The Pall XT5 and XT140 capsules were studied by analyzing breakthrough curves that have been measured under binding and non-binding conditions. A flow rate of 12 CV/min was chosen for studying the capsules under industrially relevant conditions. The effects of different flow rates in the axial flow configuration have been described in a previous publication (Francis et al., 2011).
Axial Flow Configuration at Non-Binding Conditions
Breakthrough experiments performed under non-binding conditions provide insights into solute dispersion within the studied membrane chromatography capsules. Non-binding conditions are obtained by adding 1 M NaCl to the protein solution. The analysis of non-binding data is crucial for quantifying the effect of system non-idealities that are caused by inhomogeneous flow separately from non-ideal binding mechanisms.
Breakthrough experiments under non-binding conditions provide information on the sum of the hold-up volumes in the Äkta system and in the studied chromatography capsule. The chromatography system was primed with load material up to the column switch valve in order to effectively remove the impact of the hold-up volumes before that point, as the corresponding system components, that is pumps, mixer and tubing, are already filled with protein solution when the valve is switched from bypass to the capsule. Consequently, the dispersion in the measured breakthrough curve (Fig. 5a) is caused only by the chromatography capsule and by the hold-up volumes behind that capsule that is the tubing and the detection chamber. However, the hold-up volumes behind the capsule sum up to only 18 µL and, hence, their contribution to system dispersion can be neglected.
Figure 5. Measured breakthrough curve of the axial flow XT5 capsule under non-binding conditions. a: Best fit of the symmetric Roper and Lightfoot model and of the symmetric zonal rate model (ZRM) with two membrane zones for XT5 capsule, (b): best fit of the symmetric and asymmetric ZRM with one membrane zone (Roper and Lightfoot model) for XT140 capsule.
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After an initial lag of 6 s the signal rapidly increases to half of the inlet concentration in 4 s but then gradually flattens out and takes approximately 20 more seconds for reaching the full inlet concentration. The observed tailing is far from the ideal system response but rather typical for membrane chromatography units with extreme length-to-with ratios, even though the dispersion of solute molecules on their short path through the membrane stack itself can often be neglected. Francis et al.(2011, 2012) have studied the same capsule and shown that the dispersion coefficient in the model for the membrane stack can be replaced by the molecular diffusion coefficient when the hold-up volumes are properly described. The same approach is followed in the present study. The membrane stack in the analyzed XT5 capsule has a volume of 5 mL while the hold-up volumes on the either side of the stack are 3.21 m. The membrane stack has a porosity of 0.7 (Pall XT5, which implies that the capsule contains only 1.5 mL of solid membrane. Hence, the total hold-up volume of the capsule actually exceeds the membrane volume.
As a reference, the Roper and Lightfoot model with a linear sequence of PFR and two CSTRs, one before and one after the membrane stack, is fitted to the measured breakthrough curve (see Fig. 5a). The residence times for the tanks on either side of the membrane stack are chosen identical in order to account for the respective symmetry of the studied XT5 capsule. Hence, two parameters of the Roper and Light foot model are estimated from measurement data, namely the residence times of the PFR and of the CSTRs (see Table I). The Roper and Lightfoot model can only coarsely approximate the measured breakthrough curve. The simulated curve not only shows a delay of the initial breakthrough but also a reduced tailing as compared to the measurement data.
Table I. Hold-up volumes and volumetric flow fractions as determined by fitting the zonal rate model (ZRM) with one membrane zone (Roper and Lightfoot model) and with two membrane zones to a non-binding breakthrough curve of the axial flow XT5 capsule (VPFR = QtPFR, Vinner = Qτ1, Vouter = QΦ2τ2).
