Alexander Bergmann

SAXS experiments on absolute scale with Kratky systems using water as a secondary standard

For small-angle scattering, of X-rays (SAXS) and neutrons (SANS), the importance of absolute calibration has been recognized since the inception of the technique. The work reported here focuses on SAXS measurements using Kratky slit systems. In former days, only molecular weights or scattering per particle were determined, but today absolute calibration implies the use of the unit of cm−1 for the scattering curve. It is necessary to measure the so-called absolute intensity, which is the ratio of the scattering intensity to the primary intensity P0. Basically there are two possible ways to determine the absolute intensity. The first one is the direct method, which involves the mechanical attenuation of the primary beam by a rotating disc or a moving slit. The second is the indirect method, using secondary standards. Water is well suited as a calibration standard because of the angle-independent scattering. The essential advantage is that the scattering of water only depends on the physical property of isothermal compressibility. Before presenting an example of the practical performance of this method, the most important theoretical equations for an SAS experiment on the absolute scale are summarized. With the slit collimation system, the scattering curve of water can be measured with high enough statistical accuracy. As a first example, the scattering curve of the protein lysozyme on the absolute scale is presented. The second example is the determination of the aggregation number of a triblock copolymer P94 (EO17–PO42–EO17). Taking into account that at least 10% of the polymer sample consists of diblocks, the accuracy of around 10% for the determined aggregation number is rather good. The data of P94 are also considered on the particle scale in order to obtain the radial scattering-length density distribution.

Solving the generalized indirect Fourier transformation (GIFT) by Boltzmann simplex simulated annealing (BSSA)

The structure of colloidal particles can be studied with small-angle X-ray and neutron scattering (SAXS and SANS). In the case of randomly oriented systems, the indirect Fourier transformation (IFT) is a well established technique for the calculation of model-free real-space information. Interaction leads to an overlap of inter- and intraparticle scattering effects, preventing most detailed interpretations. The recently developed generalized indirect Fourier transformation (GIFT) technique allows these effects to be separated by assuming various models for the interaction, i.e. the so-called structure factors. The different analytical behaviour of these structure factors from that of the form factors, describing the intraparticle scattering, allows this separation. The mean-deviation surface is defined by the quality of the fit for different parameter sets of the structure factor. Its global minimum represents the solution. The former non-linear least-squares approach has proved to be inefficient and not very reliable. In this paper, the incorporation of the completely different Boltzmann simplex simulated annealing (BSSA) algorithm for finding the global minimum of the hypersurface is presented. This new method increases not only the calculation speed but also the reliability of the evaluation.

Evaluation of small-angle scattering data of charged particles using the generalized indirect Fourier transformation technique

Small-angle x-ray and neutron scattering are widely used techniques to study the structure of colloidal particles in the size range up to 100 nm. The indirect Fourier transformation technique is well established to obtain model free real space information, but the interpretation of the results is limited to cases where particle interaction can be neglected. The extended generalized indirect Fourier transform (GIFT) allows one to separate inter- and intraparticle effects, but needs models for the particle interaction. We present the application of three different models for the calculation of interaction effects of charged particles, represented by the structure factor. With this extension, useful real space information can be obtained by the GIFT method for solutions with volume fractions up to about 0.3 without any assumption for the shape of the particles. Only the interaction effects need a model assumption, and the parameters determined from this model can give some additional information. Simulations show that it is impossible to determine charge and ionic strength simultaneously. There exists another ambiguity between the parameter sets for charge, radius, and volume fraction, but we show how this problem can be overcome in most cases. The practical applicability of the method is demonstrated by means of the micellar system CTAB in different concentrations from 1% up to 20% and with varying amounts of added salt to screen the charges and change the particle shape.

Dimerization of the Major Birch Pollen Allergen Bet v 1 Is Important for its In Vivo IgE-Cross-Linking Potential in Mice

In type I allergy, the cross-linking of membrane IgE on B lymphocytes and of cytophilic IgE on effector cells by their respective allergens are key events. For cross-linking two IgE molecules, allergens need at least two epitopes. On large molecules, these could be different epitopes in a multivalent, or identical epitopes in a symmetrical, fashion. However, the availability of epitopes may be limited on small allergens such as Bet v 1, the major birch pollen allergen. The present work analyzes whether dimerization is required for the cross-linking capacity of this allergen. In immunoblots, murine monoclonal and polyclonal human Bet v 1-specific Abs detected, besides a Bet v 1 monomer of 17 kDa, a dimer of 34 kDa. In dynamic light scattering, Bet v 1 appeared as dimers and even multimers, but a single condition could be defined where it behaved exclusively monomerically. Small-angle x-ray scattering of the monomeric and dimeric samples resulted in diagrams agreeing with the calculated models. Circular dichroism measurements indicated that the structure of Bet v 1 was preserved under monomeric conditions. Skin tests in Bet v 1-allergic mice were positive with Bet v 1 dimer, but remained negative using the monomer. Furthermore, in contrast to dimeric Bet v 1, the monomer was less capable of activating murine memory B cells for IgE production in vivo. Our data indicate that the presentation of two identical epitopes by dimerized allergens is a precondition for cross-linking of IgE on mast cells and B lymphocytes.

