Theoretical analysis of excipient concentrations during the final ultrafiltration/diafiltration step of therapeutic antibody

Diafiltration of a protein solution into a new buffer is a common final step in biopharmaceutical manufacturing. However, the excipient concentrations in the retentate are not always equal to their corresponding concentrations in the new buffer (diafiltration buffer). This phenomenon was observed repeatedly during diafiltration of different therapeutic monoclonal antibodies in which the concentrations of histidine and either sorbitol or sucrose (depending on which was chosen for the diafiltration buffer) in the retentate were lower than in the diafiltration buffer. Experimental studies and theoretical analyses of the ultrafiltration/diafiltration (UF/DF) step were carried out to determine the primary causes of the phenomenon and to develop a mathematical model capable of predicting retentate excipient concentrations. The analyses showed that retentate histidine concentration was low primarily because of repulsive charge interactions between positively‐charged histidine molecules and positively‐charged protein molecules, and that volume exclusion effects were secondary for like‐charged molecules. The positively‐charged protein molecules generate an electrical potential that cause an uneven distribution of charged histidine molecules. This interaction was used to construct a mathematical model based on the Poisson‐Boltzmann equation. The model successfully predicted the final histidine concentration in the diafiltered product (retentate) from the UF/DF development and production runs, with good agreement across a wide range of protein and histidine concentrations for four therapeutic monoclonal antibodies. The concentrations of uncharged excipients (sorbitol or sucrose) were also successfully predicted using previously established models, with volume exclusion identified as the primary cause of differences in uncharged excipient concentrations in the retentate and diafiltration buffer. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

Predicting diafiltration solution compositions for final ultrafiltration/diafiltration steps of monoclonal antibodies

Many liquid formulations for monoclonal antibodies (MAbs) require the final ultrafiltration/diafiltration step to operate at high protein concentrations, often at or above 100 g/L. When operating under these conditions, the excipient concentrations and pH of the final diafiltered retentate are frequently not equal to the corresponding excipient concentrations and pH of the diafiltration buffer. A model based on the Poisson-Boltzmann equation combined with volume exclusion was extended to predict both pH and excipient concentrations in the retentate for a given diafiltration buffer. This model was successfully applied to identify the diafiltration buffer composition required to achieve the desired pre-formulated bulk drug substance (retentate) conditions. Predictions were in good agreement with the experimental results, and reduced the number of experimental iterations needed to define the diafiltration buffer composition. Additionally, the predictive model was applied in a sensitivity analysis across ranges of protein charge, protein concentration, and diafiltration buffer pH and excipient concentration. This sensitivity analysis can facilitate the design of experiments for robustness testing, and allow for generalized predictions across classes of molecules such as MAbs.     

Strategies for high-concentration drug substance manufacturing to facilitate subcutaneous administration: A review

To achieve the high protein concentrations required for subcutaneous administration of biologic therapeutics, numerous manufacturing process challenges are often encountered. From an operational perspective, high protein concentrations result in highly viscous solutions, which can cause pressure increases during ultrafiltration. This can also lead to low flux during ultrafiltration and sterile filtration, resulting in long processing times. In addition, there is a greater risk of product loss from the hold-up volumes during filtration operations. From a formulation perspective, higher protein concentrations present the risk of higher aggregation rates as the closer proximity of the constituent species results in stronger attractive intermolecular interactions and higher frequency of self-association events. There are also challenges in achieving pH and excipient concentration targets in the ultrafiltration/diafiltration (UF/DF) step due to volume exclusion and Donnan equilibrium effects, which are exacerbated at higher protein concentrations. This paper highlights strategies to address these challenges, including the use of viscosity-lowering excipients, appropriate selection of UF/DF cassettes with modified membranes and/or improved flow channel design, and increased understanding of pH and excipient behavior during UF/DF. Additional considerations for high-concentration drug substance manufacturing, such as appearance attributes, stability, and freezing and handling are also discussed. These strategies can be employed to overcome the manufacturing process challenges and streamline process development efforts for high-concentration drug substance manufacturing.     

