Protein−Surface Interaction Maps for Ion-Exchange Chromatography

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Protein-Surface Interaction Maps for Ion-Exchange Chromatography Alexander S. Freed†,‡ and Steven M. Cramer*,†,‡ †

Department of Chemical and Biological Engineering, and ‡Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute (RPI), Troy, New York 12180, United States ABSTRACT: In this paper, protein-surface interaction maps were generated by performing coarse-grained protein-surface calculations. This approach allowed for the rapid determination of the protein-surface interaction energies at a range of orientations and distances. Interaction maps of lysozyme indicated that there was a contiguous series of orientations corresponding to several adjacent preferred binding regions on the protein surface. Examination of these orientations provided insight into the residues involved in suface interactions, which qualitatively agreed with the retention data for singlesite mutants. Interaction maps of lysozyme single-site mutants were also generated and provided significant insight into why these variants exhibited significant differences in their chromatographic behavior. This approach was also employed to study the binding behavior of CspB and related mutants. The results indicated that, in addition to describing general trends in the data, these maps provided significant insight into retention data of the single-site mutants. In particular, subtle retention trends observed with the K12 and K13 mutants were well-described using this interaction map approach. Finally, the number of interaction points with energies stronger than -2 kcal/mol was shown to be able to semi-quantiatively predict the behavior of most of the mutants. This rapid approach for calculating protein-surface interaction maps is expected to facilitate future method development for separating closely related protein variants in ion-exchange systems.

’ INTRODUCTION The adsorption of proteins on charged surfaces is of particular importance to a number of fields, including biomaterials,1,2 diagnostics,3 and bioseparations.4 The production of biopharmaceuticals in particular relies on the efficient separations provided by ion-exchange chromatography. It was shown by Kopaciewics et al. that protein binding on charged surfaces is the result of protein charge, surface charge density, counterion, and ionic capacity of the mobile phase.5 However, it was also shown that proteins would often adsorb at a neutral or even similar net charge as the surface. Therefore, it was inferred that regions of local charge where more important for binding than the overall protein net charge. The effects of charge distribution on protein adsorption have previously been experimentally investigated by several investigators. Whitley et al. and Gill et al. have shown that, of the total charged surface of the protein, only a few are needed to induce adsorption of a protein onto a ion-exchange surface. Gill and coworkers examined the effect of charge modification of protein adsorption to determine the preferred binding orientation of rat cytochrome b5.6 Yao and Lenhoff preformed a study using cytochome c variants to study the effect of protein shape and charge distribution on binding.7 Chicz and Regnier used genetically modified subtilisin variants to examine the effects of singlepoint (SP) mutations on protein retention.8 Work performed by Dismer et al.9 used chemical modification of lysozyme after adsorption to an ion-exchange resin to determine a preferred r 2011 American Chemical Society

conformation of the adsorbed species. We have recently examined protein charge ladders and a single-site mutant protein library to better understand the effects of charge distribution on protein retention in ion exchange. The lysozyme charge ladder10 was generated via partial acetylation of lysine residues, and the cytochrome c charge ladder was generated via partial succinylation. This resulted in homologous mixtures of protein variants with varying charge densities and distribution. A library of homologous single-site mutants of a thermostable cold-shock protein B (CspB) variant, which included single-site charge neutralizations and charge reversals, was also examined.11 These studies elucidated preferred binding orientations of these protein libraries and demonstrated how the protein electrostatic potentials (EPs) could be employed to provide insight into binding affinity. Much of the experimental work examining protein adsorption to chromatographic resins has been accompanied by mesoscale modeling efforts to examine the effects of protein charge states on adsorption. Roth and Lenhoff12 have computed the electrostatic and van der Waals energies of the interaction between a colloidal protein molecule and a planar charged surface at a fixed distance and orientation. Although the work improved our understanding of electrostatic and dispersive mechanisms for protein adsorption, the approach was limited to the depiction of Received: November 22, 2010 Revised: January 24, 2011 Published: March 04, 2011 3561

