Size and shape of detergent micelles determined by small-angle X-ray scattering

We present a systematic analysis of the aggregation number and shape of micelles formed by nine detergents commonly used in the study of membrane proteins. Small-angle X-ray scattering measurements are reported for glucosides with 8 and 9 alkyl carbons (OG/NG), maltosides and phosphocholines with 10 and 12 alkyl carbons (DM/DDM and FC-10/FC-12), 1,2-dihexanoyl-sn-glycero-phosphocholine (DHPC), 1-palmitoyl-2-hydroxy-sn-glycero-3-[phospho-rac-(1-glycerol)] (LPPG), and 3-[(3-cholamidopropyl)dimethylammonio]-1-propane sulfonate (CHAPS). The SAXS intensities are well described by two-component ellipsoid models, with a dense outer shell corresponding to the detergent head groups and a less electron dense hydrophobic core. These models provide an intermediate resolution view of micelle size and shape. In addition, we show that Guinier analysis of the forward scattering intensity can be used to obtain an independent and model-free measurement of the micelle aggregation number and radius of gyration. This approach has the advantage of being easily generalizable to protein-detergent complexes, where simple geometric models are inapplicable. Furthermore, we have discovered that the position of the second maximum in the scattering intensity provides a direct measurement of the characteristic head group-head group spacing across the micelle core. Our results for the micellar aggregation numbers and dimensions agree favorably with literature values as far as they are available. We de novo determine the shape of FC-10, FC-12, DM, LPPG, and CHAPS micelles and the aggregation numbers of FC-10 and OG to be ca. 50 and 250, respectively. Combined, these data provide a comprehensive view of the determinants of micelle formation and serve as a starting point to correlate detergent properties with detergent-protein interactions.     

X-ray small-angle scattering of bulk polyethylene

Summary On the basis of the assumption that bulk polyethylene is built up of parallel layers differing in electron density, the correlation function for the direction perpendicular to the layers is calculated from the experimental scattering curve at small angles. This function is compared with that calculated for a model consisting of alternating crystalline and amorphous layers. One scale factor and three parameters have to be adjusted to obtain good agreement. The scale factor accounts for the average periodicity in the direction perpendicular to the layers. The parameters are the crystalline fraction and the width of the distributions of the thicknesses of the crystalline and amorphous layers respectively. It is furthermore shown that especially the crystallinity thus found is not appreciably influenced by even relatively large deviations from the primary model.

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Zusammenfassung Ausgehend von der Annahme, daß aus der Schmelze erstarrtes Polyäthylen aus parallelen Schichten unterschiedlicher Elektronendichte zusammengesetzt ist, wird die Korrelationsfunktion für die Richtung, senkrecht zu den Schichten, aus der experimentellen Kleinwinkel-Streuungskurve berechnet. Diese Funktion wird mit derjenigen Funktion verglichen, welche für ein wechselweise aus kristallinen und amorphen Schichten bestehendes Modell berechnet worden ist. Es mußten zur Erreichung einer guten übereinstimmung ein Skalenfaktor und drei Parameter eingestellt werden. Im Skalenfaktor gelangt die mittlere Periodizität in der Richtung, senkrecht zu den Schichten zum Ausdruck. Die Parameter sind die Kristallinität und die Verteilungsbreite der Dicke der kristallinen, bzw. amorphen Schichten. Es wird ferner nachgewieser, daß vor allem die so ermittelte Kristallinität durch sogar relativ große Abweichungen vom primären Modell nur unwesentlich beeinflußt wird.

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With 6 figures in 7 details     

X-ray small-angle scattering of bulk polyethylene

Summary A previously described method for evaluating X-ray small-angle scattering curves was applied to a number of well-characterized polyethylene samples. The average thicknesses of the crystalline and amorphous layers were estimated by this method; furthermore, the mean square of the density fluctuations within the samples was determined from the integral small-angle scattering. From these data, combined with the overall densities of the samples, the densities of the crystalline and amorphous layers were calculated; these densities compare well with the figures generally assumed for a two-phase structure.The effects of molecular weight and cooling rate on the thicknesses of the crystalline and amorphous layers are noted, and the thicknesses of the crystalline layers are compared with the melting points of the samples.Finally, a discussion is given of the errors which may be involved ifBragg's law is applied to small-angle scattering curves.

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Zusammenfassung Eine bereits früher beschriebene Methode zur Bewertung von Röntgen-Kleinwinkelstreuungskurven wird auf eine Anzahl genau charakterisierter Polyäthylenproben angewandt. An Hand dieser Methode wird die mittlere Dicke der kristallinen und amorphen Schichten geschätzt; ferner wird an Hand der Integral-Kleinwinkelstreuung das mittlere Quadrat der Dichteschwankungen in den Proben bestimmt. Aus den so erhaltenen Unterlagen und Gesamtdichten der Proben werden die Dichten der kristallinen und amorphen Schichten berechnet; diese Werte entsprechen durchaus den im allgemeinen für eine Zweiphasenstruktur angenommenen Zahlen.Es wird der Einfluß von Molekulargewicht und Kühlgeschwindigkeit auf die Dicke der kristallinen und amorphen Schichten angegeben; außerdem werden die Dicken der kristallinen Schichten mit den Schmelzpunkten der Proben verglichen. Schließlich werden die Fehler erörtert, welche sich bei Anwendung desBragg-schen Gesetzes auf Kleinwinkelstreuungskurven ergeben.