A mechanistic model to account for the Donnan and volume exclusion effects in ultrafiltration/diafiltration process of protein formulations

Ultrafiltration/diafiltration (UF/DF) is a typical step in protein drug manufacturing process to concentrate and exchange the protein solution into a desired formulation. However, significant offset of pH and composition from the target formulation have been frequently observed after UF/DF, posing challenges to the stability, performance, and consistency of the final drug product. Such shift can often be attributed to the Donnan and volume exclusion effects. In order to predict and compensate for those effects, a mechanistic model is developed based on the protein charge, mass and charge balances, as well as the equilibrium condition across the membrane. The integrated UF/DF model can be used to predict both the dynamic behavior and the final outcome of the process. Examples of the modeling results for the pH and composition variation during the UF/DF operations are presented for two monoclonal antibody proteins. The model predictions are in good agreement with a comprehensive experimental data set that covers different process steps, protein concentrations, solution matrices, and process scales. The results show that significant pH and excipient concentration shifts are more likely to occur for high protein concentration and low ionic strength matrices. As a special example, a self-buffering protein formulation shows unique pH behavior during DF, which could also be captured with the dynamic model. The capability of the model in predicting the performance of UF/DF process as a function of protein characteristics and formulation conditions makes it a useful tool to improve process understanding and facilitate process development.     

pH and excipient profiles during formulation of highly concentrated biotherapeutics using bufferless media

Several models have been developed to describe the shifts in pH and excipient concentrations seen during diafiltration of monoclonal antibody (mAb) products accounting for both Donnan equilibrium and electroneutrality constraints. However, these models have assumed that the mAb charge is either constant or only a function of pH, assumptions that will not be valid when formulating highly concentrated mAbs using bufferless or low-buffered media due to the change in local H⁺ concentration at the protein surface. The objective of this study was to incorporate the effects of both pH and ionic strength on the mAb charge, through the use of a charge regulation model based on the amino acid sequence of the mAb, into an appropriate mass balance model to describe the pH and excipient profiles during diafiltration. The model involves no adjustable parameters, with the protein charge evaluated directly from the protonation/deprotonation of the ionizable amino acids accounting for the electrostatic interactions between the charged mAb and the H⁺ ions. Model predictions are in excellent agreement with experimental data for the pH and ion concentrations during diafiltration of a mAb and fusion protein with different isoelectric points and different formulation conditions. Model simulations are then used to obtain fundamental insights into the factors controlling the diafiltration behavior as well as guidelines for development of diafiltration processes to achieve target bufferless formulation conditions.     

Use of ultrafiltration/diafiltration for the processing of antisense oligonucleotides

Ultrafiltration/diafiltration (UF/DF) has been the hallmark for concentrating and buffer exchange of protein and peptide-based therapeutics for years. Here we examine the capabilities and limitations of UF/DF membranes to process oligonucleotides using antisense oligonucleotides (ASOs) as a model. Using a 3 kDa UF/DF membrane, oligonucleotides as small as 6 kDa are shown to have low sieving coefficients (<0.008) and thus can be concentrated to high concentrations (≤200 mg/mL) with high yield (≥95%) and low viscosity (<15 centipoise), provided the oligonucleotide is designed not to undergo self-hybridization. In general, the oligonucleotide should be at least twice the reported membrane molecular weight cutoff for robust retention. Regarding diafiltration, results show that a small amount of salt is necessary to maintain adequate flux at concentrations exceeding about 40 mg/mL. Removal of salts along with residual solvents and small molecule process-related impurities can be robust provided they are not positively charged as the interaction with the oligonucleotide can prevent passage through the membrane, even for common divalent cations such as calcium or magnesium. Overall, UF/DF is a valuable tool to utilize in oligonucleotide processing, especially as a final drug substance formulation step that enables a liquid active pharmaceutical ingredient.     

Efficiency of ultrafiltration/diafiltration in removing organic and elemental process equipment related leachables from biological therapeutics

