Pore size distributions of ion exchangers and relation to protein binding capacity

Journal of Chromatography A, 1126 (2006) 107–119

Pore size distributions of ion exchangers and relation to protein binding capacity Yan Yao 1 , Abraham M. Lenhoff ∗ Department of Chemical Engineering, University of Delaware, Newark, DE 19716, USA Available online 17 July 2006

Abstract The pore structure of chromatographic media directly influences macromolecular transport and adsorption, and consequently separation resolution and loading capacity in chromatographic separations. The pore size distribution (PSD) is therefore a central structural characteristic of chromatographic materials and a critical determinant of chromatographic behavior. In this work the PSDs of a set of commercial anion exchangers were determined by inverse size-exclusion chromatography (ISEC). The PSDs were further utilized to develop relations to functional properties of adsorbents, such as intraparticle diffusivity, and static and dynamic binding capacities. We find that the detailed PSD is useful in semi-quantitative understanding of chromatographic behavior. However, more accurate prediction of column behavior requires more thorough knowledge of the pore structure, specifically the connectivity of the pore network, as well as improved understanding of the function of grafted resins. © 2006 Elsevier B.V. All rights reserved. Keywords: Protein chromatography; Ion-exchange chromatography; Inverse size-exclusion chromatography; Intraparticle diffusion; Static binding capacity; Dynamic binding capacity; Pore connectivity

1. Introduction The porous nature of chromatographic adsorbents provides several structural features that determine important functional properties in chromatographic practice. For example, pore dimensions and geometry play a governing role in solute differentiation in size-exclusion chromatography [1]. Protein retention and uptake in adsorption chromatography are affected by pore size distributions, with access and molecular transport facilitated in wide pores [2,3], versus increased surface area and hence capacity, as well as strengthened protein–adsorbent attraction, in small pores [4,5]. Topological characteristics of the three-dimensional pore network determine the pattern of molecular migration inside microporous particles [6]. Adsorbents with a wide variety of pore architectures have been synthesized to provide specific performance attributes [7], and information on the detailed pore structure is essential for quality control and more relevant performance evaluation of adsorbents. Furthermore, advances in in-depth knowledge of

∗

Corresponding author. Tel.: +1 302 831 8989; fax: +1 302 831 4466. E-mail address: [email protected] (A.M. Lenhoff). 1 Present address: Biotechnology Development, Schering-Plough, 1011 Morris Ave., Union, NJ 07083, USA. 0021-9673/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2006.06.057

pore structure can be instrumental for a better mechanistic understanding of chromatographic behavior, which can be translated into strategies for improving the efficiency of adsorbent screening in process development. Many structural parameters have been used to describe heterogeneous porous media [6] in terms of both macroscopic measures, such as porosity, permeability and accessible surface area, and microscopic ones involving pore size and geometry, spatial distribution, and topological characteristics that depict the connections among pores. A number of microstructural parameters are relevant, among which the pore size distribution (PSD) [6], i.e., the distribution density of pore volume within a certain range of dimensions, serves as a statistical descriptor of the diverse size features. Knowledge of the PSD allows calculation of the mean pore size and the phase ratio, which can help elucidate adsorption and transport behavior [5,8]. However, detailed structural information on porous chromatographic stationary phases is rarely available from adsorbent suppliers. A variety of techniques are used to measure the PSD of porous materials [6], including gas sorption [9], mercury intrusion [10] and inverse size-exclusion chromatography (ISEC) [11]. These are indirect techniques in that they probe relevant functional properties, which are then used to derive the PSD based on an idealized model, e.g., spherical probes partitioning into parallel cylindrical pores [6,12]. Among these methods, ISEC [11,13,14]

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has the advantages [8,15–17] of: allowing in situ measurement; being based on relevant properties of functional interest in chromatographic practice and extensive exploration of the accessible pore volume as a function of probe size; and being effective in the working pore dimension range of 1–400 nm [14] of major interest for liquid chromatography. The paucity of available data on PSDs of commercial adsorbents is matched by an incomplete quantitative understanding of how the PSD affects important measures of chromatographic performance, so such comparisons are primarily descriptive in character. A relation between measures of performance and physical properties would help leverage the detailed characterization of adsorbents to make possible predictive resin screening. The principal performance measures used in preparative chromatography center around the capability of the column to maximize the production rate of pure product, and therefore include capacity, productivity and selectivity. Since the desired product is usually captured from a dilute feed, the loading step is usually rate-limiting, and its effectiveness is most often reflected in the dynamic binding capacity (DBC). The DBC is usually represented as the total amount of adsorbate fed into the packed bed per column volume until the outlet concentration reaches a certain percentage of the feed concentration [18,19]. It is bounded above by the static binding capacity, the maximum amount of bound protein at adsorption equilibrium under a given set of solution conditions. Under the dynamic conditions of column loading, however, this equilibrium is rarely attained, and the DBC is lower than the static capacity by an amount that depends on transport and kinetic events, primarily intraparticle diffusion. All these properties depend strongly on the PSD. Assuming that the surface and solution properties are suitably chosen to promote binding, the accessible surface area is the major determinant of the static binding capacity, as has been discussed for a number of adsorbents for the evaluation of loading limits [20–25]. The profile of a breakthrough curve, and hence the

DBC, is also affected by factors such as mass transfer rates and flow maldistribution in the column [19,26]. A number of models, such as the pore diffusion and homogeneous diffusion models, have been used to model uptake in studies of breakthrough behavior, with the effective intraparticle diffusivity, which can be determined from, e.g., batch uptake experiments, as the main parameter in addition to equilibrium adsorption information [19,27–29]. The intraparticle diffusion of macromolecules is restricted as a result of steric exclusion and hydrodynamic drag and therefore also depends directly on the PSD. Several hydrodynamic models of mass transfer in cylindrical pores [30–34] and gels [35–37] have been developed to relate diffusion behavior to the medium structural parameters. These models have been applied in interpreting diffusion properties in materials with uniformly sized pores or in parameterizing the medium structure [38–41]. Both the static and dynamic capacities of some model proteins are typically presented in commercial adsorbent data sheets, serving as a gauge of the performance of an adsorbent (Table 1). However, objective comparisons of adsorbents are difficult using these data, which are usually gathered under a wide variety of conditions. More consistent comparative measurements of adsorption behavior of ion exchangers have been made to help comparative performance evaluation [23–25]. However, the underlying mechanistic origins of the differences observed are not always clear, e.g., is a lower DBC a reflection of low static capacity or of slow intraparticle transport? Given that both static capacity and transport properties depend directly on pore structural characteristics, analysis of DBC data in terms of detailed structural information, such as the PSD, is an effective way to explore the possibility of basing adsorbent selection strategies at least in part on structural information. In this work, therefore, we use ISEC analysis to characterize a set of commercial anion exchangers. The resulting adsorbent performance properties, along with those from a number of previous studies

