10934-WO01-SEC Electronically Filed: April 22, 2025 METHOD FOR PREDICTING OSMOLALITY OF PROTEIN SOLUTIONS FIELD OF THE INVENTION [0001] The present disclosure relates to a method for estimating the osmolality of a protein mixture generated from an ultrafiltration and/or diafiltration operation. The results can be used with other operations to reach target protein concentrations, remove undesired excipients, and/or add desired excipients. BACKGROUND OF THE INVENTION [0002] The efficacy of drugs involving therapeutic proteins such as antibodies often requires the protein concentration of the drug to exceed certain thresholds for the final drug substance, and the safety and stability of therapeutic protein-based drugs require the presence of certain excipients and removal of others. As therapeutic proteins are typically produced via cell culture methods in appropriate media that use either mammalian or bacterial host cells engineered to produce proteins of interest, the post-cell culture protein mixtures need to undergo operations that (1) increase the protein concentration such that the protein concentration of the final mixture is above the specified threshold, (2) remove undesired impurities, and (3) add desired excipients such that the final mixture contains the right excipients at their proper concentrations to achieve the specified stability and safety. Although processes for concentrating proteins, removing undesired impurities, and adding desired excipients can vary with the properties of a particular protein of interest, the processes typically include centrifugation steps, which recover protein molecules from host cells and cell debris, and filtration steps, which remove undesired impurities and add desired excipients to the final protein solution. [0003] Protein purification processes typically include an ultrafiltration-and-diafiltration (UFDF) operation, which increases the protein concentration of the resulting mixture to a specified threshold and satisfies various specifications such as pH and osmolality. If the protein concentration is increased above 10 mg/mL, electrostatic interactions between protein molecules and charged excipients and volume-exclusion effect exerted by large protein molecules can cause differences in pH and excipient concentrations between the diafiltration (DF) buffer and the protein mixture generated from a UFDF operation. See Ladwig et al., 2020, Biotechnology Progress 36:e2993. As a result of the aforementioned differences, for a new therapeutic protein, a trial-and-error process is often used to find a DF-buffer formulation and UFDF operating conditions that produce a protein mixture satisfying all the specifications. The trial-and-error process typically starts with a DF-buffer formulation and UFDF operating conditions that have been used by other therapeutic proteins as an initial guess. If any specifications for the resulting protein mixture are not satisfied when the UFDF operation is performed under the initial guess, another UFDF operation will be performed under a new set of
operating conditions and/or a new DF-buffer formulation with a new pH and/or excipient concentrations. Since multiple factors can be varied to potentially influence whether the final protein mixture meets all the specifications, a design-of-experiment (DoE) study is often carried out, for which the influence of each factor is examined by changing one factor at a time while keeping the other factors at nominal values. Such DoE studies typically involve 10 to 20 different UFDF operations, and the resulting protein mixtures are evaluated in terms of pH, excipient concentrations, and osmolality. In short, repeated experimentation is done to find a right combination of operating conditions and DF-buffer formulation that help meet all the specifications for the final protein mixture. Since each UFDF operation can take at least one day to be completed, and the analyses of the resulting protein mixture can take days to weeks, with a typical timeline for repeated experimentation of at least several weeks. [0004] To reduce the amount of repeated experimentation to find a right combination of operating conditions and DF-buffer formulation, several UFDF models that account for physical and chemical phenomena important to UFDF operations have been developed to predict the outcome of a UFDF operation given its operating conditions and DF-buffer formulation. One UFDF model, MUD 2.0, includes microscopic description of electrostatic interactions between charged excipients and protein molecules using the Poisson-Boltzmann equation as well as macroscopic descriptions of volume exclusion and mass transfer. Through the inclusion of equations that describe physical and chemical phenomena important to UFDF operations, this UFDF model has been successfully used to predict the properties, e.g., pH and excipient concentrations, of the protein mixtures produced by UFDF operations for various therapeutic proteins. See Ladwig et al., 2020, Biotechnology Progress 36:e2993. However, the model described in Ladwig et al. predicts the osmolality of the protein mixture produced by a UFDF operation by simply adding the concentrations of all excipients, and the predicted osmolality often deviates from the corresponding experimental measurement. [0005] What is needed is an improved method to estimate the osmolality of the protein mixture produced by a UFDF operation, enabling more accurate osmolality-based determination of DF-buffer formulation and/or UFDF operating conditions. SUMMARY OF THE INVENTION [0006] The present disclosure provides a method for finding a suitable buffer formulation and/or UFDF (ultrafiltration and diafiltration) operating conditions for a protein of interest, the method comprising (1) obtaining a protein mixture comprising the protein of interest and one or more excipients from a cell culture that has been subjected to a purification process; (2) using a mathematical model, such as MUD 2.0, accounting for electrostatic interactions between charged excipients and charged protein molecules and accounting for volume exclusion of large protein molecules compared to excipient molecules, to estimate excipient concentrations in the resulting
protein mixture after the mixture from step (1) has undergone a UFDF operation given (a) the protein concentration during the DF step, (b) the DF buffer formulation, (c) the number of diavolumes, (d) the protein concentration at the end of the overconcentration (OC) step, (e) the flush buffer formulation, (f) the protein concentration for the final protein mixture, and (g) the operating temperature during the entire UFDF operation; (3) predicting the osmolality of the protein mixture that has undergone a UFDF operation by estimating its osmotic pressure based on the activity of water and Norrish constants for each excipient present in the protein mixture; (4) comparing the predicted osmolality to its specification; (5) adjusting the DF buffer and/or flush buffer formulation and/or UFDF operating conditions if necessary; and (6) repeating steps (2), (3), (4), and (5) using the adjusted DF buffer or flush-buffer formulation and/or UFDF operating conditions as necessary until a final UFDF operation meets all specifications for the protein mixture. [0007] In certain embodiments, the UFDF operation is carried out using a DF buffer formulation or flush buffer formulation that comprises essentially no buffering excipient. [0008] In certain embodiments, the UFDF operation is carried out using a DF buffer formulation or flush buffer formulation that comprises a buffering excipient, optionally at a concentration of from about 2 mM to about 300 mM. In certain aspects of these embodiments, the buffering excipient is selected from the group consisting of acetate, aspartate, ascorbate, borate, benzoate, carbonate, citrate, glycine, HEPES, MOPS, MES, N-(2-acetamido)iminodiacetic acid (ADA), histidine, lactate, phosphate, succinate, Tris, Bis-tris, and tartrate. [0009] In certain embodiments, the protein mixture obtained from the final UFDF operation comprises the protein of interest at a concentration of from about 1 mg/ml to about 200 mg/ml, from about 100 mg/ml to about 200 mg/ml, or from about 4 mg/ml to about 15 mg/ml. [0010] In one embodiment, the DF buffer or flush buffer formulation comprises a buffering excipient at a concentration of from 2 mM to about 300 mM, and the protein mixture obtained from the final UFDF operation comprises the protein at a concentration of from about 30 mg/mL to about 50 mg/mL. [0011] In certain embodiments, the UFDF operation is carried out with a DF buffer or flush buffer formulation that comprises excipients at concentrations ranging from 5 mM to 300 mM. The excipients can be selected from an amino acid, a sugar, a polyol, an anti-oxidant, a chelating agent, a lipid or a lipid derivative, a salt, a polymer, an inert protein, a surfactant, and a water-miscible co- solvent. [0012] In certain embodiments, the amino acid is one or more selected from: histidine, arginine, glycine, methionine, alanine, aspartic acid, lysine hydrochloride, proline, lysine, sarcosine, gamma- aminobutyric acid, and glutamic acid. [0013] In certain embodiments, the salt is one or more selected from: sodium chloride, sodium sulfate, sodium thiocyanate, potassium chloride, potassium phosphate, calcium lactate, and guanidine
hydrochloride. [0014] In certain embodiments, the surfactant is one or more selected from: polysorbate 20, polysorbate 40, polysorbate 60, polysorbate 80, poloxamer, PEG dodecyl ethers, and PEG tertoctylphenyl ether. [0015] In certain embodiments, the protein mixture produced by a UFDF operation comprises excipients at concentrations ranging from 5 mM to 300 mM and the protein of interest at concentrations ranging from 50 mg/ml to 200 mg/ml. In another embodiment, the protein mixture produced by a UFDF operation comprises excipients at concentrations ranging from 5 mM to 300 mM and the protein of interest at a concentration ranging from 4 mg/ml to 15 mg/ml. [0016] In certain embodiments, the purification process comprises one or more of the following steps: centrifugation, microfiltration, TFF, virus inactivation, affinity chromatography, cation exchange chromatography, anion exchange chromatography, hydrophobic interaction chromatography, ultrafiltration, diafiltration, SPTFF, depth filtration, and mixed-mode chromatography. [0017] In certain embodiments, the purification process comprises a virus filtration step and one or more of the following steps: centrifugation, microfiltration, TFF, virus inactivation, affinity chromatography, cation exchange chromatography, anion exchange chromatography, hydrophobic interaction chromatography, mixed-mode chromatography, ultrafiltration, diafiltration, SPTFF, and depth filtration, and wherein the preparation is obtained from the virus filtration step. [0018] In certain embodiments, the purification process comprises a cation exchange chromatography step, and one or more of the following steps: centrifugation, microfiltration, TFF, virus inactivation, affinity chromatography, anion exchange chromatography, hydrophobic interaction chromatography, mixed-mode chromatography, ultrafiltration, diafiltration, SPTFF, virus filtration, and depth filtration, and wherein the preparation is obtained from the cation exchange chromatography step. [0019] In certain embodiments, the purification process comprises an anion exchange chromatography step, and one or more of the following steps: centrifugation, microfiltration, TFF, virus inactivation, affinity chromatography, cation exchange chromatography, hydrophobic interaction chromatography, mixed-mode chromatography, ultrafiltration, diafiltration, SPTFF, virus filtration, and depth filtration, and wherein the preparation is obtained from the anion exchange chromatography step. [0020] In certain embodiments, the purification process comprises hydrophobic interaction chromatography step, and one or more of the following steps: centrifugation, microfiltration, TFF, virus inactivation, affinity chromatography, cation exchange chromatography, anion exchange chromatography, mixed-mode chromatography, ultrafiltration, diafiltration, SPTFF, virus filtration, and depth filtration, and wherein the preparation is obtained from the hydrophobic interaction
chromatography step. [0021] In certain embodiments, the purification process comprises a mixed-mode chromatography step, and one or more of the following steps: centrifugation, microfiltration, TFF, virus inactivation, affinity chromatography, cation exchange chromatography, anion exchange chromatography, hydrophobic interaction chromatography, ultrafiltration, diafiltration, SPTFF, virus filtration, and depth filtration, and wherein the preparation is obtained from the mixed-mode chromatography step. [0022] In certain embodiments, the protein of interest is selected from the group consisting of: etanercept, aflibercept, adalimumab, epoetin alfa, darbepoetin alfa, filgrastim, pegfilgrastim, bevacizumab, cetuximab, infliximab, rituximab, eculizumab, trastuzumab, evolocumab, denosumab, romosozumab, erenumab, blinatumomab, and a BiTE antibody construct. In certain aspects of this embodiment, the BiTE antibody construct is selected from the group consisting of blinatumomab, an anti-CD33 and anti-CD3 BiTE antibody construct, an anti-EGFRvIII and anti-CD3 BiTE antibody construct, an anti-DLL3 and anti-CD3 BiTE antibody construct, an anti-CD19 and anti-CD3 BiTE antibody construct, an anti-MSLN and anti-CD3 BiTE antibody construct, an anti-CDH19 and anti- CD3 BiTE antibody construct, an anti-FLT3 and anti-CD3 BiTE antibody construct, an anti-DLL3 and anti-CD3 BiTE antibody construct, an anti-CDH3 and anti-CD3 BiTE antibody construct, an anti- CD70 and anti-CD3 BiTE antibody construct, an anti-PSMA and anti-CD3 BiTE antibody construct, and an anti-BCMA and anti-CD3 BiTE antibody construct. [0023] In certain embodiments, the UFDF operation is carried out at a temperature of from about 25°C to about 50°C, from about 25°C to about 40°C, or from about 30°C to about 40°C. [0024] In certain embodiments, the protein mixture obtained from the final UFDF operation is a pharmaceutical formulation comprising the protein. [0025] In certain embodiments, the protein mixture obtained from the final UFDF operation is a drug substance comprising the protein. DESCRIPTION OF THE DRAWINGS [0026] Figure 1 depicts the geometry of the protein mixture. Two layers of protein cells are shown in black and grey colors. Protein cells are arranged in a lattice of closely packed spheres of radius ^^^^^^. In the center of each protein cell lies a protein molecule of radius ^^^. Between protein cells there is interstitial space. [0027] Figure 2 depicts a flow diagram for the solver algorithm used by MUD 2.0. DETAILED DESCRIPTION OF THE INVENTION [0028] The present disclosure is based on the discovery that accounting for the effects of excipients on the activity of water significantly improves the prediction accuracy for the osmolality of a protein mixture. This allows (1) a more accurate prediction of the DF-buffer formulation and UFDF operating
