A simpler analysis for the measurement of second virial coefficients by self-interaction chromatography

We describe a thermodynamic approach that supports the adoption of a simplified procedure for the determination of protein second virial coefficients (B(2)) by self-interaction chromatography. Its major advantage over the original method is a decrease in the number of parameters to which magnitudes must be assigned for the determination of B(2). Improved correlation of virial coefficients obtained by the chromatographic procedure with those obtained by light scattering is achieved by taking into account the twofold larger magnitudes of the former because of the experimental distinction between free and immobilized protein molecules in self-interaction chromatography.     

Measurement of osmotic second virial coefficients by zonal size-exclusion chromatography

Numerical simulation of protein migration reflecting linear concentration dependence of the partition isotherm has been used to invalidate a published procedure for measuring osmotic second virial coefficients (B₂₂) by zonal exclusion chromatography. Failure of the zonal procedure to emulate its frontal chromatographic counterpart reflects ambiguity about the solute concentration that should be used to replace the applied concentration in the rigorous quantitative expression for frontal migration; the recommended use of the peak concentration in the eluted zone is incorrect on theoretical grounds. Furthermore, the claim for its validation on empirical grounds has been traced to the use of inappropriate B₂₂ magnitudes as the standards against which the experimentally derived values were being tested.     

Use of dynamic light scattering to determine second virial coefficient in a semidilute concentration regime

The present work discusses an alternative procedure to obtain static light scattering (SLS) parameters in a dilute and semidilute concentration regime from a dynamic light scattering (DLS) instrument that uses an avalanche photodiode (APD) for recording the scattered intensity signal. An APD enables one to perform both SLS and DLS measurements by photon counting and photon correlation, respectively. However, due to the associated recovery time, the APDs are susceptible to saturation (above 1000 kcps), which may limit the measurements in systems that scatter too much light. We propose an alternative way of obtaining the SLS parameters with instruments that use APD for recording signal intensities.     

Negative second virial coefficients as predictors of protein crystal growth: evidence from sedimentation equilibrium studies that refutes the designation of those light scattering parameters as osmotic virial coefficients

The effects of ammonium sulphate concentration on the osmotic second virial coefficient (BAA/MA) for equine serum albumin (pH 5.6, 20 degrees C) have been examined by sedimentation equilibrium. After an initial steep decrease with increasing ammonium sulphate concentration, BAA/MA assumes an essentially concentration-independent magnitude of 8-9 ml/g. Such behaviour conforms with the statistical-mechanical prediction that a sufficient increase in ionic strength should effectively eliminate the contributions of charge interactions to BAA/MA but have no effect on the covolume contribution (8.4 ml/g for serum albumin). A similar situation is shown to apply to published sedimentation equilibrium data for lysozyme (pH 4.5). Although termed osmotic second virial coefficients and designated as such (B22), the negative values obtained in published light scattering studies of both systems have been described incorrectly because of the concomitant inclusion of the protein-salt contribution to thermodynamic nonideality of the protein. Those negative values are still valid predictors of conditions conducive to crystal growth inasmuch as they do reflect situations in which there is net attraction between protein molecules. However, the source of attraction responsible for the negative virial coefficient stems from the protein-salt rather than the protein-protein contribution, which is necessarily positive.     

Determination of the second virial coefficient of bovine serum albumin under varying pH and ionic strength by composition-gradient multi-angle static light scattering

Composition-gradient multi-angle static light scattering (CG-MALS) is an emerging technique for the determination of intermolecular interactions via the second virial coefficient B₂₂. With CG-MALS, detailed studies of the second virial coefficient can be carried out more accurately and effectively than with traditional methods. In addition, automated mixing, delivery and measurement enable high speed, continuous, fluctuation-free sample delivery and accurate results. Using CG-MALS we measure the second virial coefficient of bovine serum albumin (BSA) in aqueous solutions at various values of pH and ionic strength of a univalent salt (NaCl). The systematic variation of the second virial coefficient as a function of pH and NaCl strength reveals the net charge change and the isoelectric point of BSA under different solution conditions. The magnitude of the second virial coefficient decreases to 1.13 x 10⁻⁵ ml*mol/g² near the isoelectric point of pH 4.6 and 25 mM NaCl. These results illuminate the role of fundamental long-range electrostatic and van der Waals forces in protein-protein interactions, specifically their dependence on pH and ionic strength. Electronic supplementary material The online version of this article (doi:10.1007/s10867-014-9367-7) contains supplementary material, which is available to authorized users.     