Table 1 Properties of the anion exchangers as provided by manufacturers Adsorbent

Base matrix

dp (␮m)a

Tosoh Bioscience Super Q-650C QAE-550C

Methacrylate Methacrylate

GE Healthcare Source 30Q Q Sepharose FF Q Sepharose XL

Mean pore radius (nm)

Ion capacity (␮mol/ml)

Dynamic capacity (BSA mg/ml)

40–90 50–150

∼50 ∼25

200–300 280–380

105–155 60–80

Polystyrene/divinylbenzene Agarose Agarose with bound dextran

30 45–165 45–165

Not given Not given Not given

180–250 180–260

>40b 120 HAS >130c

Whatman Express-Ion Q

Microgranular cellulose

60–130d

Not applicable

1 meq/dry g

55

Sterogene Bioapplications Q Cellthru BigBead Plus

4% agarose

Not given

Not given

65

Applied Biosystems POROS 50 HQ

Polystyrene/divinylbenzene

Not given

Not given

60–70

a b c d

Particle diameter. 50% breakthrough. 10% breakthrough. Fiber length.

300–500 50

Y. Yao, A.M. Lenhoff / J. Chromatogr. A 1126 (2006) 107–119

[8,23–25], including mass transport and loading capacities, are applied in analyzing corresponding DBC data.

2. Materials and methods 2.1. Chromatographic stationary phases Eight strong anion exchangers from Tosoh Bioscience, GE Healthcare, Whatman, Sterogene Bioapplications and Applied Biosystems were kindly provided by Novo Nordisk (Gentofte, Denmark) for the ISEC studies. The adsorbents were designed to suit a variety of separation requirements and vary in properties such as the particle morphology, the chemical nature of the base matrix, the spacer-arm chemistry, and the density of the functional groups. The physicochemical properties of these materials as provided by the suppliers are listed in Table 1, and a more detailed description of the physical properties, functional group chemistry, and some specific features intended for improved performance is provided below. The two Toyopearl anion exchangers, Super Q-650 C and QAE-550 C, differ in both pore size and derivatization. The Toyopearl 650 series is designed onto Toyopearl HW 65, a ca. 50 nm mean pore radius base material, whereas the Toyopearl 550 series features a 25 nm mean pore radius and consequently higher surface area and capacity [8]. Toyopearl Super Q-650 contains proprietary quaternary amine functionalized polymers grafted to Toyopearl HW 65 in order to provide higher protein binding capacity than is usually found for the 650 series. Toyopearl QAE-550 C is a quaternary amine strong anion exchanger. The GE Healthcare materials cover a variety of physical and chemical characteristics. Source 30Q is a quaternary ammonium strong anion exchanger on a polystyrene-divinylbenzene matrix. The rigid mono-sized particles of 30 ␮m diameter yield high flow rate and throughput with low back pressure. Q Sepharose FF is based on 6% highly cross-linked beaded agarose with high matrix rigidity, which forms a macroporous structure suitable for protein adsorption [42]. Q Sepharose XL has dextran chains coupled to the agarose matrix to increase the exposure of the quaternary amine charged groups, resulting in higher loading capacities than those of the Sepharose FF materials. Whatman Express-Ion Q is a strong anion exchanger with microgranular cellulose as the base matrix. The N,N,N-trimethyl hydroxypropylamine group is fully ionized throughout the pH range 2–12. The adsorbent fibers are about 60–130 ␮m in length. Unlike most traditional porous adsorbents, Express-Ion Q is designed as a non-porous matrix adsorbing proteins via the particle external surface, thereby eliminating the intraparticle diffusional limitation [43,44]. Sterogene Cellthru BigBead Plus particles are 300–500 ␮m in diameter, which is markedly larger than the other resins studied here. Due to the large bead size, the medium can be used for the purification of unclarified feed streams, such as cell culture harvests and fermentation broths, on standard low-pressure columns. Q Cellthru is a strong anion exchanger with a hardened 4% agarose matrix to which functional groups are attached through spacer arms.

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POROS 50 HQ is based on 50 ␮m spherical polystyrenedivinylbenzene particles, the surface being coated with quaternized polyethyleneimine to provide complete surface ionization over a wide pH range of 1–14. As a so-called perfusion resin [45], POROS 50 HQ comprises inter-adhering microspheres that form particle clusters, intended to create throughpores (rpore > 250 nm) and diffusive pores (15 nm < rpore < 35 nm) branching from the throughpores. The large throughpores are postulated to enhance convective flow through the particles to provide access to shorter diffusive pores inside. 2.2. ISEC standards Eleven dextran standards of molecular weights ranging from 180 to 2,285,000 Da were purchased from Polymer Standards Service-USA (Silver Spring, MD). The weight-average molecular weight Mw , the number-average molecular weight Mn , the molecular weight corresponding to the elution peak Mp , the viscosity radius Rη , and the polydispersity PDI are shown in Table 2. The viscosity radii were calculated using the correlation Rη = 0.0271 × Mp0.498 , where Rη is in nm and Mp in Daltons [15]. Calf thymus DNA was obtained from Sigma Aldrich (St. Louis, MO). 2.3. Instrumentation A glass column of 70 cm × 1.6 cm i.d. (XK 16/70) and a 300 ml packing reservoir (RK 16/26) were purchased from GE Healthcare (Uppsala, Sweden). The chromatography of dextran and DNA standards was performed on a BioCAD Workstation (Applied Biosystems, Foster City, CA) equipped with a UV detector and a 100 ␮l sample loop. A Waters 410 refractometer (Waters, Milford, MA) was attached to the BioCAD as an auxiliary detector for the detection of dextrans. 2.4. ISEC of dextran standards The adsorbent was rinsed with deionized water and then equilibrated with the packing buffer prior to packing. An XK 16/70 column was equipped with the 300 ml packing reservoir and the slurry was added gradually down the inner wall of the reservoir Table 2 Molecular weights (Mw , Mn , Mp ), polydispersity (PDI) and viscosity radii (Rη ) of the dextran standards used in ISEC Mw