|Parameter||One membrane zone (mL)||Two membrane zones (mL)|
The ZRM was set-up with differently many membrane zones, also assuming symmetry of the tanks before and behind the membrane stack. Each of these configurations was fitted to the data in order to determine the minimal number of membrane zones that is required for quantitatively reproducing the measured breakthrough curve. In full agreement with previous results for the same capsule (Francis et al., 2011), a set-up with two membrane zones was found to be optimal. This set-up has four parameters, namely the PFR volume, the different volumes of two CSTRs for describing the hold-up zones before the membrane stack (the hold-up zones behind the stack are symmetrically modeled), and the volumetric flow fraction between the two membrane zones. The values of these parameters (see Table I) are completely determined by the internal geometry of the studied capsule. Although the inner tank has a smaller volume, 57% of the volumetric flow passes through the central region. The determined total hold-up volume of the capsule of 2.91 mL is reasonably close to the manufacturer specification of 3.21 mL. The ZRM is a semi-empirical approach that is based on the physical geometry, but a good reproduction of the experimental data is preferred over a perfect match of the physical volumes. A restriction of the total hold-up volume in the ZRM would remove one degree of freedom from the parameter estimation. However, the entire breakthrough curve would be shifted to the right, and this effect could not be compensated for by taking more zones, as the total hold-up volume is proportional to the area over the breakthrough curve. Computational fluid dynamics allows for a more stringent description of the internal capsule geometry, however, this would require much higher modeling and computing efforts and goes beyond the scope of the present study.
Radial Flow Configuration at Non-Binding Conditions
Non-binding breakthrough data of the radial flow XT140 capsule were also analyzed with different set-ups of the ZRM. Similar to the XT5 capsule, the impact of the system hold-up volumes is reduced by priming the chromatography system with load material up to the column-switching valve. The remaining hold-up volumes in the tubing before and behind the XT140 capsule and in the detection chamber add up to 100 mL and cannot be completely neglected. However, the analysis in the following paragraph indicates that these external hold-up volumes mainly contribute to the PFR volume and not to the CSTR volumes in the ZRM. The resulting shift of the breakthrough curve does not affect the observed performance of the XT140 capsule.
Although the internal geometry of the XT140 capsule is more complex than of the XT5 capsule, a ZRM set-up with just one membrane zone was found to be sufficient for quantitatively reproducing breakthrough curves at the studied flow rate. However, an asymmetric model with unequal volumes before and behind the membrane is required (see Fig. 5b). A second membrane zone increases the number of regression parameters, but does not significantly improve the fit (data not shown). Hence, the asymmetric model with one membrane zone is used in the following sections. The sufficiency of one membrane zone indicates that the flow is distributed more homogeneously in the XT140 capsule than in the XT5 capsule. The substantially different tank volumes upstream and downstream of the membrane stack (see Table II) reflect the fact that, in contrast to the XT5 capsule, the peripheral distribution region with 105 mL and central collection region with 45 mL in the XT140 capsule are actually not symmetric. The fitted CSTR volumes in the ZRM are smaller, which indicates that a fraction of the rather complex shaped hold-up volumes within the XT140 capsule can be modeled as a PFR. The external hold-up volumes in the tubing and in the detector chamber are much more streamlined and will, consequently, predominantly contribute to the PFR volume in the ZRM, which does not contribute to system dispersion.
Table II. Hold-up volumes as determined by fitting the symmetric and the asymmetric ZRM with one membrane zone (Roper and Lightfoot model) to a non-binding breakthrough curve of the radial flow XT140 capsule (VPFR = QtPFR, Vupstream = Qτ1, Vdownstream = Qτ2).
|Parameter||Symmetric model (mL)||Asymmetric model|
|Vdownstream||Same as Vupstream||19.32|
Axial Flow Configuration at Binding Conditions
In the previous two sections the impacts of flow non-idealities within the studied membrane chromatography capsules on experimentally measured breakthrough curves were individually analyzed under non-binding conditions. The internal geometry of the studied capsules was characterized by parameter values that represent residence times in virtual zones and flow fractions between these zones. These parameters are now fixed in order to independently analyze the impact of protein binding on the observed breakthrough curves with the Langmuir and spreading models.
In the first binding experiments, the capsule was cleaned using 1 N NaOH after each run as specified by manufacturer. The cleaning step was followed by a regeneration step with 1 M NaCl. However, this protocol resulted in a very poor reproducibility (see Fig. 6a). Huge variations are observed for subsequent runs that were performed with the same capsule and under the same conditions. The exact reasons for the observed variations between measured breakthrough curves under the same conditions cannot be cogently explained, which poses a challenge in developing a coherent model. A possible explanation could be based on the fact that individual sheets of the membrane stack can slightly move within the XT5 capsule, and that swelling and de-swelling during treatment with NaOH might cause changes in the membrane position and shape. An MRI image of the membrane capsule after repeated cleaning with 1 N NaOH (see Fig. 7a) shows an uneven membrane surface with several wedges that could potentially cause preferential flow. The MRI investigation of membrane chromatography capsules will be continued in a separate study.
