Binding of sodium n-dodecyl sulphate and protons to catalase

The binding of sodium n-dodecyl sulphate to catalase has been measured by equilibrium dialysis in the pH range 3.2 to 10.0. On the acid side of the isoelectric point (pH 5.4) the surfactant anions initially bind to cationic sites on the protein and subsequent binding is cooperative. At high pH on the alkaline side of the isoelectric point only cooperative binding is observed. The binding data have been combined with protein titration curves to calculate the Gibbs energies of formation of protein titration curves to calculate the Gibbs energies of formation of protein surfactant proton complexes. Contributions to the Gibbs energies of complex formation by surfactant and protein binding have been estimated. The average Gibbs energies of surfactant binding to specific cationic sites are ca. 28 kJ mol^?1 and for cooperative binding ca. 15 kJ mol^?1.     

Effects of fluorinated and hydrogenated surfactants on human serum albumin at different pHs

Complexation between human serum albumin (HSA) and two different surfactants, one fully fluorinated (sodium perfluorooctanoate, SPFO) and one fully hydrogenated (sodium caprylate, SO), was studied using zeta-potential measurements and difference spectroscopy. The study was carried out at three different pHs, 3.2, 6.7, and 10.0. The spectroscopy study was performed at pHs 6.7 and 10.0, given that at pH 3.2 high turbidity was observed in the wide range of surfactant concentrations. The results were interpreted in terms of the electrostatic and hydrophobic contributions to the stability of the different phases formed in the water-surfactant-HSA system. Solutions and precipitates were observed in the concentration range investigated in more detail. Using Pace methods, the thermodynamic values of the surfactant-induced conformational changes in HSA were determined for sodium perfluorooctanoate in the concentration range 2-12 mmol dm(-3) at pH 6.7 and 5-22 mmol dm(-3) at pH 10.0. Electrophoretic measurements were used to characterize surfactant adsorption by determining the number of molecules adsorbed on the surface of HSA and the Gibbs energy of adsorption. Finally, the interactions between human serum albumin and other anionic surfactants studied by other authors were compared with those observed in the present work.     

Interactions of two amphiphilic penicillins with myoglobin in aqueous buffered solutions: a thermodynamic and spectroscopy study

The interactions and complexation process of the amphiphilic penicillins sodium cloxacillin and sodium dicloxacillin with horse myoglobin in aqueous buffered solutions of pH 4.5 and 7.4 have been examined by equilibrium dialysis, zeta-potential, isothermal titration calorimetry (ITC) and UV-Vis absorbance techniques. A more opened structure of the protein molecules is detected as a consequence of the reduction of pH from 7.4 to 4.5. Binding isotherms and derived Hill coefficients reflect a cooperative binding behavior. Gibbs energies of binding per mole of drug were obtained from equilibrium dialysis data and compared with those derived from the zeta potential taking into account cooperativity. DeltaGads degrees values so obtained are large and negative at low concentrations where binding to the "high-energy" sites occurs and decreases with the drug concentration. The enthalpies of binding have been obtained from ITC and are small and exothermic so that the Gibbs energies of binding are dominated by large increases in entropy consistent with hydrophobic interactions. Other thermodynamic quantities of the binding mechanism, that is, entropy, DeltaSITCi, Gibbs energy, DeltaGITCi, the binding constant, KITCi, and the number of binding sites, ni, were also obtained, confirming the above results. From ITC data and following a theoretical model, the number of bound and free penicillin molecules was calculated, being higher at pH 4.5 than at pH 7.4. The binding of penicillin causes a conformational transition on protein structure as a consequence of the resulting intramolecular repulsion between the penicillin molecules bound to the protein. Thermodynamic quantites (the Gibbs energy of the transition in water, DeltaGw degrees , and in a hydrophobic environment, DeltaGhc degrees) of the denaturation process were calculated, indicating that at pH 4.5 some of the histidine residues are protonated, becoming accessible to solvent and giving rise to a more opened protein structure.     