Mn

Mp

PDI

Rη (nm)

180 342 1350 5200 11600 23800 48600 148000 273000 410000 3800000

180 342 1160 3300 8100 18300 35600 100000 164000 236000 1500000

180 342 1080 4400 9900 21400 43500 124000 196000 277000 2285000

1.00 1.00 1.16 1.60 1.43 1.30 1.36 1.47 1.66 1.73 2.53

0.36 0.50 0.88 1.77 2.65 3.89 5.53 9.32 11.71 13.91 39.78

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to avoid trapping of air bubbles. The reservoir was then filled with the packing buffer, and the column was flow packed at a flow rate of 4 ml/min (120 cm/h). After the bed was formed, small amounts of adsorbent were added or removed to produce a packed bed height of about 50 cm. Dextran and DNA solutions were prepared by dissolution in the operating buffer (100 mM NaCl, 20 mM Bis–Tris solution for dextran, and 1 M NaCl, 20 mM Bis–Tris solution for DNA, in both cases at pH 7) at 1 mg/ml. All solutions were stored at 4 ◦ C for a maximum of 1 day before use. All samples were filtered through 0.22 ␮m Millipore Millex-GV filters to remove possible aggregates before injection into the column. SEC was performed at a volumetric flow rate of 1 ml/min, using injection volumes of 100 ␮l. Duplicate runs were done to determine the retention volume VR for every dextran–adsorbent pair. Peak detection was by refractive index for both dextran and DNA, with UV at 260 nm used for the simultaneous detection of DNA. The interparticle volume V0 was determined using dextran with Mp 2,285,000 as the excluded solute. The total mobile phase volume VT was measured using glucose. Chromatography was performed at room temperature (ca. 23 ◦ C). PSDs were extracted from the chromatographic data using the methods discussed in several reviews of ISEC [8,16,17,46]. Specifically, the SEC distribution coefficient, Kd , is an explicit function of the PSD, and the parameters in the PSD can therefore be estimated by a least-squares fit of the Kd values. In this work the PSD was assumed to follow a log normal radius distribution,
   C 1 log(r/rp ) 2 f (r) = exp − (1) r sp 2 where rp and sp provide a measure of the core and the width of the distribution, respectively, and C is a normalization constant. The parameters rp and sp were therefore obtained from the least-squares fit. Additional pore parameters were then calculated from f(r) as described previously [8], including the mean pore radius rm , the accessible surface area per unit pore volume A(Rs ) as a function of the solute radius Rs , and the phase ratio φ(Rs ), defined as the accessible surface area per unit volume of mobile phase. 2.5. Estimation of intraparticle diffusivity of dextrans Intraparticle diffusivities of dextran standards were estimated by analysis of band broadening in the ISEC measurements. Peak widths were characterized in terms of the reduced plate height, h, which was determined for each peak from the width at half height in view of the symmetric nature of the peaks. Differences with values found from the method of moments were negligible. Extra-column dispersion was neglected in view of the large column volume, and the effect of solute polydispersity was estimated from the polydispersity index PDI [47,48] to be negligible as well. The remaining contributions to band broadening in SEC – axial dispersion, fluid-phase mass transfer and intraparticle diffusion – were dissected using standard chromatographic rate

models [49–55], specifically the relation [55]   (1 − u)2 1 m 2 + (Re Sc) + h= Pe 3(1 − εb ) Nu 10

(2)

The Peclet number Pe and the Nusselt number Nu characterize the axial dispersion and fluid-phase mass transfer terms, respectively, while Re is the Reynolds number and Sc the Schmidt number. εb is the interstitial void fraction, found from the SEC data. Re for each resin was found from the volumetric flow rate (1 ml/min), the manufacturer’s nominal mean particle size, εb , and the properties of water, while Sc was found from the diffusivity calculated from the Stokes–Einstein equation based on the Stokes radius and the properties of water. For size-exclusion chromatography, u, the fraction of solute in the moving fluid phase at long times, is calculated as u=

εb εb + (1 − εb )εp

(3)

in which εp is the fraction of adsorbent volume that is accessible to a solute. m contains information related to the restricted intraparticle diffusivity via D0 εp Dp

m=

(4)

in which D0 and Dp are the diffusivities in free solution and in the particle, respectively; the latter is the quantity of interest for modeling the DBC using the pore diffusion model. Subtraction of the axial dispersion and fluid-phase mass transfer terms from the experimentally determined plate height allows the intraparticle diffusion contribution to be calculated from Eq. (2) via the m term. The axial dispersion and fluidphase mass transfer contributions were evaluated based on previously published correlations [56–58]. Axial dispersion can be described using the correlation fitted from the data of Miller and King [58]  Pe =

Re Sc 1 − εb

−1/6 (5)

or the Gunn correlation (1 − p) 1 εb = [Y + Y 2 (e−1/Y − 1)] + Pe p τRe Sc

(6)

p(1 − P)Re Sc 23.14(1 − εb )

(7)

p = 0.17 + 0.33 e−24/Re

(8)

Y=

These two correlations were used to define the upper and lower bounds of the convective dispersion contribution [55], which are very close for Re Sc > 100. The Nusselt number was evaluated from [55,59]
Nu = 64 +



1.09 εb

1/3

3 (Re Sc)

(9)

Y. Yao, A.M. Lenhoff / J. Chromatogr. A 1126 (2006) 107–119 Table 3 Properties of the proteins used in the studies of static and dynamic binding capacities on ion exchangers [23–25]

Mw (kDa) Rs (nm)a pI a

Lipolase

BSA

Anti FVII

Aprotinin

Lysozyme

35 2.2 4.3

69 2.7 5.0–5.2

150 4.2 6–7

6 1.2 10.5

16 1.7 11

Radius of sphere of equivalent volume.

