Practical aspects to the use of indirect fourier transformation methods

We studied by small angle x-ray scattering (SAXS) the tetramethylurea (TMU) effects on the tertiary structure of lysozyme in water. Samples containing TMU with mass fractions, w, ranging from 0 to 0.7 were analyzed. The SAXS results clearly demonstrate a structural transition from a spheroidal molecule (0⩽w⩽0.6) to a highly anisometric molecule for w=0.7. Additional SAXS results for samples with w=0.7, from which the TMU was removed, showed that this transition is reversible. The variation of the maximum dimension of the molecule with w fits an equation corresponding to a “two-state” model. At w=0.6 (critical fraction) a mixture of folded (spheroidal) and unfolded (anisometric) molecules coexists in the solution.

Section: Discussionmentioning

confidence: 99%

Effects of tetramethylurea on the tertiary structure of lysozyme in water

Castelletto

Arêas

et al. 1998

“…Accordingly, the scattering at q values below this limit can be excluded from the Fourier analysis in order to minimize the interference effects that would hinder the structure determination. 38 Even within the limited range of q values retained, close inspection of the inner parts of the I(q) curves reveals a leveling off for spheres, while the scattering for cylinders increases proportional to q Ϫ1 and for planar structures to q Ϫ2 as q goes to zero. Such analysis is limited to cases where interference effects ͓i.e., S(q) 1͔ can be simply eliminated by cutting away the low q part of the scattering curve.…”

Section: A Guinier Analysismentioning

confidence: 97%

Small-angle neutron scattering of D2O–C12E5 mixtures and microemulsions with n-octane: Direct analysis by Fourier transformation

Strey

Glatter

Schubert

et al. 1996

102

106

Spherical, cylindrical, and lamellar microstructures were examined by ͑SANS͒ in the binary system water ͑D 2 O͒/pentaethylene glycol mono-perdeutero-n-dodecyl ether ͑C 12 D 25 E 5 ͒ and in the ternary system ͑D 2 O͒/pentaethylene glycol mono-n-dodecyl ether ͑C 12 E 5 ͒/perdeuterated n-octane ͑C 8 D 18 ͒. A model-independent picture of the structures emerges from Fourier transformation of the measured SANS spectra. The data analysis makes no a priori assumptions about the type of structure. Rather, the pair distribution functions obtained are so unique that an unambiguous assignment of the local geometry is possible. The different structures for a given mixture are obtained by changing temperature. For water-rich samples the sequence of spherical, cylindrical, and planar structures is obtained with increasing temperature. For oil-rich samples the same sequence occurs as a function of decreasing temperature. As an important additional result, the scattering length density profile normal to the interface is obtained. The interfacial profile is found to be rather diffuse, apparently because of solvent penetration.

“…23 The theoretical aspects of this method and its experimental applications are discussed elsewhere. 23,[29][30][31] From the approximated pair distance distribution function p IFT (r), the radius of gyration…”

Section: Inverse Fourier Transformation (Ift)mentioning

confidence: 99%

Dynamics of star-burst dendrimers in solution in relation to their structural properties

Rathgeber

Monkenbusch

Kreitschmann³

et al. 2002

133

160

We have measured both the static and dynamic structure factors of a single dendrimer with small-angle x-ray scattering ͑SAXS͒ and neutron spin-echo spectroscopy under good solvent conditions with the aim of finding a consistent correlation between the structural properties of dendrimers and their dynamic behavior. The samples under investigation were star-burst polyamidoamine dendrimers with generations gϭ0 to 8 in dilute methanol solutions. A model independent approach employing inverse Fourier transformation and square root deconvolution methods has been used to analyze the SAXS data to obtain the pair distance distribution function p(r) and the radial excess electron density profile ⌬ (r). In addition, we formulated a model that takes both the colloidal ͑globular, compact shape with form polydispersity or fuzzy surface͒ as well as the loose, polymeric ͑self-avoiding random walk͒ character of dendrimers into account. With this model we were able to describe the spectra of all dendrimer generations consistently. Parameters discussed as a function of the dendrimer generation are, among others, the correlation length of the density fluctuations ͑blob radius͒ , the radius of gyration R g , the sphere radius R s , the form polydispersity s or analogously, the width of the fuzzy surface region 2 f . Both the model-independent approach and the model fits reveal that at least down to the third generation the dendrimers exhibit a rather compact, globular shape. These findings are in agreement with the dynamic results obtained by NSE spectroscopy which probes length scales both larger and much smaller than the dimension of a single dendrimer. The method reveals that the dynamics throughout is dominated by the center-of-mass diffusion-the internal dynamics is suppressed. The diffusion coefficients obtained are close to the values calculated from the Stokes-Einstein relation using the sphere radius R s determined from the SAXS spectra. Dynamically, the dendrimers behave like ''hard'', solid spheres.