Studies of solute self-association by sedimentation equilibrium: allowance for effects of thermodynamic non-ideality beyond the consequences of nearest-neighbor interactions

A sedimentation equilibrium study of alpha-chymotrypsin self-association in acetate-chloride buffer, pH 4.1 I 0.05, has been used to illustrate determination of a dimerization constant under conditions where thermodynamic non-ideality is manifested beyond the consequences of nearest-neighbor interactions. Because the expressions for the experimentally determinable interaction parameters comprise a mixture of equilibrium constant and excluded volume terms, the assignment of reasonable magnitudes to the relevant virial coefficients describing non-associative cluster formation is essential for the evaluation of a reliable estimate of the dimerization constant. Determination of these excluded volume parameters by numerical integration over the potential-of-mean-force is shown to be preferable to their calculation by approximate analytical solutions of the integral for this relatively small enzyme monomer with high net charge (+10) under conditions of low ionic strength (0.05 M).     

Studies of the self-association of bacteriophage T4 gene 32 protein by equilibrium sedimentation.

The self-association of the bacteriophage T4 gene 32 protein has been examined in the analytical ultracentrifuge under varying conditions to determine the nature of the process. The process is not a simple indefinite association with one association constant (monomer

dimer

trimer

etc.). The complexity of the process is shown by (1) peculiarities in the molecular weight versus concentration curves, in the region of the dimer (observed with increasing ionic strength, at pH 10, in 0.04 m-MgCl₂, with aged preparations, at 19 °C and in the presence of the oligonucleotide d(pT)₁₀), (2) the increased sigmoidicity of the association curve in the presence of glycerol or oligo[d(pT)₄], and (3) the discontinuity in the association curve at the tetramer at a pH value of approximately 9.4. A model with two association constants which could vary independently (monomer

dimer

tetramer

etc.) explained many of the findings. However, a more complex model was required to explain curves which had a plateau at the dimer with increased association at higher protein concentrations. Thus, under all conditions examined there is evidence for more than one type of protein-protein interaction. These different interactions may be involved in a physiological function such as recombination.     

On the analysis of protein self-association by sedimentation velocity analytical ultracentrifugation

Analytical ultracentrifugation is one of the classical techniques for the study of protein interactions and protein self-association. Recent instrumental and computational developments have significantly enhanced this methodology. In this paper, new tools for the analysis of protein self-association by sedimentation velocity are developed, their statistical properties are examined, and considerations for optimal experimental design are discussed. A traditional strategy is the analysis of the isotherm of weight-average sedimentation coefficients s(w) as a function of protein concentration. From theoretical considerations, it is shown that integration of any differential sedimentation coefficient distribution c(s), ls-g(*)(s), or g(s(*)) can give a thermodynamically well-defined isotherm, as long as it provides a good model for the sedimentation profiles. To test this condition for the g(s(*)) distribution, a back-transform into the original data space is proposed. Deconvoluting diffusion in the sedimentation coefficient distribution c(s) can be advantageous to identify species that do not participate in the association. Because of the large number of scans that can be analyzed in the c(s) approach, its s(w) values are very precise and allow extension of the isotherm to very low concentrations. For all differential sedimentation coefficients, corrections are derived for the slowing of the sedimentation boundaries caused by radial dilution. As an alternative to the interpretation of the isotherm of the weight-average s value, direct global modeling of several sedimentation experiments with Lamm equation solutions was studied. For this purpose, a new software SEDPHAT is introduced, allowing the global analysis of several sedimentation velocity and equilibrium experiments. In this approach, information from the shape of the sedimentation profiles is exploited, which permits the identification of the association scheme and requires fewer experiments to precisely characterize the association. Further, under suitable conditions, fractions of incompetent material that are not part of the reversible equilibrium can be detected.     

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.     

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.     

Assessment by sedimentation equilibrium analysis of a heterologous macromolecular interaction in the presence of self-association: interaction of S5 with S8

The proteins S5 and S8 from the Escherichia coli 30S ribosomal subunit have been examined by sedimentation equilibrium methods for behavior in solution as isolated components and in mixtures. The means of resolving two simultaneous associations in this system is discussed, and the energy of association of S5 and S8 is reported. It was found that protein S5 from the MRE 600 strain tends to self-associate weakly at 4 degree C in a manner that can be described as an isodesmic self-association with an association constant and corresponding standard Gibbs free energy equal to (7.7 +/- 0.7) X 10(3) M-1 and -4.9 +/- 0.1 kcal/mol, respectively. Protein S8 was found to have a molecular weight of 15800 and was monomeric in a pure state. Mixtures of S5 and S8 clearly demonstrated the presence of an S5-S8 complex in addition to the self-association of S5. The equilibrium constant of association for the formation of a simple S5-S8 complex at 4 degree C and the corresponding standard Gibbs free energy were found to be (5.5 +/- 1.0) X 10(4) M-1 and -6.0 +/- 0.1 kcal/mol, respectively.     

Digitization of sedimentation equilibrium and velocity data for analysis by minicomputer

A procedure is described whereby phosphorylated seryl residues may be unequivocally identified during the sequential degradation of a polypeptide chain by the Edman technique. The phosphoseryl residue, Ser(P), was first converted by treatment with methylamine in dilute alkali to a β-methylaminoalanyl residue which was split from the polypeptide by the degradative procedure as the derived phenylthiohydantoin. This was identified by high-performance liquid chromatography. The procedure was highly effective when the Ser(P) occupied an isolated position in a polypeptide chain but was less so when grouped consecutively with other Ser(P).     

