The Surface Concentration of Parameter

Critical surface concentration of immobilized residues In 1975 we showed that a second parameter is of equal if not greater importance than the alkyl chain length. If, instead of the chain-length, the density (surface concentration) of immobilized alkyl groups is varied, protein adsorption is a sigmoidal function of the surface concentration of immobilized alkyl residues (Figure 1) (i.e., surface concentration series). Here also the strength of binding increased from retardation to very tight binding as in the homologous series of Shaltiel. Figure 1 also illustrates the effect of chain elongation in a homologous series which leads to a leftward shift of the sigmoidal curves and to a loss of sigmoidal shape. Another important finding was that a threshold value of the alkyl surface

10 20 30 40 50

limoles alkylamine mL-1 packed Sepharose

Figure 1 Dependence of the adsorption of phosphorylase kinase on the chain-length and surface concentration parameters of a homologous series of alkyl-Sepharosesat low ionic strength. The amount of adsorbed enzyme activity per mL packed Sepharose was calculated from the difference between the total amount of applied units and the amount excluded from the gel. The crude rabbit muscle extract or purified phosphorylase kinase was applied to columns containing ca. 10 mL packed gel. The alkyl agaroses were synthesized by the CNBr method. The ratio of alkyl residues to positive charges was ca.10 : 1. Inset: Double logarithmic plots of adsorbed phosphorylase kinase as a function of the degree of substitution. Experiments with purified phosphorylase kinase are included. A, Seph-C,: (•) crude extract; (O) purified phosphorylase kinase. B, Seph-C2: (A) crude extract; (A) purified phosphorylase kinase; C, Seph-C4; (□) crude extract. For further details see the text and Jennissen HP and Heilmeyer Jr LMG (1975) General aspects of hydrophobic chromatography. Adsorption and elution characteristics of some skeletal muscle enzymes. Biochemistry 14: 754-760.

10 20 30 40 50

limoles alkylamine mL-1 packed Sepharose

Figure 1 Dependence of the adsorption of phosphorylase kinase on the chain-length and surface concentration parameters of a homologous series of alkyl-Sepharosesat low ionic strength. The amount of adsorbed enzyme activity per mL packed Sepharose was calculated from the difference between the total amount of applied units and the amount excluded from the gel. The crude rabbit muscle extract or purified phosphorylase kinase was applied to columns containing ca. 10 mL packed gel. The alkyl agaroses were synthesized by the CNBr method. The ratio of alkyl residues to positive charges was ca.10 : 1. Inset: Double logarithmic plots of adsorbed phosphorylase kinase as a function of the degree of substitution. Experiments with purified phosphorylase kinase are included. A, Seph-C,: (•) crude extract; (O) purified phosphorylase kinase. B, Seph-C2: (A) crude extract; (A) purified phosphorylase kinase; C, Seph-C4; (□) crude extract. For further details see the text and Jennissen HP and Heilmeyer Jr LMG (1975) General aspects of hydrophobic chromatography. Adsorption and elution characteristics of some skeletal muscle enzymes. Biochemistry 14: 754-760.

concentration, a 'critical hydrophobicity', had to be reached before a protein adsorbed. With a ratio of alkyl residues to positive charges in the gels of about 10 : 1, the predominance of hydrophobic interactions as the basis for adsorption was strongly indicated. Thus sigmoidal adsorption curves and critical hydrophobicities could also be obtained in the presence of high salt concentrations (see Figure 2) excluding the argument that the sigmoidal shape was due to the action of charges. Finally, the same sig-moidal behaviour of protein adsorption was found on uncharged hydrophobic gels at low ionic strength and an example will be shown in this article.

Cooperative interaction of multiple immobilized residues with the protein A straightforward interpretation of the sigmoidal curves (Figures 1 and 2) was provided by the concept of multivalence and cooperativity of protein adsorption. It became clear that the sigmoidicity and the 'critical hydrophobicity' were due to the multivalence of the interaction (i.e., the necessity for a simultaneous interaction of more than one alkyl residue with the protein moiety). The term 'multivalence' is to be preferred to other terms such as 'multiple contacts' since the latter does not differentiate between the binding of a protein to separate alkyl residues or to different segments of one and the same alkyl residue. At high salt concentrations, protein binding displays a positive temperature coefficient in agreement with hydrophobic interactions (see Figure 2). A mathematical model of cooperative protein binding to an immobilized alkyl residue lattice was also developed allowing an estimation of the minimum number of alkyl residues (see Figure 2B) interacting with the protein. The model of multivalence was confirmed by equilibrium binding studies of phosphorylase b with alkylamines at high salt concentrations.

