Mass transfer of proteins in chromatographic media: Comparison of pure and crude feed solutions

Elucidation of intraparticle mass transfer mechanisms in protein chromatography is essential for process design. This study investigates the differences of adsorption and diffusion parameters of basic human fibroblast factor 2 (hFGF2) in a simple (purified) and a complex (clarified homogenate) feed solution on the grafted agarose-based strong cation exchanger Capto S.

Journal of Chromatography A 1676 (2022) 463264 Contents lists available at ScienceDirect Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma Mass transfer of proteins in chromatographic media: Comparison of pure and crude feed solutions Markus C Berg a, Jürgen Beck b, Alex Karner b, Kerstin Holzer b, Astrid Dürauer a,b, Rainer Hahn a,b,∗ a Austrian Center of Industrial Biotechnology, Muthgasse 18, Vienna 1190, Austria Department of Biotechnology, Institute of Bioprocess Science and Engineering, University of Natural Resources and Life Sciences Vienna, Muthgasse 18, Vienna 1190, Austria b a r t i c l e i n f o Article history: Received 30 March 2022 Revised 17 June 2022 Accepted 18 June 2022 Available online 19 June 2022 Keywords: Pore diffusion Solid diffusion Grafted media Ion exchange chromatography hFGF2 a b s t r a c t Elucidation of intraparticle mass transfer mechanisms in protein chromatography is essential for process design This study investigates the differences of adsorption and diffusion parameters of basic human fibroblast factor (hFGF2) in a simple (purified) and a complex (clarified homogenate) feed solution on the grafted agarose-based strong cation exchanger Capto S Microscopic investigations using confocal laser scanning microscopy revealed slower intraparticle diffusion of hFGF2 in the clarified homogenate compared to purified hFGF2 Diffusive adsorption fronts indicated a strong contribution of solid diffusion to the overall mass transfer flux Protein adsorption methods such as batch uptake and shallow bed as well as breakthrough curve experiments confirmed a 40-fold reduction of the mass transfer flux for hFGF2 in the homogenate compared to pure hFGF2 The slower mass transfer was induced by components of the clarified homogenate Essentially, the increased dynamic viscosity caused by a higher concentration of dsDNA and membrane lipids in the clarified homogenate contributed to this decrease in mass transfer Moreover, binding capacity for hFGF2 was much lower in the clarified homogenate and substantially decreased the adsorbed phase driving force for mass transfer © 2022 The Authors Published by Elsevier B.V This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) Introduction Mass transfer of proteins in chromatographic media is a slow diffusional process Typically, different transport resistances appear in adsorption systems with porous particles [1,2] Firstly, proteins must pass through a stagnant film around the particle before diffusional transport into the particle itself can occur Properties of the liquid phase surrounding each particle affect these external mass transfer mechanisms Concentration differences across the boundary layer and the film thickness define the impact of film resistance [2–4] The type of diffusion mechanism is defined by the structural properties of the chromatographic resin and buffer conditions as well as the protein characteristics Pore diffusion is dominant for macro-porous resins which can be fully penetrated by a protein of a size smaller than the pore structure During pore diffusion, surface attachments and detachments can take place repeat- ∗ Corresponding author at: Department of Biotechnology, Institute of Bioprocess Science and Engineering, University of Natural Resources and Life Sciences Vienna, Muthgasse 18, Vienna 1190, Austria E-mail address: rainer.hahn@boku.ac.at (R Hahn) edly The main driving force of this mechanism is controlled by the solute concentration gradient in the liquid phase of the pore Solid diffusion, on the other hand, occurs for proteins in the adsorbed state In contrast to pore diffusion, detachment does not typically take place for adsorbed proteins This phenomenon enables an enhanced mass transfer caused by an absorbed protein concentration gradient It is important to mention that other attributes such as narrow pores or pores blocked by adsorption of large molecules can lead to hindered diffusion [5] Pore diffusion coefficients between 10−6 – 10−8 cm²/s and solid diffusion coefficients ranging from 10−8 to 10−10 cm²/s have been reported for various proteins [1,6] The order of magnitude depends on the properties of the protein and the mobile phase as well as characteristics of the stationary phase [1,7,8] Besides conventional macro-porous chromatography resins, polymer grafted media are frequently used for protein purification [2] These special chromatographic materials contain polymer chains grafted onto the particle surface Such modifications enhance binding capacity as well as mass transfer, as compared to conventional media [9– 16] According to Tao et al [8], effective pore diffusion coefficients that are greater than the diffusivity for proteins in free solution https://doi.org/10.1016/j.chroma.2022.463264 0021-9673/© 2022 The Authors Published by Elsevier B.V This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) M.C Berg, J Beck, A Karner et al Journal of Chromatography A 1676 (2022) 463264 the pore diffusion model can be obtained when Ds = and vice