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Langmuir the protein as a low dielectric sphere. Hallgren et al.13 have employed the charge regulated slab model to evaluate the salt dependence of proteins in cation-exchange chromatography. Jonsson and Stahlberg14 have used a model based on the Poisson-Boltzmann equation to predict the ionic strength dependence of retention. Bowen et al.15 have used the nonlinear Poisson-Boltzmann equation for predicting the equilibrium constants for protein ion exchange in terms of protein size, protein and ion-exchanger ζ potential, and electrolyte concentration. Roth et al.16 have examined the electrostatic contribution to the energy and entropy of protein adsorption. Recently, Dismer and Hubbuch17 have used molecular dynamics (MD) simulations to determine the preferred binding orientation for lysozyme on an ion-exchange surface. The method employed in that study used all-atom MD simulations to determine the protein-surface energetics at a series of orientations. Further, the study correlated protein-surface binding strengths to protein retention times. While this approach allowed for both flexible surface ligands and protein side chains, this came at a significant computational expense. In this paper, a coarse-grained modeling method for determining protein-surface orientations on ion-exchange surfaces is developed. This method uses an effective charge approach and allows for rapid sampling of a large set of protein orientations. Because the effective charge calculation uses a Poisson-Boltzmann approach to account for varying electric permittivity, the calculation is able to accurately model charge-charge interactions. This efficient calculation method is employed to determine the distribution of favorable protein-surface orientations for both lysozyme and CspB protein libraries. Both general trends and subtle retention behavior are examined. Finally, a semiquantitative method is presented to predict the behavior of the variants.

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Figure 1. Diagram of the protein above the simulated surface highlighting the rotations and position axes. and the lowest protein atom. This method ensures that the protein does not intersect the surface and there is no bias toward angles that have the protein closer to the surface. The energy is calculated with a simple force field recently developed by the Elcock group24-26 to carry out energy calculations in large-scale Brownian dynamics simulations of concentrated protein solutions. For our application, this approach allows for the rapid determination of the protein-surface interaction energies at a range of orientations and distances. The force field is given as E ¼ ELJ þ EHydro þ EEle ELJ ¼ -

EHydro ¼ EEle ¼

’ THEORETICAL SECTION Structure Development. The protein structures for the native proteins were obtained from published structures. The structures were then homology modeled and parametrized according to the experimental pH. Finally, the native protein structure was modified to create the structures for the mutants and again parametrized based on the experimental conditions. The surfaces were manually constructed on the basis of a flat plane, and the charges were evenly distributed according to the desired charge density. EP Distribution. To study the distribution of EP near the protein surfaces and parametrize the effective charge model, a series of PoissonBoltzmann calculations were performed on the native protein and protein variants. Each structure of the variant was produced by mutating the native protein structure followed by minimization using the AMBER 94 force field. These structures were then parametrized with the PARSE force field, which was designed to be used for implicit solvent calculations.18 The Adaptive Poisson-Boltzmann Solver (APBS)19-22 package was employed to generate electrostatic distributions, which were then depicted and analyzed using the VMD molecular graphics viewer.23 Coarse-Grained Protein-Surface Calculations. The protein-surface interaction maps were generated by performing coarsegrained protein-surface calculations over a set of incident angles. The calculations were setup as depicted in Figure 1, where θ and j are the protein rotation about the z and y axes, respectively. The protein was oriented such that the distributions of θ and j angles were equidistant across the surface of the sphere. The height of the protein above the surface (HP) is defined as the distance between the highest surface atom

∑i ∑j 4εij

σij rij

∑i ∑j 4εij

!12

σij rij

!6

∑i qi, eff PEle

where εij and σij are the standard Lennard-Jones potential parameters for the atoms involved (for simplicity, these are assumed to be an average value for the system),26 r is the atom-atom distance, qi,eff and PEle are the effective charges for the residues and the electric field generated by the surface as described by Gabdoulline, respectively.27 The effective charges are a method of coarse-graining charge-charge interactions, removing the need for full Poisson-Boltzmann calculations. In this procedure, the electrostatic protential around the protein is calculated. The protein is then broken down into distinct charges, in this case, on the basis of charged residues (e.g., one charge at the Nþ of lysine and the N terminus and two charges for the delocalized charges in arginine, aspartic acid, glutamic acid, and the C terminus). The charge values are then adjusted such that they will be able to generate the same EP distribution in a constant dielectric medium. Because the resin surface is fixed in the simulation, it is only necessary to consider the EP field generated by the surface charges. As a result, the computational expense associated with the calculation of the protein-surface interaction energy is dramatically decreased. While relatively simplistic, this approach is able to provide very good estimates of electrostatic interaction strengths, which is the primary mechanism of interaction in ionexchange chromatography. Further, this dramatic gain in computational efficiency enables many more angles of interest to be calculated, giving a better picture of protein adsorption. In the current work, a background salt concentration of 150 mM was employed in all calculations. It is also important to consider the effect of the protein-surface distance on the calculations. While the surface is represented with discrete charges, at sufficient protein-surface separation distance 3562

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Figure 2. EP in the x-y plane at three distances above the surface: (a) 25 Å, (b) 15 Å, and (c) 5 Å.