Figure 6. Measured breakthrough curve of the axial flow XT5 capsule under binding conditions. a: Using 1 N NaOH for cleaning after each run, (b): using 1 M NaCl for cleaning after each run, (c): best fit of the ZRM combined with the Langmuir binding model and the spreading model, and (d): simulated concentrations of bound molecules in the end-on orientation (q1: red line) and in the sideways orientation (q2: black line) during the loading process over time.
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Figure 7. a: Cross-sectional MRI scan through the center of the membrane stack of an axial flow XT5 capsule that has been cleaned using 1 N NaOH, (b): Cross-sectional MRI scan of the XT140 capsule. The membrane pleats are clearly visible in gray, due to their water content.
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This study was continued with a fresh capsule and with a revised cleaning protocol in which 20 CV of 1 M NaCl were passed through the capsule after each completed cycle of load, wash and elution. Moreover, the time between two experiments was minimized by performing all runs immediately one after another. The revised protocol resulted in a much improved reproducibility of the breakthrough curve shapes (see Fig. 6b).
Rapid execution of the experiments was observed to be crucial, as the breakthrough curves were shifted to the right after the membrane was stored in the cleaning buffer (1 N NaOH) for several hours (data not shown). Similar shifts of the breakthrough curves are observed for the radial flow XT140 capsule that contains the same type of membrane (Radial Flow Configuration at Binding Conditions Section). These shifts, which are also observed in industrial applications of the same capsules, indicate that the overall binding capacity increases with storage time in the cleaning buffer. The cause is unclear, but the capacity would increase if the polyethylene sulfone (PES) backbone of the membrane had an inherent binding capacity for BSA and if the storage in NaCl would expose more of this backbone to the protein. Alternatively, more of the Q ligands could be exposed after storage in the cleaning buffer.
The measured breakthrough curves in Figure 6b are asymmetric and show a sharp increase from the initial breakthrough point to ca. 90 percent of the inlet concentration, which is followed by a very slow rise towards 100% of the inlet concentration. Without further analysis, the experimental data does not reveal the origin of the observed tailing. The tailing could be exclusively caused by non-ideal flow in the hold-up volumes, but the binding process can also influence the breakthrough curve in a non-ideal way. Hence, a model-based data analysis is proposed for separately quantifying the impact of flow non-idealities and binding non-idealities. The ZRM was combined with the Langmuir model and the spreading model for analyzing the binding data.
The complexity of the spreading model was reduced by assuming that BSA cannot directly adsorb or desorb from or to the sideways orientation. The resulting model reproduces the measurements equally well (data not shown) with a lower number of regressed parameters and is hence preferred in order to avoid over-parameterization and over-fitting.
Figure 6c shows the best fit of the ZRM with the Langmuir model, and the estimated parameters are summarized in Table III. The Langmuir model can reproduce the initial breakthrough but not the tailing. The spreading model reproduces the entire breakthrough curve much better than the Langmuir model (see Fig. 6c), even with neglected adsorption and desorption of the second bound state. The spreading model involves six parameters, ka1, kd1, k12, k21, qm, and β, that are also estimated from binding breakthrough data (see Table IV).
Table III. Parameters of the Langmuir model for the axial flow configuration as determined by fitting the ZRM to a binding breakthrough curve of the axial flow XT5 capsule.
|ka (L/(g s))||6.4 × 10−2|
|kd (L/s)||6 × 10−3|
Table IV. Parameters of the spreading model for the axial flow configuration as determined by fitting the ZRM to a binding breakthrough curve of the axial flow XT5 capsule.
|ka1 (L/(g s))||8.08 × 10−2|
|kd1 (L/s)||1.06 × 10−5|
|k12 L/(g s))||7.37 × 10−4|
|k21 (L/s)||9.41 × 10−3|
The spreading factor β is larger than one and, hence, the molecules that are bound in the first orientation require less space as in the second orientation. This indicates that the first orientation is with one end towards the surface, whereas the second bound state is in a sideways orientation. However, the fact that the spreading model fits the experimental data very well cannot be taken as final proof for the underlying hypothesis of different binding orientations, and conformational changes of the bound molecule might also be involved.