versa for the solid diffusion model when De = For column adsorption operations Eq (1d) is replaced by: can be achieved on dextran grafted resins for ion exchange processes This result may be explained by a transport enhancement facilitated by an electrostatic driving force or a coupling transport of proteins and ions [2,9] The mass transfer mechanisms of single or two component systems on ion exchange media as well as proteins on affinity resins (such as protein A) have been previously investigated [1,7,17–21] However, little data is available on diffusional adsorption processes of proteins in complex solution such as clarified bacterial homogenates [22,23] In general, most isoelectric points of E coli host cell proteins are in the acidic range [24] This enables purification of positively charged recombinant proteins on cation exchangers with hardly any coeluting process-related impurities if binding conditions are adjusted properly In principle, this high selectivity should allow the determination of protein mass transport parameters with single component adsorption models The aim of the present study was to elaborate the differences in mass transfer mechanisms of purified basic human fibroblast growth factor (hFGF2) and a clarified homogenate containing hFGF2 overexpressed in E coli This basic protein exhibits an isoelectric point of 9.6 at a molecular size of 17.2 kDa in monomeric form [25,26] and is therefore well suited for the purification by cation exchangers For all our main investigations, the strong cation exchange resin Capto S from Cytiva (Uppsala, Sweden) was chosen as the stationary phase This resin is based on an agarose backbone grafted with dextran inclusions [8,9] Since host cell-related impurities such as DNA and membrane lipids are present in the clarified homogenate, dynamic viscosity is increased significantly compared to the pure protein solution which affects the diffusion mechanisms [27,28] For determining parameters describing the mass transfer of the protein of interest, batch and packed bed methods were performed εb ∂C ∂ q¯ ∂C ∂ 2C + ( − εb ) +u = εb DL ∂t ∂t ∂z ∂z with boundary conditions: t = 0C = (2a) z = 0uCF = uC − r = r p De ∂c ∂q + Ds = k f (C − c ) ∂r ∂r (2c) For a rectangular isotherm, an analytical solution for batch adsorption and film and pore diffusion control has been obtained by Teo and Ruthven [30]: C0 De t = 1− I2 − I1 qmax r p Bi (3) with: I1 = 1 √ tan−1 λ I2 = ln = VM qm V C0 (1) λ= (1a) λ3 + η3 λ + λ3 + λ + η ln 6λ + with boundary conditions: ∂c =0 ∂r (2b) 2.2 Analytical solutions for film and pore diffusion control A general model for mass transfer for batch adsorption assuming parallel mass transfer of pore and solid diffusion mechanisms within the bead pores as given by [29]: r=0 ∂C ∂z where ε b is the extra-particle void fraction, z is the bed length coordinate, DL is the axial dispersion coefficient and L is the bed length 2.1 General model for pore and solid diffusion t = 0c = 0q = εb DL ∂C =0 ∂z z=L Theory ∂q ∂ ∂c ∂q = r De + Ds ∂ t r2 ∂ r ∂r ∂r (2) −1 2η − λ √ λ 3 − tan−1 2−λ √ λ λ3 + η3 λ3 + (3a) (3b) (3c) 1/3 (3d) η = (1 − F )1/3 (3e) k f rp De (3f) (1b) Bi = (1c) where qmax is the maximum binding capacity, Bi is the Biot number, and F is the frictional approach to equilibrium The solutions for film mass transfer control are 3k f VM VM dq¯ dC = − C − c|r=r p = − dt r pV V dt (1d) 3k f VM C = exp − t C0 rp V C = C0t = (1e) and and material balance: 3k f VM q = − exp − t qm rp V where q is the solute concentration in particle, t is the time, r the particle radial coordinate, De the effective pore diffusivity, Ds is the effective solid diffusivity, c is the solute concentration in the pore fluid, rp is the particle radius, C the solute concentration in the bulk fluid, C0 is the initial protein concentration, VM is the volume of the particles, V is the bulk solution volume and q¯ is the particleaverage solute concentration A reduction of the general model to (4) (5) For shallow-bed adsorption operations the solution is [29]: ε p Det C0 r p qm = 1 1 − 1− F − (1 − F )2/3 Bi (6) M.C Berg, J Beck, A Karner et al Journal of Chromatography A 1676 (2022) 463264 A constant pattern solution for film and pore diffusion in column adsorption described by Weber et al [31] is given as: C δ =1− exp {[−τ + ξ + − ln (1 + δ )]/δ} C0 1+δ 15 2η − N pore (τ1 − ) = √ tan−1 √ 3 for − 15 ln + η + η2 − 5π + ln − η3 + − √ Bi 3 τ − ξ ≥ − ln(1 + δ ) when δ ≤ τ is the dimensionless time and ξ is the bed length parameter These parameters are defined as: (7) where τ1 = ut L N pore = − εb = ξ= (7d) CF 1/2 Re ε S c 1/3 hFGF2 was produced in Escherichia coli according to the procedure published by Sauer et al [25] BL21 cells containing hFGF2 were resuspended in 50 mM Na2 HPO4 /NaH2 PO4 pH 6.5 to yield in a 60 gCDM/L suspension The suspension was homogenized at 700/70 bar for passages on a Niro Soavi PANDAPlus 20 0 (GEA, Parma, Italy) Removal of cell debris was achieved by centrifugation and a filtration step on a 0.2 μm sterile filter (Fluorodyne EX EDF, PALL, Dreieich, Germany) Purification of hFGF2 was performed on a 10 mL Capto S column The filtered homogenate (100 mL) was loaded and eluted using a linear gradient ranging from to M NaCl The protein eluate was buffer exchanged via a PD-10 desalting column (Cytiva, Uppsala, Sweden) into 50 mM Na2 HPO4 /NaH2 PO4 , 30 mM NaCl pH 6.5 Both the clarified homogenate as well as the purified and buffer exchanged protein solutions were used to