The likelihood of aggregation during protein renaturation can be assessed using the second virial coefficient

Protein aggregation is commonly observed during protein refolding. To better understand this phenomenon, the intermolecular interactions experienced by a protein during unfolding and refolding are inferred from second virial coefficient (SVC) measurements. It is accepted that a negative SVC is indicative of protein-protein interactions that are attractive, whereas a positive SVC indicates net repulsive interactions. Lysozyme denatured and reduced in guanidinium hydrochloride exhibited a decreasing SVC as the denaturant was diluted, and the SVC approached zero at approximately 3 M GdnHCl. Further dilution of denaturant to renaturation conditions (1.25 M GdnHCl) led to a negative SVC, and significant protein aggregation was observed. The inclusion of 500 mM L-arginine in the renaturation buffer shifted the SVC to positive and suppressed aggregation, thereby increasing refolding yield. The formation of mixed disulfides in the denatured state prior to refolding also increased protein solubility and suppressed aggregation, even without the use of L-arginine. Again, the suppression of aggregation was shown to be caused by a shift from attractive to repulsive intermolecular interactions as reflected in a shift from a negative to a positive SVC value. To the best of our knowledge, this is the first time that SVC data have been reported for renaturation studies. We believe this technique will aid in our understanding of how certain conditions promote renaturation and increase protein solubility, thereby suppressing aggregation. SVC measurements provide a useful link, for protein folding and aggregation, between empirical observation and thermodynamics.     

Characterization of weak protein dimerization by direct analysis of sedimentation equilibrium distributions: the INVEQ approach

Closer scrutiny has been accorded a recently reported procedure for characterizing weak protein dimerization by sedimentation equilibrium (INVEQ) in which the equilibrium distribution is analyzed as a dependence of radial distance on solute concentration rather than of solute concentration on radial distance. By demonstrating theoretically that the fundamental parameter derived from the analysis is simply the difference between the dimerization constant and the osmotic second virial coefficient for monomer-monomer interaction, this investigation refutes the original claim that independent estimates of these two parameters can be obtained by nonlinear curve fitting of the sedimentation equilibrium distribution. This criticism also applies to conventional analyses of sedimentation distributions by the commonly employed Beckman Origin and NONLIN software. Numerically simulated distributions are then analyzed to demonstrate limitations of the procedure and also to indicate a means of improving the reliability of the returned estimate of the dimerization constant. These features are illustrated by applying the original and revised analytical procedures to a sedimentation equilibrium distribution for alpha-chymotrypsin (pH 4.0, I 0.05 M).     

Direct analysis of protein sedimentation equilibrium in detergent solutions without density matching

Characterizing membrane proteins by sedimentation equilibrium is challenging because detergents and/or lipid molecules, usually required for solubilization, form a complex with the protein. The most common way to overcome this problem is Tanford and Reynolds' density matching method, which eliminates the buoyant mass contributions of detergents/lipids by adjusting the solvent density with D2O/H2O mixtures to render either detergent or lipid molecules neutrally buoyant. Unfortunately, the method is practical only for detergent densities between 1.0 (H2O) and 1.1 (D2O) g ml(-1), excluding many of the more commonly used detergents for membrane protein studies. Here, we present a modern variant of Tanford and Reynolds' method that (1) is applicable to any detergent regardless of its specific density, (2) does not compromise accuracy and precision, and (3) provides additional information about the number of detergent molecules that are bound to each protein. The new method was applied successfully to Delta(1-43)A-I, an amino-terminal deletion mutant of human apolipoprotein A-I. Interestingly, we observed a significantly lower Delta(1-43)A-I/octyl-glucoside complex partial specific volume than that expected from volume additivity rules, indicative of specific protein-detergent interactions.     