In the production of biological therapeutics such as monoclonal antibodies (mAbs), ultrafiltration and diafiltration (UF/DF) are widely regarded as effective downstream processing steps capable of removing process equipment related leachables (PERLs) introduced upstream of the UF/DF step. However, clearance data available in the literature are limited to species with low partition coefficients (log P) such as buffer ions, hydrophilic organic compounds, and some metal ions. Additional data for a wide range of PERLs including hydrophobic compounds and elemental impurities are needed to establish meaningful, comprehensive safety risk assessments. Herein, we report the results from studies investigating the clearance of seven different organic PERLs representing a wide range of characteristics (i.e., log P (−0.3 to 18)), and four model elements with different chemical properties spiked into a mAb formulation at 10 ppm and analyzed during clearance using gas chromatography–mass spectrometry (GC–MS), liquid chromatography-photodiode-array-mass spectrometry (LC-PDA-MS), and inductively coupled plasma mass spectrometry (ICP-MS). The clearance data showed ideal clearance and sieving of spiked organic PERLs with log P < 4, partial clearance of PERLs with 4 < log P < 9, and poor clearance of highly hydrophobic PERLs (log P > 9) after nine diafiltration volumes (DVs). Supplemental clearance studies on seven additional PERLs present at much lower concentration levels (0.1–1.5 ppm) in the mAb formulation upstream of UF/DF and three PERLs associated with the tangential flow filtration (TFF) equipment also demonstrated the similar correlations between log P and % clearance. For model elements, the findings suggest that UF/DF in general provides ideal clearance for elements. Evidence showed that the UF/DF process does not only help mitigate leachables risk from PERLs introduced upstream of UF/DF, but also from the TFF operation itself as all three TFF-related PERLs were effectively cleared. Overall, the UF/DF clearance presented in this work demonstrated whereas highly hydrophobic PERLs and elements that exist as charged species, particularly transition metal ions, may not be as effectively cleared and thus warrant further risk assessment; hydrophilic and some hydrophobic PERLs (log P < 4) are indeed well-cleared and thus present a lower overall safety risk.     

Streamlining process characterization efforts using the high throughput ambr® crossflow system for ultrafiltration and diafiltration processing of monoclonal antibodies

Commercial process development for biopharmaceuticals often involves process characterization (PC) studies to gain process knowledge and understanding in preparation for process validation. One common approach to conduct PC activities is by using design-of-experiment, which can help determine the impact process parameter deviations may have on product quality attributes. Qualified scale-down systems are typically used to conduct these studies. For an ultrafiltration/diafiltration (UF/DF) application, however, a traditional scale-down still requires hundreds of milliliters of material per run and can only conduct one experiment at a time. This poses a challenge in resources as there could be 20+ experiments required for a typical UF/DF PC study. One solution to circumvent this is the use of high-throughput systems, which enable parallel experimentation by only using a fraction of the resources. Sartorius Stedim Biotech has recently commercialized the ambr® crossflow high-throughput system to meet this need. In this study, the performance of this system during a monoclonal antibody UF/DF step was first compared with a pilot- and a manufacturing-scale tangential flow filtration (TFF) system at a single operating condition. Due to material limitations, it was then compared to only the pilot-scale TFF system across wider ranges of transmembrane pressure; crossflow rate; and diafiltration concentration in a PC study. Permeate flux, aggregate content, process yield, pH/conductivity traces, retentate concentration, axial pressure drop, and turbidity values were measured at both scales. A good agreement was attained across scales, further supporting its potential use as a scale-down system.     

Introduction and clearance of beta-glucan in the downstream processing of monoclonal antibodies

β-Glucan process-related impurities can be introduced into biopharmaceutical products via upstream or downstream processing or via excipients. This study obtained a comprehensive process-mapping dataset for five monoclonal antibodies to assess β-glucan introduction and clearance during development and production runs at various scales. Overall, 198 data points were available for analysis. The greatest β-glucan concentrations were found in the depth-filtration filtrate (37–2,745 pg/ml). Load volume correlated with β-glucan concentration in the filtrate, whereas flush volume was of secondary importance. Cation-exchange chromatography significantly cleared β-glucans. Furthermore, β-glucan leaching from the Planova 20N virus removal filter was reduced by increasing the flush volume (1 vs. 10 L/m²). β-glucan concentrations after filter flush with 10 L/m² were consistently <10 pg/ml. No or only limited β-glucan clearance was attained via ultrafiltration/diafiltration (UF/DF). However, during the first run with monoclonal antibody (mAb) 4, β-glucan concentration in the UF/DF retentate was 10.8 pg/mg, potentially due to β-glucan leaching from the first run with a regenerated cellulose membrane. Overall, β-glucan levels in the final mAb drug substance were 1–12 pg/mg. Assuming high doses of 1,000–5,000 mg, a β-glucan contamination at 20 pg/mg would translate to 20–100 ng/dose, which is below the previously suggested threshold for product safety (≤500 ng/dose).     