conduct the experiments as described in the subsequent sections A hFGF2 concentration of mg/mL was chosen for all experiments unless otherwise stated (8) 2.3 Analytical solution for film and solid diffusion control For solid diffusion control an analytical solution is given by [32]: π ∞ n=1 n π Ds t exp − n r p2 (9) Eq (9) is valid for intraparticle mass transfer control if δ ≥ δ is the diffusion resistance parameter which determines the controlling mechanism and is described as: δ k f r p C0 = Ds qmax 3.2 Sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) (10) SDS–PAGE was performed in an XCell SureLockTM Mini-Cell Electrophoresis System (Thermofisher Scientific, Dreieich, Germany) with an EPS 301 power supply (Cytiva, Uppsala, Sweden) A NuPage 4–12% BIS-Tris gel (Thermofisher Scientific, Dreieich, Germany) was used for separation All samples were 10-fold diluted in 50 mM Na2 HPO4 /NaH2 PO4 pH 6.5 prior to application onto the gel Separation was carried out according to the manufacturer’s directions after μL of 4x sample buffer (Thermofisher Scientific, Dreieich, Germany), μL of DTT, and 13 μL of the diluted sample aliquots were combined and an aliquot (14 μL) was loaded onto the gels The separated proteins were fixed with a solution containing 50% ethanol and 10% glacial acetic acid Protein bands were stained with Coomassie blue G 250 for 30 Destaining was performed with a solution containing 25% ethanol and 8% glacial acetic acid Destained gels were scanned on an Epson Perfection V700 Photo scanner (EPSON, Meerbusch, Germany) SeeBlueTM Plus2 pre-stained protein standard (7 μL) (Thermofisher Scientific, Dreieich, Germany) was used as the molecular mass marker on each gel An analytical solution for the column adsorption for external mass transfer and solid diffusion has been obtained by Yoshida et al [33]: C = exp C0 δ (16) 3.1 Sample preparation where Sh is the Sherwood number, Re is the Reynolds number and Sc is the Schmidt number (1 − ε ) k f L rp u Materials and method where u is the superficial velocity, τ is the dimensionless time and CF is the feed protein concentration The film mass transfer coefficient kf for packed bed operation can be obtained from the following correlation: F =1− (15) (7c) (1 − εb )qmax Sh = 1.15 3k f C0 εL t− r p qmax u and (7b) 1/3 C CF η = 1− τ= (7a) 15(1 − εb )De L ur 2p (14) τ −ξ +δ−1− δ for τ − ξ ≤ −δ + + δ − ln C δ =1− exp C0 1+δ 1+δ (11) δ −τ + ξ − δ + + δ ln 1+δ δ /δ for τ − ξ ≥ −δ + + δ − ln 1+δ δ (12) when δ ≥ 1, and: C = exp (τ − ξ − ) C0 3.3 Adsorption isotherms for τ − ξ ≤ − ln(1 + δ ) A 50 mM Na2 HPO4 /NaH2 PO4 30 mM NaCl pH 6.5 buffer was used for slurry preparation of the Capto S resin (Cytiva, Uppsala, (13) M.C Berg, J Beck, A Karner et al Journal of Chromatography A 1676 (2022) 463264 Sweden) Specific amounts of slurry were mixed with fixed volumes of either clarified homogenate consisting of hFGF2 or purified hFGF2 In general, the protein concentration of hFGF2 in both matrices was set to 2–2.1 mg/mL The resin-protein mixtures were incubated in mL vials at room temperature for 24 h on an endover-end rotator (Stuart SB3, Cole-Parmer, Stone, Staffordshire, UK) at 13 rpm Afterwards, all samples were filtered through 0.22 μm syringe filters (Millex-GV PDFV, Merck Millipore, Darmstadt, Germany) The filtrate was then quantified via HPLC on a Propac WCX10 (Thermofisher Scientific, Dreieich, Germany) with the dimensions mm x 250 mm A linear gradient over 2.5 CV ranging from to M NaCl in 100 mM Na2 HPO4 /NaH2 PO4 pH 6.5 was applied at a volumetric flow rate of mL/min The amount of bound hFGF2 per mL resin was determined by mass balance calculation Equilibrium constant KL and maximum binding capacity qmax were determined by fitting the data to the Langmuir model Adsorption profiles were fitted to pore and solid diffusion models Eqs (6) and ((9)) 3.7 Confocal laser scanning microscopy Fluorescent labeling of hFGF2 was performed with Rhodamine RedTM – X dye (Thermofisher Scientific, Dreieich, Germany) Prior to labeling, hFGF2 was transferred into 500 mM bicarbonate pH 8.5 buffer by using a PD-10 desalting column labeling dye was added into a mL vial in a 1:3 dye: protein molar ratio and incubated for h wrapped in aluminum foil Unbound dye was then removed by using a desalting column A labeling ratio of 0.28 was obtained Labelled hFGF2 was then added to the protein solution in a 1:40 mass ratio Adsorption kinetic experiments were performed with the labelled protein solutions as described above Moreover, microscopy images were recorded with a 40x dry objective and a resolution of 512 × 512 pixels at a frequency of 400 Hz 3.4 Adsorption kinetics For all batch uptake experiments, a 10 mL glass beaker was filled with mL protein solution The slurry of Capto S in 50 mM Na2 HPO4 /NaH2 PO4 (0.078–0.15 mL) was added and stirred on a magnetic stirrer at 300 rpm Samples (150 μL) of the protein-resin suspension were drawn at the predefined time points and immediately filtered through 0.22 μm syringe filters The filtrate was then quantified analogously as described for adsorption isotherms The film mass transfer coefficient kf was determined by a correlation for external mass transfer [1,4] Data obtained via adsorption kinetics were fitted to pore and solid diffusion models by applying Eqs (3)–(5) and (9) Experiments at increased dynamic viscosity were conducted by adding specific amounts of glycerol (Thermofisher Scientific, Dreieich, Germany) to the protein solutions Further studies