Analysis of sedimentation equilibrium distributions reflecting nonideal macromolecular associations

A rigorous statistical-mechanical approach is adopted to derive general quantitative expressions that allow for the effects of thermodynamic nonideality in equilibrium measurements reflecting interaction between dissimilar macromolecular reactants. An analytical procedure based on these expressions is then formulated for obtaining global estimates of equilibrium constants and the corresponding reference thermodynamic activities of the free reactants in each of several sedimentation equilibrium experiments. The method is demonstrated by application to results from an ultracentrifugal study of an electrostatic interaction between ovalbumin and cytochrome c (Winzor, D. J., M. P. Jacobsen, and P. R. Wills. 1998. Biochemistry. 37:2226-2233). It is demonstrated that reliable estimates of relevant thermodynamic parameters are extracted from the data through statistical analysis by means of a simple nonlinear fitting procedure.     

Early time expansions for sedimentation of weakly nonideal solutions

An expansion valid for short times is presented for the rectangular approximation to the Lamm equation when the sedimentation coefficient can be expressed as s = S₀(1?kc). The expansion allows the study of meniscus perturbations on the Faxén approximation, as well as a determination of when reflections from the base become significant.     

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.     

Quantitative characterization of weak self-association in concentrated solutions of immunoglobulin G via the measurement of sedimentation equilibrium and osmotic pressure

The sedimentation equilibrium of solutions of immunoglobulin G in saline buffer, over a concentration range up to 125 g/L, was measured and analyzed in the context of a model that takes into account the possibility of attractive intermolecular interaction leading to the reversible formation of oligomeric species and repulsive intermolecular interaction leading to nonideal solution behavior. Additionally, previously published data on the concentration dependence of the osmotic pressure of immunoglobulin G under similar conditions, over a concentration range up to 400 g/L, were analyzed in the context of a newly developed thermodynamic formalism describing the osmotic pressure of a solution containing multiple nondiffusible solute species at an arbitrary concentration. Both sets of data are quantitatively accounted for by a model in which IgG self-associates at very high concentration to form (predominantly) trimers under the conditions of these experiments.     

Activity coefficients of KCl in highly concentrated protein solutions

As a contribution to the understanding of the thermodynamic state of single salts in living systems, the activity coefficients of KCl were determined in concentrated bovine serum albumin (BSA) solutions. The concentration range studied was 0.01 to 0.5 M KCl and zero to 18% wt BSA, thus amply covering physiological conditions. The activity coefficients of the salt were measured using the EMF method with ion exchange membrane electrodes. Keeping the salt concentration constant, the activity coefficients of the salt decrease linearly with protein concentration, the effect being more pronounced for low salt content. The maximal deviations of the activity coefficients with respect to those in pure salt solution amount to ca. 40% for 0.01 M KCl and 18% wt BSA. The results were interpreted on the assumption of the superposition of three effects i.e. water bound to BSA molecules as non-solvent water, specific Cl^– ion binding and the electrostatic interactions of the polyions with the salt ions. In view of the results it can be concluded that only a small portion of simple intracellular ions are bound, based on the assumption that the cytoplasm of living cells may be regarded as a concentrated protein-salt solution.     

Scaling of the equilibrium sedimentation distribution in dense DNA solutions

DNA molecules, several persistence lengths long in sedimentation equilibrium at speeds high enough to maintain fairly close packing, show a dense, sharply-bounded turbid phase and an isotropic phase (as with shorter fragments) and also an intermediate, somewhat turbid region. The concentration distribution in the isotropic phase is in satisfactory agreement with a simple extension of scaled particle theory in which semiflexible chains are equivalent to straight rods of the same length. The net intermolecular interactions, as inferred from the Zimm cluster integral, are purely repulsive. As in our previous study with short fragments, the results are compatible with a hard-core electrostatic radius, decreasing with increasing salt concentration. However, for the longer fragments it is necessary to infer either a slightly greater mass per unit length or a slightly smaller electrostatic radius for closest agreement with scaled particle theory. The properties of the solution at the boundary with the turbid, presumably strongly ordered phase are consistent with those found for shorter fragments and with theoretical scaling expectation for a hard, asymmetric particle.     

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.     

Non-ideal tracer sedimentation equilibrium: a powerful tool for the characterization of macromolecular interactions in crowded solutions

Non-ideal tracer sedimentation equilibrium is a technique devised to quantify the effect of high concentrations of unrelated macromolecules on the self- or hetero-associations of dilute macromolecules. Principles and experimental techniques are reviewed, and previous experimental work summarized. A new analysis of experimental data is presented that requires no a priori assumptions regarding the nature of weak repulsive interactions between solute species and the concentrated (crowding) species.     