Study of the interactions between lysozyme and a fully-fluorinated surfactant in aqueous solution at different surfactant-protein ratios

The interactions of a fluorinated surfactant, sodium perfluorooctanoate, with lysozyme, have been investigated by a combination of UV absorbance, electrical conductivity and dynamic light scattering to detect and to characterize the conformational transitions of lysozyme. By using difference spectroscopy, the transition was followed as a function of surfactant concentration, and the data were analyzed to obtain the Gibbs energy of the transition in water (DeltaGw(o)) and in a hydrophobic environment (DeltaGh(o)) for saturated protein-surfactant complexes. Electrical conductivity was used to determine the critical micelle concentration of the surfactant in the presence of different lysozyme concentration. From these results, the average number of surfactant monomer per protein molecule was calculated. Finally, dynamic light scattering show that only changes in the secondary structure of the protein can be observed.     

Ultraviolet-circular dichroism spectroscopy and potentiometric study of the interaction between human serum albumin and sodium perfluorooctanoate

The interaction of a fluorinated surfactant, sodium perfluorooctanoate, with human serum albumin (HSA) has been investigated by a combination of ultraviolet-circular dichroism (UV-CD) spectroscopy and potentiometry (by a home-built ion-selective electrode) techniques to detect and characterize the conformational transitions of HSA. By using difference spectroscopy, the transition was followed as a function of temperature, and the data were analyzed to obtain the parameters characterizing the thermodynamics of unfolding. The results indicate that the presence of surfactant drastically changes the melting unfolding, acting as a structure stabilizer and delaying the unfolding process. Potentiometric measurements were used to determine the binding isotherms and binding capacity for this system. The isotherm shows a high affinity of surfactant molecules for HSA. The average number of surfactant molecules absorbed per protein molecule (at 28 mM of surfactant concentration) was found to be approximately 900, about 6 g of surfactant per gram of protein. The shape of the binding capacity curve and the relation between binding capacity and extend of cooperativity were examined. From these analysis, the values of g (number of ligand-binding sites), KH (Hill binding constant), and nH (Hill coefficient) were determined.     

Rheological properties of ovalbumin hydrogels as affected by surfactants addition

The gel properties of ovalbumin mixtures with three different surfactants (sodium perfluorooctanoate, sodium octanoate and sodium dodecanoate) have been studied by rheological techniques. The gel elasticities were determined as a function of surfactant concentration and surfactant type. The fractal dimension of the formed structures was evaluated from plots of storage modulus against surfactant concentration. The role of electrostatic, hydrophobic and disulfide SS interactions in these systems has been demonstrated to be the predominant. The viscosity of these structures tends to increase with surfactant concentration, except for the fluorinated one. Unfolded ovalbumin molecules tend to form fibrillar structures that tend to increase with surfactant concentration, except for the fluorinated one. This fact has been related to the particular nature of this molecule.     

Cooperativity and effects of ionic strength on the binding of sodium n-dodecyl sulphate to lysozyme

The binding of sodium n-dodecyl sulphate to lysozyme has been measured by equilibrium dialysis at 25°C and pH 3.2 over a range of ionic strengts from 0.0119 to 0.2119. Binding isotherms in the region corresponding to ionic binding between the surfactant anions and cationic amino acid residues on the protein have been interpreted in terms of the Hill equation and exhibit positive cooperativity with Hill coefficients in the region of 7–11. The Gibbs energies of binding have been calculated from the Hill binding constants and from the Wyman binding potentials. The stability of the surfactant-protein complexes is discussed in relation to the stability of surfactant micelles. Ionic binding of the surfactant is weakened and hydrophobic binding strengthened by increasing ionic strength.     

Thermodynamics of the interaction of sodium-n-dodecyl sulphate with Aspergillus niger catalase in high ionic strength aqueous solutions

The thermodynamic parameters for the interaction between sodium n-dodecyl sulphate (SDS) and Aspergillus niger catalase in aqueous solution at pH 3.2 and 6.4 have been measured by microcalorimetry and equilibrium dialysis over a range of ionic strength from 0.05 to 0.2 at 25 degrees C. Binding isotherms have been interpreted in terms of theoretical models (Hill equation and Wyman binding potential). The Gibbs energies of interaction become increasingly negative with increase in ionic strength and the entropies of interaction become increasingly positive. The ionic strength dependence of the Gibbs energies are much greater than predicted by the Debye-Hückel limiting law indicating a strongly ionic strength dependent hydrophobic contribution to the interactions.     