with pure lysozyme as a model protein as well as Toyopearl Gigacap S (Tosoh, Griesheim, Germany) and SP Sepharose FF (Cytiva, Uppsala, Sweden) as alternative stationary phases were performed analogously Results and discussion 4.1 Purification of hFGF2 Based on the purification procedure published by Sauer et al [25], a cation exchange chromatography system was selected to capture the basic hFGF2 To increase capture efficiency the polymer grafted cation exchanger Capto S was chosen instead of CM Sepharose FF and buffer concentration was reduced Clarified homogenate containing hFGF2 was loaded onto a Capto S column In total, 40 mg of hFGF2 were loaded per mL resin Fig 1A shows the absorbance and conductivity profiles of the capture step A gaussian-shaped elution peak was obtained without any visible shoulders Analysis of the collected fractions by SDS-PAGE revealed a highly pure eluate fraction as shown in Fig 1B, lane 14 No additional bands other than the one of monomeric hFGF2 were detected Since most host cell components of E coli strain BL21 are negatively charged at the chosen buffer conditions hardly any impurities were captured and co-eluted in the desorption step Increasing concentrations of hFGF2 could be detected in the flow through fractions at the end of the loading step (lanes 3–13) Apparently, hFGF2 was loaded beyond the maximum binding capacity of Capto S Nevertheless, replacing CM-Sepharose FF by Capto S substantially increased capacity, and even more importantly, purity of the eluate was very high Due to this high selectivity, modeling of the adsorption was simplified and competitive adsorption models, as described for hFGF2 capture by Kołodziej et al [20], were not required 3.5 Breakthrough curve experiments Columns packed with Capto S and SP Sepharose FF resin were purchased from Repligen (Weingarten, Germany) Breakthrough curves (BTC) were recorded on columns with 0.2 mL and 1.0 mL column volume corresponding to column dimensions of 0.5/1 and 0.5/5 cm A 50 mM Na2 HPO4 /NaH2 PO4 30 mM NaCl pH 6.5 buffer was used for column equilibration Residence time for all BTC experiments varied between and 10 The breakthrough for hFGF2 in the clarified homogenate was monitored by quantifying collected fractions via HPLC on a WCX column as described above Analytical solutions including external mass transfer were used to fit all breakthrough profiles for obtaining solid and pore diffusion coefficients Eqs (7) and ((11)–(14)) 4.2 Adsorption isotherm A first estimation of the binding capacity was done by evaluating the capture run profile Hence, for obtaining accurate values for the maximum binding capacity qmax as well as for the equilibrium constant KL adsorption isotherms were established from batch uptake measurements Both purified hFGF2 and clarified homogenate containing hFGF2 were investigated For pure hFGF2, 50 mM Na2 HPO4 /NaH2 PO4 30 mM NaCl pH 6.5 was chosen as the buffer system which exhibited a comparable conductivity as determined for the homogenate (8 mS/cm) Fig shows the adsorption isotherms including a fit of the Langmuir adsorption model to the experimental data Pure hFGF2 yielded in a maximum binding capacity of 100 mg/mL whereas a qmax of 24 mg/mL was determined for hFGF2 in the clarified homogenate Additionally, a 32-fold reduction of the equilibrium constant KL was obtained for the clarified homogenate containing hFGF2 3.6 Shallow bed adsorption Capto S resin (5 μL) was transferred into a HR 5/50 column (Cytiva, Uppsala, Sweden) Silica beads (20 μL of 100 μm beads) were added for emulating the conditions of a fixed bed [34] Prior to sample application the column was equilibrated with 50 mM Na2 HPO4 /NaH2 PO4 30 mM NaCl pH 6.5 Protein solutions were pumped onto the column in a circular manner at a flow rate of mL/min Elution of bound protein after specific timepoints was achieved by applying a step gradient of 1.0 M NaCl in the equilibration buffer for The amount of protein bound was determined by using a linear equation describing the correlation of the absorbance signal at 280 nm and the protein concentration M.C Berg, J Beck, A Karner et al Journal of Chromatography A 1676 (2022) 463264 Fig Capture run of clarified homogenate containing hFGF2 on Capto S (CV = mL) (A) 40 mg hFGF2 per mL column volume were loaded A linear gradient from to M NaCl in 50 mM Na2 HPO4 /NaH2 PO4 pH 6.5 over CV was applied to elute the protein (B) SDS-PAGE under reduced conditions with Coomassie staining of load, flow through and eluate fractions of Capto S run shown in (A) Lane molecular weight marker SeeBlue; Lane clarified homogenate/load containing hFGF2 (black); Lane to 13 corresponding to the flow through fractions (blue); Lane 14 represents the eluate fraction (green) Note that hFGF2 has a molecular weight of 17.2 kDa (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Fig Adsorption isotherms of purified hFGF2 (A) and clarified homogenate containing hFGF2 (B) on Capto S Absorbed concentration q was plotted against the fluid phase concentration C Solid curves represent fits with the Langmuir model 4.3 Adsorption kinetics agreement with the isotherm measurements, binding capacity for hFGF2 in the clarified homogenate was much lower compared to pure hFGF2 In addition, for both experimental methods, batch uptake and shallow bed adsorption, a significant decrease of the adsorption kinetics of hFGF2 on Capto S in the clarified homogenate compared to purified hFGF2 was confirmed For quantitative analysis of