SED88: a Pascal program for the analysis of sedimentation equilibrium data

Analytical ultracentrifugation is commonly used for the determinationof molecular weights (sedimentation equilibrium) and sedimentationcoefficients (sedimentation rate) of biological macromoleculesin solution. A Turbo Pascal program for the analysis of sedimentationequilibrium centrifugation data produced by absorbance opticalsystems is described. The user may enter data from a scan ofabsorbance versus distance from the centre of rotation, viaa graphics tablet (or ASCII file). This is subsequently manipulatedto yield an apparent weight average molecular weight for thegiven sample. Plots of In (absorbance) versus (radius²) mayalso be produced. The method described uses readily availablecomputational equipment requiring only a graphics tablet inaddition to an IBM PC compatible computer. This technique andthe software developed have been used to investigate the molecularweight range of two International Humic Substances Society (IHSS)reference samples from the Suwannee River. Received on October 7, 1988; accepted on December 12, 1988     

Direct analysis of solute self-association by sedimentation equilibrium

An improved procedure is described for the characterization of solute self-association by sedimentation equilibrium. Whereas previous statistical-mechanical approaches to allowance for the effects of thermodynamic nonideality have entailed tedious iteration because of their specification of activity coefficients in terms of the equilibrium concentrations of all species, such reliance upon knowledge of the solution composition is avoided by the adaptation of an alternative statistical-mechanical formulation [T. L. Hill and Y. D. Chen (1973) Biopolymers, Vol. 12, pp. 1285–1312] in which thermodynamic nonideality is expressed in terms of total solute concentration. The development of an analysis in terms of a relationship with total solute concentration as the experimental variable allows this attribute of the Adams-Fujita approach to be retained without sacrifice of statistical-mechanical rigor. Its use is illustrated by application to Rayleigh interferometric records of sedimentation equilibrium distributions reflecting α-chymotrypsin dimerization and lysozyme self-association. © 1996 John Wiley & Sons, Inc.     

Beyond the second virial coefficient: Sedimentation equilibrium in highly non-ideal solutions

The general theory of sedimentation equilibrium (SE), applicable to mixtures of interacting sedimentable solutes at arbitrary concentration, is summarized. Practical techniques for the acquisition of SE data suitable for analysis are described. Experimental measurements and analyses of SE in concentrated protein solutions are reviewed. The method of non-ideal tracer sedimentation equilibrium (NITSE) is described. Experimental studies using NITSE to detect and quantitatively characterize intermolecular interactions in mixtures of dilute tracer species and concentrated proteins or polymers are reviewed.     

The analysis of macromolecular interactions by sedimentation equilibrium

The study of macromolecular interactions by sedimentation equilibrium is a highly technical method that requires great care in both the experimental design and data analysis. The complexity of the interacting system that can be analyzed is only limited by the ability to deconvolute the exponential contributions of each of the species to the overall concentration gradient. This is achieved in part through the use of multi-signal data collection and the implementation of soft mass conservation. We illustrate the use of these constraints in SEDPHAT through the study of an A+B+B?AB+B?ABB system and highlight some of the technical challenges that arise. We show that both the multi-signal analysis and mass conservation result in a precise and robust data analysis and discuss improvements that can be obtained through the inclusion of data from other methods such as sedimentation velocity and isothermal titration calorimetry.     

Lipase-catalyzed acylation of naringin with palmitic acid in highly concentrated homogeneous solutions

Acylation reactions of naringin with palmitic acid were performed by a lipase after formation of highly concentrated homogeneous solutions. Their initial naringin concentration was 840–950 mM, which is 20–60 times greater than that in organic solvent media. The overall productivity of highly concentrated solutions was more than 15 times greater than those of organic phase media. The addition of DMSO (20–40%, w/w) to substrate mixtures lowered the melting temperature of a naringin–palmitic acid mixture (1:1 molar ratio) to about 40 °C. Reactions at 80 °C apparently followed Michaelis–Menten kinetics despite extremely high substrate concentrations. As the temperature increased from 60 °C to 80 °C, the apparent viscosity of the highly concentrated solution decreased remarkably from 4.31 Pa s to 0.063 Pa s. An activation energy of 7.65 kcal/mol obtained in a range of 60–75 °C suggests a diffusion-control. On the other hand, an activation energy of 17.09 kcal/mol in a range of 75–90 °C indicates a reaction-control. The highest product conversion yield of 33% (mol/mol) was obtained in a 10 h reaction at 80 °C. Addition of activated molecular sieves to the highly concentrated solution increased the product conversion yield by 7% (mol/mol), suggesting that the original equilibrium was disrupted by removing water and then a new equilibrium was reached.