Otto Ristau

Analysis of the thermodynamic non-ideality of proteins by sedimentation equilibrium experiments.

This paper presents a modified method to determine experimentally the second virial coefficient of protein solutions by sedimentation equilibrium experiments. The improvement is based on the possibility of fitting simultaneously up to seven radial concentration distribution curves of solutions with different loading concentrations. The possibility of precise determination of the second virial coefficient allows estimation of the net charge and the excluded volume of a monomeric protein. Application of the method is demonstrated for lysozyme and ovalbumin. In 0.1 M sodium acetate buffer, pH 4.5, the second virial coefficient of hen egg white lysozyme amounts to 24 +/- 1 ml/g. Analysis based on spherical particle theory yield an excluded volume of 3.5 ml/g and a charge dependent value of 20.5 ml/g which is induced by a net charge number of 14.1 +/- 1. Under low salt conditions self-association processes on lysozyme are unfavorable due to electrostatic repulsion. To overcome these repulsive contributions, either a shift to neutral pH or addition of at least 2% NaCl is necessary. In this way the charge dependent contribution decreases below the value responsible for the excluded volume and allows crystallization of the protein. Similar effects can be observed with ovalbumin. The high virial coefficient observed at pH 8.5 is induced by the high net charge number of 27 +/- 1.

A new approximate whole boundary solution of the Lamm differential equation for the analysis of sedimentation velocity experiments

Sedimentation velocity is one of the best-suited physical methods for determining the size and shape of macromolecular substances or their complexes in the range from 1 to several thousand kDa. The moving boundary in sedimentation velocity runs can be described by the Lamm differential equation. Fitting of suitable model functions or solutions of the Lamm equation to the moving boundary is used to obtain directly sedimentation and diffusion coefficients, thus allowing quick determination of size, shape and other parameters of macromolecules. Here we present a new approximate whole boundary solution of the Lamm equation that simultaneously allows the specification of sedimentation and diffusion coefficients with deviations smaller than 1% from the expected values.

Self-association studies on the EphB2 receptor SAM domain using analytical ultracentrifugation

Abstract. The self-association behavior of the Eph-kinases SAM domain has been studied in phosphate buffer, pHxa07.4, containing 0.14xa0M NaCl using concentration-dependent sedimentation equilibrium experiments. Only weak interactions typical for a monomer-dimer equilibrium up to at least 12xa0mg/mL were observed. Such concentrated solutions require a consideration of the non-ideality expressed by virial coefficients. A special centrifuge equation was used for the global analysis to estimate equilibrium constants based on the thermodynamic activities of the reactants. When neglecting this, the parameters deviate by about 20%. Association constants for dimerization of the EphB2-SAM domain vary between 163xa0M–1 at 10xa0°C and 395xa0M–1 at 32xa0°C, indicating hydrophobic forces are involved in the dimerization process. In solutions of about 12xa0mg/mL, less than 50% dimers are in solution and higher oligomers can be excluded.

Molecular parameters from sedimentation velocity experiments: Whole boundary fitting using approximate and numerical solutions of lamm equation

Publisher Summary This chapter describes the molecular parameters from sedimentation velocity experiments. The chapter discusses two types of approaches that are recently implemented in software adapted for data obtained from the Beckman XL-A. In the first approach, the finite element method is used to solve the Lamm equation (and modifications of the Lamm equation) numerically, whereas in the second approach is analytical solutions of the Lamm equation, subjected to various approximations. Both approaches involve nonlinear least-squares, fitting of the moving boundary of sedimentation velocity, and approach-to-equilibrium experiments to solutions of the Lamm equation. Recent advances in analytical ultracentrifugation hardware brought about substantial improvements in the accuracy, precision, and range of data obtained from this instrumentation. These improvements are made possible by digital data acquisition, microprocessor-controlled experimental parameters, high-quality optical components, and by the introduction of a Raleigh interference system that permits the acquisition of data at lower protein concentration, with a higher signal-to-noise ratio and a higher data density than possible, with absorbance optics.

Analysis of interacting biopolymer systems by analytical ultracentrifugation.