the uptake data, we followed a stepwise approach considering different contributions to the overall mass transport For that purpose, we used established correlations and structural parameters that had been previously determined Analytical solutions for batch uptake are available for both mass transfer mechanisms, pore and solid diffusion as described in the theory section These solutions have been derived assuming a rectangular adsorption isotherm For pure hFGF2, the isotherm is highly favorable but not for the clarified homogenate containing hFGF2 All experiments were performed at an hFGF2 concentration of mg/mL which yielded a constant separation factor of ∼ 0.15 for the clarified homogenate To investigate if the analytical solution would lead to a significant error, we compared the analytical to the numerical solution (Fig A2 in supportive information) We found only minor differences and as such the analytical solutions can be used To gain an insight into the mass transfer mechanism, investigation by confocal laser scanning microscopy (CLSM) of the intraparticle mass transport was performed In general, pore diffusion and steep isotherms result in a shrinking core behavior with visible sharp fronts In contrast, solid diffusion is distinguished by diffusive profiles and fast progression to the center of the particle As previously shown by Beck et al [35], pore diffusion only leads to diffusive fronts if the isotherm is extremely shallow (KL < 0.1) Fig shows the CLSM images of pure hFGF2 (A) as well as hFGF2 in clarified homogenate (B) Both systems exhibit diffusive fronts and progression to the particle center that occurred rapidly, suggesting a significant contribution of solid diffusion to the mass transfer A difference in the mechanism between the two feed solutions is not apparent in this analysis, but it can clearly be seen that mass transfer of hFGF2 in the clarified homogenate was substantially reduced Adsorption kinetics was analyzed via batch uptake in a stirred tank as well as in a shallow bed adsorption system [34] Experimental adsorption kinetics at 2.0 mg/mL are shown in Fig In M.C Berg, J Beck, A Karner et al Journal of Chromatography A 1676 (2022) 463264 Fig CLSM measurements of the adsorption process of purified hFGF2 (A) and clarified homogenate containing hFGF2 (B) on Capto S hFGF2 was labelled with Rhodamine Red-X Measurement points from left to right: 30 s, 60 s, 120 s, 300 s, 600 s and 1800 s of incubation Fig Adsorption of purified hFGF2 ( ) and clarified homogenate containing hFGF2 (o) via batch uptake (A) and Shallow bed adsorption (B) on Capto S hFGF2 concentration was 2.0 mg/mL for both model systems Solid lines represent a fit with the solid diffusion model (Eq (9)) as a good estimate From a mechanistic point of view, a pore or solid diffusion model assuming only a single mass transfer mechanism is not fully physically representative, as both diffusion mechanisms contribute to the overall mass transfer Despite that, experimental data can be well approximated with both models and the derived diffusion coefficients can be considered as apparent diffusion coefficients Adsorption data shown in Fig were fitted with both models yielding basically identical curves For clarity, only the solid diffusion model is plotted For the case of pore diffusion, an ab initio estimation of the effective pore diffusion coefficient De can be derived from characteristic parameters of the solute and the stationary phase, respectively [1,32]: De = ψ p ∗ ε p∗ D0 τ pore diffusivity is reasonably low which is mainly attributed to the small pore radius of nm Effectively, this is a truly theoretical value that only would apply in the case of sole pore diffusion Calculated De was then compared to effective pore diffusion coefficients derived from experimentally performed batch uptake and shallow bed adsorption systems Again, a maximum binding capacity qmax of 100 mghFGF2 /mLCaptoS was obtained for the pure protein solution After fitting the experimental data to the corresponding model, an effective pore diffusivity of D˙ e of 1.4 ± 0.2 × 10−6 cm²/s was determined, which was 34-fold higher compared to the De calculated from Eq (17) In accordance with the CLSM profiles, a strong contribution of solid diffusion to mass transfer is supposed We followed the approach of Hunter et al [29], interpreting the effective De determined with the pore diffusion model as an overall mass transfer flux, which can be written as (17) D˙ e = De + Ds In Eq (17) ψ p is the hindrance parameters for pore diffusion, εp the intraparticle porosity, D0 the free diffusivity of the protein and τ is the tortuosity factor for intraparticle diffusion The hindrance parameter ψ p is proportional to the ratio of the pore and protein radius and can be calculated by [1,36]: qmax C (19) Eq (19) considers the coherence of two individual mass transfer mechanisms where the first term represents pore diffusion and the second term solid diffusion As can be seen from Eq (19), the effect of solid diffusion depends on the magnitude of the solid diffusion coefficient Ds and the driving force expressed as the ratio of qmax over the initial protein concentration C [2] To further investigate the individual solid diffusion contribution, the experimental data were fitted to a solid diffusion control model (Eq (9)) A solid diffusion coefficient Ds of 1.7 ± 0.1 × 10−8 cm²/s was determined for pure hFGF2 via batch uptake and shallow bed adsorption Inserting all parameters (De , Ds , qmax and C) into Eq (19) yields D˙ e,calc of 1.4 × 10−6 cm²/s This value is identical to the overall effective pore diffusivity D˙ e,exp obtained from the experimental data and the fitting to the pore diffusion model ψ p = 0.865 ∗ (1 − λm )2 ∗ − 2.1044 ∗ λm + 2.089 ∗ λ3m ∗ 0.984 ∗ λ5m (18) where λm is the ratio of pore over protein radius The free diffusivity D0 of hFGF2 can be estimated by the TynGusek equation [37] if the dynamic viscosity and temperature of the solution are known An intraparticle porosity of 0.74 and a tortuosity of 1.5 have previously been determined for Capto S [38] Calculated parameters are listed in Table Using Eq (17) De was estimated as 3.9 × 10−8 cm²/s for pure hFGF2 The calculated M.C Berg, J Beck, A Karner et al Journal of Chromatography A 1676 (2022) 463264 Table Summary of the adsorption kinetics data obtained for purified hFGF2 and hFGF2 in the clarified homogenate via shallow bed adsorption and batch uptake experiments λm is the ratio of protein and pore radii ψ p is the hindrance parameters for pore diffusion and τ is the tortuosity D0 is the solution diffusivity The overall effective pore diffusivity D˙ e,calc was calculated by Eq (19) The reported values for D˙ e,exp and Ds are arithmetic means and standard deviations determined from batch uptake and shallow bed experiments Sample Purified hFGF2 hFGF2 in cl homog λm 0.418 ψp 0.076 τ 1.5 D˙ e, calc (cm²/s) D0 (cm²/s) −6 1.0 × 10 1.8 × 10−7 −6 1.4 × 10 6.8 × 10−8 D˙ e,exp (cm²/s) Ds (cm²/s) −6 1.4 ± 0.2 × 10 3.3 ± 0.3 × 10−8 1.7 ± 0.1 × 10−8 3.2 ± 0.3 × 10−9 Fig Breakthrough curves of purified hFGF2 (A) and clarified homogenate containing hFGF2 (B) on a Capto S column (CV = mL) with residence time Filled circles (●) and filled squares ( ) represent experimental data at residence time of Dotted lines represent prediction with pore diffusion model Eq (7)) and dashed lines represent prediction with solid diffusion model (Eqs (11)–((14)) using parameters determined by batch uptake kinetics As with pure hFGF2, we conducted a quantitative analysis of the mass transfer for hFGF2 in the clarified homogenate Due to higher dynamic viscosities of the solution an even lower hypothetical De of 7.0 × 10−9 cm²/s was estimated Again, the quantitative analysis was compared to the effective diffusion coefficients derived from experimental data In contrast to pure hFGF2, a lower solid diffusion contribution was determined, which was due to the lower maximum binding capacity and the lower Ds of 3.2 × 10−9 cm²/s Consequently, under these conditions, the overall mass transfer flux was drastically reduced to D˙ e,exp = 3.3 × 10−8 cm²/s This value corresponded to half of D˙ e,calc which was based on the hypothetical De calculated from Eq (17) A summary of the adsorption kinetics data obtained can be found in Table fied homogenate, the experimentally observed early breakthrough of hFGF2 at a residence time of was also well captured by the model (Fig 6B) To verify if this overprediction was specific for pure hFGF2 on Capto S, a series of supporting experiments was carried out First, lysozyme adsorption on Capto S was studied at the same experimental conditions Lysozyme has a molecular mass of 14.3 kDa and an isoelectric point (11.0) comparable to hFGF2 Thus, adsorption properties were expected to be similar In fact, almost identical behavior in terms of batch uptake rate (Fig 7A) and protein breakthrough including overprediction by the model was observed (Fig 7B) Mass transfer parameters are included in Table To further investigate this phenomenon, adsorption of pure hFGF2 was studied on two other cation exchangers: Toyopearl Gigacap S has similar properties as Capto S, but with a polymethacrylate backbone and grafted surface extenders functionalized with sulfopropyl modifiers The batch uptake curve and fitting of the experimental data yielded almost the same diffusion coefficients as obtained for the Capto S resin, confirming the very fast uptake rates on grafted media Diffusion coefficients are listed in Table and the uptake curve is provided in the supportive information (Fig A3) We also investigated a macro-porous resin without grafted polymers, SP Sepharose FF (Fig 8) The batch uptake was substantially reduced, and the diffusion coefficients obtained from the fit were one order of magnitude lower as compared to Capto S Correspondingly, BTCs were less steep compared to those obtained on the grafted media and exhibited a stronger dependence on velocity The profiles were well predicted by the pore diffusion model for the most part of the mass transfer zone A summary of the diffusivity values obtained for all methods and stationary phases used can be found in Table Adsorption of basic proteins on SP Sepharose FF has been investigated by several researchers Dziennik et al [39] have shown that the diffusion coefficients for lysozyme varied considerably with buffer conditions For higher ionic strengths, protein uptake was comparably fast as on grafted media Martin et al [40] showed that the uptake rates were also dependent on the protein characteristics, as shown for 4.4 Breakthrough curves Predictions for column operation were made based on mass transfer parameters derived from batch uptake kinetics The calculated BTCs were then compared to experimental data of pure hFGF2 Fig 5A) and hFGF2 in clarified homogenate (Fig 5B) Analytical solutions for column adsorption are available for both mass transfer mechanisms (Eqs (7) and ((11)–(14)) In