Characterization of macromolecular heterogeneity by equilibrium sedimentation techniques

New graphical procedures have been developed to investigate the heterogeneity of protein preparations using sedimentation equilibrium. The heterogeneous systems that can be studied include self-associating systems contaminated by incompetent monomer, self-associating systems contaminated by non-dissociating oligomer and simple non-interacting monomer-oligmer disperse systems. The new procedures are based on the concentration dependence of the apparent association constants estimated by a non-linear least square fitting program (NONLIN), on the assumption of conservation of mass during sedimentation and on the applications of several standard techniques for statistical inferences of NONLIN estimations. The procedures outlined here can detect various types of heterogeneity, discriminate amongst different types of heterogeneity, estimate the amount of contaminant causing heterogeneity and determine the true equilibrium constant of the self-associating components. The procedures appear to be sensitive, accurate and easily applicable when tested using both protein samples and computer simulated data.     

Reduced sedimentation equilibrium time by two-step initial loading

Computer simulation shows that the time required to attain near sedimentation equilbrium is dramatically reduced by a two-step initial loading in which a macromolecular solution at low or zero concentration is layered above one at a higher concentration. To achieve the minimum time requires a good estimate of the molecular weight, but at least a 50% reduction in time can be achieved if the molecular weight of the macromolecule is known only within a factor of 2. Numerical solutions to the differential equation of the ultracentrifuge are calculated using the finite element method. An efficient Gaussian elimination algorithm can be used to minimize calculation time and computer storage requirements.     

Analyses of sedimentation equilibrium data

A numerical procedure is presented which can quite adequately compute the molecular weight averages as a function of solute concentration from sedimentation equilibrium data for homogeneous systems and for monomer-dimer associating systems with a possible extension to heterogeneous systems where monotonic variation in the weight average molecular weight is observed such as in weakly associating or dissociating systems. The procedure utilizes the method of orthogonal polynomials for curve fitting which allows for a rapid determination of best fit with minimal round off error. The procedure is particularly applicable in cases where the concentration of solute at the meniscus can be considered to be neither appreciable and reasonably well determined as in low speed sedimentation equilibrium experiments, nor essentially zero as in high speed sedimentation equilibrium experiments where the calculations become somewhat more simplified. The use of moderate speed sedimentation equilibrium has the advantage of providing a more broad concentration distribution in the centrifuge cell which yields more extensive information concerning dissociating systems yet still provides results at low solute concentrations where most solutes can be considered to be behaving ideally.     

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.     

Direct observation of the self-association of dilute proteins in the presence of inert macromolecules at high concentration via tracer sedimentation equilibrium: theory, experiment, and biological significance.

The technique of tracer sedimentation equilibrium [Rivas, G., et al. (1994) Biochemistry, 2341-2348 (1); Rivas, G., et al. (1996) J. Mol. Recognit. 9, 31-38 (2)] is utilized, together with an extension of the theory of sedimentation equilibrium of highly nonideal solutions [Chatelier and Minton, (1987) Biopolymers 26, 1097-1113 (3)], to characterize the thermodynamic activity and/or the state of association of a dilute, labeled macromolecular solute in the presence of an arbitary concentration of a second, unlabeled macromolecular solute. Experiments are performed on solutions of labeled fibrinogen (0.25-1 g/L) in bovine serum albumin (0-100 g/L) in the presence and absence of divalent cations (Ca(2+), Mg(2+)), and on solutions of labeled tubulin (0.2-0.6 g/L) in dextran (0-100 g/L). It is found that in the absence of the divalent cations, the large dependence of the thermodynamic activity of fibrinogen on BSA concentration is well accounted for by a simple model for steric repulsion. In the presence of the cations and sufficiently large concentrations of BSA (>30 g/L), fibrinogen appears to self-associate to a weight-average molar mass approximately twice that of monomeric fibrinogen. Tubulin appears to self-associate to an extent that increases monotonically with increasing dextran concentration, reaching a weight-average molar mass almost 3 times that of the alphabeta dimer in the presence of 100 g/L dextran. Possible biological ramifications are discussed.     

The effect of temperature on the self-association of S5 and on the association of S5 with S8 as determined by sedimentation equilibrium

Solutions of proteins S5 and S8 from the Escherichia coli 30 S ribosomal subunit have been examined by sedimentation equilibrium methods as a function of temperature for their behavior in solution as isolated components and in mixtures. The standard enthalpy and entropy at 4 °C for the isodesmic self-association of S5 were determined from a study over the temperature range of 3 to 33 °C to be 0.1 ± 0.9 kcal/mol and 18 ± 3 cal/(mol × deg), respectively. The protein S8 remained monomeric over the same range of temperature. The standard enthalpy and entropy at 4 °C for the association of S5 and S8 were determined on mixtures from a study over the temperature range of 3 to 27 °C to be ?0.4 ± 1.6 kcal/mol and 20 ± 6 cal/(mol × deg), respectively. Based on these values and the previously determined standard Gibbs free energies (S. H. Tindall and K. C. Aune, 1981, Biochemistry20, 4861–4866), the driving force for the self-association of S5 and the association of S5 with S8 could be interpreted as being derived from the expulsion of water upon ion pair formation at the interaction sites.