistic model for the purification of rAAV with anionexchange membrane chromatography was developed to optimize the removal of ECs and the enrichment of full rAAV.
The mechanistic model, a reactive-dispersive model with F I G U R E 8 Yield for different purity requirements and total elution lengths with a two-step elution (for a pH of 9.0).
F I G U R E 9 Simulated chromatogram corresponding to the selected optimal point with two-step elution (for a purity requirement of 90%, a total elution length of 20 CV, and a pH of 9.0).
T A B L E 1 Results summary with the simulated and the experimental values.multiple-component Langmuir isotherm with salt and pH dependance (Andersson et al., 2014;Saleh et al., 2020;Seidel-Morgenstern, Schmidt-Traub, et al., 2012), was calibrated using linear gradient experiments with different conditions of flow rate, gradient slope, pH and loading density, achieving observable agreement between the simulations and the experiments, and allowing to study the effect of these process conditions on the process performance and the model parameters.
The calibrated model was used to optimize the separation of EC and FC using single-step and two-step isocratic elution, by maximizing yield with different elution lengths, pH, and purity requirements.
The following conclusions were obtained from the optimization: 1. Two-step elution turned out to be better than single-step elution.
2. Purity and yield are impacted by Step 1 pH, and pH 9.0 was the optimal.
3. The higher the purity requirement, the lower the yield although industrially relevant yields could still be obtained at high, relevant purity levels.
4. Constraining to shorter elution lengths led to lower yields although the elution length could be reduced from 40 to 20 CV without a significant effect on yield, with the consequent gain on productivity, buffer consumption, and pool concentration.
5. Load challenge impacts selectivity, with EC and FC bands less resolved at higher load challenges.
6.In a two-step paradigm, there is a strong relationship between Step 1 (empty wash) salt concentration and wash length when considering their impact on Step 2 (FC elution) pool yield and purity.
Given all of these interactions, defining Step 1 parameters for expected loading approaches is the key industrially relevant goal.
Under the assumption that one knows to study all of the variables and interactions that were revealed by the model as important, approximating an optimal Step 1 through brute-force iterative approaches-that is, omitting designed experiments matched to chromatography theory (modeling)-is possible.Empirically, one or two fairly shallow linear gradient elution experimentsat one chosen pH-can in principle be used to define an approximate salt concentration in the general range of that Step 1 optimum.The authors have observed that the conductivity (and corresponding salt concentration) at approximately 15% of the average "peak 1" height under gradient conditions which result in a typical unresolved but multi-peak chromatogram, is a reasonable approximation (data not shown) for a first attempt at defining a Step 1 salt concentration.From there, developers can then choose a selection of salt concentrations-for example, n = 5-in proximity to that first pass, perhaps in 0.5 mS/cm increments.By running independent experiments with extended isocratic Step 1 washes at those selected salt concentrations, fractionating, and analyzing fraction content, one might empirically define a reasonable optimum wash conductivity and length for yield and purity.Previous efforts to develop analytical (Lock et al., 2012) and manufacturing (Dickerson et al., 2021;Joshi et al., 2021) relevant empty:full separations have successfully employed similar methodologies; however, there has not typically been significant attention paid to the interactive effect of Wash 1 conductivity and length on yield and fold enrichment.In an alternative approach, one could skip the linear gradient and go directly to isocratic elution with stepwise increases in conductivity.Hejmowski et al. (2022) reported the development of a Mustang-Q enrichment step for AAV5 through the application of 1 mS/cm isocratic steps, and even more recently Cytiva presented on the application of 0.5 mS/cm isocratic steps across a range of serotypes (Cytiva, 2023a(Cytiva, , 2023b)).Neither case leveraged a linear gradient and instead screened wash 1 and 2 conductivities with the isocratic-step-gradient approach, establishing ideal wash 1 and 2 conductivities based on semi-quantitative interpretation of elution peaks and empty-full crossover to minimize "full capsid leakage."In both cases, no initial linear gradient was needed, and significant enrichment (e.g., as high as >4-fold enrichment with 70% recovery) was shown to be successfully developed with high efficiency and short cycle time, although neither approach rigorously investigated the impact of wash 1 length.While there is clearly evidence that purely empirical approaches can lead to successful-even great-outcomes, the limitations of this approach relative to mechanistic modeling are numerous.While an acceptable condition can perhaps be found, even if wash length was more commonly incorporated into existing approaches finding a more global optimum Step 1 might remain elusive given how fine the EC and FC separation can be and how much the many factors interact.In addition, for truly robust processes, the empirical experiments described would likely need to be repeated at multiple pH, load densities (load challenges), and load purities (load % full).Furthermore, should design requirements change significantly-for instance, finding you may only need 50% purity-a model might, by its application of testable theory, have greater predictive and extrapolative power.Perhaps, more simplistically, the number of experiments and sampling required to perform the aforementioned empirical approach-especially at numerous pHs and load challenges-is at least as many as were performed to develop the model, without all of the benefits of a model.
In this work, an optimal solution with a two-step elution of 20 CV of length, pH 9.0, 90.0% purity, and 84.1% yield, was selected for experimental validation, where the purity was 64.5% and the recovery yield was 88.2%.The model was thus able to deliver the expected recovery yield with remarkable fidelity.While the model overpredicted the purity, it nonetheless was able to identify a significant enrichment regime.It is possible that this is an example of quality-in, quality-out; whereas recovery yield is based on samples analyzed by a single method, and within the same analytical assaykeeping variability to a minimum-purity is based on the combination of two methods and, consequently, it is subject to greater variability.
It is our experience that it is not uncommon to see ±10%-15% variability when determining purity by these two analytical methods.
Thus, it is important to consider when training and calibrating mechanistic models that the robustness of outputs can be impacted Probing utilized HEX fluorophore with Iowa Black quencher.The standard curve was generated via serial dilutions of known quantities of linearized, double-stranded gBlock DNA fragments designed specifically for the assay.Sample preparation included various enzymatic and processing steps (e.g., nuclease, DNAse, proteinase, heat, and quenching) to ensure results faithfully reported only transgene-containing viral capsids.Samples were plated in 384-well format, enabling higher throughput and the inclusion of multiple standard assay controls, technical replicates, and dilutional ranges.Thermocycler amplification and fluorescence detection utilized BioRad C1000 and BioRad CFX, respectively (Bio-Rad).Viral vector percent recovery was determined by mass balance calculated from the qPCR method and known process volumes.Total capsid titer was determined by a qualified capsid ELISA method based on the Progen AAV6 Titration ELISA Kit, p/n PRAA6 (Progen).Samples were read using a BioTek Synergy H1 plate reader (BioTek Instruments).Percent full rAAV6 was determined by dividing qPCR titer by total capsid titer.Enrichment was determined by dividing pool percent full by load percent full.Orthogonal confirmation of fold enrichment and recovery utilized Stunner (Unchained Labs), a microfluidic technology that couples UV-VIS with multi-angle light scattering (data not shown).
Experimental and simulated chromatograms at gradient lengths 20.0, 40.0, and 80.0 CV (panels a-

F
I G U R E 6 Yield for different purity requirements.(a) Comparison between single-step with one decision variable (DV), two-step elution with two DV, and two-step elution with three DV (for a pH of 9.0).(b) Comparison between different pH values.The total elution length is 40 CV for all points in the figures.F I G U R E 7 Response surface plot of the salt concentration and the length of in the first elution step and their effect on the yield (for a purity requirement of 90%, total elution length of 40 CV, and a pH of 9.0).The black point represents the optimal point.The two plots correspond to two different views of the same figure.