conditions needed to meet the osmolality target specification for the protein mixture produced by a UFDF operation and (2) a reduction of the experiments needed to develop an appropriate combination of the DF buffer and/or flush buffer formulation and UFDF operating conditions that produce a protein mixture meeting all the specifications. [0029] In the methods disclosed herein, in silico UFDF design utilizing mathematical modeling reduces the amount of laboratory experimentation. An in silico UFDF model is used to design the DF buffer and/or flush buffer formulation and UFDF operating conditions such that the desired pH, excipient concentrations, and/or osmolality of the final protein mixture are met with a reduced amount of experimentation. Obtaining a Protein Mixture from a Cell Culture [0030] In the methods disclosed herein, a protein mixture containing the protein of interest is obtained by subjecting a protein mixture comprising the protein of interest and one or more impurities, for example, from a cell culture harvest, to a purification process. Processes for purifying a protein of interest encompass all process steps from cell culture harvest up to UFDF and typically include at least the steps of recovering the protein from host cells and/or cell debris, e.g., using centrifugation and/or filtration methods, and steps for purifying the proteins, e.g., using one or more chromatography and/or filtration methods, to separate the protein from various impurities. Purification steps typically used in the art are described below. [0031] For the methods disclosed herein, a protein of interest is typically produced in recombinant systems, e.g., using host cells and appropriate cell culture media, using cell culture methods known to those skilled in the art. In recombinant expression systems, proteins may be secreted from host cells into growth media or may be made intracellularly. Purification processes start from recovering a protein of interest from the cell culture, from host cells or the cell culture media, and comprise one or more steps selected from centrifugation, microfiltration, and single-pass tangential-flow filtration (SPTFF) to recover the protein of interest from host cells. For example, if the protein is produced intracellularly, the host cells are lysed, e.g., by mechanical homogenization, osmotic shock, or enzymatic treatment, as a first step to release the protein from the host cells. The resulting cell debris can be removed by subjecting the mixture to centrifugation, microfiltration, and/or SPTFF. [0032] The protein recovered from the host cells is then purified using various methods known and used in the art, including viral inactivation steps, various chromatography methods, and various filtration methods. [0033] The purification process can comprise affinity chromatography steps. Affinity chromatography refers to a protein separation technique in which a protein of interest (e.g., an Fc- region containing protein of interest or antibody) is specifically bound to a ligand specific for the target protein. In certain embodiments, the purification process comprises the use of a Protein-A-
based affinity resin for use in the affinity chromatography steps. The Protein A can be native Protein A (from S. aureus), recombinant Protein A, or functional variant thereof. Examples of Protein-A- based affinity resins that may be used include: ProSep®-vA HC (Millipore Sigma), ProSep® Ultra Plus (Millipore Sigma), MabSelect™ (Cytiva), MabSelect™ SuRe™ (Cytiva) and other commercially available affinity resins. Other affinity ligands/resins that can be utilized in the purification methods described herein include Protein G and other Fc-binding proteins like single-chain camelid antibodies. The protein of interest generally retains its specific binding affinity for the ligand during the chromatographic steps, while other impurities in the mixture do not bind appreciably or specifically to the ligand. After binding to the ligand and consequently being separated from impurities not binding to the ligand, the protein of interest is eluted from the affinity chromatography column through the usage of solutions known in the art, e.g., solutions recommended by the manufacturer of the affinity resin used in the affinity chromatography step. [0034] The purification process can comprise ion exchange chromatography steps. Ion exchange chromatography can be membrane ion exchange chromatography or column ion exchange chromatography. Ion exchange chromatography separates proteins based on the difference in their respective ionic charges and includes cationic exchange chromatography and anionic exchange chromatography. The use of a cationic exchange chromatography versus an anionic exchange chromatography is based on the overall charge of the protein. It is within the skill of a person of ordinary skill in the art to determine whether to use only cation exchange chromatography, only anion exchange chromatography, or a combination of the two to purify a protein of interest. In some embodiments, the purification process employs only a cation exchange step. In some embodiments, the purification process employs only an anion exchange step. In some embodiments, the purification process employs an anionic exchange step prior to the use of a cationic exchange step. In certain embodiments, the purification process employs a cationic exchange step prior to the use of an anionic exchange step. [0035] In ion exchange chromatography, the protein of interest in the protein mixture is attracted by opposite charges attached to a chromatography matrix, provided that the ionic strength of the surrounding solution or buffer is low. Elution is generally achieved by increasing the ionic strength of the elution buffer through the addition of salt ions that compete with the protein molecules for the charged sites of the ion exchange matrix. The salt ions which may be used will depend on the pH of the protein mixture and can be readily identified by one of ordinary skills in the art. In some embodiments, the amount of salt added ranges from 25 mM to 500 mM. In other embodiments, the amount of salt added ranges from 100 mM to 250 mM. Changing the pH of the protein mixture present in the chromatography matrix, which thereby alters the charge of the protein of interest, is another way to achieve the elution of the protein from the matrix. The increase in the ionic strength of the elution buffer or the pH of the protein mixture may be gradual (gradient elution) or stepwise (step
elution). [0036] Cation exchange materials or resins are available from commercial sources. Nonlimiting cationic materials suitable for cation exchange chromatography include carboxymethyl (CM), sulfoethyl (SE), sulfopropyl (SP), phosphate (P), sulfonate (S) and Fractogel® EMD cation exchange materials (Millipore Sigma). Cellulose ion exchange resins include DE23™, DE32™, DE52™, CM- 23™, CM-32™, and CM-52™ (Whatman Ltd.). SEPHADEX®-based and cross-linked ion exchange materials are also known, for example, diethylaminoethyl- (DEAE)-, QAE-, CM-, and SP- SEPHADEX®, DEAE-, Q-, CM- and S-SEPHAROSE®, and SEPHAROSE® Fast Flow (Pharmacia AB). Further, DEAE and CM derivatized ethylene-glycol-methacrylate copolymer such as TOYOPEARL™ DEAE-650S/M and TOYOPEARL™ CM-650S/M (Tosoh Bioscience) can be used. Fractogel® EMD cation exchange materials include Fractogel® EMD SO3- (S), Fractogel® EMD COO- (S), Fractogel® EMD SO3- (M), Fractogel® EMD SE Hicap (M), and Fractogel® EMD COO- (M). [0037] Anion exchange materials or resins are available from commercial sources. Non-limiting examples of anionic exchange substituents include DEAE, quaternary aminoethyl (QAE) and quaternary amine (Q) groups. Exemplary anion exchange materials include Fractogel® EMD TMAE (S), Fractogel® EMD DEAE (S), Fractogel® EMD DMAE (S), Fractogel® EMD TMAE (M), Fractogel® EMD TMAE Hicap (M), Fractogel® EMD DEAE (M), Fractogel® EMD DMAE (M) (Millipore Sigma). [0038] The purification process can comprise hydrophobic interaction chromatography (HIC) steps. Generally, HIC is useful for removing protein aggregates, such as antibody aggregates and process-related impurities. In some embodiments, HIC is performed after salt precipitations or ion exchange procedures as hydrophobic interactions are the strongest at high ionic strength. Many HIC columns are available commercially. Nonlimiting examples include: Phenyl Sepharose™ 6 Fast Flow column with low or high substitution (Pharmacia LKB Biotechnology, AB), Phenyl Sepharose™ High Performance column (Pharmacia LKB Biotechnology, AB), Octyl Sepharose™ High Performance column (Pharmacia LKB Biotechnology, AB), Fractogel™ EMD Propyl or Fractogel™ EMD Phenyl columns (Millipore Sigma), Macro-Prep™ Methyl or Macro-Prep™ t-Butyl Supports (Bio-Rad), WP HI-Propyl (C3)™ column (J. T. Baker), Phenyl Sepharose HiSub FF (Cytiva), and Toyopearl™ ether, phenyl or butyl columns (Tosoh Bioscience). [0039] The purification process can comprise mixed-mode or multimode chromatography (MMC). MMC is a chromatographic method in which solutes interact with stationary phase through more than one interaction modes or mechanisms. Using multimodal functional ligands, MMC achieves the adsorption of the protein molecules of interest with the combination of ionic interactions, hydrogen bonds, and hydrophobic interactions. Mixed-mode resins can directly capture target proteins at relatively high salt concentrations without dilution or other additives due to their multiple binding
interactions. Non-limiting exemplary commercially available mixed-mode resins include: Capto MMC, Capto adhere, and Capto Core 700 (Cytiva), PPA Hypercel, HEA Hypercel, and MEP Hypercel (Pall Corporation), Eshmuno HCX (Millipore Sigma), Toyopearl MX-Trp-650 M (Tosoh Bioscience), and Nuvia cPrime, CHT Ceramic Hydroxyapatite, and CFT Ceramic Fluoroapatite (Bio- Rad). [0040] The protein purification process can comprise a virus filtration step between and/or after any of the steps described above, as appropriate. In certain embodiments, the purification process comprises a virus filtration step after viral inactivation, or after affinity chromatography, or after cation exchange chromatography, or after anion exchange chromatography, or after HIC, or after mixed-mode chromatography. In certain embodiments, the purification process comprises a virus filtration step before cation exchange chromatography, or before anion exchange chromatography, or before HIC, or before mixed-mode chromatography. In certain embodiments, the purification process comprises a virus filtration step as the final step of the purification, or the penultimate of purification, e.g., before the final UFDF operation. [0041] Virus filtration may be achieved via the use of appropriate filters. Non-limiting examples of suitable filters for virus filtration include: Ultipor DV50™ filter (Pall Corporation), Viresolve™ filters (Millipore Sigma), CUNO Zeta Plus™ VR filters (3M) and Planova™ filters (Asahi Kasei Pharma). In some embodiments, the virus filtration step employs a pre-filter which can be of any format and includes but is not limited to a membrane, a depth filter, a chromatography column, or combinations thereof. Non-limiting examples of a depth filter that can be used for virus filtration include the Cuno™ model 30/60 ZA depth filters (3M Corporation) and 0.45/0.2 μm Sartopore™ bi- layer filter cartridges (Sartorius). [0042] Many virus-inactivating agents are known and can be used in addition to or in lieu of viral filtration. See, e.g., Gail Sofer, “Virus Inactivation in the 1990s—and into the 21st Century, Part 4, Culture Media. Biotechnology Products, and Vaccines,” Biopharm International, pp.50-57 (2003). Exemplary virus inactivation methods include solvent/detergent inactivation (e.g., with Triton X 100), pasteurization (heating), acidic pH inactivation (e.g., at pH 3-5), and ultraviolet (UV) inactivation. It is also possible to combine two or more of the forementioned methods, e.g., performing acidic pH inactivation at elevated temperature, to inactivate viruses. [0043] The purification process can include additional process steps including formulation and/or concentration steps. In one embodiment, the purification process further comprises sterile filtration and/or absolute filtration. Sterile filtration is typically carried out using Normal Flow Filtration (NFF) where the direction of the fluid stream is perpendicular to the filter medium (e.g., a membrane) under an applied pressure.