Figure 2 Dependence of the adsorption of phosphorylase b on the surface concentration parameter of Seph-C4 at 5°C and 34°C at high ionic strength. The adsorbed amount of phosphorylase in the presence of 1.1 M ammonium sulfate was calculated from adsorption isotherms measured at each point at an apparent equilibrium concentration of free bulk protein of 0.07 mg mL~1. The adsorbed amount of enzyme (v) is expressed in relation to the anhydrodisaccharide content of agarose in moT1 anhydrodisaccharide. Similarly C indicates the immobilized butyl residue concentration in relation to the anhydrodisaccharide content of agarose in moles of alkyl residue per mole of anhydrodisaccharide. A monomer molecular mass of 105 was employed for phosphorylase b. The alkyl agaroses were synthesized by the CNBr method. (A) Adsorption isotherms ('lattice site binding function') of phosphorylase b in Cartesian coordinates. Inset: Scatchard plots of the sigmoidal binding curves with extrapolation of fractional saturation of 610 (5°C) and 1220 (34°C) ^moles enzyme per mole of anhydrodisaccharide (corresponding to 6.2 and 13.4 mg mL~1 packed gel respectively). The broken lines indicate the mode of extrapolation. (•) 5°C; (O) 34°C. (B) Hill plots of the sigmoidal binding curves. d the fractional saturation was calculated from the extrapolated saturation values of the Scatchard plot (A). The Hill coefficients nH are given in the graph. The apparent dissociation constants of half-maximal saturation (^D05) are 0.137 and 0.167 mole butyl residue per mole of anhydrodisaccharide at 5°C and 34°C respectively (which corresponds to 14.0 and 17.0 ^mole butyl residues per ml packed gel, respectively). (•) 5°C; (O) 34°C. For further details see the text and for the source see Jennissen HP (2000) Hydrophobic (interaction) chromatography. In: Vijayalakshmi MA (ed.). TheoryandPractice ofBiochromatography. Amsterdam: Harwood Academic Publishers.

Figure 2 Dependence of the adsorption of phosphorylase b on the surface concentration parameter of Seph-C4 at 5°C and 34°C at high ionic strength. The adsorbed amount of phosphorylase in the presence of 1.1 M ammonium sulfate was calculated from adsorption isotherms measured at each point at an apparent equilibrium concentration of free bulk protein of 0.07 mg mL~1. The adsorbed amount of enzyme (v) is expressed in relation to the anhydrodisaccharide content of agarose in moT1 anhydrodisaccharide. Similarly C indicates the immobilized butyl residue concentration in relation to the anhydrodisaccharide content of agarose in moles of alkyl residue per mole of anhydrodisaccharide. A monomer molecular mass of 105 was employed for phosphorylase b. The alkyl agaroses were synthesized by the CNBr method. (A) Adsorption isotherms ('lattice site binding function') of phosphorylase b in Cartesian coordinates. Inset: Scatchard plots of the sigmoidal binding curves with extrapolation of fractional saturation of 610 (5°C) and 1220 (34°C) ^moles enzyme per mole of anhydrodisaccharide (corresponding to 6.2 and 13.4 mg mL~1 packed gel respectively). The broken lines indicate the mode of extrapolation. (•) 5°C; (O) 34°C. (B) Hill plots of the sigmoidal binding curves. d the fractional saturation was calculated from the extrapolated saturation values of the Scatchard plot (A). The Hill coefficients nH are given in the graph. The apparent dissociation constants of half-maximal saturation (^D05) are 0.137 and 0.167 mole butyl residue per mole of anhydrodisaccharide at 5°C and 34°C respectively (which corresponds to 14.0 and 17.0 ^mole butyl residues per ml packed gel, respectively). (•) 5°C; (O) 34°C. For further details see the text and for the source see Jennissen HP (2000) Hydrophobic (interaction) chromatography. In: Vijayalakshmi MA (ed.). TheoryandPractice ofBiochromatography. Amsterdam: Harwood Academic Publishers.

Adsorption hysteresis An important consequence of cooperative multivalent protein binding on alkyl-sub-stituted surfaces is protein adsorption hysteresis. Protein adsorption hysteresis implies that the adsorption isotherm is not retraced by the desorption isotherm, due to an increase in binding affinity after the protein is adsorbed. The binding affinity increase can be attributed to an increase in the number of interactions (multivalence) which can either be due to a reorientation of the protein on the surface or to a conformational change in which buried hydropho-bic contact sites (valences) are exposed due to the surface binding strain on the adsorbed protein. Adsorption hysteresis provides evidence for the concept that protein adsorption to multivalent surfaces in general is thermodynamically irreversible (AS > 0) and that a true equilibrium has not been reached. Another conclusion from this concept is that protein adsorption in hysteretic systems is, moreover, not thermodynamically but kinetically controlled. Thus adsorption hysteresis has a strong influence on hydrophobic interaction chromatography by leading to nonlinearity and skewed elution peaks in zonal chromatography and to 'irreversibility' in adsorption chromatography. Hysteresis can, however, be easily reduced by decreasing the surface concentration of immobilized alkyl residues.

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