2.6. Static and dynamic binding capacities

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centration gradient of the adsorbed solute in the particle. Again an analytical solution has been developed, in this case for a linear driving force model [67]. The equations used based on both models are also summarized elsewhere [68]. The pore diffusivity values used for the pore diffusion model were based on those measured for dextrans of comparable size, as described in the previous section. The effective diffusivity for the homogeneous diffusion model, Ds , was estimated by [27] εp Dp Ds qs ∼ 0.6 D0 D0 Cf

(10)

where Cf is the feed concentration and qs is the static capacity. Measurements of static and dynamic binding capacities of several model proteins on a number of cation and anion exchangers were conducted at Novo Nordisk, as reported previously [23–25]. Proteins with different molecular sizes were included in the study, namely bovine serum albumin, anti-FVII mAb and lipolase in the anion exchange systems, and anti-FVII mAb, lysozyme and aprotinin on the cation exchangers. The size parameters of proteins described as spheres are listed in Table 3. Based on studies of hydrodynamics and low-angle X-ray scattering, BSA is often described as a prolate ellipsoid with dimensions of 14 nm × 4 nm [60], although more detailed analysis of human serum albumin suggests that this is misleading [61,62]. Here we described BSA as an equivalent sphere 2.7 nm in radius. The experiments reported previously [23–25] were performed at pH 8 and pH 5.5 for the anion and cation exchange experiments, respectively. Static binding capacities were determined from batch adsorption with adsorbents incubated in 1 mg/ml protein solution overnight. Frontal experiments were performed on the adsorbents at two flow rates (25 and 75% of the maximum recommended flow rate or pressure) to characterize the breakthrough extents. The published static and dynamic capacity data were used to test the extent to which PSD data can be used as the basis for predicting capacities. Static capacities were estimated by assuming monolayer adsorption of spheres, with the maximum coverage assessed in two different ways. The lower limit was calculated from the jamming limit predicted by random sequential adsorption (RSA) theory [63], namely a fractional surface coverage of 0.547, and the upper limit is given by hexagonal close packing, which gives a fractional surface coverage of 0.907. These values are used here to estimate static adsorption considering the molecular size of the protein and the accessible surface area of the adsorbent, and they neglect such effects as molecular anisotropy, electrostatic exclusion and attenuation of protein–surface attraction at higher salt concentrations [64,65]. Breakthrough profiles and hence dynamic binding capacities were calculated using standard chromatographic rate models [26], specifically the pore diffusion and homogeneous diffusion models. In the pore diffusion model, diffusion is envisioned as occurring in a liquid-filled pore, with the driving force expressed as the pore fluid concentration gradient. Adsorption is assumed to be described by the limiting case of a rectangular isotherm (the shrinking core model), for which an analytical solution for the breakthrough curve is available [66]. Homogeneous diffusion, on the other hand, assumes a driving force in terms of the con-

3. Results and discussion 3.1. Pore size distribution The SEC calibration curves for the different stationary phases are shown in Fig. 1a (Toyopearl Super Q-650 C and QAE-550 C), Fig. 1b (Source 30Q, Q Sepharose FF and Q Sepharose XL), Fig. 1c (Toyopearl Super Q-650C, Express-Ion Q and Q Cellthru BigBead Plus) and Fig. 1d (POROS 50HQ and Toyopearl QAE550C). For each curve the viscosity radii of the dextran standards are plotted against the Kd values on a log scale. The PSD parameters for log normal distributions were fitted from the Kd curves, and the phase ratios and the mean pore radius of each stationary phase were calculated (Table 4). Super Q-650 C, Q Sepharose XL, Express-Ion Q and Cellthru Bigbead Plus contain significant amounts of pore volume below 10 nm radius, with distributions that are restricted to a comparatively narrow size range (Fig. 2a). For the other, larger-pore materials, i.e., QAE-550 C, Source 30Q, Q Sepharose FF and POROS 50 HQ, the PSDs cover a much wider range, and the mode of the pore size distribution curve deviates further from the mean pore radius (Fig. 2b). 3.1.1. Toyopearl Super Q-650 C and QAE-550 C The calibration curves for these two adsorbents (Fig. 1a) show that Super Q-650 C and QAE-550 C comprise pores of very different sizes. For Super Q-650 C the Kd values drop rapidly for even small dextran molecules (up to 2.7 nm in radius), and probes of radius 5.5 nm and greater are essentially fully excluded. In contrast, most of the calibration curve for QAE-550C is linear, with substantial access to the pore space even for the 13.9 nm probe. The mean pore radius of 54.5 nm for QAE-550 C is in reasonable agreement with the general size specification for the 550 family, but the mean pore radius of 4.8 nm found for Super Q-650 C is much smaller than the ca. 50 nm mean pore radius base matrix used for the Toyopearl 650 series. This constriction in characteristic pore dimensions, which was confirmed by measurements on different lots of the adsorbent (Fig. 3), is explained by the presence of grafted polymer chains in the Super Q material. Previous ISEC analysis [8] of a “tentacle” Fractogel cation exchanger, also prepared on the 650 base matrix, showed a similar constriction in the mean pore size. These measurements also showed that the pore radius generally increased with increasing

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Fig. 1. Dextran calibration curves. (a) Toyopearl Super Q-650 C (䊉) and QAE-550 C (
). (b) GE Healthcare Source 30Q (䊉), Q Sepharose FF (
) and Q Sepharose XL (). (c) Toyopearl Super Q-650 C (䊉), Whatman Express-Ion Q (
) and Sterogene Q Cellthru BigBead (). (d) Toyopearl QAE-550 C (䊉) and Applied Biosystems POROS 50 HQ (
).