UFDF Operation [0044] The protein purification process can comprise ultrafiltration-and-diafiltration (UFDF) steps. Ultrafiltration (UF) is a separation process through the usage of a semi-permeable membrane that retains macromolecules, while allowing smaller solvent and excipient molecules to pass through. See, e.g., Zeman et al., Microfiltration and Ultrafiltration: Principles and Applications, Marcel Dekker, Inc., pp.299-301 (1996). Diafiltration (DF) is a buffer exchange process during which a DF buffer is added to a protein mixture, and the resulting mixture is passed through a semi-permeable membrane that retains macromolecules, while allowing smaller solvent and excipient molecules to pass through. In this manner, diafiltration can be used to add desired excipient molecules as well as remove undesired excipient and/or solvent molecules from the protein mixture. UFDF operations utilize selectively permeable membranes which retain protein based on size, while allowing smaller solvent and excipient molecules to permeate through. During a UFDF operation, UF is used to increase the protein concentration of the mixture, and DF adds a buffer (“DF buffer”) to the remaining protein mixture to change its initial composition, pH, and/or osmolality to their desired values. UFDF steps may be used for concentrating proteins and/or formulating a protein of interest into a mixture with the desired composition, pH, and/or osmolality. [0045] In an exemplary manufacturing process, an incoming pool from a cell culture harvest is concentrated in terms of its protein content by being subjected to a UF step that removes solvent and excipient molecules. Subsequently, the resulting mixture is diafiltered after a DF buffer is added to the mixture. Multiple DF operations can be executed, and the post-DF protein mixture is overconcentrated (OC) via another UF step. Finally, the post-OC protein mixture is diluted to the concentration specified for the final protein mixture after a flush buffer is added to the mixture. [0046] In certain embodiments, the UFDF operation is carried out using a DF buffer or flush buffer that comprises excipients at concentrations ranging from 5 mM to 300 mM. The excipients can be an amino acid, a sugar, a polyol, an anti-oxidant, a chelating agent, a lipid or a lipid derivative, a salt, a polymer, an inert protein, a surfactant, and a water-miscible co-solvent. [0047] A UFDF operation (any one or all) can be carried out at a temperature ranging from about 20°C to about 50°C. In some embodiments, the UFDF operation is carried out at a temperature ranging from about 20°C to about 40°C. In some embodiments, the UFDF operation is carried out at a temperature ranging from about 30°C to about 50°C. Calculating Excipient Concentrations Using MUD 2.0 [0048] To accurately predict the outcome of a UFDF operation given the DF buffer and UFDF operating conditions, mathematical models describing the interactions between the protein and excipients must be employed. Such models must take into consideration (1) electrostatic interactions between charged excipients and charged protein molecules and (2) volume exclusion of significantly
larger protein molecules compared to many excipient molecules. These are the two dominant molecular interactions influencing the partitioning of each excipient molecule across the semi- permeable membranes during a UFDF operation. Because a protein of interest often possesses a net positive or negative electrostatic charge, the electrostatic interactions between the charged protein molecules and charged excipient molecules, either attraction if the protein molecules and the excipient molecules are oppositely charged or repulsion if similarly charged, can result in an unequal partitioning of charged excipients across the semi-permeable membranes. At high concentrations of a protein of interest, volume exclusion occurs because the significantly larger protein molecules occupy a significant portion of the mixture volume. During a UFDF operation, since protein molecules are confined to one side of a selectively permeable membrane, the volume occupied by the protein molecules reduces the volume available for solvent and excipient molecules. In addition to these effects, additional minor molecular interactions, such as specific and nonspecific bindings, may also be applicable to certain types of excipients and conditions of the protein mixture. [0049] The electrostatic interactions during a UFDF operation account for the partitioning of charged excipients across the UFDF membrane based on the presence of charged protein molecules on the retentate side of the membrane. Two main models, Donnan equilibrium and Poisson– Boltzmann models, can be employed to model such electrostatic interactions. The Donnan equilibrium model assumes a homogenous distribution of electrical potential throughout the retentate side of the membrane, representing a special case of the more general Poisson–Boltzmann model. The Poisson–Boltzmann model is based on mean-field theory using equations that describe electrostatic interactions at the microscopic scale. The Poisson-Boltzmann model combines the Poisson equation, which calculates the electric potential generated by the charged protein molecules, and the Boltzmann distribution equation, which describes the distribution of charged excipient molecules as a function of the electric potential generated by the charged protein molecules. Note that the Poisson–Boltzmann equation is generally applicable to excipients of any valency. [0050] The mathematical UFDF model, MUD 2.0, is a multi-scale model that describes the microscopic electrostatic interactions between charged protein molecules and charged excipient molecules and the macroscopic volume exclusion due to the presence of significantly larger protein molecules on the retentate side of the UFDF membrane. The model simulates the electrostatic- interaction-based excipient partition across the UFDF membrane by assuming that the charged protein surfaces generate local regions which attract oppositely charged excipient molecules and repel like- charged excipient molecules. This assumption requires specifications of the parameters that govern the geometry of the protein molecules, the local surrounding volume of each protein molecule, and the surface charges of the protein molecules. In addition, the mathematical UFDF model describes the mass transfer of excipient molecules across the UFDF due to spatial concentration gradients. This allows the calculation of excipient concentrations during all phases of a UFDF operation, including
the dynamic, nonequilibrium periods like the initial UF, DF, and OC steps. [0051] In the methods of the invention, excipient concentrations of the post-UFDF preparation are estimated using a mathematical model, which accounts for electrostatic interactions between charged excipients and charged protein molecules and accounts for volume exclusion of large protein molecules compared to excipient molecules, e.g., MUD 2.0 (See Ladwig et al., 2020, Biotechnology Progress 36:e2993) based on (a) the protein concentration during the DF step; (b) the DF buffer formulation; (c) the number of diavolumes; (d) the protein concentration at the end of the OC step; (e) the flush buffer formulation; (f) the protein concentration for the final protein mixture; (g) the operating temperature during the entire UFDF operation. Note that (a), (d), and/or (f) can be the same, and (b) and (e) can be the same. In certain embodiments, the system of equations can be implemented in MATLAB. Model performance is assessed through statistical comparisons between model predictions and the corresponding experimental measurements from lab-scale and manufacturing- scale UFDF operations. [0052] MUD 2.0 specifies the geometry of the protein and its surrounding volume by dividing the mixture volume into spherical protein cells which are arranged in a regular, close-packed lattice. Each protein cell contains a single spherical-shaped protein molecule. The volume of each protein cell is a function of the protein concentration. This geometry specifies three regions within the system as shown in Figure 1. The first region is the spherical region occupied by a single protein molecule, which is characterized by the protein radius. The second region is the protein cell, which takes the form of a spherical annulus characterized by inner and outer radii. The third region is the interstitial space between protein cells which encompasses the remaining volume of the protein mixture that undergoes the UFDF operation. The interstitial space between protein cells can be calculated from the following formula (See Ladwig et al., 2020, Biotechnol Progress 36:e2993 for a complete derivation): ^^^^௧^^^௧^௧^^^ = ^1 − గ ଷ√ଶ^ ^^, (1) where V is the volume of operation.