Figure 4. Protein-surface interaction map for lysozyme on the cationic surface. Three orientations of interest are labeled spanning the strong interaction region.

Figure 3. Chromatographic profile of the lysozyme charge ladder mixture separated in a linear gradient with the native and four singlesite variants identified. (e.g., 25 Å), the EP as a function of x and y positions is essentially flat (Figure 2a). At this distance, the surface acts like an infinite surface of uniform electrical density and the x-y position of the protein does not affect the protein-surface interaction map. Prior work by our group, which employed protein EP isosurfaces, was essentially limited to this level of analysis.11 However, the EP generated by the surface becomes more variable at shorter protein-surface separation distances. At 15 Å (Figure 2b), although the EP is relatively uniform, there is distinct “structure” in the profile. This is even more pronounced at 5 Å, where the higher values of the EP are focused in the vicinity of the charges (Figure 2c). At these distances, where the protein can distinguish the EP generated by individual surface charges, the preferred orientation of the protein becomes a function of the protein location. This necessitates the use of a minimization algorithm to align the protein to the surface charges. In this work, a simple Monte Carlo search algorithm was employed for the minimization of the protein over the model surface.

’ RESULTS AND DISCUSSION Lysozyme Charge Ladder. Previous work in our laboratory has employed a lysozyme charge ladder to study the effects of protein surface modification on protein retention in cationexchange chromatography.10 In that work, acetic anhydride was used as an acetylating agent to modify protein surface lysine residues. Partial acetylation of lysozyme resulted in the formation of a homologous set of modified proteins with varying charge densities and distribution. The resulting protein charge ladder was separated on a cation-exchange column (Figure 3), and eluent fractions were subsequently analyzed using capillary zone electrophoresis and direct infusion electrospray ionization mass spectrometry to determine the number and location of the acetylated sites for a number of fractions. While the proteins showed the expected trend, with higher levels of acetylation (less positive charge) resulting in lower retention on the cation exchanger, as compared to the native lysozyme, there were several unexpected results. Several fractions contained coelution

of variants, some with differing net charge. In addition, several cases were observed where variants with more positive surface charge eluted from the column prior to variants with less positive charge. The elution times of four single-site variants are shown in Figure 3. As seen in the figure, the retention decrease was highest for neutralization of lysine 1 or the N terminus. This was followed closely by residue 33. Finally, residue 97 eluted last and showed significantly less effect from the neutralization. Clearly, because all single-site variants have the same net charge, the change in protein retention was due to the location of the charge. In a previous paper, we demonstrated that EP isosurfaces could be employed to identify two potential preferred binding regions on the lysozyme surface. To examine this in more depth, the coarse-grained modeling approach was employed to study the surface binding behavior of the single-site variants. Figure 4 shows the results for the binding of lysozyme on the model cation-exchange surface. The map represents the binding energy as the protein is rotated above the surface. The x axis of the map corresponds to the θ rotations, and the y axis corresponds to the j rotations. The blue regions represent weak interactions, while the red regions represent strong interactions. As seen in the figure, there is a distinct strong interaction region of this binding map. This contiguous series of orientations corresponds to several adjacent preferred binding regions on the protein surface. It is instructive to examine the protein orientation with respect to the surface in this strong interaction region. The orientations corresponding to points A, B, and C in Figure 4 are given in panels a, b, and c of Figure 5, respectively (note that the spheres represent the charged residues in their conformation above the surface). For site A, the protein is oriented such that residues Lys 1, Lys 33, Arg 128, and Arg 5 are facing the surface (Figure 5a). For site B, residues Lys 1, Arg 128, and Arg 14 are primarily involved in the interaction with the surface. Finally, site C on the very edge of the strong interactions region involves residues Lys 13, Arg 14, His 15, Arg 21, Lys 96, Lys 97, and Arg 128. While there appears to be more charges interacting with the surface at site C than at the other two, the large number of negatively charged residues also involved in the binding face makes this site the weakest of the three. It should be noted that the binding orientations obtained in this method agree well with not only those previously hypothesized from the experimental results10 but also those observed in a separate orientation study carried out with lysozyme.9 While discrete binding orientations are depicted in Figure 5, it is clear from the binding map (Figure 4) that there is a continuum 3563

