Peter Zipper

Calculation of Partial Specific Volumes and Other Volumetric Properties of Small Molecules and Polymers

Volumetric properties of macromolecules and low-molecular compounds are necessary auxiliary means for the determination of molar masses from solution-scattering and hydrodynamic techniques. In many cases experimental determinations of partial volumes can or have to be replaced by calculative procedures. A universal approach for the calculation of both low-molecular organic compounds and polymers of different chemical composition and structure in aqueous solution is described. It is based on volume increments for the constituent atoms, ions and/or groups and allows corrections for covolume, ring formation, micellization, ionization etc. Application of this approach is of particular interest in connection with: (i) nonionic and ionic organic solutes; (ii) inorganic electrolytes; (iii) monomeric and micellar detergents and lipids; (iv) carbohydrates and polysaccharides; (v) nucleobases, nucleosides, nucleotides, polynucleotides, nucleic acids; (vi) amino acids, amino-acid residues, peptides, polyaminoacids, nonconjugated and conjugated proteins; (vii) synthetic polymers. The results of the volume predictions show a high degree of reliability, if compared to experimental data. Special approaches dealing with simple and conjugated proteins and protein-ligand complexes in two- and multicomponent solutions allow the prediction of both isomolal and isopotential volumes under a variety of native and denaturing conditions, including the presence of high amounts of additives.

Comparative investigations of biopolymer hydration by physicochemical and modeling techniques

The comparative investigation of biopolymer hydration by physicochemical techniques, particularly by small-angle X-ray scattering, has shown that the values obtained differ over a wide range, depending on the nature of the polymer and the environmental conditions. In the case of simple proteins, a large number of available data allow the derivation of a realistic average value for the hydration (0.35 g of water per gram of protein). As long as the average properties of proteins are considered, the use of such a default value is sufficient. Modeling approaches may be used advantageously, in order to differentiate between different assumptions and hydration contributions, and to correctly predict hydrodynamic properties of biopolymers on the basis of their three-dimensional structure. Problems of major concern are the positioning and the properties of the water molecules on the biopolymer surface. In this context, different approaches for calculating the molecular volume and surface of biopolymers have been applied, in addition to the development of appropriate hydration algorithms.

Molecular Shape, Dissociation, and Oxygen Binding of the Dodecamer Subunit of Lumbricus terrestris Hemoglobin

Small angle x-ray scattering of the 213-kDa dodecamer of Lumbricus terrestris Hb yielded radius of gyration = 3.74 ± 0.01 nm, maximum diameter = 10.59 ± 0.01 nm, and volume = 255 ± 10 nm3, with no difference between the oxy and deoxy states. Sedimentation velocity studies indicate the dodecamer to have a spherical shape and concentration- and Ca2+-dependent equilibria with its constituent subunits, the disulfide-bonded trimer of chains a-c and chain d. Equilibrium sedimentation data were fitted best with a trimer-dodecamer model, ln K4 = 7 (association K in liters3/g3) at 1°C and 4 at 25°C, providing ΔH = −20 kcal/mol and ΔS = 4.4 eu/mol. Oxydodecamer dissociation at pH 8.0, in urea, GdmCl, heteropolytungstate K8[SiW11O39] and of metdodecamer at pH 7, was followed by gel filtration. Elution profiles were fitted with exponentially modified gaussians to represent the three peaks. Two exponentials were necessary to fit all the dissociations except in [SiW11O39]−8. Equilibrium oxygen binding measurements at pH 6.5-8.5, provided P50 = 8.5, 11.5-11.9 and 11.9-13.5 torr, and n50 = 5.2-9.5, 3.2-4.9, and 1.8-2.7 for blood, Hb, and dodecamer, respectively, at pH 7.5, 25°C. P50 was decreased 3- and 2-fold in ~100 mM Ca2+ and Mg2+, respectively, with concomitant but smaller increases in cooperativity.

Calculation of hydrodynamic properties of macromolecular bead models with overlapping spheres.

Abstract For the calculation of hydrodynamic properties of rigid macromolecules using bead modelling, models with overlapping beads of different sizes are used in some applications. The hydrodynamic interaction tensor between unequal overlapping beads is unknown, and an oversimplified treatment with the Oseen tensor may introduce important errors. Here we discuss some aspects of the overlapping problem, and explore an ad hoc form of the interaction tensor, proposed by Zipper and Durchschlag. We carry out a systematic numerical study of the hydrodynamic properties of a two-spheres model, showing how the Zipper-Durchschlag correction removes efficiently the numerical instabilities, and predicts the correct limits.