[0053] MUD 2.0 also accounts for the concentration of each ionic excipient and its dissociation state(s). Chemical equilibrium reactions are incorporated into MUD 2.0 to determine the concentration and charge state of each dissociable ionic excipient. ^^ ^^,భ^^,బ ^,^ = (2) )
where ^^^,^ is the concentration of the completely protonated form of dissociable ionic excipient i, which has a charge of ^^^,^. Subsequent dissociations result in the singly deprotonated state with concentration ^^^,^ and charge ^^^,^ = ^^^,^ − 1; the doubly deprotonated state with concentration ^^^,ଶ with charge ^^^,ଶ = ^^^,^ − 2; and so on until the final deprotonation, ^^^^ . The concentration of the dissociation forms of ionic excipient i is dependent on the activity-adjusted equilibrium constants, ^^^,^. Equation (6) represents a mole balance, which can be used to solve for the concentration of the completely protonated excipient i in terms of the overall concentration of all states of ionic excipient i, ^^^,௧^௧^^, ^^ ^^,^^^ೌ^ ^^,^^^ೌ ^,^ = ಿೖ = ^ ಿೖ . (6) ಿ ^ା∑ ೖ^ ∏ ^ ೕసభ ೖ^,ೕ ^ା ೖ ∏ ^ ೕసభ ೖ^,ೕ ^ ା⋯ା Using Equations (4) and ions in terms of ^^^,௧^௧^^, ^^ శ, and the equilibr
ு ium ^,^. [0054] To accurately estimate the equilibrium constants, ^^^,^, MUD 2.0 uses the Davies equation to account for an activity-coefficient correction established by thermodynamic considerations. See Christian, 1986, Analytical Chem.4th ed. New York and Davies, 1962, Ion association. London: Butterworths. Based on the Debye-Huckel theory, the Davies equation extends the applicability of the theory to higher ionic strengths: − log^^ ^^^,^ = ^^൫^^^,^൯ଶ ^ √ூ ^ା^.ଷଷఈ√ூ − ^^^^^, (7) where ^^ is the
i, ^^^,^ the charge of the jth deprotonated state of ionic excipient i, I the ionic strength, and ^^ an ion size parameter. A and B are unitless constants of values 0.509 and 0.3, respectively. See Bowen and Williams, 1996, The Osmotic Pressure of Electrostatically Stabilized Colloidal Dispersions. J of Colloid Interface Sci. The ionic strength of the protein mixture, I, is defined by the sum of ^^^,^, and ^^ , the ionic charge and the conc th ^,^ entration of the j deprotonated state of ionic excipient i, respectively, over all deprotonated states of all ionic excipients: ^^ = ^ ∑ே^ ∑^^ ^ ଶ ଶ ^ ^ୀ^ ^^,^൫^^^,^൯ , (8) where ^^ is the total
coupling among the deprotonated states of each ionic excipient, since the values of ^^^,^ in Equations (4) and (6) are dependent on ionic strength I through the activity coefficients, ^^^,^: ^^ ^ = ఊ^,ೕషభ ^, ఊ ఊ ^^^,^బ, (9) where ^^ is the
and ^^ శ the coefficient for H+ ions calculated from the Davies equation, Equation (7).
[0055] As MUD 2.0 often simulates the UFDF operations of protein mixtures with high protein concentrations, e.g., 10 – 200 g protein/L, the protein molecules exhibit significant contributions to the acid-base equilibrium of the protein mixtures. MUD 2.0 treats proteins’ acid-base behavior as an ion with many dissociation constants, which are estimated based on the idealized behavior of the protein's residues. Table 1 lists the dissociation constant values used by MUD 2.0 for each amino acid potentially present in the protein. Table 1: Dissociation constants, pKa, and fully protonated charges of various amino acid groups. Amino Acid Group pKa Fully Protonated Charge COOH terminus 3.2 0 [0056]
differences between the pH at the protein surface and in the interstitial space. MUD 2.0 uses a charge regulation model to account for the ionization reactions at the protein surface wherein equilibrium equations for protein molecules’ amino acid residues are calculated with respect to the local hydrogen concentration at the protein surface. The protein residue analogues of Equations (2-5) take the same form except with p subscripts and incorporation of the hydrogen concentration at the protein surface. For example, the equation for the first protein removal takes the following form: ^^^,^ = ^^^^,బ (10) for which the
without activity- coefficient correction: ^^^^^ = − log^^ ^^^, (11) and the surface hydrogen concentration, ^^ுశ,^௨^^^^^, is calculated by the Boltzmann distribution: ^^ = ^^ ^ ^ట൫ோ^൯ శ శ,^ ^^^^^ ൬− ^, (12) for which ^^ுశ,^
space between protein cells. The values for ^^ு శ ,^ and the electric potential, ^^(^^^), are calculated from the Poisson–
Boltzmann equation. [0057] The net charge of the protein's primary structure, ^^^బ, is calculated from the concentration and charge state of each amino acid: ^^^బ = ^ேಲ ே^ ∑^^^,^^^^,^. (13) Note that Equation (13) does not take influences of the folded protein on the net charge of the
MUD 2.0 incorporates a calibration constant ^^^ௗ^, which accounts for the charge adjustment due to the folded structure of a protein and is empirically fit for each protein of interest. The net charge of the folded protein, ^^^, is estimated by applying this empirically fit charge adjustment to the net charge of the protein solely based on its amino acid sequence, ^^^,^: ^^^ = ^^^బ − ^^^ௗ^ . (14) [0058] The protein surface charge density, σ, is specified in alignment with work by Miao et al. (Miao et al., 2009, Biotechnol Prog 25:964-972), wherein the protein charge is uniformly distributed across the surface of the spherical protein, ^^ = ^ொ^ ^^ , (15) for which e is the protein.
[0059] MUD 2.0 a the pH of the protein mixture. An overall charge neutrality can be written for all excipients, hydrogen ions and hydroxide ions, as shown in Equations (16-18): ^^ுశ − ^^ைுష + ^^ொ = 0 (16) Equation (16) of all
components in the protein mixture except H+ and OH−. Equation (17) represents the dissociation of water, for which the equilibrium constant for water, kw, is fixed at 10−14. The activity coefficients of H+ and OH-, ^^ு శ and ^^ைு ష, respectively, are calculated with Equation (7), the Davies equation. Furthermore, the activity coefficient for water, ^^ுమை, is set to 1, because H2O is neutral, i.e., does not possess net positive or negative charge. [0060] MUD 2.0 applies the Poisson–Boltzmann theory to establish the electrostatic potential field and the distribution of ionic excipients around each protein molecule that typically possesses a net charge. In a spherical coordinate system, the Poisson– Boltzmann equation results in a non-linear, second-order ordinary differential equation ^ ௗ ^^^ଶ ௗట^ = −^ ∑ ^^ ௭^,ೕ^ట ^,^^^ ^^^^^^ ^− ^. (19)
The left-hand side of Equation (19) describes the radial diffusion of electrostatic potential. The right- hand side gives a Boltzmann weighting to describe the distribution of ionic excipients based on the electrostatic potential. For Equation (19), r is the radial coordinate, e the charge of a proton, ɛ the permittivity of water, and ^^^,^ the charge of the jth deprotonated state of ionic excipient i. Furthermore, the infinity subscript included in ^^^,^ಮ represents the concentration of the jth deprotonated state of ionic excipient i at the outer radius of the cell volume, ^^ = ^^^^^^, and in the interstitial space. This equation is solved for the electric potential, ^^(^^). [0061] Solving Equation (19) requires two boundary conditions. The first boundary condition assumes that at the interface between protein and solution (r = Rp), the net charge of the protein is uniformly distributed across its surface with a surface charge density of σ. Gauss's law relates the slope of the electrical potential at r = Rp to the enclosed charge: ௗట ൫^^ = ^^ ൯ ఙ ௗ^ ^ = − ఌ . (20) The second boundary condition is applied at the outer boundary, ^^ = ^^^^^^, and is chosen in MUD 2.0 as ^^(^^ = ^^^^^^) = 0. (21) Equation (21)
are continuous and constant between the protein cell and interstitial space, i.e., ^^^,^(^^ = ^^^^^^) = ^^^,^ಮ . [0062] Equations (20) and (21) represent the boundary conditions for Equation (19). The inputs are the concentrations of ionic excipients, charges of ionic excipients, the permittivity of water, the protein charge approximated charge density of protein molecules, and the two radii of the protein and the cell. The output is the electrostatic potential established by typically charged protein molecules as a function of radius, i.e., distance from each protein molecule. After calculating the electrostatic potential, the local concentrations of the jth deprotonated state of ionic excipient i, ^^^,^(^^), are calculated from the Boltzmann distribution:
^^^,^(^^) = ^^^,^ಮ^^^^^^ ^− ௭^,ೕ^ట(^) ^் ^. (22) [0063] The Poisson- the mass of ionic
excipients. To preserve the mass balance of each ionic excipient, MUD 2.0 accounts for the significant volume-exclusion effect of large protein molecules at high concentrations on the concentrations of ionic excipients on the retentate side of the UFDF membrane. For each ion excipient, its total mass is divided into the mass within the protein cell, ^^^,^^^^^ , and the mass within the interstitial space, ^^^,^^^^^^ೞ^^^^ೌ^ . The total mass of the jth deprotonated state of ionic excipient i within the protein cell, ^^^,^^^^^ , is calculated by integrating ^^^,^(^^) from Equation (22): ^^ ோ^^^^ ^,^ ଶ ^^^^ = ^^^ ^ 4^^^^ ^^^,^(^^)^^^^ . (23) To calculate the mass
2.0 assumes that the
ion concentrations are continuous and constant at the boundaries between the protein cells and interstitial space. Thus, the mass of interstitial ionic excipient is: ^^^,^^^^^^ೞ^^^^ೌ^ = ^^^,^ಮ^^^^௧^^^௧^௧^^^ (24) for which ^^^^௧^^^௧^௧^^^ denotes the volume of the interstitial space. The bulk concentration of each ionic excipient is defined as the mass of the ionic excipient divided by the volume of the entire protein mixture, V, including the volume occupied by the protein molecules: ^ ^^ ^,ೕ^^^^ା^^,ೕ^^^^^ೞ^^^^ೌ^ ^,^ = ^ (25) Equations (23–25) for both the chemical equilibrium