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Figure 5. Structures of the protein-surface complexes identified in Figure 4. The protein is show in the cartoon with the charged groups shown in the spheres. The surface groups are shown along the bottom.

Figure 6. Protein-surface interaction maps for native lysozyme and three single-site neutralization variants (1, 33, and 97).

of high-affinity orientations. Thus, the protein is able to easily reorient between the various configurations shown in Figure 5. This reorientation between binding configurations is expected to be an important contributor to the binding energy because the improved rotational degrees of freedom will decrease the entropy loss associated with adsorption. As seen in panels a and b of Figure 5, residue 1 and the N-terminal amine are located at the hinge between sites A and B. Thus, neutralization of these amines would be expected to have a larger effect on retention than neutralization of residue 33, which is not as centrally located in the binding region. In other words, when residue 33 is lost, there is a decrease in binding associated with the removal of charge from a favored site. However, when lysine 1 or the terminal amine are neutralized, there is a greater effect because many more preferred orientations are affected as well as the ability of the protein to sample multiple conformations. As seen in Figure 5c,

residue 97 plays a minor role in the binding for this particular orientation. Thus, when this residue is neutralized, it would be expected to have a less pronounced effect on the protein retention. These results agree with the retention time trends of the mutants shown in Figure 3. It is also important to note that, while the discussion thus far has focused on the strong interaction region, moderate and weak binding regions can also contribute to protein binding. While the protein will favor stronger interaction regions, it is also likely to sample other adjoining weaker binding conformations. To examine this in more depth, it is instructive to compare the binding maps between the native and mutant forms. The binding maps for the native, variant 1, variant 33, and variant 97 are presented in Figure 6. The N-terminal variant is not being examined because the charge characteristics for both the Lys 1 and N terminus variants are indistinguishable from one another. For variant 1, the removal of this crucial charge had a dramatic affect on the binding map. A large portion of the strong interaction region was affected, leaving only two restricted conformations. For variant 33, the change is significant within the area around site A, but clearly the effect is not nearly as widespread as was observed for neutralization of Lys 1. For variant 97, only a minor change was observed in the binding map, leaving most of the strong interaction region intact. These results qualitatively agree with the order of the retention times of these variants (Figure 3). Further, these binding maps provide significant insight into why these variants have significant differences in their chromatographic behavior. CspB Mutant Library. The binding map analysis was also employed to evaluate data obtained from a previous study11 on the chromatographic behavior of a CspB mutant library in a cation-exchange system. CspB was chosen as a model protein because it is small, monomeric, well-characterized, and stable after undergoing a range of SP mutations. The surface used in these simulations was the same charged surface used in the previous analysis of lysozyme. In this prior work, single-site mutations were performed on charged amino acids on the protein surface, resulting in a homologous protein set with varying charge density and distribution. As seen in Figure 7, the retention times of the mutants varied significantly during linear gradient chromatography. While the expected trends were observed with increasing or decreasing positive charge on the protein surface, the degree of change was a strong function of the location and microenvironment of the mutated amino acid. The chromatographic results indicated that, while mutations of residues 3, 12, 13, and 55 resulted in significant changes in retention, changes in residues 5, 7, 20, 39, and 42 resulted in 3564

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Langmuir minor changes. These results along with the EP isosurface analysis presented in that paper indicated the presence of potential preferred binding regions on the surface of the protein. While informative, this previous work was limited to a qualitative analysis of the electrostatic properties of the protein. To examine this in more depth, the coarse-grained modeling approach was employed to study the surface binding behavior of CspB on the simulated SP surface (Figure 8). As seen in the resulting binding map, there was a contiguous series of orientations corresponding to several adjacent preferred binding regions on the protein surface. It is instructive to examine the protein