Surface characterization of human serum albumin and sodium perfluorooctanoate mixed solutions by pendant drop tensiometry and circular dichroism

The interfacial behavior of mixed human serum albumin (HSA)/sodium perfluorooctanoate (C8FONa) solutions is examined by using two experimental techniques, pendant drop tensiometry and circular dichroism spectroscopy. Through the analysis of the surface tension of the mixed solutions, surface competitive adsorption at the air-water interface between C8FONa and HSA is detected. The dynamic adsorption curves exhibit the distinct regimes in their time-dependent surface tension. The nature of these regimes is further analyzed in terms of the variation of the molecules surface areas. As a consequence, a compact and dense structure was formed where protein molecules were interconnected and overlapped. Thus, a reduction of the area occupied per molecule from 100 to 0.2 nm(2) is interpreted as a gel-like structure at the surface. The presence of the surfactant seems to favor the formation of this interfacial structure. Finally, measurements of circular dichroism suggests a compaction of the protein due to the association with the surfactant given by an increase of alpha-helix structure in the complexes as compared to that of pure protein.     

Energetics and conformational changes upon complexation of a phenothiazine drug with human serum albumin

The interactions and complexation process of the amphiphilic phenothiazine fluphenazine hydrochloride with human serum albumin in aqueous buffered solutions of pH 3.0 and 7.4 have been examined by zeta-potential, isothermal titration calorimetry (ITC), UV-vis spectroscopy, and dynamic light scattering (DLS) techniques with the aim of analyzing the effect of hydrophobic and electrostatic forces on the complexation process and the alteration of protein conformation upon binding. Thus, the energetics and stoichiometry of the binding process were derived from ITC data. The enthalpies of binding obtained are small and exothermic, so the Gibbs energies of binding are dominated by large increases in entropy, consistent with hydrophobic interactions at a acidic pH. However, at physiological pH, binding to the first class of binding sites is dominated by an enthalpic contribution due to the existence of electrostatic interactions and probably some hydrogen bonding. Binding isotherms were obtained from microcalorimetric data by using a theoretical model based on the Langmuir isotherm. zeta-Potential data showed a reversal in the sign of the protein charge at pH 7.4, as a consequence of the binding of the drug to the protein. Gibbs energies of drug binding per mole of drug were also derived from zeta-potential data. On the other hand, binding of the phenothiazine that causes a conformational transition on the protein structure was followed as a function of drug concentration using UV-vis spectroscopy, and the data were analyzed to obtain the Gibbs energy of the transition in water (deltaG(degree)w) and in a hydrophobic environment (deltaG(degree)hc). Finally, the population distribution of the different species in solution and the size of the complexes were analyzed through dynamic light scattering. The existence of an aggregation process of drug/protein complexes, as a consequence of the expanded structure of the protein induced by the drug and subsequent further binding, is in agreement with ITC data. In addition, detection of drug aggregates at concentrations below the drug critical micelle concentration was also detected by this technique.     

Interaction of glucose oxidase with ionic surfactants: a microcalorimetric study

The enthalpies of interaction of glucose oxidase at 25°C with a homologous series of n-alkyltrimethylammonium bromides (TABs) at pH 10 and a homologous series of n-alkylsulfates at pH 3.2 have been measured by microcalorimetry. For the n-dodecyl member of each series, DTAB and sodium n-dodecylsulfate (SDS), the binding of the surfactants to glucose oxidase as measured by equilibrium dialysis has been used in combination with the enthalpy data to obtain the Gibbs energy ( ), enthalpy ( ) and entropy ( ) of binding per surfactant molecule as a function of the number of surfactant molecules bound ( ). The thermodynamic parameters for the glucose oxidase interaction with DTAB at pH 10 and SDS at pH 3.2 are very similar and show that the interactions are entropically driven. The observed enthalpies of interaction of glucose oxidase with the homologous n-alkylsulfates have been analysed in terms of the interactions between the anionic surfactant head group and cationic sites on the protein, hydrophobic binding and the thermal contributions arising from protein unfolding. At surfactant concentrations of 0.5 c.m.c., the enthalpy of unfolding of glucose oxidase is estimated to be 3610 ± 560 kJ mol⁻¹.     