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With 6 figures in 7 details and 2 tables     

Simultaneous small-angle X-ray scattering and wide-angle X-ray diffraction

The simultaneous SAXS/WAXD technique is shown to provide an unambiguous method for following structural changes taking place during the programmed heating of a range of multiphase polymeric materials. Results are given for polyethylene, block copolyurethanes and block copolyesters containing liquid crystalline hard segments. UK Thermal methods Group Award Lecture     

The effect of spherulitic truncation on small-angle light scattering

The effects of spherulitic truncation on the H_v small-angle light-scattering (SALS) patterns are determined by computer simulation of spherulite nucleation and growth. The simulation is carried out for simultaneous and sporadic nucleation of two-dimensional spherulites and simultaneous nucleation of three-dimensional spherulites. The scattered intensity differences between truncated spherulites and round spherulites are determined as functions of the type of growth and the volume (or area) fraction of spherulites. Methods for the determination of certain geometrical characteristics of spherulites systems by SALS are developed. These characteristics include the volume (or area). fraction of spherulites, the average spherulite radius, and the average spherulite volume (or area). The results of this study are essential in the quantitative analysis of H_v SALS from spherulitic systems. The simulation process is readily extendable to the examination of other morphological phenomena by SALS.     

Understanding fluorine-free electrolytes via small-angle X-ray scattering

Fluorine-free electrolytes have attracted great attention because of its low-cost and environmental friendliness. However, so far, little is known about the solution structures of these electrolytes. Here,we compare the solvation phenomenon of sodium tetraphenylborate(NaBPh₄) salt dissolved in organic solvents of propylene carbonate(PC), 1,2-dimethoxyethane(DME), acetonitrile(ACN) and tetrahydrofuran(THF). Small-angle X-ray scattering(SAXS) reveals a unique two-peak structural feature...     

Investigation of humate-cetyltrimethylammonium complexes by small-angle X-ray scattering

The structural examination of the complexes formed between humic acid and cationic surfactants has environmental implications. A humic acid (HA) dissolved in 0.1 M NaOH (5 g/L) was reacted with a cationic surfactant (hexadecyltrimethylammonium bromide or CTAB) at initial solution concentrations of 1, 5, 10, 20, 30, 40 and 50 mM. The HA precipitated at CTAB concentrations of 20, 30, and 50 mM but the complexes were soluble at 40 mM and below 20 mM. The charge neutralization between humic acid anions and CTAB micelles and the subsequent charge reversal due to hydrophobic interactions explain the behavior of the HA-CTAB complexes. The HA solution (5 g/L), reaction products (supernatants and precipitates), and pure cationic surfactant solutions were studied by the small-angle X-ray scattering (SAXS) technique in order to determine the structure of HA-CTAB complexes. The scattering intensity (I(q)) of various HA-CTAB systems were recorded over a range of scattering vectors (q=0.053-4.0 nm(-1)). HA forms networks in an alkaline solution with a characterization length of 7.8 nm or greater. The HA-CTAB precipitates and the 50-mM CTAB solution gave d(100) and d(110) reflections of a hexagonal structure. The hexagonal array of cylindrical CTAB micelles has a lattice parameter of 5.01 nm in pure solution, and the parameter decreases in the order: 4.96, 4.91, and 4.85 nm for the precipitates of HA-CTAB (50, 30, and 20 mM, respectively), indicating that the structure of CTAB micelles was disturbed by the addition of HA. The molecular properties and behavior of HA in solution were discussed.     

Size-exclusion chromatography combined with small-angle X-ray scattering optics

Size-exclusion chromatography with on-line synchrotron radiation solution small-angle X-ray scattering optics, absorbance and/or refractive index detectors was evaluated by protein characterizations. The radius of gyration value and zero-angle scattering intensity of protein molecules eluted from the chromatography column were estimated using this measurement system. In addition, the characterization of the conformation of the eluted proteins was demonstrated for hen egg lysozyme and bovine submaxillary mucin. The present technique will be useful for not only the determination of the radius of gyration value and molecular weight of proteins with dimensions of 1–10 nm, but also for the structural characterization of the macromolecules during the chromatography.     

Sas_analyzer software for small-angle X-ray scattering data treatment

New approaches to the analysis of small-angle X-ray scattering data from nanoscale systems based on the optimization and direct multiple shooting methods are presented. A program is developed, which bears on these new approaches and allows a user to model small-angle X-ray diffraction data, introduce collimation corrections, and analyze dispersions in the samples. The program results for a number of typical nanosized systems (sols, catalysts) are reported and the comparison with currently available programs for small-angle data processing is presented.     