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orientation with respect to the surface in this strong interaction region. The orientations corresponding to points A, B, and C in the binding map are presented in Figure 9. In orientation A, residues 12, 13, 55, and 56 are near the surface. This agrees with the significant reduction in retention time when residues 12, 13, and 55 were neutralized or a negative charge was introduced (Figure 7). In orientation B, residues 3, 20, amino terminus, and 55 are near the surface. This agrees with the significant reduction in retention time when residues 3 and 55 were neutralized or a negative charge was introduced (Figure 7). Finally, in orientation C, residues 12, 29, 39, 55, and 56 are near the surface. This agrees with the reduction in retention time observed when residues 12, 39, and 55 were neutralized or a negative charge was introduced (Figure 7). Mutant Binding Maps. To examine this in more depth, it is instructive to compare the binding maps between the native and some of the mutant forms of CspB. Three sets of binding map comparisons were carried out. First, a comparison between the native CspB, E50K, and K55E mutants was performed to show the overall effect of increasing and decreasing the protein charge. Comparisons were then carried out to examine the underlying cause of the subtle effects shown for the K13 and E50 mutations. Figure 10 shows a comparison between the native, E50K, and K12E forms of CspB. As seen, the overall intensity of the E50K

Figure 7. Elution salt concentration of the single-site CspB mutants relative the native protein.

Figure 8. Protein-surface interaction map for CspB on the cationic surface. Three orientations of interest are labeled spanning the strong interaction regions.

Figure 10. Protein-surface interaction maps for native CspB and examples of strong (E50K) and weak (K12E) binding variants.

Figure 9. Structures of the protein-surface complexes identified in Figure 8. The protein is show in the cartoon with the charged groups shown in the spheres. The surface groups are shown along the bottom. 3565

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Figure 11. Protein-surface interaction maps for native CspB compared to the K12 and K13 mutants.

variant was significantly higher than the native CspB. In addition, the K12E mutant exhibited much weaker interactions with the surface, as compared to the native protein. These results are in qualitative agreement with what was observed with the experimental retention times (Figure 7). The much weaker interactions between the K12E mutant and the surface lead to an overall weaker binding, and therefore, a lower amount of salt is needed to elute the protein. On the other hand, the higher overall binding energy of E50K as compared to native CspB results in stronger adsorption, which requires higher salt concentrations to elute the protein. While the E50K and K12E mutants show how the interaction maps can be used to understand the general adsorption trend, the real advantage of this approach is how it can provide insight into some of the more subtle effects in protein surface binding. One of the more puzzling results from the retention data was the relative behavior of the K12 and K13 mutants. As seen in Figure 7, while neutralization resulted in decreased retention of both the K12Q and K13Q mutants, only the K12E mutant was further affected by charge reversal. This result is interesting because the K12 and K13 mutants reside near each other on the protein surface. As seen from the interaction maps in Figure 11, while the binding of mutants K12Q and K13Q were very similar, there were clear differences that were observed with K12E and K13E. While the interaction map of K12Q was further reduced upon mutation to K12E, the maps for K13Q and K13E were quite similar. Importantly, this is exactly what was observed with the chromatography, indicating that this modeling approach is indeed capable of describing subtle behavior in these protein adsorption systems. While the interaction maps were able to explain the behavior of the K13 mutants, they were not as successful in describing the K50 mutants. As seen in Figure 7, while neutralization resulted in a minimal effect on protein adsorption, charge reversal produced a dramatic increase in protein binding, producing the highest binder of all of the mutants. A comparison between the interaction maps for the native, E50Q, and E50K proteins is presented in Figure 12. As seen in the figure, while E50K exhibited increased binding, as compared to E50Q, both mutants had higher binding than the native protein. Thus, while the E50K

Figure 12. Protein-surface interaction maps for native CspB compared to the E50 mutants.

mutant results agree with the chromatography, the E50Q interaction map does not appear to agree with the retention data. This indicates that a qualitative examination of the interaction maps while useful may not be sufficient to describe the behavior of all cases. It was of interest to determine what properties of the binding maps could be employed to perform a semi-quantitative analysis of the retention data. The top and middle panels of Figure 13 show the minimum and average energies for each of the protein mutants examined, respectively. As seen, there did not appear to be any significant agreement between these energies and the retention times on the column. The bottom panel of Figure 13 presents the number of interaction points with energies stronger than -2 kcal/mol. As seen in the figure, in contrast to the other properties, this approach seems to work reasonably well for many of the mutants. In addition, the relative retention behavior of the K12 and K13 mutants is captured well using this approach, as well as the behavior of the K55 and E43 mutants. Again, while the 3566