Protein adsorption at solid-liquid interfaces: Part II--Adsorption from binary protein mixture

Extent of adsorption of proteins at alumina-water interface from solutions containing binary mixture of beta-lactoglobulin and bovine serum albumin (BSA), beta-lactoglobulin and gelatin, and gelatin and bovine serum albumin has been estimated as functions of protein concentrations at varying pH, ionic strength, temperature and weight fraction ratios of protein mixture. The extent of adsorption (gamma lacw) of lactoglobulin in the presence of BSA increases with increase of protein concentration (Clac) until it reaches a maximum but a fixed value gamma lacw(m). Extent of adsorption gamma serw also initially increases with increase of protein concentrations until it reaches maximum value gamma serw(m). Beyond these protein concentrations, adsorbed BSA is gradually desorbed due to the preferential adsorption of lactoglobulin from the protein mixture. In many systems, gamma serw at high protein concentrations even becomes negative due to the strong competition of BSA and water for binding to the surface sites in the presence of lactoglobulin. For lactoglobulin-gelatin mixtures, adsorption of both proteins is enhanced as protein concentration is increased until limiting values for adsorption are reached. Beyond the limiting value, lactoglobulin is further accumulated at the interface without limit when protein concentration is high. For gelatin-albumin mixtures, extent of gelatin adsorption increases with increase in the adsorption of BSA. The limit for saturation of adsorption for gelatin is not reached for many systems. At acid pH, adsorbed BSA appears to be desorbed from the surface in the presence of gelatin. From the results thus obtained the role of electrostatic and hydrophobic effects in controlling the adsorption process has been analysed.     

A multitechnique approach in protein/surfactant interaction study: physicochemical aspects of sodium dodecyl sulfate in the presence of trypsin in aqueous medium

Interaction of sodium dodecyl sulfate (SDS) with a globular protein, trypsin, has been physicochemically studied in aqueous medium in detail using tensiometric, conductometric, calorimetric, fluorimetric, viscometric, and circular dichroism techniques. The results indicate that SDS-trypsin aggregates start to form at a surfactant concentration higher than the critical micelle concentration of pure SDS micelle. In contrast, the counterion binding decreases in the presence of trypsin. The free energies and enthalpies of micellization, interfacial adsorption, and entropy of micellization associated with the interaction have also been calculated. The values show that the interaction phenomenon is entropy controlled and endothermic in nature. The increase in viscosity is observed for the system of SDS-trypsin cluster above the critical micelle concentration of SDS micelle only. The aggregation number and interface polarity decrease compared to the values of micelles without protein. Circular dichroism spectra show the high alpha-helical content and unfolded structure of trypsin in the presence of SDS due to strong electrostatic repulsion leading to a probable "necklace and bead" model in the case of biopolymer-surfactant complexes.     

The thermodynamic principles of ligand binding in chromatography and biology

In chromatography, macromolecules do not adsorb in the traditional sense of the word but bind to ligands that are covalently bonded to the surface of the porous bead. Therefore, the adsorption must be modelled as a process where protein molecules bind to the immobilised ligands. The paper discusses the general thermodynamic principles of ligand binding. Models of the multi-component adsorption in ion-exchange and hydrophobic chromatography, HIC and RPLC, are developed. The parameters in the models have a well-defined physical significance. The models are compared to the Langmuir model. In the traditional adsorption models, the standard state Gibbs energy change of adsorption does not depend level of occupancy, but when it depends on the level of occupancy it gives rise to an adsorptive behaviour known as cooperativity. The binding of oxygen to haemoglobin is a well-known example from biology but it is also observed in chromatography due to protein-protein interactions. Retention measurements on beta-lactoglobulin A demonstrate this. A discussion of salt effects on hydrophobic interactions in precipitation and chromatography of proteins concludes the paper.     

Interaction between sodium n-undecyl sulfate and insulin

The binding of sodium n-undecyl sulfate with bovine insulin was studied at pH 3.2 and 10 by equilibrium dialysis at 25°C. The binding data have been used to determine the Gibbs energies of interaction using the theoretical model of the Wyman binding potential. The curves of Gibbs energies as a function of the number of bound ligands ( ) tend to limiting values of around −14 kJ mol⁻¹ at high values of . The enthalpies of in interaction have been measured directly by microcalorimetry showing an increase of exothermicity at lower pH. The results have been compared with similar data for the interaction of anionic surfactants with insulin.     