Effect of protein and solution properties on the Donnan effect during the ultrafiltration of proteins

Formulation of protein biopharmaceuticals as highly concentrated liquids can improve the drug substance storage and supply chain, improve the target product profile, and allow greater flexibility in dosing methods. The Donnan effect can cause a large offset in pH from the target value established with the diafiltration buffer during the concentration and diafiltration of charged proteins with ultrafiltration membranes. For neutral formulations, the pH will typically increase above the diafiltration buffer pH for basic monoclonal antibodies and decline below the diafiltration buffer pH for acidic Fc-fusion proteins. In this study, new equations for the Donnan effect during the diafiltration and concentration of proteins in solutions containing monovalent and divalent ions were derived. The new Donnan models obey mass conservation laws, account for the buffering capacity of proteins, and account for protein-ion binding. Data for the pH offsets of an Fc-fusion protein and a monoclonal antibody were predicted in both monovalent and divalent buffers using these equations. To compensate for the pH offset caused by the Donnan effect, diafiltration buffers with pH and excipient values offset from the ultrafiltrate pool specifications can be used. The Donnan offset observed during the concentration of an acidic Fc-fusion protein was mitigated by operating at low temperature. It is important to account for the Donnan effect during preformulation studies. The excipients levels in an ultrafiltration pool may differ from the levels in a protein solution obtained by adding buffers into concentrated protein solutions due to the Donnan effect.     

Clearance of solvents and small molecule impurities in antibody drug conjugates via ultrafiltration and diafiltration operation

Ultrafiltration and diafiltration (UF/DF) processes by tangential flow filtration (TFF) are frequently used for removal of solvents and small molecule impurities and for buffer exchange for biopharmaceutical products. Antibody-drug conjugates (ADCs) as an important class of biological therapeutics, carry unique solvents and small molecule impurities into the final UF/DF step as compared to standard antibody preparation. The production process of ADCs involves multiple chemical steps, for example, reduction and conjugation. The clearance of these solvents and small molecules by UF/DF, specifically the DF step, has been assessed and described herein. The rates of clearance for all the impurities in this study are close to the ideal clearance with no apparent interaction with either the protein or the TFF membrane and system. The effect of process variables during DF, such as pH, temperature, membrane loading, transmembrane pressure, and cross flow rate, has also been evaluated and found to have minimal impact on the clearance rate. These results demonstrate efficient clearance of solvents and small molecule impurities related to the ADC process by the DF process and provide a general data package to facilitate risk assessments based on the sieving factors and program specific needs.     

Continuous ultrafiltration/diafiltration using a 3D-printed two membrane single pass module

A 3D printed ultrafiltration/diafiltration (UF/DF) module is presented allowing the continuous, simultaneous concentration of retained (bio-)molecules and reduction or exchange of the salt buffer. Differing from the single-pass UF concepts known from the literature, DF operation does not require the application of several steps or units with intermediating dilution. In contrast, the developed module uses two membranes confining the section in which the molecules are concentrated while the sample is passing. Simultaneously to this concentration process, the two membranes allow a perpendicular in and outflow of DF buffer reducing the salt content in this section. The module showed the continuous concentration of a dissolved protein up to a factor of 4.6 while reducing the salt concentration down to 47% of the initial concentration along a flow path length of only 5 cm. Due to single-pass operation the module shows concentration polarization effects reducing the effective permeability of the applied membrane in case of higher concentration factors. However, because of its simple design and the capability to simultaneously run UF and DF processes in a single module, the development could be economically beneficial for small scale UF/DF applications.     

Mass Balance Model with Donnan Equilibrium Accurately Describes Unusual pH and Excipient Profiles during Diafiltration of Monoclonal Antibodies

There is extensive experimental data showing that the final pH and buffer composition after protein diafiltration (DF), particularly with monoclonal antibodies, can be considerably different than that in the DF buffer due to electrostatic interactions between the charged protein and the charged ions. Previous models for this behavior have focused on the final (equilibrium) partitioning and are unable to explain the complex pH and concentration profiles during the DF process. The objective of this study is to develop a new model for antibody DF based on solution of the transient mass balance equations, with the permeate concentrations of the charged species evaluated assuming Donnan equilibrium across the semipermeable membrane in combination with electroneutrality constraints. Model predictions are in excellent agreement with experimental data obtained during DF of both acidic and basic monoclonal antibodies, with the protein charge determined from independent electrophoretic mobility measurements. The model is able to predict the entire pH/histidine concentration profiles during DF, providing a framework for the development of DF processes that yield the desired antibody formulation.     