The initial adsorption rate of solute molecules to the unsaturated membrane in the end-on orientation is 1/(ka1 × qm) = 0.042 s and the reorientation rate to the sideways orientation is 1/(k12 × qm) = 4.69 s. Both rates are quite fast, but the desorption rate is 1/kd1 = 157 min, which indicates almost irreversible binding under the observed conditions with an overall loading time of 15 min. However, the reorientation rate from the sideways to the end-on orientation is 1/k21 = 106 s and, consequently, both directions of the reorientation process are relevant during the loading process. Figure 6d shows the simulated amounts of bound molecules in both orientations over time. The BSA molecules are first bound in end-on orientation but rapidly transferred to the sideways orientation, which requires more space. Hence the surface is quickly saturated within 20 s. Then bound molecules in sideways orientation are more slowly transferred back to the end-on orientation, making room for further binding in end-on state. More than 15 min are required for reaching the complete equilibrium between both bound states. These two phases can also be seen in the measured breakthrough curves. The first phase corresponds with the initial sharp increase and the second phase with the long tail of the experimental curve. The maximum in the sideways orientation curve occurs at the inflection point in the breakthrough curve at 420 s where approximately 90% of the inlet concentration is reached (compare with Fig. 6b).
Radial Flow Configuration at Binding Conditions
With the manufacturer protocol for cleaning, the slopes of the measured breakthrough curves of the radial flow XT140 capsule were found to be better reproducible as compared to the XT5 capsule (see Fig. 8a). This might be due to the fact that in the XT140 capsule the membrane is not stacked but tightly arranged in fixed pleats, which effectively prevent position and shape changes. However, the breakthrough curves are also shifted to the right with increasing cycle numbers. Hence, the XT140 experiments were also performed with a fresh capsule and the revised cleaning protocol using 1 M NaCl instead of 1 N NaOH. The resulting breakthrough curves are not shifted but have similar shapes as compared to the original cleaning protocol (see Fig. 8b). The breakthrough curve in Figure 8b shows a sharply increasing section after the initial breakthrough point at 380 s in which 70% of the inlet concentration is reached within 420 s. The curve then gradually flattens out and reaches the full inlet concentration after approximately 850 more seconds.
Figure 8. Measured breakthrough curve of the axial flow XT140 capsule under binding conditions. a: Using 1 N NaOH and (b): using 1 M NaCl for cleaning after each run.
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In Radial Flow Configuration at Non-Binding Conditions Section, the flow non-idealities in the XT140 capsule were described by an asymmetric ZRM with one membrane zone, and in Radial Flow Configuration at Binding Conditions Section, the kinetic parameters of the spreading model were determined independently from the flow configuration. Hence, the flow related parameters of the XT140 capsule (Table II) could be combined with the binding related parameters (Table IV) that have been determined for the same membrane type in the XT5 capsule. With this information, the ZRM can be applied for predicting breakthrough curves of the XT140 capsule under binding conditions. The result of this model-based prediction is compared to the corresponding measurement data in Figure 9. The simulated breakthrough curve closely matches the breakthrough point and the initial slope of the measured data. The model also correctly predicts the flattening of the breakthrough curve after 420 s, however, the predicted tail starts at 90% of the inlet concentration whereas the measured tail starts at 70% of the inlet concentration.
Figure 9. Predicted and measured breakthrough curve of the axial flow XT140 capsule under binding conditions. The asymmetric ZRM with one membrane zone was solved with the flow related parameters from Table III and the binding related parameters from Table V.
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The ZRM quantitatively accounts for non-ideal flow in the void volumes of the XT140 capsule, and the binding parameters are determined independently from the flow regime. Hence, the observed deviations must be caused by capsule specific issues that are negligible under non-binding conditions. An MRI scan reveals that the membrane pleats are not perfectly arranged in the used XT140 capsule. The red arrows in Figure 7b indicate irregular pleats with varying membrane areas. These variations can cause local deviations in the linear velocity that are not accounted by the ZRM, as configured according to Figure 3c. Hence, the data is re-analyzed with a novel configuration of the ZRM in which the axial membrane zone is splitted into several angular sectors with different linear velocities (see Fig. 10a).