Table 4 The phase ratio φ as a function of dextran size for the anion exchangers, the fitting parameters rp , sp for the log normal PSD and the resulting calculated mean pore radius rm . Also shown are the particle porosity εp , the included volume VT and the void volume V0 expressed as a fraction of the bed volume Probes

Phase ratio (m2 /ml)

Rη (nm)

Super Q-650 C

QAE-550 C

Source 30Q

Q Sepharose FF

Q Sepharose XL

Express-Ion Q

Q Cellthru BigBead Plus

0.36 0.50 0.88 1.77 2.65 3.89 5.53 9.32 11.71 13.91 39.78

177.4 162.3 123.0 50.9 21.3 3.4 0.1 0 0 0 0

66.8 62.4 43.0 34.6 26.6 19.3 10.9 7.8 5.8 0 0

44.8 43.4 40.1 34.6 30.2 24.3 18.3 9.2 5.7 3.9 0

49.4 48.5 46.5 42.3 38.5 33.3 27.5 16.1 10.0 0 0

187.5 179.2 158.1 91.5 51.2 13.5 0.3 0 0 0 0

164.4 145.2 88.7 25.8 8.1 1.1 0.02 0 0 0 0

119.5 117.3 108.4 86.8 70.7 41.5 0.1 0 0 0 0

0.76 0.85 0.38 28.53 1.20 58.73

0.53 0.71 0.39 25.10 0.72 32.41

0.79 0.87 0.36 25.78 0.47 28.79

εp VT V0 rp (nm) sp rm (nm)

0.53 0.71 0.39 4.73 0.17 4.79

0.79 0.86 0.36 5.88 0.006 5.88

0.61 0.82 0.53 3.88 0.21 3.96

0.92 0.95 0.40 9.93 0.014 9.93

POROS 50 HQ 37.1 31.5 22.5 13.1 9.3 5.8 3.7 1.9 1.1 0.8 0.1 0.49 0.76 0.53 78.9 2.19 868

Y. Yao, A.M. Lenhoff / J. Chromatogr. A 1126 (2006) 107–119

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Fig. 4. Dextran calibration curves for Toyopearl Super Q-650 C (lot no. 65QAC02AM) at different ionic strengths, 1 M NaCl (䊉) and 0.1 M NaCl (
).

Fig. 2. Fitted pore size distributions for (a) Toyopearl Super Q-650 C, Q Sepharose XL, Express-Ion Q and Cellthru BigBead Plus, and (b) Toyopearl QAE-550 C, Source 30Q, Q Sepharose FF and POROS 50 HQ.

Fig. 3. Dextran calibration curves for Toyopearl Super Q-650 C lot numbers 65QAC18Y (䊉) and 65QAC02AM (
).

salt concentration, presumably due to collapse and compaction of the polyelectrolyte tentacles [8]. The susceptibility to pore size changes of Super Q-650 C at different salt concentrations (1 M NaCl and 0.1 M NaCl) was therefore investigated using ISEC (Fig. 4), which showed that the salt concentration does not greatly change the pore dimension of this material, probably because of more extensive cross-linking in Super Q-650 than in Fractogel. As seen in the phase ratio data (Table 4), Super Q-650 C provides very high surface areas for smaller molecules, but its capacity for proteins may be somewhat limited. Conversely, the phase ratios of QAE-550 C for small molecules (Rη < 2 nm) are much lower than those provided by Super Q-650 C, but decline more slowly over a wider radius range to allow adsorption of larger molecules. 3.1.2. GE Healthcare Source 30Q and Sepharose materials The calibration curves for Source 30Q and Q Sepharose FF are quite similar (Fig. 1b), the only significant difference being for the largest dextran standard (13.9 nm radius), which permeates Source 30Q with a measured Kd of 0.26, while being almost totally excluded from Q Sepharose FF. The linear portions of the calibration curves for Source 30Q and Q Sepharose FF span dextran radii of ca. 0.88–13.6 nm. The extent of permeation in Q Sepharose XL is much lower than that in the other two resins, with only the two smallest probes having Kd values similar to those for Source 30Q and Q Sepharose FF, and probes larger than 5.5 nm being completely excluded. The smaller apparent pore size of Q Sepharose XL is also seen in the linear portion of the calibration curve, which spans dextran radii of 0.88–5.5 nm. An ISEC mean pore radius of 32.4 nm was calculated for Source 30Q, as against 28.8 nm for Q Sepharose FF and 5.9 nm for Q Sepharose XL. The noticeably smaller pores of Q Sepharose XL, as compared to other Sepharose materials, are due to the random coiled dextran coupled to the agarose backbone, which presumably divides the pore spaces constructed by agarose bundles into smaller subvolumes.

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The phase ratio data show corresponding trends. Those of Source 30Q and Q Sepharose FF (Table 4) are very close, with Source 30Q showing slightly lower capacities for most dextran molecules. The phase ratio of Q Sepharose XL increases sharply with decreasing probe size, indicating lower capacity than the other two materials for probes of radius larger than 4 nm, and much greater capacity for smaller probes. 3.1.3. Whatman Express-Ion Q and Sterogene Q Cellthru BigBead Plus Express-Ion Q and Q Cellthru BigBead Plus are small-pore materials as characterized by ISEC (Table 4), so their calibration curves and that of Super Q-650 C are presented together for comparison (Fig. 1c). The major difference between Express-Ion Q and Super Q-650 C is that the former has lower distribution coefficients for dextrans of radii 0.5, 0.88 and 1.77 nm. Q Cellthru BigBead Plus has a linear Kd for probes of radii 0.88–3.89 nm, with partitioning more favorable in this range than for Super Q-650 C and Express-Ion Q; however, probes larger than 9.3 nm were totally excluded. The calculated mean pore radii are 4.0 nm for Express-Ion Q and 9.4 nm for Q Cellthru BigBead Plus. Although the manufacturer defines Express-Ion Q as non-porous, the Kd values indicate that the base matrix still contains accessible pore space. Express-Ion Q has high phase ratios (Table 4) for small dextrans, but the phase ratio decreases sharply with increasing probe size, and reaches zero when the probes are larger than its mean pore size. Q Cellthru BigBead Plus has a flatter phase ratio curve over the dextran radius range, which indicates capacity for a broader set of probes. 3.1.4. Applied Biosystems POROS 50 HQ The calibration curve for POROS 50 HQ is plotted in Fig. 1d, with QAE-550 C providing a comparison as another wide-pore material. The whole POROS curve follows a linear trend, with consistently higher Kd than that of QAE-550 C over all the probes used. The difference in Kd for the two materials becomes increasingly pronounced for larger probes, where POROS 50 HQ admits even the largest probe (40 nm radius), which is excluded by QAE-550 C. Particles with radii well in excess of those of typical available SEC standards, such as micron-size latex particles, can be used for quantifying the sizes of macropores, in which case extra care is needed in choosing the filters and frits in the chromatography system. The enormous permeation of POROS 50 HQ is due to the presence of large throughpores [69], and their capacity to admit the largest probe in this study prevents quantitative characterization of the macropores and interstitial pore space. The bed porosity for the POROS material was therefore taken as 0.35 [70,71] for the PSD calculations. The resulting PSD is very wide, with rp of 78.9 nm and sp of 2.19, the effective mean pore radius being 868 nm. The phase ratios of POROS 50 HQ for most probes calculated based on these parameters (Table 4) are about half of those for QAE-550 C. The presence of clear categories of macropores and micropores in the POROS material suggests that a bimodal distribution would provide a better representation of the pore structure. How-

