UF/DF experimentsExperimental setup

The custom-made setup from Rüdt et al. [20] and Rolinger et al. [12] was adjusted for automation of the UF/DF process. Figure 1 shows the setup as a Piping and Instrumentation Diagram (P&ID). A KrosFlo KRIIi CFF unit (Spectrum Labs, Rancho Dominguez, USA) was equipped with a FlowVPE Variable Pathlength (VP) Ultraviolet and Visible (UV/Vis) spectrometer (C Technologies, Bridgewater, USA), a non-bypass version of a flow-through micro Liquid Density Sensor (microLDS) (TrueDyne Sensors AG, Reinach, CH), a MarqMetrix BioReactor Ballprobe (MarqMetrix, Seattle, USA) inserted into an in-house made flow cell for Raman measurements and a T-piece with injection plug (Fresenius Kabi, Bad Homburg, DE) placed after the retentate reservoir of the CFF unit for drawing samples for off-line analytics. The ball probe was connected to a HyperFlux PRO Plus 785 Raman analyzer with Spectralsoft 2.8.0 (Tornado Spectral Systems, Toronto, CA). Additionally, a fractionation valve of an Äkta prime (Cytiva, Chicago, USA) was connected to a relay module, which was controlled via a NI USB-6008 data acquisition device (National Instruments, Austin, USA) to switch between air and DF buffer. A Topolino magnetic stirrer (IKA Werke GmbH & Co. KG, Staufen im Breisgau, DE) and a stir bar ensured homogeneous mixing in the retentate reservoir.

Fig. 1

Piping and instrumentation diagram of the experimental setup. A VP UV/Vis spectrometer, a microLDS and a Raman probe are incorporated into the flow of the Tangential Flow Filtration (TFF). Additionally, a three-way valve is incorporated to change between UF and DF phase. All sensors are connected to a computer for capturing the data centrally. Electronic communication lines are indicated by dashed lines. The letters indicate: C control, D density, I indicate, P pressure, R record, U multivariable, V viscosity, W weight

Lysozyme

The protocol for the UF/DF process for Lysozyme (Hampton Research, Aliso Viejo, USA) from our previous publication [21] was slightly adjusted by changing the DF buffer to 50mM phosphate buffer (VWR Chemicals, Leuven, B) at pH 7.1. In short, the process consisted of an UF phase concentrating the protein from 10gL− 1 to 20gL− 1, a DF phase, where a buffer exchange from citrate buffer at pH 6.0 to a phosphate buffer at pH 7.1 occurred, and a second DF phase to achieve a final concentration of 40gL− 1.

mAb

The mAb UF/DF process was adjusted from our previous publication [21]. In the first UF phase, the filtered mAb stock solution at a concentration of 2.79gL− 1 was concentrated to 25gL− 1. A Pellicon 3 Cassette with an Ultracel membrane (type C screen with 3kDa cutoff, 88cm2 membrane area) in a Pellicon Mini Cassette Holder was used (both Merck) in the UF/DF setup. The process was run at a Transmembrane Pressure (TMP) of 1.5bar and a feed flow of 45mLmin− 1. In the DF phase, the solution was diafiltrated with eight Diafiltration Volumes (DVs) of DF buffer (250mM glycine, 25mM histidine at pH 5.8). In the second UF phase, the solution was concentrated to approximately 100gL− 1. The mAb was provided by an industrial partner who may not be disclosed due to the established confidentiality agreement.

bsAb

For the Antibody (bsAb), the membrane, TMP and feed flowrate settings from the mAb process were used. The bsAb stock solution (concentration 11.49gL− 1) was adjusted with a 2M Tris(hydroxymethyl)amino methane (TRIS) buffer to pH 7.1 and filtered before use. In a first UF step, the concentration was raised to 25gL− 1. Next, the solution was diafiltrated with eight DVs of DF buffer (2.2mM sodium phosphate, 1.3mM TRIS). A second UF step concentrated the product to approximately 80gL− 1. The bsAb was provided by an industrial partner who may not be disclosed due to the established confidentiality agreement.

Data acquisition and analysis

During experiments, all integrated sensors and devices communicated with and were controlled (except for the Raman analyzer) by a custom-made application developed in MATLAB (version R2020a, The Mathworks, Natick, USA) and adapted from Rüdt et al. [20] and Rolinger et al. [12]. Besides connecting the devices and starting and stopping measurements, the application gathered the signals from the integrated sensors and calculated quality attributes and process parameters. Communication and control were performed through software libraries provided by the different instrument manufacturers. In contrast to the previous publications, no Graphical User Interface (GUI) was used to display the signals to save computational power. Data acquisition and analysis of the density and viscosity measurements, Raman measurements, and UV measurements were performed as described below.