Figure 10. a: Virtual partitioning of hold-up volumes and of the membrane for a radial flow configuration in which one axial membrane zone is splitted into three angular sectors with different linear velocities, (b): distribution of the volumetric flow relative to the total volumetric flow, f, over the linear velocity relative to the average linear velocity, v, in the respective sector.
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The configurations in Figures 3c and Figure 10a can be combined for a ZRM with more than one membrane zone and several sectors with different linear velocities. However, one axial membrane zone has been shown already to accurately describe the XT140 capsule under non-binding conditions (Radial Flow Configuration at Non-Binding Conditions Section), and a second axial membrane zone does not improve the model-based prediction of the XT140 binding data in Figure 9 (data not shown). Varying linear velocities in different sectors of the membrane zone are negligible under non-binding conditions, because the membrane stack is very thin and, consequently, the residence time of the solute molecules in the membrane stack is much shorter as in the hold-up volumes. Nonetheless, varying linear velocities do significantly impact on the loading of the membrane sectors, as the solute molecules are supplied at different rates. The ZRM has two additional parameters for each angular section, the volumetric flow through this section and the linear velocity within this section. However, the overall model has one degree of freedom less when the total volumetric flow rate is given, for example in a three sector model, the relation Q1 + Q2 + Q3 = Q allows to compute Q3 from Q1 and Q2.
The measured breakthrough data is first re-analyzed with ZRM configurations with one axial membrane zone and two to four angular sectors (see Fig. 11a–c). Table V shows the fitted volumetric flow through the angular sectors relative to the overall volumetric flow and the linear velocities in these sectors relative to the average linear velocity. Figure 11a–c illustrates that the revised configuration of the ZRM can quantitatively reproduce the measured breakthrough curve. The simulated breakthrough curve increasingly adapts to the measurement data with increasing numbers of sectors. The visible steps in Figure 11a,b are due to the fact, that the ZRM with two and three sectors only coarsely approximates the true velocity distribution. The fitted parameters in Table V reveal that more than 85% of the overall volumetric flow has only a slightly increased linear velocity, whereas the remaining fraction of the volumetric flow has significantly decreased linear velocities. This coincides with the observation that most of the pleats in the used XT140 capsule are quite regular (see Fig. 7b).
Figure 11. Measured breakthrough curve of the axial flow XT140 capsule under binding conditions. Best fit of the ZRM with one axial membrane zone and (a) two, (b) three, (c) four, and (d) sixteen angular sectors.
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Table V. Volumetric flow relative to the total volumetric flow and linear velocity relative to the average linear velocity for the asymmetric ZRM with one axial membrane zone and one to four angular membrane sectors as determined by fitting the ZRM to a binding breakthrough curve of the radial flow XT140 capsule.
|Sectors||ZRM with 1 sectors||ZRM with 2 sectors||ZRM with 3 sectors||ZRM with 4 sectors|
|Volumetric velocity (%)||Linear velocity (%)||Volumetric velocity (%)||Linear velocity (%)||Volumetric velocity (%)||Linear velocity (%)||Volumetric velocity (%)||Linear velocity (%)|
The ZRM with four sectors describes the measurement data very well but comprises too many parameters that need to be estimated from experimental data. The following approach is applied for reducing the number of parameters and at the same time to account for the fact, that the true velocity distribution is a continuous function: The ZRM is configured with 16 sectors, and a series of equidistantly spaced linear velocities is assigned to these sectors. The distribution of the total volumetric flow through these sections is approximated by a function that depends on only three parameters (see Fig. 10b). The first two parameters describe the position and the width of the main peak, which is modeled by a Gaussian distribution. The third parameter describes the slope of a linear increase starting at the origin. On the left hand side of the peak, the maximum of these curves is taken. The area under the curve is normalized such as to maintain the total volumetric flow rate. The parameters for the sectors are simultaneously estimated by fitting the ZRM to the measured breakthrough curve.
Figure 11d shows an excellent fit with only three additional parameters. The volumetric flow rate and the linear velocity in the sectors are expressed in relation to their total or average values, respectively. The peak in Figure 10b is slightly shifted to the right, because the average is decreased by the existence of smaller velocities. As before, approximately 85% of the total volumetric flow has almost the same linear velocity, whereas the remaining 15% have significantly different linear velocities.