ion concentrations, ^^^,^ಮ , used in the Poisson–Boltzmann equation must ensure that the bulk ion concentrations, ^^^,^, calculated from Equation (25) are consistent with those from the chemical equilibrium Equations (4) and (6). This system of equations is coupled and solved through an iterative procedure, as discussed below. [0064] MUD 2.0 also accounts for the transfer of solute components across a UFDF membrane. MUD 2.0 assumes that the protein molecules are too large to move through the membrane and remain at the retentate side of the membrane, i.e., in the protein mixture, throughout the simulation. In addition, the oppositely charged ionic excipients near the surface of charged protein molecules are unable to move through the membrane and are trapped in the protein mixture. As a result, only the ionic excipients at a sufficiently far radial distance from the protein surface as well as in the interstitial space are actively involved in mass transfer through the UFDF membrane, while the region sufficiently close to the protein surface is not. The radial distance, beyond which the region is available for the mass transfer through the UFDF membrane is denoted by ^^௧^^^: ^^௧^^^ = ^^^^^^ ∙ ^^^^^^, (26) for which ^^^^^^ denotes the fraction of ^^^^^^, the radius of the protein cell, available for the mass transfer through the UFDF membrane. The concentration of each ion excipient in the permeate, ^^^,^^ೠ^ , is considered equal to that in the retentate volume available for mass transfer through the membrane: ே ೃ ^ ^ ^^^^ ೃ^^ೌ ସ గ^మ^^,ೕ(^)ௗ^ା^^,ೕಮ^^^^^^ೞ^^^^ೌ^ ^^ = ^ ^ ^^ ^ for which the
than ^^௧^^^ from the center of the protein cell in the protein cell and (b) that in the interstitial space, and the denominator is the volume of the protein mixture available for mass transfer through the membrane. [0065] Mass transfer during a UFDF operation is dependent on whether the retentate volume is held constant. During the DF phase, the retentate volume is held constant and a feed stream of the DF buffer is added to the recirculated retentate pool at a rate equal to the flow rate, q, of the solution permeating the UFDF membrane. Under this constant volume condition, the mass conservation of the
system is expressed as: ௗ^^,ೕ ^^^,ೕ ି^^,ೕ^ ^ ௗ௩^ = ^^ ೠ^ ^ , (28) for which ^^^,^^^ ionic excipient i and ^^^ the amount of
phases of a UFDF operation, solution permeates the membrane with no feed stream. Under this condition, the mass conservation of the system is expressed as: ௗ^^,ೕ ൫^^,ೕି^^,ೕ ൯ ௗ௩^ = ^ೠ^ ^ . (29) [0066] MUD 2.0 versions of MATLAB®. Within
is used to simultaneously converge pH, surface potential around protein molecules, and mass balance of each ionic excipient. Figure 2 shows the overall structure of the solver algorithm. The inner-most iteration procedures converge chemical equilibria such as pH and the overall charge of the protein mixture for a given set of excipients and protein. At the converged chemical equilibria, the overall charge of the system converges to zero. Explicitly writing the charge balance for the protein mixture provides an objective function that reveals the pH of the mixture by driving the calculated charge of the protein mixture to zero. An initial pH guess is made. If the resulting overall charge of the protein mixture is positive, the pH guess is too low and thus should be increased by a certain step size. On the other hand, if the resulting overall charge of the protein mixture is negative, the pH guess is too high and thus should be decreased by a certain step size. Using an initial pH step size of 1 for the solver, the pH of the mixture generally converges within 0.001 units in 15 to 20 iterations. The next layer of the solver solves the Poisson–Boltzmann equation, Equation (19), to find the ^^^,^ಮ values for each ionic excipient such that the mass balance for every ionic excipient closes to within a tolerance of 10−7 mol/L. The second- order Poisson–Boltzmann equation is solved numerically as a system of ordinary differential equations using the boundary value problem solver BVP4C within MATLAB® for the radial range of R୮ ≤ r ≤ Rୡ^୪୪. A closed mass balance is achieved by initially guessing values for each ^^^,^ಮ . When applicable, the previously converged result is used as an initial guess; otherwise, the bulk concentration, ^^^,^, is used. The resulting distributions of ionic excipients are then integrated and compared to the known bulk concentrations. Values of ^^^,^ಮare iteratively improved until the algorithm converge within tolerance. The solution to the Poisson–Boltzmann equation provides an updated surface potential around protein molecules which perturbs the initial pH equilibrium calculation. Typically, pH, surface potential around protein molecules, and mass balance for each ionic excipient converge within 3 to 5 iteration cycles. Following convergence of pH, surface potential around protein molecules, and mass balance for each ionic excipient, mass transfer across the UFDF membrane is simulated across a small timestep. Once the simulation of mass transfer is
completed, a new timepoint is reached. The pH, surface potential around protein molecules, and mass balance for each ionic excipient are converged again for the updated composition of the protein mixture. The simulation of an entire UFDF operation typically requires 3 to 5 minutes of computational time using an Intel® Core™ i5 processor. [0067] Table 2 summarizes the constants and parameters utilized by MUD 2.0. In addition to these model parameters, a protein-charge adjustment parameter is calibrated for each protein molecule. Calibration of the charge adjustment parameter is performed by simulating an experimental UFDF operations for which the pH of the final protein mixture has already been measured with various values of the adjustment parameter and by optimizing the charge adjustment parameter value when the simulated pH of the final protein mixture matches with the experimental measurement. The calibration process is performed with a native optimization algorithm, fminbnd, in MATLAB®. The protein-charge adjustment parameter can be estimated from a single experimental data point. However, the average of charge adjustment parameters calibrated by multiple experimental UFDF operations of the same protein can account for potential experimental variation. Aside from the charge adjustment parameter, no other fitting parameters is used by MUD 2.0. Following its calibration with data from experimental UFDF operations, the protein-charge adjustment parameter is fixed for the given protein and is not adjusted during subsequent simulations of UFDF operations. However, due to the dependence of amino acid pKa values on salt concentrations, significant changes to the composition of excipients can require re-calibration of the charge adjustment parameter. Table 2: Model parameters and their values for MUD 2.0. Symbol Model Value Units Description i l h i l ki f es
k 1.381×10-23 Joule/Kelvin Boltzmann constant NA 6.022×1023 Molecules/mole Avogadro constant C I
[0068] In the methods disclosed herein, the osmolality of the protein mixture generated by a UFDF operation is predicted by estimating its osmotic pressure based on the activity of water and Norrish constants for all excipients present in the mixture. [0069] To predict osmolality, the MUD 2.0 model described in the previous section first adds together the concentrations of all the excipients present in the protein mixture generated by a UFDF operation to obtain osmolarity, which has a unit of Osm/L mixture. The calculated osmolarity is then adjusted to osmolality, which has a unit of Osm/kg water, by using the following equation: ^^^^^^^^^^^^^^^^^^^^ = ை^^ ^ ^^௫௧௨^^ ^ ௪^௧^^ ^ ^^௫௧௨^^ ^ ௪^௧^^ ^ ^^௫௧௨^^ ∙ ^ ௪^௧^^ ∙ ^^ ௪^௧^^ ≈ ^^^^^^^^^^^^^^^^^^^^^^ ⋅ ^ ^^௫௨^^ି^ ^^^௧^^^ ⋅ ^^ ௪^௧^^, for which the volume of water is estimated to be the volume of the protein mixture subtracted by the volume of all protein molecules. [0070] At the manufacturing level, the accuracy of the osmolality-estimation method described in the previous section has been proved to be inadequate for real-world purposes. To achieve the accuracy of osmolality prediction sufficient for commercial-scale UFDF operations, the osmolality- prediction model described herein estimates the effect of excipients on the activity of water, ^^௪, via the usage of the Norrish equation. See Petro S. Taoukis and Michelle Richardson, Water Activity in Foods: Fundamentals and Applications, 393 (2nd edition, 2020). The estimated ^^௪ is then translated into osmotic pressure ^^. See Janacek et al., 1996, Folia Microbiol 41:2-9. Finally, the osmotic pressure ^^ is translated into osmolality. See Winzor, 2004, Biophys Chem 107:317-23. This osmolality-prediction scheme is described by the following equations: ^^ = ^^ ^^^ೄ^ೄమ ,^^^^^^^^^^ ^ ௪ ^^ , the Norrish equation; (30) (31)
(32) for which ^^^ denotes the Norrish constant for excipient i and ^^^^^ = 2.271 ^^^^ ⋅ ^^^^^^/^^^^^^ if osmolality is measured via freezing point depression. Table 3 lists the Norrish constant for commonly used excipients. Table 3: Binary interaction constants for Norrish equation. Humectant K Humectant K
a-Aminobutyric acid -2.57 ± 0.37 Lysine -9.3 ± 0.3 1.3-Butylene glycol -3.47 Malic acid - 1.82 ± 0.13 Sou