ever, this has the drawback of requiring a larger number of fitting parameters: even for the simplest bimodal distribution, there are five independent parameters. Thus it is difficult to determine the distribution parameters reliably, and this approach was not pursued here. 3.2. Intraparticle diffusion The intraparticle diffusivities of the dextran standards used in ISEC were estimated from the band broadening measured in the ISEC of anion exchangers here and in an earlier study of cation exchangers [8,72]. Intraparticle transport resistance is typically the dominant contribution to the plate height. The effective intraparticle diffusivities, Dp , derived from the plate height analysis and normalized by the free-solution diffusivities D0 , are plotted against the ratio of solute size and mean pore size, λ = Rs /rm , which is often used as a dimensionless parameter in quantifying extents of hindrance (Fig. 5). The intraparticle diffusivities of the dextran standards are reduced relative to the values in free solution to extents that increase with increasing molecular size, except in POROS 50 HQ. A possible reason for this anomalous behavior is the perfusive behavior that this material is intended to allow. Although differences in adsorbent pore dimensions have been taken into account via scaling of the solute radius by the mean pore radius, there are still pronounced differences in the hindrance extents presented in this way (Fig. 5), suggesting the dependence of hindrance on properties beyond just the mean pore size. The overall attenuation of diffusion represents the combined effects of porosity, tortuosity, partitioning and hindered diffusion, although these are cumulatively often represented simply in terms of an empirical tortuosity value in the range of 2–6 [50,73]. The porosity can be accounted for directly from the values for the different probes determined by ISEC, while the effects of partitioning and hindered diffusion can be calculated,

Fig. 5. Normalized measured hindered diffusivities of dextran standards as a function of the solute-to-pore size ratio. Dp is the effective intraparticle diffusivity, and D0 the diffusivity in free solution. Rs is the solute radius, and rm the mean pore radius of the adsorbent. The line is calculated using the Renkin equation [31].

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e.g., from the Renkin equation [31], Dp D0

≈ (1 − λ)2 (1 − 2.1044λ + 2.089λ3 − 0.948λ5 )

(11)

This relation is also shown in Fig. 5, and is noticeably higher than the experimental values. The inadequacy of the mean pore size in elucidating molecular transport in porous resins is not surprising, as adsorbents with the same mean pore size can have completely different pore size distributions and consequently significantly different transport behavior. In the absence of more detailed pore structural information, the combined effects of the PSD can be taken into account in an effort to rationalize the discrepancies. Here we estimate the hindrance that a solute experiences in an adsorbent using the additive contributions of the diffusivities in all accessible pores by  Dp =

∞

Rm

f (r)Dp dr

(12)

115

or by considering the additive contributions of the resistances by ∞ 2  1 R +δ (f (r)/r Dp ) dr = m∞ (13) 2 Dp Rm +δ (f (r)/r ) dr As Dp of a solute of radius Rs is zero in a pore of the same size, a cutoff value of δ is used to define the lower limit of the integral in the latter equation. δ was arbitrarily set to 0.1 nm in the calculation here. A slight improvement in the calculation based on the PSD compared to the mean pore size case is seen for the calculation based on Eq. (12) (Fig. 6a and b), but the intraparticle diffusivity is still overestimated in all materials. The estimated diffusivities of small solutes using Eq. (13) (Fig. 6c and d) are comparable to those from Eq. (12), but the calculated diffusivity decreases much more sharply as a function of the probe size, with the calculated values for some large probes even lower than the measured values. The significantly reduced calculated diffusivities from the combined resistance approach can be attributed to the bottleneck effect of severe retardation that a large solute

Fig. 6. Measured hindered diffusivities (symbols) compared with calculated values (lines) from the combined contributions from all pores described using the PSDs. (a) Cation exchangers and base matrices, with calculations from Eq. (12). HW-65 F (䊉, —), HW-55 F (, – –), SP-650 M (, · · ·), SP Sepharose FF (
, – · –). (b) Anion exchangers, with calculations from Eq. (12). Super Q-650 C (䊉, —), QAE-550 C (, – –), Source 30Q (♦, · · ·), Q Sepharose FF (, – · –), Q Sepharose XL (
, – ·· –), POROS 50 HQ (×, - - -). (c) Cation exchangers and base matrices, with calculations from Eq. (13). Legend as in a. (d) Anion exchangers, with calculations from Eq. (13). Legend as in b.