Fig 5A, the experimental breakthrough curve for pure hFGF2 is plotted against predictions using Ds = 1.6 × 10−8 cm²/s for solid diffusion model and D˙ e,exp = 1.2 × 10−6 cm²/s for the pore diffusion model Film mass transfer coefficients were calculated from the correlation as given by [4] It is evident that both models yielded almost identical breakthrough profiles However, both models captured only the first 30% of the experimental BTC and predicted faster mass transfer as occurred experimentally In contrast, breakthrough of hFGF2 in clarified homogenate was very well predicted by both models using Ds = 3.2 × 10−9 cm²/s and D˙ e,exp = 3.3 × 10−8 cm²/s, respectively (Fig 5B) Further experimental runs were conducted at varying residence times (Fig 6) Predictions based on the mass transfer parameters as used above yielded essentially the same results with strong overprediction for pure hFGF2 For the clari7 M.C Berg, J Beck, A Karner et al Journal of Chromatography A 1676 (2022) 463264 Fig (A) Breakthrough curve (BTC) of purified hFGF2 on Capto S column (CV = 0.2 mL) with varying residence time Filled circles (●) represent residence time of Residence time of is represented as open circle (o) (B) Breakthrough curve of clarified homogenate containing hFGF2 on Capto S column (CV = mL) with varying residence time Filled squares ( ) represent residence time Residence time of 10 represented as open squares ( ) Analytical solution for solid diffusion by Yoshida et al Eqs (11)–((14)) used for data prediction is shown as dashed lines Fig Adsorption of lysozyme on Capto S (A) Solid diffusion model used for fitting data Eq (9)) Breakthrough curve of lysozyme on Capto S (CV = 0.2 mL) with varying residence time (B) Filled circles (●) represent residence time of Residence time of is represented as open circle (o) Predictions via analytical solution for solid diffusion by Yoshida et al (Eqs (11)–((14)) are shown as dashed lines Table Summary of all mass transfer coefficients obtained for purified hFGF2 and clarified homogenate containing hFGF2 and additional experiments with lysozyme Mass transfer coefficient (cm²/s) purified hFGF2 Method/Sample Batch uptake on Capto S Shallow-bed on Capto S Batch uptake on Gigacap S Batch uptake on SP Sepharose FF Cl homogenate lysozyme D˙ e Ds D˙ e Ds D˙ e Ds 1.3E-6 1.6E-6 1.2E-6 1.5E-7 1.6E-8 1.8E-8 1.4E-8 2.6E-9 3.0E-8 3.5E-8 3.0E-9 3.6E-9 2.0E-6 1.2E-8 lysozyme and cytochrome c The latter had a diffusion coefficient that was almost one order of magnitude higher than lysozyme although the molecular weight and the isoelectric point are very similar Apparently, the amino acid composition and the binding strength can have an important impact on the adsorption properties Taking all these factors and variations into account, the uptake rates determined for hFGF2 on SP Sepharose FF in this work seem very reliable Furthermore, we investigated if extra-column contributions could be responsible for deviations of the experimental BTCs and the model predictions shown in Figs 5, 6A and 7B We performed BTCs under non-binding conditions and bypassing the column As shown in Fig A1 in supportive information, extra-column effects could not be responsible for the discrepancy as the upper part of the BTCs reached the plateau rapidly without any tailing or washout effects Bowes and Lenhoff [41] investigated protein adsorption on grafted media including Capto S Under weak binding conditions, and more pronounced for smaller proteins, they observed a slow approach to equilibrium reflected by a tailing behavior in the upper part of the BTC They concluded that a rearrangement of the initially bound proteins on the dextran layer could be responsible for the observed effects All of these studies are indicative of such a behavior of pure hFGF2 and lysozyme on grafted media which made the prediction of BTCs challenging Tao et al [8] predicted BTCs of a mAb on Capto S by a solid diffusion model However, since mAb has a molecular mass of 150 kDa, solid diffusion coefficients were 3-fold lower than those we determined for the smaller proteins hFGF2 and lysozyme In contrast, when the uptake rates M.C Berg, J Beck, A Karner et al Journal of Chromatography A 1676 (2022) 463264 Fig (A) Batch uptake kinetics of purified hFGF2 on SP Sepharose FF Pore diffusion model for rectangular isotherms used for fitting data (Eq (3)) Breakthrough curve experiments with hFGF2 on SP Sepharose FF (CV = 0.2 mL) (B) Filled circles (●) represent residence time of Residence time of is represented as open circles (o) Predictions via analytical solution for pore diffusion (Eq (7)) are shown as dashed lines Fig Solid diffusion coefficients of purified hFGF2 in solutions adapted to different dynamic viscosities by adding glycerol (A) Solid diffusion coefficients of purified hFGF2 adapted to different dynamic viscosities against maximum binding capacities (B) Addition of 23 mg/mL BSA represented as (x) Dashed line represents Ds determined for purified hFGF2 without additives and dotted line represents Ds of hFGF2 in clarified homogenate Analytical solution for solid diffusion (Eq (9)) was used for fitting the experimental data (C) Dynamic viscosities of different glycerol concentrations ( ), correlation of dynamic viscosity and clarified homogenates with varying cell dry mass concentrations (●) as well as dynamic viscosity of purified hFGF2 represented as dotted line were lower, as was the case for hFGF2 in the clarified homogenate, model predictions