Multi‐criteria manufacturability indices for ranking high‐concentration monoclonal antibody formulations

The need for high‐concentration formulations for subcutaneous delivery of therapeutic monoclonal antibodies (mAbs) can present manufacturability challenges for the final ultrafiltration/diafiltration (UF/DF) step. Viscosity levels and the propensity to aggregate are key considerations for high‐concentration formulations. This work presents novel frameworks for deriving a set of manufacturability indices related to viscosity and thermostability to rank high‐concentration mAb formulation conditions in terms of their ease of manufacture. This is illustrated by analyzing published high‐throughput biophysical screening data that explores the influence of different formulation conditions (pH, ions, and excipients) on the solution viscosity and product thermostability. A decision tree classification method, CART (Classification and Regression Tree) is used to identify the critical formulation conditions that influence the viscosity and thermostability. In this work, three different multi‐criteria data analysis frameworks were investigated to derive manufacturability indices from analysis of the stress maps and the process conditions experienced in the final UF/DF step. Polynomial regression techniques were used to transform the experimental data into a set of stress maps that show viscosity and thermostability as functions of the formulation conditions. A mathematical filtrate flux model was used to capture the time profiles of protein concentration and flux decay behavior during UF/DF. Multi‐criteria decision‐making analysis was used to identify the optimal formulation conditions that minimize the potential for both viscosity and aggregation issues during UF/DF. Biotechnol. Bioeng. 2017;114: 2043–2056. © 2017 The Authors. Biotechnology and Bioengineering Published by Wiley Perodicals, Inc.     

pH variations during diafiltration due to buffer nonidealities

Diafiltration is used for final formulation of essentially all biotherapeutics. Several studies have demonstrated that buffer/excipient concentrations in the final diafiltered product can be different than that in the diafiltration buffer due to interactions between buffer species and the protein product. However, recent work in our lab has shown variations in solution pH that are largely independent of the protein concentration during the first few diavolumes. Our hypothesis is that these pH variations are due to nonidealities in the acid‐base equilibrium coefficient. A model was developed for the diafiltration process accounting for the ionic strength dependence of the pK_a. Experimental results obtained using phosphate and histidine buffers were in excellent agreement with model predictions. A decrease in ionic strength leads to an increase in the pK_a for the phosphate buffer, causing a shift in the solution pH, even under conditions where the initial feed and the diafiltration buffer are at the same pH. This effect could be eliminated by matching the ionic strength of the feed and diafiltration buffer. The experimental data and model provide new insights into the factors controlling the pH profile during diafiltration processes. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 33:1555–1560, 2017     

Assessing the impact of sanitization methods for regenerated cellulose ultrafiltration/diafiltration membrane on membrane integrity and protein quality

Ultrafiltration/diafiltration (UF/DF) is typically the final step in downstream processing of recombinant monoclonal antibody (mAb) products, which serves for protein concentration and buffer exchange. For UF/DF membranes composed of regenerated cellulose (RC), sanitization with 0.1 M sodium hydroxide is generally recommended by the supplier, but it may not be sufficient for reducing bioburden during large scale manufacturing. Therefore, more stringent sanitization methods for RC membranes are required. However, chemicals used in such sanitization step may disrupt membrane integrity, while the corresponding residuals may reduce product quality. Previous work has shown that high concentration of sodium hydroxide or addition of peracetic acid (PAA) can effectively reduce bioburden, but their effects on the RC membranes remain unknown. In this work, we assessed the impact of two sanitization methods, 0.5 M sodium hydroxide and 30 mM PAA in combination with 0.5 M sodium hydroxide, on membrane integrity and protein quality of Millipore and pall corporation (PALL) membranes. Both methods showed a similar impact as the control after performing 15 cycles. However, the addition of PAA may cause residual chemical concerns, therefore, 0.5 M sodium hydroxide was recommended as an effective and safe sanitization method for RC UF/DF membranes.     