Measurement of the second osmotic virial coefficient for protein solutions exhibiting monomer-dimer equilibrium

The second osmotic virial coefficient (B) is a measure of solution nonideality that is useful for predicting conditions favorable for protein crystallization and for inhibition of aggregation. Static light scattering is the technique most commonly used to determine B values, typically using protein concentrations less than 5 mg/mL. During static light scattering experiments at low protein concentrations, frequently the protein is assumed to exist either as a single nonassociating species or as a combination of assembly states independent of protein concentration. In the work described here, we examined the limit for ignoring weak reversible dimerization (Kd > or =1 mM) by comparing B values calculated with and without accounting for self-association. Light scattering effects for equilibrium dimer systems with Kd <20 mM and Kd <1 mM will significantly affect apparent B values measured for 20 and 150-kDa proteins, respectively. To interpret correctly light scattering data for monomer-dimer equilibrium systems, we use an expanded coefficient model to account for separate monomer-monomer (B(22)), monomer-dimer (B(23)), and dimer-dimer (B(33)) interactions.     

Static light scattering studies of OmpF porin: implications for integral membrane protein crystallization

Integral membrane proteins carry out some of the most important functions of living cells, yet relatively few details are known about their structures. This is due, in large part, to the difficulties associated with preparing membrane protein crystals suitable for X-ray diffraction analysis. Mechanistic studies of membrane protein crystallization may provide insights that will aid in determining future membrane protein structures. Accordingly, the solution behavior of the bacterial outer membrane protein OmpF porin was studied by static light scattering under conditions favorable for crystal growth. The second osmotic virial coefficient (B22) was found to be a predictor of the crystallization behavior of porin, as has previously been found for soluble proteins. Both tetragonal and trigonal porin crystals were found to form only within a narrow window of B22 values located at approximately -0.5 to -2 X 10(-4) mol mL g(-2), which is similar to the "crystallization slot" observed for soluble proteins. The B22 behavior of protein-free detergent micelles proved very similar to that of porin-detergent complexes, suggesting that the detergent's contribution dominates the behavior of protein-detergent complexes under crystallizing conditions. This observation implies that, for any given detergent, it may be possible to construct membrane protein crystallization screens of general utility by manipulating the solution properties so as to drive detergent B22 values into the crystallization slot. Such screens would limit the screening effort to the detergent systems most likely to yield crystals, thereby minimizing protein requirements and improving productivity.     

Automated measurement of the static light scattering of macromolecular solutions over a broad range of concentrations

A method and apparatus for automated measurement of the concentration dependence of static light scattering of protein solutions over a broad range of concentrations is described. The gradient of protein concentrations is created by successive dilutions of an initially concentrated solution contained within the scattering measurement cell, which is maintained at constant total volume. The method is validated by measurement of the concentration dependence of light scattering of bovine serum albumin, ovalbumin, and ovomucoid at concentrations up to 130 g/L. The experimentally obtained concentration dependence of scattering obtained from all three proteins is quantitatively consistent with the assumption that no significant self-association occurs over the measured range of concentrations.     

Characterization of protein detergent complexes by NMR, light scattering, and analytical ultracentrifugation