., , . . irife et al., 1980, International Journal of Food Science & Technology 15.1:59-70. Leiras et al., 1990, Journal of Food Science 55.4:1174-1174. Alzamora c1 al., 1994, Food Research International 27.1: 65-67. Bell and Labuza (2000) Moisture Sorption: Practical Aspects of Isotherm Measurement and Use, 2e. St. Paul, MN: American Association of Cereal Chemists. Compare Predicted Osmolality to Specification and Adjusting the Composition of DF Buffer and/or UFDF Operating Conditions [0071] In the methods disclosed herein, once the osmolality is predicted, the value is compared to the osmolality specification or target for the protein of interest. If the predicted osmolality is outside the specified range, the composition of the DF buffer and/or UFDF operating conditions are adjusted so that the predicted osmolality under the new conditions may meet the osmolality specification. This process can be performed iteratively until the predicted osmolality meets the specification. One example for adjusting the DF buffer and/or flush buffer formulation and/or UFDF operating conditions to meet the osmolality specification is to change the concentration of sugars like sucrose and glucose in the DF buffer or flush buffer. As another example, the number of diavolumes can be
increased such that the protein mixture obtained after diafiltration reaches a steady osmolality. Protein Mixture Obtained from a UFDF Operation [0072] The methods disclosed herein include performing a UFDF operation using the adjusted DF buffer and/or flush buffer formulation and/or UFDF operating conditions to obtain a mixture comprising the protein of interest that meets all the target specifications. In some embodiments, the composition obtained from the UFDF operation is a drug substance (DS) comprising the protein. In some embodiments, the protein mixture obtained from the UFDF operation is a pharmaceutical formulation comprising the protein. In other words, the adjusted UFDF operation puts the protein of interest into a mixture that meets all the specifications intended for the protein mixture. In some embodiments, the method further comprises sterile filtration and/or absolute filtration steps after the UFDF operation. In some embodiments, the UFDF operation is the penultimate or the final step of a purification process used to achieve the specified pH, osmolality, and/or concentrations of specific excipients. [0073] In some embodiments, the protein mixture obtained from the final UFDF operation comprises the protein of interest at a concentration ranging from 50 mg/mL to 100 mg/mL. In other embodiments, the protein mixture obtained from the final UFDF operation comprises the protein of interest at a concentration ranging from 1 mg/mL to 10 mg/mL, from 100 mg/mL to 200 mg/mL, and from 1 mg/mL to 15 mg/mL. [0074] In some embodiments, the protein mixture obtained from the UFDF operation comprises buffering excipients that help the protein mixture meet the pH specification. Any buffer disclosed above may be comprised in the composition. In some embodiments, the composition obtained from the UFDF operation comprises buffering excipients at concentrations of from 2 mM to 35 mM, from 2 mM to 50 mM, or from 2 mM to 10 mM, or about 10 mM to 50 mM, or from 50 to 500 mM. In some embodiments, the composition obtained from the final UFDF operation comprises a buffer at a concentration of from about 50 mM to about 300 mM, from about 60 mM to about 300 mM, from about 70 mM to about 300 mM, from about 80 mM to about 300 mM, from about 90 mM to about 300 mM, from about 100 mM to about 300 mM, from about 120 mM to about 300 mM, from about 140 mM to about 300 mM, from about 160 mM to about 300 mM, from about 180 mM to about 300 mM, from about 200 mM to about 300 mM, from about 220 mM to about 300 mM, or from about 250 mM to about 300 mM. In some embodiments, the composition obtained from the final UF DF operation comprises a buffer at a concentration of 2 mM, about 2.5 mM, about 5 mM, about 10 mM, about 20 mM, about 30 mM, about 40 mM, about 50 mM, about 70 mM, about 90 mM, about 100 mM, about 120 mM, about 150 mM, about 170 mM, about 200 mM, about 220 mM, about 250 mM, about 270 mM, or about 300 mM. In embodiments where the composition obtained from the final UFDF operation comprises a buffer, the protein of interest comprised in the composition can be at any
of the concentrations described above. [0075] The protein mixture obtained from the UFDF operation can comprise a buffer with low buffering capability, which can be a result of buffering excipients at low concentrations and/or a buffer pH that is outside the buffering capabilities of the excipients. In some embodiments, the protein mixture obtained from the UFDF operation comprises a buffering excipient at a concentration of from 2 mM to 30 mM and has a pH within the buffering capability of the buffering excipient and a protein concentration that ranges from about 1 mg/mL to about 100 mg/mL. In some embodiments, the protein mixture obtained from the UFDF operation has a pH outside the buffering capabilities of the buffering excipients, the concentrations of which range from 2 mM to 50 mM, and comprises the protein of interest at a concentration ranging from about 1 mg/mL to about 50 mg/ml, or from about 1 mg/mL to about 40 mg/mL, or at about 10 mg/mL, or at about 20 mg/mL, or at about 30 mg/mL, or at about 40 mg/mL, or at about 50 mg/mL. In some embodiments, the protein mixture obtained from the UFDF operation has a pH outside the buffering capabilities of the buffering excipients, the a concentrations of which range from about 2 mM to about 40 mM, and comprises the protein of interest at a concentration ranging from about 1 mg/mL to about 50 mg/ml, or from about 1 mg/mL to about 40 mg/mL, or at about 10 mg/mL, or at about 20 mg/mL, or at about 30 mg/mL, or at about 40 mg/mL, or at about 50 mg/mL. Methods for Concentrating Proteins [0076] Proteins may be concentrated using methods known in the art. Non-limiting exemplary methods that may be used for concentrating proteins include membrane filtration, e.g., using cellulose membrane filters, centrifugal filtration, dialysis against a water-absorbing material, e.g., a water- absorbing polymer, salting out, e.g., using ammonium sulfate, and chromatography, e.g., size exclusion chromatography. Excipients [0077] In some embodiments, the method disclosed herein comprises adding one or more excipients to the protein mixture to increase, promote, or maintain the stability of proteins of interest. In some embodiments, the excipient can be an amino acid, a sugar, a polyol, an anti-oxidant, a chelating agent, a lipid or a lipid derivative, a salt, a polymer, an inert protein or polypeptide, a surfactant, a water-miscible co-solvent, or a combination thereof. [0078] Non-limiting examples of amino acid stabilizers that may be used in the methods disclosed herein include histidine, arginine, glycine, methionine, alanine, aspartic acid, lysine hydrochloride, proline, lysine, sarcosine, gamma-aminobutyric acid, and glutamic acid. [0079] Non-limiting examples of antioxidants include ascorbic acid, glutathione, vitamin E, and poly(ethylenimine).
[0080] Non-limiting examples of chelating agents include ethylenediaminetetraacetic acid (EDTA), diethylenetriaminepentaacetic acid (DTPA), citric acid, hexaphosphate, and thioglycolic acid. [0081] Non-limiting examples of sugars include sucrose, trehalose, xylitol, maltose, dextrose, glucose, raffinose, and lactose. [0082] Non-limiting examples of polyols include sugar alcohols, e.g., sorbitol, inositol, mannitol, glycerol, erythritol, caprylate, tryptophanate, and sarcosine. [0083] Non-limiting examples of polymers and inert proteins include protamine sulfate, polygalactouronic acid, phytic acid, polyfumaric, polysebacic acid, polyethylene glycol (PEG)- poly(lysine), polyaspartic acid block copolymer, carboxyphenoxypropane-sebacic acid copolymer, chitosan, chitin, palmitoyl glycol chitosan, glycated chitosan, N,N,N-trimethyl chitosan, chlorogenic acid chitosan, polymers of acylated amino acids, poly(ethyl acrylic acid), poly(propyl acrylic acid), long chain alkyl amine substituted poly (acrylic acid), proteinoids (condensation polymers of modified acylated amino acids), heparin, heparin sulfate, dextran sulfate, bases with conjugations such as PEG, e.g., PEG-succinate, polyrotaxanes, galacosylated poly(lysine), alpha-2- macroglobulin:poly(lysine), galactosylated poly(ethyleneimine), N-(beta-hydroxyethyl)-lactaminde, poly(amidoamine) dendrimers, steryl-poly(L-lysine), poly(phosphoesters), PEG-caprlyic-capric triglycerides, sucrose laurate, tocopheryl PEG-acetate, tocopheryl PEG-succinate, gelatin, lactoglobulin, serum albumin, e.g., human serum albumin (HSA), bovine serum albumin (BSA), and recombinant HA, hyaluronic acid, polyvinylpyrrolidone (PVP), poly(lactic-co-glycolic acid) (PLGA), polyacrylic acid (PAA) and derivatives thereof (e.g., Amphipol A8-35, PAA5-25C8-40C3, Carbopol® 934, Carbopol® 980), PEG, hydroxyethyl starch, sulfated polysaccharides, polyamino acids, dextran, diethylaminoethyl-dextran, cyclodextrin and derivatives thereof, e.g., hydroxypropyl- beta-cyclodextrin, sulfobutylether-beta-cyclodextrin, polyethyleneimine (PEI), and carboxymethyl cellulose. [0084] Non-limiting examples of salts include sodium chloride, sodium sulfate, sodium thiocyanate, potassium chloride, potassium phosphate, lactic acid salts, e.g., calcium lactate, dioleoyl propyl-trimethylammonium chloride (DOTMA), sodium caprylate, cholesterol sulfate, protamine sulfate, and guanidine hydrochloride. [0085] Non-limiting examples of lipids and lipid derivatives thereof include fatty acids, e.g., oleic acid, phospholipids and phospholipid derivatives, diethanolamine (DEA) phospohate, DEA cetyl phosphate, oleth-10 phosphate, DEA cetyl phosphate, mannosylglycerate, polidocanol, sulfobetaine cholate, phospholipids, and C12-15 alcohols benzoate. [0086] Non-limiting examples of surfactants include non-ionic surfactants like polysorbate 20, polysorbate 40, polysorbate 60, polysorbate 80, poloxamer, e.g., Pluronic F68 and F127, PEG dodecyl ethers, e.g., Brij 35 and Brij 30, and PEG tert-octylphenyl ether, e.g., Triton X-100.