were accurate (Fig 5B) It can be assumed that the rearrangement effect, if occurring at all, had little impact on the shape of the BTC Finally, we addressed the question of the cause for the reduced mass transfer rate in the clarified homogenate We identified that the lower driving force, which is a major factor for solid diffusionbased mass transfer, was due to the low capacity The question remains: why is the capacity so much lower compared to pure hFGF2 since Capto S was very selective for hFGF2 and the eluate fraction was highly pure? This outcome indicates very little competition from host cell proteins for binding, although the homogenate contained around 25 mg/mL of proteins To further prove the assumption that host cell proteins not interfere with the mass transfer rates, we spiked 23 mg BSA/mL to the pure hFGF2 solution and performed batch uptake experiments on Capto S The uptake data were then fitted with the solid diffusion model As can be seen in Fig 9, Ds values and qmax were identical to pure hFGF2 without BSA spiked This suggests that other impurities are responsible for the reduced mass transfer E coli homogenates contain numerous low molecular weight compounds in high concentrations which potentially were competing with hFGF2 adsorption On one hand the identification and further quantification of these compounds is very difficult On the other hand, even if the nature and concentration of these compounds were known, the resulting multi-component adsorption system would be extremely complex Furthermore, we investigated if the reduced Ds was caused by a general decrease of diffusivity due to viscosity effects Therefore, specific amounts of glycerol were added to pure hFGF2 solutions to emulate the dynamic viscosity of hFGF2 in clarified homogenate Batch uptake kinetics were recorded and qmax and Ds were determined Fig shows the decrease of the solid diffusivity with increasing glycerol concentration A glycerol addition of 44%, which corresponded to the viscosity of clarified homogenate, yielded the same Ds value as obtained for hFGF2 in the clarified homogenate Also, in this case, qmax was not affected Overall, the glycerol spiking experiments supported the explanation that the reduction of D0 is affected by higher viscosity In combination with the reduced driving force caused by lower qmax , the overall lower diffusivity of hFGF2 in the homogenate was plausible Moreover, process design for a preparative capture step can easily be performed with either model using the respective diffusion coefficients Conclusion In general, mass transfer on the grafted chromatography medium Capto S is very fast due to enhanced solid diffusion transport We have shown that mass transfer of a protein from a clarified homogenate is significantly reduced when compared to a feed solution of pure protein The reduction of the transport rate from the clarified homogenate was caused by two factors: (1) higher viscosity intrinsically results in lower diffusion coefficients and (2) the solid diffusion driving force is much reduced at lower maximum binding capacities, which was shown to be the case for hFGF2 in the clarified homogenate From an engineering point of view, both diffusion models, the pore diffusion with an apparent M.C Berg, J Beck, A Karner et al Journal of Chromatography A 1676 (2022) 463264 pore diffusion coefficient as well the solid diffusion model, were able to describe the experimental data The models can easily be applied for process design calculations and scale-up It 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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper CRediT authorship contribution statement Markus C Berg: Conceptualization, Methodology, Formal analysis, Investigation, Data curation, Writing – original draft, Visualization Jürgen Beck: Investigation, Data curation Alex Karner: Methodology, Formal analysis, Investigation Kerstin Holzer: Methodology, Formal analysis, Investigation Astrid Dürauer: Conceptualization, Investigation, Methodology, Writing – review & editing, Writing – original draft Rainer Hahn: Conceptualization, Investigation, Methodology, Writing – original draft Acknowledgment The COMET center: acib: Next Generation Bioproduction is funded by BMK, BMDW, SFG, Standortagentur Tirol, Government of Lower Austria und Vienna Business Agency in the framework of COMET - Competence Centers for Excellent Technologies The COMET-Funding Program is managed by the Austrian Research Promotion Agency FFG We thank the colleagues M Martinetz, N Hammerschmidt, S Krahulec, M Graf and C Brocard of our company partner BI RCV for their scientific input in fruitful continuous discussions Furthermore, the authors thank Dr Monika Debreceny from the Imaging Center and the Doctoral School “BioProEng” for their support Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.chroma.2022.463264 References [1] G Carta, A Jungbauer, Protein chromatography, 2010 10.1002/9783527630158 [2] R Hahn, Methods for characterization of biochromatography media, J Sep Sci (2012), doi:10.10 02/jssc.20120 0770 [3] F.T Sarfert, M.R Etzel, Mass transfer limitations in protein separations using ion-exchange membranes, J Chromatogr A 764 (1997) 3–20, doi:10.1016/ S0 021-9673(96)0 0894-1 [4] P.M Armenante, D.J Kirwan, Mass transfer to microparticles in agitated systems, Chem Eng Sci 44 (1989) 2781–2796, 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an insight into the mass transfer mechanism, investigation by