Real-time monitoring of quality attributes by in-line Fourier transform infrared spectroscopic sensors at ultrafiltration and diafiltration of bioprocess

Technologies capable of monitoring product quality attributes and process parameters in real time are becoming popular due to the endorsement of regulatory agencies and also to support the agile development of biotherapeutic pipelines. The utility of vibrational spectroscopic techniques such as Fourier transform mid-infrared (Mid-IR) and multivariate data analysis (MVDA) models allows the prediction of multiple critical attributes simultaneously in real time. This study reports the use of Mid-IR and MVDA model sensors for monitoring of multiple attributes (excipients and protein concentrations) in real time (measurement frequency of every 40 s) at ultrafiltration and diafiltration (UF/DF) unit operation of biologics manufacturing. The platform features integration of fiber optic Mid-IR probe sensors to UF/DF set up at the bulk solution and through a flow cell at the retentate line followed by automated Mid-IR data piping into a process monitoring software platform with pre-loaded partial least square regression (PLS) chemometric models. Data visualization infrastructure is also built-in to the platform so that upon automated PLS prediction of excipients and protein concentrations, the results were projected in a graphical or numerical format in real time. The Mid-IR predicted concentrations of excipients and protein show excellent correlation with the offline measurements by traditional analytical methods. Absolute percent difference values between Mid-IR predicted results and offline reference assay results were ≤5% across all the excipients and the protein of interest; which shows a great promise as a reliable process analytical technology tool.     

Countercurrent staged diafiltration for formulation of high value proteins

A number of groups have studied the application of continuous bioreactors and continuous chromatographic systems as part of efforts to develop an integrated continuous biomanufacturing process. The objective of this study was to examine the feasibility of using a countercurrent staged diafiltration process for continuous protein formulation with reduced buffer requirements. Experiments were performed using a polyclonal immunoglobulin (IgG) with Cadence? Inline Concentrators. Model equations were developed for the product yield, impurity removal, and buffer requirements as a function of the number of stages and the stage conversion (ratio of permeate to feed flow rate). Data from a countercurrent two‐stage system were in excellent agreement with model calculations, demonstrating the potential of using countercurrent staged diafiltration for protein formulation. Model simulations demonstrated the importance of the countercurrent staging on both the extent of buffer exchange and the amount of buffer required per kg of formulated product. The staged diafiltration process not only provides for continuous buffer exchange, it could also provide significant reductions in the number of pump passes while providing opportunities for reduced buffer requirements.     

Multistage continuous countercurrent diafiltration for formulation of monoclonal antibodies

There is growing interest in the development of fully integrated and continuous biomanufacturing processes for the production of monoclonal antibody products. A recent study has demonstrated the feasibility of using a two-stage countercurrent diafiltration (DF) process for continuous product formulation, but this system did not provide sufficient levels of buffer exchange for most applications. The objective of this study was to design and test a three-stage countercurrent DF system that could achieve at least 99.9% buffer exchange over 24 hr of continuous operation. Experimental data were obtained using concentrated solutions of human immunoglobulin G as a model protein, with the extent of vitamin B₁₂ removal used to track the extent of DF. Pall Cadence™ inline concentrators with Delta 30 kD regenerated cellulose membranes were used in the three stages to achieve high conversion in a single pass. The three-stage system showed stable operation with >99.9% vitamin B₁₂ removal and a minimal increase in pressure over the full 24 hr. Modules were effectively cleaned using sodium hydroxide, with nearly complete recovery of water permeability. A simple economic analysis was presented that accounts for the trade-offs between quantity of buffer used and membrane costs for this type of countercurrent staged DF process. The results provide important insights to the design and operation of a continuous process for antibody formulation.     

Separation of alpha-lactalbumin and beta-lactoglobulin using membrane ultrafiltration

There is considerable commercial interest in the preparation of individual whey proteins as high-value food additives, nutraceuticals, and therapeutics. This study examined the use of membrane filtration for the separation of alpha-lactalbumin and beta-lactoglobulin. Stirred cell filtration experiments were performed using both cellulosic and polyethersulfone membranes to determine the optimal pH, ionic strength, and filtration conditions. Selectivities of greater than 55 could be achieved at pH 5.5 and 50 mM ionic strength using a 30-kD cellulose membrane. A diafiltration process was then designed for the protein separation. A 16-diavolume filtration yielded beta-lactoglobulin as the retentate product with a purification factor of 100 and recovery of 90%. The alpha-lactalbumin was recovered in the filtrate with a purification factor of more than 10 and nearly 99% yield. Model calculations were in good agreement with the experimental data.