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provided significant insight into why these variants exhibited significant differences in their chromatographic behavior. The coarse-grained modeling approach was also employed to study the surface-binding behavior of CspB and related mutants on the simulated SP surface. The results indicated that, in addition to describing general trends in the data, these maps provided significant insight into retention data of the single-site mutants. For example, while the interaction map of K12Q was further reduced upon mutation to K12E, the maps for K13Q and K13E were quite similar. These results were in good agreement with those observed with the chromatography, indicating that this modeling approach was indeed capable of describing subtle behavior in these protein adsorption systems. However, while the binding maps worked for most mutants, it may not be sufficient to describe the behavior of all cases. Finally, the number of interaction points with energies stronger than -2 kcal/mol was shown to be able to semi-quantitatively predict the behavior of most of the mutants. The shape of the energy well is likely to be correlated to protein-surface conformational entropy, which is expected to have a significant effect on protein adsorption. This may be important for understanding the behavior of the individual shifts observed with the protein mutant libraries. Previous studies have shown that residue mutations in preferred binding regions affect the adsorption strength more than those outside the preferred region. However, the exact degree of shift is often highly variable even for neighboring residues, and the exact cause of this is still an area of exploration. In addition, statistical analysis to correlate protein retention times to the shape and strength of the protein-surface interaction maps may also be useful. Finally, it will be important to extend this approach to other protein chromatographic systems, such as multi-modal chromatography.

’ AUTHOR INFORMATION Figure 13. Comparison of binding map properties for the K12, K13, and E50 mutant sets.

E50K is well-described, the E50Q is still problematic. The number of low-energy interaction sites is to some extent a measure of the configurational degrees of freedom experienced by the surface-bound protein. Thus, it is not only the strength of the interactions but also the number of favorable interactions that impact the protein adsorption. The fact that the E50Q mutant is still not properly described suggests that there are other factors that may come into play, such as the number of contiguous binding poses and the local energy wells that are present within a series of binding configurations.

’ CONCLUSIONS In this paper, protein-surface interaction maps were generated by performing coarse-grained protein-surface calculations. The approach employed here allows for the rapid determination of the protein-surface interaction energies at a range of orientations and distances. Interaction maps of lysozyme indicated that there was a contiguous series of orientations corresponding to several adjacent preferred binding regions on the protein surface. Examination of these orientations provided insight into the residues involved in surface interactions, which qualitatively agreed with the retention data for single-site mutants. Interaction maps of lysozyme single-site mutants were also generated and

Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by National Science Foundation Grant CBET 0933169. ’ REFERENCES (1) Lavenus, S.; Ricquier, J. C.; Louarn, G.; Layrolle, P. Cell interaction with nanopatterned surface of implants. Nanomedicine 2010, 5 (6), 937–947. (2) Raynor, J. E.; Capadona, J. R.; Collard, D. M.; Petrie, T. A.; Garcia, A. J. Polymer brushes and self-assembled monolayers: Versatile platforms to control cell adhesion to biomaterials (Review). Biointerphases 2009, 4 (2), FA3–FA16. (3) Bilitewski, U. Protein-sensing assay formats and devices. Anal. Chim. Acta 2006, 568 (1-2), 232–247. (4) Yigzaw, Y.; Hinckley, P.; Hewig, A.; Vedantham, G. Ion exchange chromatography of proteins and clearance of aggregates. Curr. Pharm. Biotechnol. 2009, 10 (4), 421–426. (5) Kopaciewicz, W.; Rounds, M. A.; Fausnaugh, J.; Regnier, F. E. Retention model for high-performance ion-exchange chromatography. J. Chromatogr. 1983, 266, 3–21. (6) Gill, D. S.; Roush, D. J.; Willson, R. C. Presence of a preferred anion-exchange binding-site on cytochrome b5—Structural and thermodynamic considerations. J. Chromatogr., A 1994, 684 (1), 55–63. 3567