UV absorbance measurements and processing

UV slope spectra were recorded from 280nm to 300nm for lysozyme, mAb, and bsAb with a resolution of 5nm. For concentration calculations, the absorbance at 280nm was used without scatter correction. The settings resulted in a measurement speed of 0.9min per spectrum. To improve the measurement speed, measuring at a wavelength of 280nm would be sufficient. Measuring more wavelengths can give information about the formation of aggregates in the solution, as large aggregate scatter increases the background scatter signal in the UV range.

Temperature and protein concentration correction of density measurements

In general, the density ρ of solutions is affected by the buffer components, protein concentration, and temperature. For the obtained data, this was important as the used microLDS dissipates a noticeable amount of heat into the measured liquid. To obtain comparable results, the measured viscosity and density were corrected to a standard process temperature yielding \(\eta _}}\) and \(\rho _}}\), respectively. As the temperature differences were relatively small (ΔT ≤ 5K), it was assumed that the deviations from the ideal solution behavior were neglectable [22,23,24]. The temperature correction was thus performed by cross-multiplication for viscosity and density measurements.

$$ \rho_} = \frac, T_}},T}}\rho $$

(1)

This approach is similar to the temperature correction of the sedimentation coefficient performed in analytical ultracentrifugation [25, 26]. Reference values for the density/viscosity of water were obtained from the National Institute of Standards and Technology (NIST) chemistry webbook [27].

To calculate the buffer density \(\rho _}\), the influence of the protein concentration on the density was subtracted from the temperature corrected density \(\rho _}\).

$$ \rho_} = \rho_}- a_ \cdot c_ $$

(2)

where cprot is the protein concentration and aprot is a buffer-dependent factor, also referred to as partial specific volume of the protein. To obtain aprot serial dilutions of the protein in buffer solutions were performed and aprot was estimated as the slope of an ordinary linear regression of \(\rho _} = \rho _} + a_ \cdot c_\) since a linear relationship is expected [28]. As the applied buffer conditions in this paper are fairly narrow in terms of pH range and ionic buffer strength, only small changes in aprot are expected during the DF phase [29]. We therefore used aprot for the DF buffer as an approximation for the whole process phase.

Raman measurements

The laser power during acquisition was set to 495mW with an exposure time of 800ms and 10 acquisitions per spectrum for lysozyme and the bsAb. Due to the lower concentration of the mAb, an initial exposure time of 1200ms was chosen. As the mAb showed a significant level of background scattering, which increased with increasing mAb concentration, the exposure time was step-wise lowered, every time the maximum intensity reached the saturation limit of the detector. X-axis, Y-axis, and laser calibration were done before the experiment according to the manual.

For Partial-least Squares (PLS) modeling, Solo 8.9 (Eigenvector Research, Inc., Wenatchee, USA) was used. First, different spectral preprocessing steps were evaluated to improve the model prediction and linearity based on the recorded dilution series. However, the raw spectra provided the best model accuracy during cross-validation and initial optimization. Consequently, no spectral preprocessing was done and no wavelength selection was done. Only mean centering was applied as it is a standard treatment for spectral data. More information on the PLS models is provided in the Electronic Supplementary Material. For visualization purposes, the automatic asymmetric Whittaker Filter was used along with the Savitzky-Golay filter (15 points, second-order, no derivative) to remove the background/baseline signal and to smooth the data.

Extended Kalman filter implementation

An EKF was used to smooth the data during DF. The EKF concept was selected, because it is the classical concept for extending the Kalman filter concept to non-linear state transitions and observer models, where the direct derivation of the Hessian and Jacobian matrix is possible [30, 31]. However, other alternatives like Particle filters, the Unscented Kalman Filter, or an EKF based on a second-order Taylor expansion [32] would have been also a valid choice for smoothing the data during the DF phase. The basic idea behind the EKF is to combine measurements with a non-linear process model to estimate the current true state of the process. This approach also makes predictions into the future possible by leveraging the predictive abilities of the non-linear process model. Predictions may be used to timely terminate reactions, anticipate unwanted behavior or control the process in other ways.

For DF processes, the process may be approximated by the buffer exchange in a Continuously Stirred Tank Reactor (CSTR) under the assumption that the retentate flow is much bigger than the permeate flow and the process volume remains constant. We thus describe the buffer exchange in our CFF setup by following differential equation:

$$ \beginrcl@} \frac=c_ \frac- c \frac, \end $$

(3)

where c and cin are the concentration of the considered species in the retentate tank resp. the DF buffer, F is the constant permeate flowrate, V is the constant volume of the retentate tank and κ is an empirical sieving coefficient. For free membrane passing ions, κ is close to 1 [33]. If a Donnan effect occurs, the sieving coefficient κ can increase or decrease depending on the kind of interaction between the ions of the excipient, protein and membrane [33]. For the differential equation integration and for the EKF transfer function, we assume that κ is constant over time. Since κ is recursively estimated by the EKF, the estimate may change over the course of the run. By integration from tk− 1 to tk, we obtain:

$$ \beginrcl@} \frac} - c_= \left( \frac} - c_\right) \exp t\right)} \end $$

(4)