TraA and its N-terminal relaxase domain of the Gram-positive plasmid pIP501 show specific oriT binding and behave as dimers in solution

TraA is the DNA relaxase encoded by the broad-host-range Grampositive plasmid pIP501. It is the second relaxase to be characterized from plasmids originating from Gram-positive organisms. Full-length TraA (654 amino acids) and the N-terminal domain (246 amino acids), termed TraAN246, were expressed as 6xHis-tagged fusions and purified. Small-angle X-ray scattering and chemical cross-linking proved that TraAN246 and TraA form dimers in solution. Both proteins revealed oriTpIP501 (origin of transfer of pIP501) cleavage activity on supercoiled plasmid DNA in vitro. oriT binding was demonstrated by electrophoretic mobility shift assays. Radiolabelled oligonucleotides covering different parts of oriTpIP501 were subjected to binding with TraA and TraAN246. The KD of the protein-DNA complex encompassing the inverted repeat, the nick site and an additional 7 bases was found to be 55 nM for TraA and 26 nM for TraAN246. The unfolding of both protein constructs was monitored by measuring the change in the CD signal at 220 nm upon temperature change. The unfolding transition of both proteins occurred at approx. 42 degrees C. CD spectra measured at 20 degrees C showed 30% a-helix and 13% b-sheet for TraA, and 27% alpha-helix and 18% beta-sheet content for the truncated protein. Upon DNA binding, an enhanced secondary structure content and increased thermal stability were observed for the TraAN246 protein, suggesting an induced-fit mechanism for the formation of the specific relaxase-oriT complex.

Interpretation of small-angle scattering data of inhomogeneous ellipsoids

Small-angle scattering data of inhomogeneous ellipsoidal particles are discussed in terms of their pair distance distribution functions p(r). Special attention is given to the determination of core and shell thicknesses and axis ratios as well as to large distances within the particles, since cross terms between parts of positive and negative contrast within the particle can produce misleading results, similar to homogeneous particles or Janus particles. Cross-section pair distance distribution functions p c (r) of cylinders with elliptical cross sections show similar behaviour. Theoretical calculations are compared with small-angle X-ray and neutron scattering (SAXS and SANS) data of cetyltrimethylammonium bromide in aqueous KCl solutions.

Electrospray ionization mass spectrometry, circular dichroism and SAXS studies of the (S)-hydroxynitrile lyase from Hevea brasiliensis.

We report on experiments pertaining to solution properties of the (S)-hydroxynitrile lyase from Hevea brasiliensis (HbHNL). Small angle X-ray scattering unequivocally established the enzyme to occur in solution as a dimer, presumably of the same structure as in the crystal. The acid induced, irreversible deactivation of HbHNL was examined by electrospray ionization mass spectrometry (ESI-MS), circular dichroism (CD) and by measuring the enzyme activity. The deactivation is paralleled by an unfolding of the enzyme. ESI-MS of this 30000 Da per monomer heavy protein demonstrated that unfolding took place in several stages which are paralleled by a decrease in enzyme activity. Unfolding can also be observed by CD spectroscopy, and there is a clear correlation between enzyme activity and unfolding as detected by ESI-MS and CD.

SAXS instruments with slit collimation : investigation of resolution and flux

Six small-angle X-ray cameras with block collimation systems were simulated, namely the original Kratky camera, a high-flux version of the Kratky camera, a SAXSess (Anton Parr) camera with a focusing mirror in a linear collimation setup and in a pin-hole setup, as well as a similar camera with a parallelizing mirror in a linear and a pin-hole setup. Their performance was examined using Monte Carlo ray-tracing. The Kratky and the SAXSess camera gave resolutions of 64–65 nm, the high-flux Kratky camera gave a resolution of 44 nm, and the camera with parallelizing mirror gave a resolution of 32 nm. The flux of the camera with parallelizing mirror was 1.47 times higher than for the SAXSess camera, and 18.6 times the flux of the Kratky camera. On changing the alignment, the camera with parallelizing mirror exhibited the best performance up to a resolution of 44 nm; the SAXSess camera was better for higher resolutions. Experimental flux measurements agree if no collimation system is added. Measurements of beam profiles and flux including collimation systems show only qualitative agreement because of user-dependent factors during alignment.

Real space functions from experimental small angle scattering data

A model free evaluation of small angle scattering data of interacting particles results in real space curves that are often difficult to interpret. It is then easier to use a model for the inter and/or the intra particle effects. Such a procedure requires the selection of appropriate models. The selection of the correct model is facilitated by interpreting parts of the purely model free real space results of the scattering data. The corresponding functions for hard, charged, and attractive spheres are simulated as well as the curves of spheres in BCC crystalline order and of cylinders in hexagonal order. The simulated results are compared to experimental data obtained from concentrated emulsions. Estimations for particle diameter, type of interaction, next neighbour distance, and volume fraction can be deduced from most of the data.