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experiences in pores of comparable size. The simplification of sampling all pores for the estimation of intraparticle diffusion does not account for the effective exclusion of solutes from such restricted regions, or for the overall topology of pore paths, particularly the connectivity structure. A number of methods have been developed to estimate transport properties in a disordered pore space with a distribution of permeabilities, among which the critical path method describes transport as dominated by paths with lower resistance [74,75], but these are beyond the scope of the present study. 3.3. Relation of ISEC results to chromatographic performance The dynamic binding capacity is widely used as a performance measure in preparative chromatography. It is usually determined empirically, and any ability to estimate it a priori would improve the efficiency of adsorbent selection. Here the ISEC results are used in an effort to explore this possibility, using previously published static and dynamic capacities for several proteins on a number of ion exchangers under a systematic and consistent set of experimental conditions [23–25]. Comparisons among different proteins were made in that work to explore the effects of protein size on the binding capacities. More complete adsorption data were presented for BSA and lysozyme on anion and cation exchangers, respectively, and these cases are used here in exploring the quantitative estimation of breakthrough behavior using the adsorbent properties determined from our structural characterization. 3.3.1. Static binding capacity The static binding capacities of nine adsorbents are shown for BSA or lysozyme in Fig. 7, plotted against the accessible surface area per unit accessible volume. The experimental values are those reported previously [23–25] and the calculated ranges are found from the ISEC-derived accessible surface areas, based on the random sequential adsorption (RSA) model and hexagonal close packing, with BSA and lysozyme treated as spheres of equivalent volume. Of the anion exchangers for which ISEC data were presented earlier, capacity data are not shown for Q Cellthru BigBead Plus, for which the measured capacities were very low. The experimental values in Fig. 7 are quite widely scattered around the predicted ranges, with most deviations showing underprediction of the capacities. Although some discrepancies are expected due to uncertainties in the accessible surface areas resulting from the ideal sphere-in-cylinder model used in the ISEC analysis, the magnitude of the deviations seen generally would suggest at first sight that the accessible surface area does not provide a reasonable basis for predicting static capacities. However, a closer examination indicates that the discrepancies may in fact be systematic and may shed light on adsorption and transport mechanisms. The three adsorbents displaying the most significant deviations from the predicted trend are Super Q-650 C, Q Sepharose XL and Whatman Express-Ion Q. These materials are noteworthy for having fitted pore size distributions that are highly skewed toward small pores (Fig. 2a), which in the first two of these

Fig. 7. Comparison of measured [24,77] and calculated static binding capacities of BSA on anion exchangers (solid symbols) and of lysozyme on cation exchangers (open symbols). Symbols represent measured values and bars show range of calculations bounded by RSA jamming limit coverage and hexagonal close packing. Symbols: () Toyopearl Super Q-650, (䊉) Toyopearl QAE-550 C, () Source 30Q, () Q Sepharose FF, () Q Sepharose XL, () POROS 50 HQ, () Whatman Express-Ion Q, (
) Toyopearl SP-550, (♦) Toyopearl SP-650.

materials is due largely to the free polymer chains attached to the base matrix that serve as attachment points for the bulk of the charged ligands. The ISEC sphere-in-cylinder assumption is especially questionable for the space between these polymer chains, but more importantly, the mobility of the chains may yield misleading results in ISEC performed using uncharged dextran probes. The ISEC data (Fig. 1a and b) show that dextrans of radius equivalent to that assumed for BSA have Kd values of only 0.12, 0.27 and 0.11, respectively, for the three materials. Oppositely charged proteins may be able to enter narrow pore space in significant quantities even though neutral SEC probes would suggest otherwise [76], and this is a likely explanation for the discrepancies seen for these three materials. For the other four adsorbents for which BSA static capacities are examined, the experimental values lie largely in the predicted range, primarily near the lower end (RSA model prediction). All these materials, including the gel-like Q Sepharose FF, have wider pores than those examined above and present more rigid adsorptive surfaces, suggesting that the monolayer adsorption model is more appropriate here. The measured capacity of POROS 50 HQ is at the upper end of the range, but it is still significantly lower than the specification (saturation capacity of BSA at pH 8.0 >110 mg/ml) provided by the manufacturer. These discrepancies may be due in part to the uncertainties in the PSD fit noted in Section 3.1.4, but beyond this the perfusion material sacrifices adsorption capacity as a fraction of void space because it is designed to provide macropores for convection. The two cases for lysozyme static capacities show reasonable agreement between prediction and experiment. The poorer of the two fits is that for SP 550 C, which is again noteworthy for being a very narrow-pore material, although the Kd value of 0.50 [8]

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indicates reasonable accessibility of the lysozyme-sized dextran. However, the ISEC data were obtained numerous years earlier with resin from a different lot, adding an additional element of uncertainty. 3.3.2. Dynamic binding capacity The dynamic binding capacities previously reported [23,24] show a general trend toward higher dynamic binding capacity in adsorbents comprising mainly small pores, such as Q Sepharose XL and Super Q-650 C. These can be rationalized based on the static capacities discussed above (Fig. 7). Clear decreases in dynamic capacity are seen for most adsorbents with increasing in protein size [23,24], which can be explained in part by the reduced accessible surface area for adsorption, but also by slower transport. Indeed, the relation between the static and dynamic capacities depends strongly on transport considerations, and accounting for this requires more detailed calculations. Quantitative comparisons of measured and predicted dynamic binding capacities are presented for BSA on anion exchangers and lysozyme on cation exchangers, for which measured static binding capacities [23,24,77] are available. For comparison with the experimental data, the dynamic binding capacities were calculated at 10 and 50% breakthrough using both the pore diffusion and homogeneous diffusion models (Fig. 8), with intraparticle pore diffusivities taken to be those of dextran molecules of the same size as the respective protein molecules. The diffusivities were adjusted for the homogeneous diffusion model using Eq. (10). At the lower flow rates (25% of the maximum recommended flow rate or pressure) the calculated dynamic binding capacities differ little from the static ones, as is expected given the longer contact times and therefore longer times available for diffusion into the particles. In general the calculations for these cases slightly overestimate the 50% breakthrough measurements and more appreciably overestimate the 10% breakthrough measurements. These differences suggest that the calculations underestimate the extent of dispersion in the column, for which several explanations are possible. One is that the diffusivities may be overestimated, but this seems unlikely, as one would expect the protein–surface electrostatic attraction to enhance uptake, if anything. A second possible explanation is the omission of an explicit axial dispersion (“eddy diffusion”) contribution from the model calculations, but this is usually small at the high P´eclet numbers typical for protein chromatography. Similarly, external mass transfer resistance is neglected, which may have an effect during initial stages of uptake and therefore in the early part of the breakthrough curve. A more likely explanation is the contribution of unaccounted-for dispersive effects such as those due to non-uniform flow distribution and particle size heterogeneity. Slower intraparticle transport than expected from the dextran diffusivities may occur for reasons that include narrowing of pores when covered by adsorbed protein, and uncertainties in assigning a diffusivity of dextran, a flexible polymer, to more rigid proteins [78]. Another possible cause of the discrepancies is the analytical approximations used for the calculations. In all cases, the results are most sensitive for the 10% breakthrough, where the slope of the breakthrough curve is often shallow, contribut-