Abstract Many of the functions of biological macromolecules are based on specific interactions. Extended concentration dependent studies of sedimentation coefficients or molecular masses of biopolymers are highly useful for describing the different kinds of association phenomena. These studies allow one to determine the partial concentrations of monomers and associates or reactants and complexes in self-associating systems or heterologous associations, respectively. Furthermore, in combination with corresponding measurements of biological activity these data allow one to estimate the individual activity parameters of components involved in equilibrium processes. The study of self-association and heterologous association using analytical ultracentrifugation, some recent developments therein, and its application to different examples are outlined here.

Quantum-chemical interpretation of the unusual absorption spectrum of the cytochrome P-450CO complex

Abstract The electronic transitions of COue5f8hemoglobin and cytochrome P-450ue5f8CO were calculated using the PPP method with inclusion of one-centre exchange integrals between the iron orbitals d xz and d yz . It is suggested from the calculations that a mercaptide sulfur may be the fifth ligand in cytochrome P-450.

Analysis of protein self-association under conditions of the thermodynamic non-ideality

Analysis of protein-protein interactions in highly concentrated solutions requires a consideration of the non-ideality in such solutions which is expressed by the virial coefficients. Different equations are presented to estimate effects of the thermodynamic non-ideality on the macromolecular interaction of self-associating proteins in sedimentation equilibrium experiments. Usually the influence of thermodynamic non-ideal behavior are described by concentration power series. The convergence of such power series is limited at high solute concentration. When expressing the thermodynamic non-ideality by an activity power series this disadvantage can be minimized. The developed centrifuge equations are the basis for a global analysis to estimate equilibrium constants and the corresponding thermodynamic activities of the reactants. Based on fit analysis of synthetic concentration profiles it was established that marked deviations from the expected association constants are observed for proteins with strong association forces between solute molecules. Considerable differences were also observed in weakly interacting systems. This was due to the excluded volume of the protein which is similar in magnitude to the binding constant. For interactions with moderate affinities values extremely close to the true binding values were obtained, as confirmed by experimental results with concanavalin A.

An INDO-CI method in π-approximation for the calculation of transition metal complexes with organic ligands—application to iron(II)-trisdiimine complexes

An INDO-CI method in π-approximation extended for transition metal complexes with organic ligands is presented. The σ-polarization in the complex is estimated using a two-dimensional EHT calculation and considered in the π-calculation by means of the diagonal Fock matrix elements. The method is tested for four trisdiimine iron(II) complexes. In agreement with the experimental absorption spectra the calculations show that diimine complexes with non-heterocyclicly bound nitrogen atoms exhibit a large red-shift of the characteristic charge-transfer transition increasing the number of aromatic rings. Contrarily, for diimine complexes with heterocyclicly bound nitrogen atoms no shift of the charge-transfer transition was obtained.

Sedimentation equilibrium: a valuable tool to study homologous and heterogeneous interactions of proteins or proteins and nucleic acids

We present a short overview of our experience in analyzing the affinity and stoichiometry of self-associating and heterologous interactions by using the sedimentation equilibrium technique. Data acquisition and the fitting procedure employing the computer programs that we have developed, Polymole and Virial, are utilized for obtaining reliable results under ideal as well as non-ideal conditions. Such data derived from biologically important macromolecules find utility in understanding physiological events such as cell regulation.

An improved approximate solution of the Lamm equation for the simultaneous estimation of sedimentation and diffusion coefficients from sedimentation velocity experiments

Sedimentation and diffusion coefficients are important parameters to describe size and shape of macromolecules in solution. The data can be obtained from sedimentation velocity experiments by a nonlinear fitting procedure using approximate solutions for the Lamm equation. Here, we present a modification of such a model function that was originally proposed by Fujita [H. Fujita, Mathematical Theory of Sedimentation Analysis, Wiley, New York, 1962]. The extended model function is well suitable to study low molecular mass compounds. The improvement of this solution given here is based on using an adjustable value for the explicit integration variable, z, the reduced radius. This modification leads to more accurate sedimentation and diffusion coefficients compared to using a constant value of 0.5 as used by Fujita. The advantage of our modification was demonstrated by the analysis of noise-free curves calculated using the finite element method, as well as experimental curves obtained for the peptides angiotensin I and II. The relatively low sedimentation and diffusion coefficients found for both substances indicate that the peptides exist as extended chains of about 3.65 nm (angiotensin I) or 3.04 nm length (angiotensin II) in solution. The lack of higher-order structure of the peptides that was derived also from CD spectra might facilitate receptor binding, and could be one reason for the fast proteolytic digestion of the free peptides.