Comparative investigations of the effects of X- and UV-irradiation on lysozyme in the absence or presence of additives

Abstract The radiation damage of lysozyme has been investigated in aqueous solution, after preceding X- and UV-irradiation in the absence or presence of various additives. Activity measurements and UV absorption and fluorescence spectroscopy turned out to be powerful screening techniques for disclosing the damages (inactivation, aggregation, loss of aromatics) and modifications (protection) provided by many additives. Advanced computer modeling approaches were used to visualize the protein atoms and the water molecules bound preferentially on the protein surface. Correlations between the position of radiosensitive amino acid residues and occurring radiation damages are discussed.

An X-ray diffraction study of the crystalline to amorphous phase change in cellulose during high-energy dry ball milling

In methods used widely for determining crystallinity of cellulose substrates by X-ray wide angle diffraction the scattering characteristics of truly amorphous cellulose is needed. So far, such scattering curves have not been available. It was the aim of this study to arrive at an experimentally determined scattering curve of amorphous cellulose. For this purpose, two cellulose samples (a pine wood pulp and a microcrystalline powder) were ball milled in a high-energy equipment in order to destroy the crystalline structure. The structural changes in the cellulose samples and the kinetics of amorphization were followed by taking X-ray diffractograms. After 30min of milling, no more change in the structure could be observed and the diffraction curve of amorphous cellulose with two diffuse maxima at spacings of 0.427nm (strong) and 0.247nm (weak) was obtained. The amorphization was found to follow a first order kinetics, the rate constant of k=(0.0033±0.0004)s -1 holding for both samples. However, while the amorphization of the microcrystalline cellulose started immediately, with the wood pulp sample an induction period of about 300 seconds was observed, which is probably due to residual morphological structures present in this sample.

Detection of small conformational changes of proteins by small‐angle scattering

In the past the technique of small-angle scattering has been a powerful tool for studying conformational changes of proteins which occur, for example, upon binding with ligands. Results obtained by different authors from X-ray and neutron experiments on a variety of proteins and under various conditions have been compiled. This offers the possibility of comparing the extent of changes in the molecular parameters investigated (e.g. change of the radius of gyration). Problems encountered with the detection of small changes are discussed. As an example, conformational changes of the enzyme citrate synthase upon substrate binding (oxaloacetate) are presented. X-ray crystallography had already found distinct changes between open and closed forms of the enzyme. Small-angle X-ray scattering studies registered slight changes of some parameters in solution. These changes could be paralleled with the results of other solution techniques (UV absorption, fluorescence and circular dichroism spectroscopy, analytical ultracentrifugation). The results found for citrate synthase are also compared with previous findings for malate synthase, an enzyme of similar enzymatic function. Above all, this study shows that care has to be taken when studying small conformational changes. It is absolutely necessary to use different methods and conditions and to study the problem from different points of view to avoid pitfalls.

Lack of size and shape alteration of oxygenated and deoxygenated Lumbricus terrestris hemoglobin

The giant extracellular hemoglobin of Lumbricus terrestris was investigated in the oxygenated, deoxygenated and reoxygenated state using small angle X-ray scattering. Scattering experiments of the oxygenated state of the protein yielded a radius of gyration of 10.71 +/- 0.02 nm, a maximum diameter of 29.37 +/- 0.21 nm and a volume of 6200 +/- 200 nm3. The values for the deoxygenated state of the hemoglobin are smaller than the values for the oxygenated state, but the differences hardly exceed the limits of error.

Small-angle X-ray studies on malate synthase from Baker's yeast

Abstract Malate synthase was investigated in solution by the small-angle X-ray scattering technique. The substrate-free enzyme was shown to have a molecular weight of 186000, a radius of gyration of 3.96 nm, a maximum particle diameter of 11.2 nm, a volume of 343 nm3, a radius of gyration of the thickness of 1.04 nm, and an axial ratio of 1:0.33. The enzyme molecule undergoes small changes in overall structure upon binding substrates. Investigation of the enzyme under prolonged exposure to X-rays led to an aggregation of the enzyme and allowed statements concerning the way of aggregation and factors influencing aggregation.

SMALL-ANGLE X-RAY SCATTERING STUDIES ON CELLOBIOSE DEHYDROGENASE FROM PHANEROCHAETE CHRYSOSPORIUM

Limited proteolysis of cellobiose dehydrogenase (CDH) from the white rot fungus Phanerochaete chrysosporium by papain cleaves the enzyme into two fragments containing flavin (FAD) and heme, respectively. Small-angle X-ray scattering (SAXS) was employed to investigate size and shape of intact CDH and of its fragments in solution. The largest dimension of CDH amounts to about 18 nm, whereas the corresponding quantity of each of the two fragments is only around 9 nm. CDH as well as its fragments appear to be of prolate shape, the cross-section of the FAD fragment (diameter 4.3 to 5.1 nm) being considerably larger than that of the heme fragment (diameter 3.3 nm). These findings suggest a collinear arrangement of the two domains in the CDH particle. Simulations based on the method of finite elements corroborate this structure model and furthermore suggest the existence of a possibly flexible linker between the two domains.