Fig. 8. Comparison of experimental and calculated dynamic binding capacities (DBC) (in mg/ml) of BSA on anion exchangers [23,24] and lysozyme on cation exchangers [77] at two flow rates F1 (a) and F2 (b) (F1 < F2). Capacities shown for each adsorbent are, from left: measured static binding capacity (), DBCs for 10% breakthrough (measured (
), calculated using pore ( ) and homogeneous diffusion ( ) models, respectively), DBCs for 50% breakthrough (measured ( ), calculated using pore ( ) and homogeneous diffusion ( ) models, respectively).

ing both to the sensitivity of the experimental measurements and possible inaccuracies in the calculations. The mass transfer limitations at the higher flow rates (75% of the maximum recommended flow rate or pressure) are expected to result in a larger decrease in capacity from the static values, and this is indeed seen for most of the materials. In most cases the relation between the calculated and measured dynamic binding capacities is similar to that at the lower flow rates, but some cases deserve individual attention. Dramatic exceptions to the relation between measured and calculated values are that the calculated loading capacities of Super Q-650 C are far lower than the experimental results (Fig. 8). This suggests that a much higher diffusivity is needed for the models to attain the measured capacity. Super Q-650 C is among the three very narrow pore materials discussed in the previous section as barely admitting even the relatively small dextran probe molecules similar in size to BSA. That the DBC

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is in fact quite respectable may be due to the electrostatic contribution to transport that is not present for the dextran probes and was also mentioned in the discussion of static capacities [76]. For two other adsorbents, Q Sepharose XL and POROS 50 HQ, the decreases in the dynamic binding capacity at the higher flow rate are also noticeably overpredicted by the model calculations, but much less so than for Super Q-650 C discussed in the previous paragraph. For Q Sepharose XL the reasons are also presumably similar, but the effect is less dramatic because of the greater penetration of the dextran probes, as reflected in the Kd values discussed above. As a material designed to be perfusive, POROS 50 HQ is specifically intended to display enhanced transport due to intraparticle convection [69], and it is possible that this contributes to the relative invariance of DBC to flow rate in this case. In general, though, an apparent transport enhancement of this kind is presumably due to an underestimate of the effective rate of diffusion. This may stem in part from the electrostatic driving force discussed above, as well as other manifestations of changes in uptake mechanisms resulting from a complex dependence of transport on the stationary-phase structure, the protein and the salt concentration [79]. Such enhanced transport has in fact been observed for lysozyme uptake in SP-650 [79]. Overall, however, reasonable semi-quantitative estimates of dynamic capacities are obtained for materials other than Super Q-650 C, with slight differences between the two diffusion models (Fig. 8). This reasonable agreement is due mainly to use of the experimental static binding capacity for each material, which provides an upper bound for the dynamic binding capacity. The calculated dynamic binding capacities are generally higher than the measured results, indicating unaccounted-for sources of dispersion.

well-defined geometry is well established, intraparticle diffusion in chromatographic adsorbents cannot be accurately predicted using only the size-hindrance relation and the PSD. Even beyond the difficulties of predicting pore diffusivities, discrepancies in transport properties are seen under non-binding versus binding conditions, which may be related to the flexibility of dextrans versus the rigidity of proteins, as well as to the deviation of proteins from a spherical shape. Nevertheless, the information obtainable from ISEC allows approximate quantification of the underlying effects driving partitioning and adsorptive behavior, and its ease of implementation can make it a valuable chromatographic science tool to aid in interpretation of empirical results. The calculations shown here are not intended to provide precise predictions of breakthrough curves, such as those [19,27,79] that use directly measured mass transfer parameters at identical solution conditions or manipulate the controlling parameters. Rather, the efforts here are intended as a test of the feasibility of using knowledge gained solely from the pore structure to obtain a quick estimate of process features, specifically static capacity, diffusivity and hence dynamic capacity. These calculations were performed using parameters estimated from completely independent ISEC experiments, and therefore constitute predictions using a minimum of independent information. Given this situation, the calculations are, in many cases, in surprisingly good agreement with experimental data. The significant discrepancies seen in other cases appear to be associated with distinctive structural features, such as the presence of grafted polymers, and they may therefore provide useful mechanistic insights for those systems. Overall, therefore, the very rough engineering estimates presented can be helpful in narrowing down choices of media for screening.

4. Conclusions

Acknowledgements

The ISEC measurements presented here were based on established procedures, and demonstrate once again the relatively straightforward nature of this method. The more important contribution of this paper is, however, in showing the utility of these results, obtained in the absence of adsorption, for estimating important practical measures of performance of the materials under adsorptive conditions. Here the behavior of those materials bearing grafted polymers appears to be different from the more traditional ones. In particular, for the latter, static binding capacity appears to be related to the accessible surface area, which can be estimated from the PSD. With the information on surface area and a physical model that describes protein adsorption, reasonable estimates of static binding capacity are feasible in these cases, at least for the purpose of capturing trends among different materials. The discrepancies seen for adsorbents with pore space that is poorly accessible to neutral probes, e.g., those bearing grafted polymers, are quite large and probably reflect important mechanistic differences that can be exploited to enhance capacity. Prediction of breakthrough behavior and dynamic binding capacity presents a greater challenge, and our results suggest several sources of uncertainty in estimating transport properties. Although the correlation of hindrance with transport in a

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