[0087] Non-limiting examples of water-miscible co-solvents include dimethyl sulfoxide (DMSO), dimethylformamide (DMF), dimethylacetamide (DMA), N-methylpyrrolidone (NMP), ethanol, PEG- 40 castor oil, and camphorsulfonic acid (CSA). [0088] A combination of one or more excipients from the lists above may be used in the method disclosed herein. [0089] As can be appreciated by one skilled in the art, some of the excipients disclosed herein can impact the pH of the protein mixture. For example, certain amino acids are acidic, e.g., aspartic acid and glutamic acid, or basic, e.g., lysine and arginine, and can function as an acid or base. Amino acids can also form a buffer with added bases or acids. Similarly, certain acids or bases disclosed herein can function as an excipient, e.g., ascorbic acid, citrate acid, hyaluronic acid, and lactic acid, all of which have stabilizing properties. [0090] In certain embodiments, the one or more excipients are added before the UFDF operation. In certain embodiments, the one or more excipients are added after the UFDF operation. In certain embodiments, the one or more excipients are added before the UFDF operation, and then removed during the UFDF operation (e.g., using a DF buffer that does not contain the excipients) such that the excipients are not present in the protein mixture obtained after the UFDF operation. Typically, such excipients can stabilize the protein of interest before and during the UFDF operation, but may not be suitable for being administrated to patients, e.g., humans. Proteins of Interest [0091] Proteins that may be prepared by the methods disclosed herein include therapeutic proteins such as those approved for human therapeutic use by regulatory agencies, e.g., FDA and EMA. In certain embodiments, the therapeutic proteins are therapeutic antibodies include, but are not limited to, a chimeric antibody, a human antibody, a humanized antibody, a bispecific antibody, and a domain antibody (dAb). [0092] Non-limiting examples of therapeutic proteins that may be prepared by the methods disclosed herein include Aflibercept (Eylea®), Etanercept (ENBREL®), Epoetin alfa (EPOGEN®), Pegfilgrastim (Neulasta®), Filgrastim (NEUPOGEN®), darbepoetin alfa (Aranesp®), Dornase alfa (Pulmozyme®), IL-2 mutein Fc fusion protein (AMG592), Becaplermin (REGRANEX®), Alteplase (Activase®), Laronidase (Aldurazyme®), Alefacept (Amevive®), Interferon beta-1b (BETASERON®), Rasburicase (Elitek®), Asparaginase (Elspar®), Agalsidase beta (Fabrazyme®), Interferon alfacon-1(INFERGEN®), Interferon alfa-2a (INTRON A®), Anakinra (Kineret®), Oprelvekin (NEUMEGA®), Denileukin diftitox (Ontak®), Peginterferon alfa-2a (PEGASYS®), Aldesleukin (Proleukin®), Dornase alfa (Pulmozyme®), Interferon beta-1a (Rebif®), Becaplermin (REGRANEX®), Reteplase (Retavase®), Interferon alfa-2 (Roferon-A®), Tenecteplase (TNKase®), and Drotrecogin alfa (Xigris®), Rilonacept (ARCALYST®), Romiplostim (Nplate®),
methoxypolyethylene glycol-epoetin beta (MIRCERA®), C1 esterase inhibitor (Cinryze®), idursulfase (Elaprase®), alglucosidase alfa (Myozyme®), abatacept (ORENCIA®), galsulfase (Naglazyme®), palifermin (Kepivance®) and interferon gamma-1b (ACTIMMUNE®). [0093] Non-limiting exemplary antibodies that may be prepared using the methods disclosed herein include bevacizumab (Avastin®), cetuximab (Erbitux®), adalimumab (HUMIRA®), infliximab (Remicade®), rituximab (Rituxan®), natalizumab (Tysabri®), eculizumab (Soliris®), trastuzumab (Herceptin®), Alemtuzumab (Campath®), Arcitumomab (CEA-Scan), Imciromab Pentetate (Myoscint®), Capromab Pendetide (ProstaScint®), Abciximab (ReoPro®), Rituximab (Rituxan®), Basiliximab (Simulect®), Palivizumab (Synagis®), Omalizumab (Xolair®), Daclizumab (Zenapax®), Muromonab-CD3 (Orthoclone OKT3®), Edrecolomab (Panorex®), golimumab (Simponi®), Certolizumab pegol (Cimzia®), ustekinumab (Stelara®), panitumumab (Vectibix®), tositumomab (Bexxar®), panitumumab (Victibix®), evolocumab (Repatha®), denosumab (Prolia®), romosozumab (Eventiy®), tezepelumab, anti-PAC1 (pituitary adenylate cyclase activating type 1) receptor antibody (WO2014/144632), anti-IL-15 antibody (WO2007/087384), bispecific antibody- peptide conjugate that targets BAFF and ICOS ligand (US 9,458,241), human monoclonal antibody that inhibits c-fms and decreases tumor-associated macrophage (TAM) function (WO2009/026303), prezalumab (WO2007/011941), erenumab (Aimovig™, WO2010/075238), and bispecific T cell engager (BiTE) antibody constructs including blinatumomab (Blicyto®), anti-CD33 and anti-CD3 BiTE antibody construct, anti-EGFRvIII and anti-CD3 BiTE antibody construct, anti-DLL3 and anti- CD3 BiTE antibody construct, anti-CD19 and anti-CD3 BiTE antibody construct, anti-MSLN and anti-CD3 BiTE antibody construct, anti-CDH19 and anti-CD3 BiTE antibody construct, anti-FLT3 and anti-CD3 BiTE antibody construct, anti-DLL3 and anti-CD3 BiTE antibody construct, anti-CDH3 and anti-CD3 BiTE antibody construct, anti-CD70 and anti-CD3 BiTE antibody construct, anti-PSMA and anti-CD3 BiTE antibody construct, and anti-BCMA and anti-CD3 BiTE antibody construct (as described in WO2008/119567 and WO2017/134140). [0094] The invention will be more fully understood by reference to the following examples. The examples should not, however, be construed as limiting the scope of the invention. [0095] All references cited in this application are incorporated by reference herein. EXAMPLES [0096] Two half-life extended (HLE) bispecific T-cell engager (BiTE®) antibodies and two monoclonal antibodies (mAbs) were used to evaluate the prediction accuracy of MUD for the osmolality of the protein mixtures produced by UFDF operations. The HLE BiTE antibodies have molecular weights of approximately 105,000 Da. The mAbs are either immunoglobulin G1 (IgG1) or IgG2 with molecular weights of approximately 150,000 Da. The isoelectric points (PIs) of the mAbs range from 7.5 to 8.12.
[0097] Table 4 lists the values of the charge adjustment parameters for four proteins used herein as case studies. Table 4: Charge adjustment parameters for four proteins used herein as Examples Protein-Charge Adjustment Protein Parameters Example 1
[0098] The protein mixtures that underwent UFDF were prepared by diluting mAb 1 to 6 g/L with potassium phosphate/NaMES pH 7.0 buffer (MES stands for 2-(N-morpholino)ethanesulfonic). [0099] Method: 6 g/L mAb 1 mixture was concentrated to approximately 49, 70, and 91 g/L by ultrafiltration and then diafiltrated with 12 diavolumes of DF buffer. These UFDF processes, which were conducted at ambient room temperature (20 ± 5oC) and used three pieces of 88 cm2 membrane cassettes with a total membrane area of 264 cm2, was executed under an automated GE Healthcare ÄKTA Crossflow with UNICORN software version 7.3. The DF buffer had a pH of 4.7 and contained 20 mM sodium acetate, 40 mM L-phenylalanine, and 4.2 %w/v sorbitol. At the end of each UFDF process, the osmolality of the resulting protein mixture was measured. The following table lists the measured osmolalities and the corresponding MUD predictions with and without the improved osmolality prediction model disclosed herein.
Table 5 noi t n a o r i yt t t t li a i u h f r tl ) l a o h t l yt i ti l i r e l t o ) i e l d a l ) we d o M no i t c i d e r P y ti l a l o ms O d e v o r p m I [0100] after ultrafiltr
ation, MUD predicts it to contain 23.45 mM acetate, 221.49 mM sorbitol, 38.43 mM L- phenylalanine, and 8.55 mM sodium. Since the improved osmolality prediction model requires the mole fractions of water and that of sorbitol, the first step is to estimate the volume fraction of non- protein solution from the actual protein concentration and assume that protein has a density of 0.73 mL/gram, 1 − ହଷ.଼ଽ ^ ^.^ଷ mL protein mL non-protein solution L mixture ⋅ g protein = 0.9607 L mixture . (33) [0101] All the
with respect to non-protein solution with the assumption that the non-protein solution has a density of 1 L/kilogram: 23.45 mmol acetate ⋅ 1 L mixture ⋅ 1 L non-protein solution = 24 mmol acetate L mixture 0.9607 mL non-protein solution kg non-protein solution .41kg non-protein solution (34) 221.49 mmol sorbitol L mixture ⋅ 1 L mixture 0.9607 mL non-protein solution ⋅ 1 L non-protein solution kg non-protein solution = 230.56 mmol sorbitol kg non-protein solution (35)
mixture 0.9607 mL non-protein solution kg non-protein solution kg non-protein solution (36) 8.55 mmol sodium 1 L mixture 1 L non-protein solution mmol sodi L mixture ⋅0.9607 mL non- solution ⋅ non- solution = 8.90 um non- solution. (37)
the excipients from that of non-protein solution: 1 kg non-protein solution − 24.41 mmol acetate⋅ 59.044 g acetate mol acetate −
230.56 mmol sorbitol⋅ 182.17 g sorbitol − 40.00 m 165.19 g L-phenylalanine mol sorbitol mol L-phenylalanine⋅ mol L-phenylalanine − 8.90 mmol sodium⋅ 23 g sodium = 949.75 g water mol water mol sodium ⋅ 18 g water = 52.76 mol water. (38) [0103] The mole fractions of water and sorbitol can be calculated as follows: Total number of moles of non-protein components = 52.76 mol water + 24.41 mmol acetate + 230.56 mmol sorbitol + 40.00 mmol L-phenylalanine + 8.90 mmol sodium = 53.06 mol (39) mol fraction of water = ହଶ.^^ mol water ହଷ.^^ mol = 0.9943 (40) mol fraction of sorbitol = ଶଷ^.ହ^ mmol sorbitol ହଷ.^^ mol = 0.0043. (41) [0104] The activity water can be estimated by using Equation (30): ^^^ ≈ ^^௪^^^sorbitol^sమ orbitol = 0.9943 ⋅ ^^ି^.^ହ⋅^.^^ସଷమ = 0.9942. (42) [0105] The osmotic pressure can be calculated by using Equation (31): ି଼ ^ ^^ = ିோ் ௩ೈ ln ^^^ = .ଷ^ସ^^^⋅ଶ^ଷ.^ହ ^ ⋅ ln 0.9942 = 0.73 MPa. (43) ^ షయ ^య .^^଼⋅^^ ^^^ [0106] The
(32): Osmolality = గ ^.^ଷ MPa mOsm ோ బ் = ଶ.ଶ^^ kg⋅MPa = 320.8 mol kg water. (44) Example 2 [0107] Before undergoing UFDF, the protein mixtures of HLE BiTE® 2 underwent purification steps including protein A affinity chromatography, low pH viral inactivation, cation exchange gradient chromatography, mixed mode anion exchange chromatography, and viral filtration. The concentration of HLE BiTE 2 was 1.60 mg/mL and was equilibrated with a buffer that contained 13.66 g/L sodium chloride, 16.29 g/L MES sodium salt anhydrous, and 5.67 g/L MES hydrate before UFDF. [0108] Method: 1.60 mg/mL HLE BiTE® 2 mixture was concentrated to approximately 4.0 mg/mL by ultrafiltration and then diafiltrated with 10 diavolumes of DF buffer. Subsequently, the protein mixture was diluted to a final protein concentration of 1.00 mg/mL. These UFDF processes were conducted at ambient room temperature (20 ± 5oC) and used Millipore’s P3 Regenerated Cellulose 10 kDa filters that had areas of 0.11 m2, 0.57 m2, and 1.14 m2 and max filter sizing ranging from 55 to 140 g/m2. Diafiltration and dilution used the same buffer that contained 90 g/L beet derived sucrose and 1.47 g/L L-glutamic acid and had a pH of 4.2 that was achieved with the addition of 10N sodium hydroxide. At the end of UFDF, the osmolality of the protein mixture was measured to be 312 mOsm/kg water. The following table lists the measured osmolality and the corresponding MUD predictions with and without improved osmolality prediction model.