Abstract  Bottlenecks in expression, solubilization, purification and crystallization hamper the structural study of integral membrane proteins (IMPs). Successful crystallization is critically dependent on the purity, stability and oligomeric homogeneity of an IMP sample. These characteristics are in turn strongly influenced by the type and concentration of the detergents used in IMP preparation. By utilizing the techniques and analytical tools we earlier developed for the characterization of protein-detergent complexes (PDCs) [21], we demonstrate that for successful protein extraction from E. coli membrane fractions, the solubilizing detergent associates preferentially to IMPs rather than to membrane lipids. Notably, this result is contrary to the generally accepted mechanism of detergent-mediated IMP solubilization. We find that for one particular member of the family of proteins studied (E. coli receptor kinases, which is purified in mixed multimeric states and oligomerizes through its transmembrane region), the protein oligomeric composition is largely unaffected by a 10-fold increase in protein concentration, by alteration of micelle properties through addition of other detergents to the PDC sample, or by a 20-fold variation in the detergent concentration used for solubilization of the IMP from the membrane. We observed that the conditions used for expression of the IMP, which impact protein density in the membrane, has the greatest influence on the IMP oligomeric structure. Finally, we argue that for concentrating PDCs smaller than 30 kDa, stirred concentration cells are less prone to over-concentration of detergent and are therefore more effective than centrifugal ultrafiltration devices.     

Donnan membrane equilibrium,sedimentation equilibrium,and coil expansion of DNA in salt solutions

This is a review of applications of the McMillan-Mayer-Hill virial theory and the ionic double-layer theory to dilute colloidal solutions, in particular, solutions of DNA. Interactions of highly charged colloidal rods are developed in terms of the second virial coefficients between two rods, and between one rod and one small co-ion. The relevant cluster integrals are evaluated with interaction potentials based on the Poisson-Boltzmann equation. The treatment is extended to the intrachain repulsion responsible for the statistical swelling of coiled DNA (excluded volume effect). The theory is compared with three sets of experimental data: The salt distribution in Donnan membrane equilibria of DNA-salt solutions, sedimentation equilibria of short DNA fragments at different ionic strengths, and the intrinsic viscosity of T7 DNA in NaCl solutions. In all cases the theory agrees well with the experiments. The agreement is not convincing for the sedimentation equilibrium at low ionic strength, because here the experimental DNA concentration is too high for the truncated dilute solution expansion of the DNA-salt repulsion.     

Characterization of reacting solutions of macromolecules by laser light scattering and Airfuge centrifugation

Simple, fast and accurate measurements combining centrifugation in a table top Airfuge and laser light scattering in the Airfuge tube are described. The procedure achieves quantitative separation of particles according to their sedimentation coefficient in microliter volumes. By scanning through the sedimenting boundary association equilibrium constants are evaluated.     

Interactions of lysozyme in guanidinium chloride solutions from static and dynamic light-scattering measurements

The interactions of partially unfolded proteins provide insight into protein folding and protein aggregation. In this work, we studied partially unfolded hen egg lysozyme interactions in solutions containing up to 7 M guanidinium chloride (GdnHCl). The osmotic second virial coefficient (B(22)) of lysozyme was measured using static light scattering in GdnHCl aqueous solutions at 20 degrees C and pH 4.5. B(22) is positive in all solutions, indicating repulsive protein-protein interactions. At low GdnHCl concentrations, B(22) decreases with rising ionic strength: in the absence of GdnHCl, B(22) is 1.1 x 10(-3) mLmol/g(2), decreasing to 3.0 x 10(-5) mLmol/g(2) in the presence of 1 M GdnHCl. Lysozyme unfolds in solutions at GdnHCl concentrations higher than 3 M. Under such conditions, B(22) increases with ionic strength, reaching 8.0 x 10(-4) mLmol/g(2) at 6.5 M GdnHCl. Protein-protein hydrodynamic interactions were evaluated from concentration-dependent diffusivity measurements, obtained from dynamic light scattering. At moderate GdnHCl concentrations, lysozyme interparticle interactions are least repulsive and hydrodynamic interactions are least attractive. The lysozyme hydrodynamic radius was calculated from infinite-dilution diffusivity and did not change significantly during protein unfolding. Our results contribute toward better understanding of protein interactions of partially unfolded states in the presence of a denaturant; they may be helpful for the design of protein refolding processes that avoid protein aggregation.     