with ck− 1 and ck being the concentration at tk− 1 and tk, respectively, and Δt being the step in time. Consequently, a buffer signal during DF follows an exponential decay towards a new steady-state concentration. It is worth noting that Eq. 4 can directly be used for the EKF as long as a measurement calibration is available. This allows to directly estimate the empirical sieving coefficient κ by the EKF. For the current application, the goal was to implement an EKF which does not require prior calibration. To this end, we now replace the concentrations c with the more general concept of a signal linearly correlated to the concentration. The signal may either be a Raman band intensity, a density measurement, or indeed also a buffer component concentration. The signal may either be increasing or decreasing depending on the nature of the measurement. Transforming Eq. 4 and lumping the signal terms \(\frac } - x(t)= x(t)\) results in:

$$ x(t_)= x(t_) \exp t\right)}. $$

(5)

Starting from Eq. 5, the EKF is now implemented as described in [30]. Equation 6 is used to predict the state vector \(\boldsymbol }_\) at the time point k based on the measurements up to the time point k − 1. The first entry in the state vector \(\boldsymbol }_\) is the estimated delta buffer signal \(\hat _=E( x)\). \(\hat _\) is the estimated buffer exchange rate \(E\left (-\frac t\right )\). As discussed above, the model assumes that the buffer exchange rate \(\hat _\) is constant over time. \(\hat _\) is the estimated offset, i.e., the terminal signal height \(E\left (\frac }\right )\). The offset of the measurement signal \(\hat _\) and the buffer signal \(\hat _\) is then used to predict the observation \(\hat _\) with Eq. 7.

$$ \beginrcl@} &\text & \boldsymbol}_= \left[\begin \hat_ \cdot e^_} \\ \hat_ \\ \hat_ \end\right] \end $$

(6)

$$ \beginrcl@} &\text & \hat_= ~\hat_ + \hat_ \end $$

(7)

Equation 8 is used to predict the covariance matrix Pk|k− 1 from the previous covariance matrix Pk− 1|k− 1 and the Jacobian matrix Fk to linearize the state function on the local point by a first-order Taylor series expansion. The process covariance matrix Qk is added to account for the model uncertainty. σv is the covariance coefficient of the process error.

$$ \text \boldsymbol_= \boldsymbol_ \boldsymbol_ \boldsymbol_^ + \boldsymbol_ $$

(8)

$$ \beginrcl@} \text ~ \boldsymbol_ = \left[\begin e^_ } & -e^_} \cdot \hat_ & 0 \\ 0 & 1 & 0\\ 0 & 0 & 1 \end\right] \end $$

$$ \beginrcl@} ~ \text~ \boldsymbol_ = \left[\begin ^} & 0 & 0 \\ 0 & 0 & 0\\ 0 & 0 & 0 \end\right] \end $$

The innovation covariance matrix Sk is calculated via Eq. 9 based on the Jacobian of the sensor transfer functions [Hk], the covariance matrix Pk|k− 1 and the sensor covariance matrix [Rk]. σw is the covariance coefficient of the sensor error.

$$ \text \boldsymbol_= \boldsymbol_ \boldsymbol_ \boldsymbol_^ + \boldsymbol_ $$

(9)

$$ \beginrcl@} \text ~ \boldsymbol_ = \begin 1 \\ 0 \\ 1 \end \text ~ \boldsymbol} = \begin ^} & 0 & 0 \\ 0 & 0 & 0\\ 0 & 0 & 0 \end \end $$

Now, the Kalman gain Kk can be calculated via Eq. 10 from the covariance matrix Pk|k− 1 and the sensor transfer functions Hk, scaled by the innovation covariance matrix Sk.

$$ \text \boldsymbol_= \boldsymbol_ \boldsymbol_^ \boldsymbol_^ $$

(10)

With the calculated Kalman gain Kk, the prediction of the state estimate \(\boldsymbol }_\) and the covariance matrix Pk|k can be updated via Eqs. 11 and 12, respectively.

$$ \beginrcl@} \text \quad \boldsymbol}_&=& \boldsymbol}_ + \boldsymbol_ (z_ - \hat_) \end $$

(11)

$$ \beginrcl@} \text \quad \boldsymbol_&=& (I-\boldsymbol_ \boldsymbol_) \boldsymbol_ \end $$

(12)

In principle, the peak height of the buffer component in question in the Raman spectrum may be used as an input signal for the EKF. To improve the prediction and reduce noise levels, Raman spectra were factorized by a Principal Component Analysis (PCA) and the principal component score of the buffer component was used as input for the EKF.

Off-line analytics by SE-HPLC

The off-line Size Exclusion High Performance Liquid Chromatography (SE-HPLC) analytic was done according to our previous publication [21], with the difference that already mAb and bsAb samples with concentrations higher than 30gL− 1 were diluted 10-fold. bsAb samples were analyzed according to the protocol for the mAb.