Adsorption of biopolymers at hydrophilic cellulose-water interface

The extent of adsorption (Gamma2(1)) of bovine serum albumin (BSA), beta-lactoglobulin, lysozyme, gelatin, and DNA from aqueous solution onto the hydrophilic surface of cellulose has been measured as function of biopolymer concentration at different temperatures, pHs, and ionic strengths, and in the presence of a high concentration of inorganic salts and denaturants. In all cases, the value of Gamma2(1) increases with the increase of biopolymer concentration (X2) in bulk and it attains a maximum value at a critical mole fraction concentration X2m. The value of Gamma2m depends upon the nature of protein, temperature, pH, and ionic strength, as well as the nature of neutral salts present in excess. Gamma2m for proteins at a fixed physicochemical condition stands in the following order: Gelatin>betalactoglobulin>lysozyme>BSA. The isotherms for adsorption of DNA nucleotides on cellulose surface at pH 4.0 have been compared at different temperatures and ionic strengths, and in the presence of high concentration of inorganic salts LiCl, NaCl, KCl, and Na2SO4. Values of Gamma2m for different systems have been evaluated and critically compared. At pH 6.0 and 8.0, Gamma2(1) values of DNA nucleotides on cellulose are all negative due to the excess positive hydration of cellulose. At pH 4.0, adsorption of nucleotides of acid, alkali, and heat-denatured DNA widely differ from each other and in the presence of excess concentration of urea becomes negative. The probable mechanisms of biopolymer-cellulose adsorption in terms of polymer hydration, steric interaction, London-van der Waals, hydrophobic, and other types of interactions have been discussed qualitatively. The standard free energy change for the adsorption of protein and DNA nucleotides on the cellulose surface at the state of adsorption saturation has been calculated in kJ per kg of cellulose using an integrated form of the Gibbs adsorption equation. The relation between DeltaG degrees and maximum affinities between biopolymers and the polysaccharide interface have been discussed for various systems.     

Effects of the molecular structure of two amphiphilic antidepressant drugs on the formation of complexes with human serum albumin

Interactions of two amphiphilic antidepressant drugs, imipramine and desipramine hydrochlorides, with the blood protein human serum albumin (HSA) were investigated to gain an understanding of the effects of drug molecular structure on the complex formation of drug-protein molecules. To elucidate the mechanisms of such effects, the protein-antidepressant interactions in aqueous buffered solutions of pH 3.0 and 5.5 (isoelectric point of HSA = 4.9) were investigated using conductivity, zeta potential, and dynamic light scattering. An increase of the critical micelle concentration of both antidepressants was detected as a consequence of extensive binding to the protein. From zeta-potential measurements, the Gibbs energies of adsorption of the drugs onto the protein were derived using the proposed models of Kayes and Ottewill and Watanabe. Measurements of the hydrodynamic radii of HSA-antidepressant complexes as a function of the drug concentration have shown a gradual increase of size of a saturation rather than a denaturation process of the protein. A larger drug adsorption at pH 5.5 than at pH 3.0 was also observed, as a consequence of a more important specific binding at the former pH.     

Complexation of beta-lactam antibiotic drug carbenicillin to bovine serum albumin: energetics and conformational studies

Binding of the antibiotic drug carbenicillin to bovine serum albumin (BSA) has been studied using isothermal titration calorimetry (ITC) in combination with fluorescence and circular dichroism (CD) spectroscopies. The thermodynamic parameters of binding have been evaluated as a function of temperature, ionic strength, and in the presence of anionic, cationic and nonionic surfactants, tetrabutylammonium bromide, and sucrose. The values of van't Hoff enthalpy do not agree with the calorimetric enthalpy indicating conformational changes in the protein upon drug binding. These observations are supported by the intrinsic fluorescence and CD spectroscopic measurements. A reduction in the binding affinity of carbenicillin to BSA is observed with increase in ionic strength of the solution, thereby suggesting, prevailing of electrostatic interactions in the binding process. The involvement of hydrophobic interactions in the binding of the drug to the protein is also indicated by a slight reduction in binding constant in the presence of tetrabutylammonium bromide. The experiments in the presence of sucrose suggest that hydrogen bonding is perhaps not dominant in the binding. The anionic surfactant sodium dodecyl sulphate (SDS) is observed to completely interfere in the ionic interactions in addition to its partial denaturing capacity. However, the presence of cationic surfactant hexadecyl trimethylammonium bromide (HTAB) and nonionic surfactant Triton-X 100 induce a slight reduction in the values of binding affinity. These calorimetric and spectroscopic results, provide quantitative information on the binding of carbenicillin to BSA and suggests that the binding is dominated by electrostatic interactions with contribution from hydrophobic interactions. (c) 2008 Wiley Periodicals, Inc. Biopolymers 89: 831-840, 2008.This article was originally published online as an accepted preprint. The "Published Online" date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com.     