Addition of a polypeptide stretch at the N-terminus improves the expression, stability and solubility of recombinant protein tyrosine phosphatases from Drosophila melanogaster

The production of recombinant proteins in Escherichia coli involves substantial optimization in the size of the protein and over-expression strategies to avoid inclusion-body formation. Here we report our observations on this so-called construct dependence using the catalytic domains of five Drosophila melanogaster receptor protein tyrosine phosphatases as a model system. Five strains of E. coli as well as three variations in purification tags viz., poly-histidine peptide attachments at the N- and C-termini and a construct with Glutathione-S-transferase at the N-terminus were examined. In this study we observe that inclusion of a 45 residue stretch at the N-terminus was crucial for over-expression of the enzymes, influencing both the solubility and the stability of these recombinant proteins. While the addition of negatively charged residues in the N-terminal extension could partially rationalize the improvement in the solubility of these constructs, conventional parameters like the proportion of order promoting residues or aliphatic index did not correlate with the improved biochemical characteristics. These findings thus suggest the inclusion of additional parameters apart from rigid domain predictions to obtain domain constructs that are most likely to yield soluble protein upon expression in E. coli.     

The chlorosome of Chlorobaculum tepidum: size, mass and protein composition revealed by electron microscopy, dynamic light scattering and mass spectrometry-driven proteomics

Chlorosomes, the antenna complexes of green bacteria, are unique antenna systems in which pigments are organized in aggregates. Studies on isolated chlorosomes from Chlorobaculum tepidum based on SDS-PAGE, immunoblotting and molecular biology have revealed that they contain ten chlorosomal proteins, but no comprehensive information is available about the protein composition of the entire organelle. To extend these studies, chlorosomes were isolated from C. tepidum using three related and one independent isolation protocol and characterized by absorption spectroscopy, tricine SDS-PAGE, dynamic light scattering (DLS) and electron microscopy. Tricine SDS-PAGE showed the presence of more than 20 proteins with molecular weights ranging between 6 and 70 kDa. The chlorosomes varied in size. Their hydrodynamic radius (R(h) ) ranged from 51 to 75 nm and electron microscopy indicated that they were on average 140 nm wide and 170 nm long. Furthermore, the mass of 184 whole chlorosome organelles determined by scanning transmission electron microscopy ranged from 27 to 237 MDa being on average 88 (±28) MDa. In contrast their mass-per-area was independent of their size, indicating that there is a strict limit to chlorosome thickness. The average protein composition of the C. tepidum chlorosome organelles was obtained by MS/MS-driven proteomics and for the first time a detailed protein catalogue of the isolated chlorosomal proteome is presented. Based on the proteomics results for chlorosomes isolated by different protocols, four proteins that are involved in the electron or ion transport are proposed to be tightly associated with or incorporated into C. tepidum chlorosomes as well as the ten Csm proteins known to date.     

Interactions of surfactants with a water treatment protein from Moringa oleifera seeds in solution studied by zeta-potential and light scattering measurements

Protein extracted from Moringa oleifera (MO) seeds has been advocated as a cheap and environmental friendly alternative to ionic flocculants for water purification. However, the nature and mechanism of its interaction with particles in water, as well as with dissolved surface-active molecules, are not well understood. In this article, we report studies of the protein and its interaction with four surfactants using dynamic light scattering (DLS), zeta-potential and turbidity measurements. Zeta-potential measurements identified points of charge reversal and the turbidity and DLS measurements were used to characterize the microstructure and size of protein-surfactant complexes. From the points of charge reversal, it was estimated that 7 anions are required to neutralize the positive charges of each protein molecule at pH 7. For protein mixtures with sodium dodecyl sulfate and dodecyl di-acid sodium salt, the peak in turbidity corresponds to concentrations with a large change in zeta-potential. No turbidity was observed for protein mixtures with either the nonionic surfactant Triton X-100 or the zwitterionic surfactant N-dodecyl-N,N-dimethyl-3-ammonio-1-propanesulfonate. Changes of pH in the range 4-10 have little effect on the zeta-potential, turbidity, and the hydrodynamic radius reflecting the high isoelectric point of the protein. Addition of small amounts of salt has little effect on the size of protein in solution. These results are discussed in the context of the use of the MO protein in water treatment.