Table 6 n e o r i d t e v u o n o i d e t e r c i r t v x i u t d e p c r m i o d r p e d o M not c d e P yt a o ms O [0109] UFDF, MUD
2.0 predicts it to contain 9.88 mM glutamate, 262.74 mM sucrose, and 5.79 mM sodium. Since the improved osmolality prediction model requires the mole fractions of water and that of sucrose, the first step is to estimate the volume fraction of non-protein solution from the actual protein concentration and assume that protein has a density of 0.73 mL/gram, 1 − ^.^ଷ ^ ^.^ଷ mL protein mL non-protein solu mixture ⋅ g protein = 0. tion L 9992 L mixture . (45) [0110] All the
with respect to non-protein solution with the assumption that the non-protein solution has a density of 1 L/kilogram: 9.88 mmol glutamate 1 L mixture 1 L non-protein solution mmo L mixture ⋅0.9992 mL non-protein solution ⋅ kg non-protein solution = 9.89 l glutamate kg non-protein solution (46) 262.74 mmol sucrose ⋅ 1 L mixture ⋅ 1 L non-protein solution on-protein solution = 262.94 mmol sucrose L mixture 0.9992 mL non-protein solution kg n kg non-protein solution (47) 5.79 mmol sodium 1 L mixture 1 L non-protein solutio L mixture ⋅0.9992 mL non-protein solution ⋅ n kg non-protein solution = 5.79 mmol sodium kg non-protein solution. (48) [0111] The amount of water in the solution can be estimated by subtracting the masses of all the excipients from that of non-protein solution: 1 kg non-protein solution − 9.89 mmol glutamate⋅ 146.12 g glutamate mol glutamate − 262.94 mmol sucrose⋅ 342.3 g sucrose 23 g sodium mol water mol sucrose − 5.79 mmol sodium⋅ mol sodium = 908.43 g water ⋅ 18 g water = 50.47 mol water. (49)
[0112] The mole fractions of water and sorbitol can be calculated as follows: Total number of moles of non-protein components = 50.47 mol water + 9.89 mmol glutamate + 262.94 mmol sucrose + 5.79 mmol sodium = 50.75 mol (50) mol fraction of water = ହ^.ସ^ mol water ହଷ.^^ mol = 0.9945 (51) mol fraction of sucrose = ଶ^ଶ.ଽସ mmol sucrose ହଷ.^^ mol = 0.0052. (52) [0113] The activity water can be estimated by using Equation (30): ^^^ ≈ ^^௪^^^sucrose^sమucrose = 0.9945 ⋅ ^^ି^.ସ^⋅^.^^ହଶమ = 0.9943. (53) [0114] The by using Equation (31):
ିோ் ି଼.ଷ^ସ ^ ⋅ଶ^ଷ.^ହ ௩ೈ ln ^^^ = ^ ^ ^^ = ^^ ^.^^଼⋅^^షయ ^య ⋅ ln 0.9943 = 0.72 MPa. (54) ^^^ [0115] The osmolality can be calculated by using Equation (32): Osmolality = గ ^.^ଶ MPa mOsm ோ బ் = ଶ.ଶ^^ kg⋅MPa = 315.5 . (55) mol kg water Example 3 [0116] The protein mixture that underwent UFDF contained 70 mg/mL mAb 3, 10 mM acetate, and 9 w/v% sucrose and had a pH of 5.2. [0117] Method: 70 mg/mL mAb 3 was diafiltrated without ultrafiltration, i.e., it was diafiltrated at 70 mg/mL with 7 diavolumes of DF buffer. Subsequently, the protein mixture was overconcentrated to approximately 160 mg/mL and then diluted to approximately 140 mg/mL with dilution buffer. The DF buffer contained 15 mM acetate and 8.5 w/v% sucrose and had a pH of 4.83, and the dilution buffer contained 15 mM acetate and 8.5 w/v% sucrose and had a pH of 5.20. At the end of UFDF, the osmolality of the protein mixture was measured to be 334 mOsm/kg water. The following table lists the measured osmolality and the corresponding MUD predictions with and without improved osmolality prediction model. Table 7
f o g d no i ) k e / v o l e Dd l e d e l e D l e t a L m m s r p d mo Ue v d M o o v o r d o Ud M e d v o M not c d e P yt a o ms O [011 , MUD 2.0 p
. , . , . . the improved osmolality prediction model requires the mole fractions of water and that of sucrose, the first step is to estimate the volume fraction of non-protein solution from the actual protein concentration and assume that protein has a density of 0.73 mL/gram, 1 − ^ସ^ ^ ^.^ଷ mL protein mL non-protein solut e ⋅ g protein = 0.897 ion L mixtur 8 L mixture . (56) [0119] All the
with respect to non-protein solution with the assumption that the non-protein solution has a density of 1 L/kilogram: 21.54 mmol acetate 1 L mixture 1 L non-protein soluti L mixture ⋅0.8978 mL non-protein solution ⋅ on kg non-protein solution = 23.99 mmol acetate kg non-protein solution (57) 222.58 mmol sucrose 1 L mixture 1 L non-protein solution m ixture ⋅0.8978 mL non-protein solution ⋅ mol sucrose L m kg non-protein solution = 247.92kg non-protein solution (58) 6.62 mmol sodium ⋅ 1 L mixture 1 L non-protein solution mmol s 0.8978 mL non-protein solution ⋅kg non-protein solution = 7.37 odium L mixture kg non-protein solution. (59) [0120] The amount of water in the solution can be estimated by subtracting the masses of all the excipients from that of non-protein solution: 1 kg non-protein solution − 23.99 mmol acetate⋅ 59.044 g acetate mol acetate − 247.92 mmol sucrose⋅ 342.3 g sucrose − 7.37 mmol sodium⋅ 23 g sodium = 913.55 g mol water mol sucrose mol sodium water ⋅18 g water = 50.75 mol water. (60) [0121] The mole fractions of water and sorbitol can be calculated as follows: Total number of moles of non-protein components = 50.75 mol water + 23.99 mmol acetate + 247.92 mmol sucrose + 7.37 mmol sodium = 51.03 mol (61) mol fraction of water = ହ^.^ହ mol water ହ^.^ଷ mol = 0.9945 (62) mol fraction of sucrose = ଶ^ଶ.ଽସ mmol sucrose ହଷ.^^ mol = 0.0049. (63) [0122] The activity water can be estimated by using Equation (30):
^^ ≈ ^^ ^^^sucrose^sమucrose = 0.994 ି^.ସ^⋅^.^^ସଽమ ^ ௪ 5 ⋅ ^^ = 0.9944. (64) [0123] The osmotic pressure can be calculated by using Equation (31): ି଼.ଷ^ସ ^ ⋅ଶ^ଷ ^ = ି .^ହ ^ ^ ோ் ௩ೈ ln ^^^ = ^^^ ^.^^଼⋅^^షయ ^య ⋅ ln 0.9944 = 0.71 MPa. (65) ^^^ [0124] The (32):
= ோ బ் = ଶ.ଶ^^ kg⋅MPa = 313.4 mOsm . (6 mol kg water 6) Example 4 [0125] Before undergoing UFDF, the protein mixtures of HLE BiTE® 4 underwent purification steps including protein A affinity chromatography, low pH viral inactivation, cation exchange gradient chromatography, mixed mode anion exchange chromatography, and viral filtration. The concentration of HLE BiTE 4 was 1.26 mg/mL and contained 0.233 M sodium, 0.177 M chloride, 0.045 M acetate, and 0.016 M MES before UFDF. [0126] Method: 1.26 mg/mL HLE BiTE® 4 mixture was concentrated to 8.0 mg/mL by ultrafiltration and then diafiltrated with 10 diavolumes of DF buffer. Subsequently, the protein mixture was diluted to a final protein concentration of 5.51 mg/mL. These UFDF processes were conducted at ambient room temperature (20 ± 5oC) and used Millipore’s P3 Regenerated Cellulose 10 kDa filters that had area of 1.14 m2 and max filter sizing no more than 110 g/m2. Diafiltration and dilution used the same buffer that contained 90 g/L beet derived sucrose and 1.47 g/L L-glutamic acid and had a pH of 4.2 that was achieved with the addition of 10N sodium hydroxide. At the end of UFDF, the osmolality of the protein mixture was measured to be 315 mOsm/kg water. The following table lists the measured osmolality and the corresponding MUD predictions with and without improved osmolality prediction model. Table 8 la d ni g e F k / v o l r e d D d e l e d e d v l e d D l d e d o M no c d e P y a o ms O
[0127] Calculation: For the protein mixture that contained 5.51 mg/mL protein after UFDF, MUD 2.0 predicts it to contain 9.76 mM glutamate, 261.86 mM sucrose, and 5.77 mM sodium. Since the improved osmolality prediction model requires the mole fractions of water and that of sucrose, the first step is to estimate the volume fraction of non-protein solution from the actual protein concentration and assume that protein has a density of 0.73 mL/gram, 1 − ହ.ହ^ ^ ^.^ଷ mL protein mL non-protein solution L mixture ⋅ g protein = 0.9960 L mixture . (67) [0128] All the converted from molarity to molality with respect to non-protein
the non-protein solution has a density of 1 L/kilogram: 9.76 mmol glutamate ⋅ 1 L mixture 0.9960 mL non-protein solution ⋅ 1 L non-protein solution kg non-protein solution = 9. mmol glutamate L mixture 80 kg non-protein solution (68)
(69) 5.77 mmol sodium 1 L mixture 1 L non-protei L mixture ⋅0.9960 mL non-protein ⋅ n solution kg non-protein solution = 5.79 mmol sodium kg non-protein solution. (70) [0129] The amount of water in the solution can be estimated by subtracting the masses of all the excipients from that of non-protein solution: 1 kg non-protein solution − 9.80 mmol glutamate⋅ 146.12 g glutamate mol glutamate − 263.80 mmol sucrose⋅ 342.3 g sucrose 23 g sodium mol water mol sucrose − 5.79 mmol sodium⋅ mol sodium = 908.14 g water ⋅ 18 g water = 50.45 mol water. (71) [0130] The mole fractions of water and sorbitol can be calculated as follows: Total number of moles of non-protein components = 50.45 mol water + 9.80 mmol glutamate + 263.80 mmol sucrose + 5.79 mmol sodium = 50.73 mol (72) mol fraction of water = ହ^.ସହ mol water ହ^.^ଷ mol = 0.9945 (73) mol fraction of sucrose = ଶ^ଷ.଼^ mmol sucrose ହ^.^ଷ mol = 0.0052. (74) [0131] The activity water can be estimated by using Equation (30): ^^^ ≈ ^^௪^^^sucrose^sమucrose = 0.9945 ⋅ ^^ି^.ସ^⋅^.^^ହଶమ = 0.9943. (75) [0132] The
by using Equation (31): ି ^ ି ଼.ଷ^ସ ⋅ଶ^ଷ.^ହ ^ ^^ = ோ் ln ^^ = ^^^ ⋅ ln 0.9943 = 0.72 MPa. (76) [0133] The
(32): Osmolality = గ ^.^ ோ బ் = ଶ MPa ଶ.ଶ^^ kg⋅MPa = 315.4 mOsm . mol kg water (77)