NMR studies on binding sites and aggregation–disassociation of fluorinated surfactant sodium perfluorooctanoate on protein ubiquitin

The fluorinated surfactant sodium perfluorooctanoate (SPFO) could bind onto ubiquitin (UBQ) and induce the unfolding of UBQ. By using ¹⁵N-edited heteronuclear single-quantum coherence (HSQC) NMR and ¹⁹F NMR to monitor ¹⁵N-labeled UBQ and SPFO, respectively, the binding sites and the aggregation process of SPFO on UBQ at various SPFO concentrations were observed. A detailed process from specific binding to cooperative binding of SPFO on UBQ, and a detailed structure change of UBQ upon the increase of SPFO concentration were obtained. The refolding of UBQ in UBQ–SPFO complex was carried out by adding cationic surfactant. It was shown that added cationic surfactants formed mixed micelles with SPFO and resulted in the dissociation of the UBQ–SPFO complex, and consequently, most ubiquitin could be refolded to its native state.     

Direct observation of intraparticle equilibration and the rate-limiting step in adsorption of proteins in chromatographic adsorbents with confocal laser scanning microscopy

The adsorption of different proteins in a single biospecific and hydrophobic adsorbent particle for preparative protein chromatography has been observed directly by confocal laser scanning microscopy as a function of time at a constant bulk concentration c(b). The bulk concentration was in the non-linear part of the adsorption isotherm. At all times the concentration of free protein at the particle surface was almost equal to the bulk content indicating that external mass transfer resistance is not rate limiting for the adsorption under these conditions. Inside the particles a distinct maximum in adsorbed and free protein concentration that moved inside to a distance of approximately 0.2 R (R particle radius) from the particle surface, was observed. This is due to a decreasing solid-phase density and adsorptive capacity in the particle between 0.8 R and R indicating that the fraction of macropores (or void space) is larger in the outer than in the inner part of the adsorbent particles. By increasing the bulk concentration by a factor of 10 the equilibration time was reduced by about the same magnitude. This is in agreement with the concentration dependence of the effective pore diffusion coefficient D(p,eff)=D(p)/[epsilon(p)[1+nK/(K +c)(2)]] derived from the mass conservation relations describing the adsorption process. The time dependence protein adsorption up to approximately 90% of the equilibration value q* could be described by a bilinear free driving force model. The rapid equilibration in the outer part of the particle with a half-life time of approximately 100 s in the studied systems accounted for 0.3-0.4 q*. The slower equilibration with a up to ten times longer half-life time, was the adsorption in the inner part of the particle that outside 0.5 R accounts for 0.5-0.6 q*. These data were compared with literature data for batch adsorption of proteins in biospecific, hydrophobic and ion-exchange adsorbents. They could also be described by a bilinear free driving force model, with about the same quantitative results as obtained for similar conditions in the single particle experiments. The static adsorption parameters, maximum binding site concentration n, and dissociation constant for the protein binding to a binding site K, were determined from Scatchard plots. For the same protein-adsorbent system the plots changed from linear to non-linear with increasing n. This change occurred when the average distance between adjacent binding sites become of the same order of magnitude as the size of the binding site or adsorbed protein. This causes a shielding of free binding sites increasing with n and the concentration of adsorbed protein, yielding a concentration dependence in K. These results show that for a high throughput and rapid adsorption in preparative chromatography, the adsorption step should be carried out in the non-linear part of the adsorption isotherm with concentrations up to c(b) where q*/c(b)>/=10 to obtain high protein recoveries. To avoid tailing due to the flow of adsorbed proteins in the inner part of the particles further into the particles at the start of the desorption, and to speed up desorption rates, protein adsorption in the particle within 0.5 R from the particle center should be avoided. This requires the further development of suitable pellicular particles for preparative protein chromatography that meet this requirement.