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(7) Yao, Y.; Lenhoff, A. M. Electrostatic contributions to protein retention in ion-exchange chromatography. 1. Cytochrome c variants. Anal. Chem. 2004, 76 (22), 6743–6752. (8) Chicz, R. M.; Regnier, F. E. Single amino-acid contributions to protein retention in cation-exchange chromatography—Resolution of genetically engineered subtilisin variants. Anal. Chem. 1989, 61 (18), 2059–2066. (9) Dismer, F.; Hubbuch, J. A novel approach to characterize the binding orientation of lysozyme on ion-exchange resins. J. Chromatogr., A 2007, 1149 (2), 312–320. (10) Chung, W. K.; Evans, S. T.; Freed, A. S.; Keba, J. J.; Baer, Z. C.; Rege, K.; Cramer, S. M. Utilization of lysozyme charge ladders to examine the effects of protein surface charge distribution on binding affinity in ion exchange systems. Langmuir 2010, 26 (2), 759–768. (11) Chung, W. K.; Hou, Y.; Freed, A.; Holstein, M.; Makhatadze, G. I.; Cramer, S. M. Investigation of protein binding affinity and preferred orientations in ion exchange systems using a homologous protein library. Biotechnol. Bioeng. 2009, 102 (3), 869–881. (12) Roth, C. M.; Lenhoff, A. M. Electrostatic and van der Waals contributions to protein adsorption: Computation of equilibrium constants. Langmuir 1993, 9 (4), 962–972. (13) Hallgren, E.; Kalman, F.; Farnan, D.; Horvath, C.; Stahlberg, J. Protein retention in ion-exchange chromatography: Effect of net charge and charge distribution. J. Chromatogr., A 2000, 877 (1-2), 13–24. (14) Jonsson, B.; Stahlberg, J. The electrostatic interaction between a charged sphere and an oppositely charged planar surface and its application to protein adsorption. Colloids Surf., B 1999, 14 (1-4), 67–75. (15) Bowen, W. R.; Sharif, A. O. Long-range electrostatic attraction between like-charge spheres in a charged pore. Nature 1998, 393 (6686), 663–665. (16) Roth, C. M.; Sader, J. E.; Lenhoff, A. M. Electrostatic contribution to the energy and entropy of protein adsorption. J. Colloid Interface Sci. 1998, 203 (1), 218–221. (17) Dismer, F.; Hubbuch, J. In silico prediction of protein binding using molecular dynamic simulations: A future tool for accelerated process development. J. Biosci. Bioeng. 2009, 108, S60–S60. (18) Tan, C.; Yang, L.; Luo, R. How well does Poisson-Boltzmann implicit solvent agree with explicit solvent? A quantitative analysis. J. Phys. Chem. B 2006, 110 (37), 18680–18687. (19) Baker, N. A.; Sept, D.; Joseph, S.; Holst, M. J.; McCammon, J. A. Electrostatics of nanosystems: Application to microtubules and the ribosome. Proc. Natl. Acad. Sci. U.S.A. 2001, 98 (18), 10037–10041. (20) Holst, M.; Saied, F. Multigrid solution of the Poisson-Boltzmann equation. J. Comput. Chem. 1993, 14 (1), 105–113. (21) Holst, M. J.; Saied, F. Numerical solution of the nonlinear Poisson-Boltzmann equation—Developing more robust and efficient methods. J. Comput. Chem. 1995, 16 (3), 337–364. (22) Bank, R. E.; Holst, M. A new paradigm for parallel adaptive meshing algorithms. SIAM J. Sci. Comput. 2000, 22 (4), 1411–1443. (23) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual molecular dynamics. J. Mol. Graphics 1996, 14 (1), 33–38. (24) Donald, L. E.; McCammon, J. A. Brownian dynamics with hydrodynamic interactions. J. Chem. Phys. 1978, 69 (4), 1352–1360. (25) Elcock, A. H. Molecular simulations of diffusion and association in multimacromolecular systems. Methods Enzymol. 2004, 383, 166–198. (26) McGuffee, S. R.; Elcock, A. H. Atomically detailed simulations of concentrated protein solutions: The effects of salt, pH, point mutations, and protein concentration in simulations of 1000-molecule systems. J. Am. Chem. Soc. 2006, 128 (37), 12098–12110. (27) Gabdoulline, R. R.; Wade, R. C. Effective charges for macromolecules in solvent. J. Phys. Chem. 1996, 100 (9), 3868–3878.

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