Structural characterization of flexible proteins using small-angle X-ray scattering

Structural analysis of flexible macromolecular systems such as intrinsically disordered or multidomain proteins with flexible linkers is a difficult task as high-resolution techniques are barely applicable. A new approach, ensemble optimization method (EOM), is proposed to quantitatively characterize flexible proteins in solution using small-angle X-ray scattering (SAXS). The flexibility is taken into account by allowing for the coexistence of different conformations of the protein contributing to the experimental scattering pattern. These conformers are selected using a genetic algorithm from a pool containing a large number of randomly generated models covering the protein configurational space. Quantitative criteria are developed to analyze the EOM selected models and to determine the optimum number of conformers in the ensemble. Simultaneous fitting of multiple scattering patterns from deletion mutants, if available, provides yet more detailed local information about the structure. The efficiency of EOM is demonstrated in model and practical examples on completely or partially unfolded proteins and on multidomain proteins interconnected by linkers. In the latter case, EOM is able to distinguish between rigid and flexible proteins and to directly assess the interdomain contacts.     

Theory of tagged polymer method in small-angle X-ray scattering

Summary It was shown that the conformation of a single polymer chain in concentrated solutions and in undiluted state can be estimated from the small-angle X-ray scattering of randomly tagged polymer mixed in the systems. The randomly tagged polymer means the polymer containing heavy atoms at randomly selected positions along the molecule. The excess scattering of the tagged polymer is obtained by subtracting the scattering of the untagged polymer solution (or bulk) from that of the mixture solution (or bulk) containing the tagged and untagged polymers. The excess scattering obtained in this way contains the contributions of some undesirable cross terms of the scattering amplitude. The method for the experimental evaluation of these terms and the conditions under which these terms are negligible are discussed. It was found that the cross terms can be neglected when the contrast in scattering power between the tagged and untagged scattering units is sufficiently large, and the number of the tags per tagged molecule is not so small.The distribution of the tags in the tagged molecules was also taken into consideration. By averaging the theoretical scattered intensity over all possible positions of the tags, it was found that the excess scattering is practically proportional to the scattering function of the untagged polymer when the number of the tags per tagged molecule is not so small. Experimental verification of this theory was shown.It was also shown experimentally that the conformational change, which may be caused by the effect of the tags, can be eliminated by the extrapolation of the results obtained for a series of tagged polymers with various tag contents to zero tag content.With 2 figures     

A small-angle X-ray scattering study of bromine-containing latex particles

A small-angle X-ray scattering (SAXS) study of two-stage latices (TSL), composed of polystyrene (PS) and polytribromostyrene (PTBrS), is presented. The analysis of the scattering curves leads to the conclusion that the TSL particles have a concentric core-shell structure. When a PTBrS latex was used as a seed, its particles were overcoated with a PS shell during the second-stage polymerization. However, only a small portion of the seed particles were overcoated with a PTBrS shell when using a PS seed. The size distributions of the TSL and the PTBrS latex particles were determined from the scattering curves, using the method of Indirect Fourier Transformation. The resulting average radii were in good agreement with the values obtained from TEM observations. © 1996 John Wiley & Sons, Inc.     

Analysis of a polydisperse system using small-angle X-ray scattering

The small-angle X-ray data from a polydisperse solution of sodium silicate have been measured in the concentration range 3.6–169 mg/cm³ using aKratky camera. The following values of the particle parameters were obtained: the average radius of gyration =7.5 nm, the average particle weight =900 000, the average volume =671 nm³, and the average particle surface area =717 nm².From the above parameters and the apparent specific volume, analysed to be 0.422 cm³/g, the water content of the silicate particles was determined to be 3% (by weight).From small-angle X-ray measurements, performed on solutions exposed to a hydrodynamic field, it is indicated that at least the larger particles in the solution have a relatively symmetric shape. Based on this observation it was assumed that the particles in solution are spherical, and particle size distribution functions were calculated using a least-squares program. It was found that the distribution cannot be described by a simple function, such as aGaussian function; instead, the distribution follows a histogram with three local maxima.Dedicated to Prof. Dr. Dr.Otto Kratky, Graz, on the occasion of his 80th birthday.     

Interaction of blockcopolymer micelles as probed by small-angle neutron and by small-angle X-ray scattering

 The analysis of the interaction of micelles formed by a blockcopolymer is given by means of small-angle X-ray (SAXS) and small-angle neutron scattering (SANS). The blockcopolymer consists of poly(styrene) and poly(ethylene oxide) (molecular weight of each block: 1000 g/mol) and forms well-defined micelles (weight-association number: 400, weight-average diameter: 15.4 nm) in water. The internal structure has been studied previously (Macromolecules 29:4006 (1996)) by SAXS. There it has been shown that the micelles are spherical objects. The structure factor S(q) as a function of the scattering vector q (q=(4π/λ) sin (θ/2); λ: wavelength of the radiation in the medium; θ: scattering angle) can be extracted from both sets of small-angle scattering data (SANS: q≤0.4 nm^-1; SAXS: q≤0.6 nm^-1). It is shown that particle interaction in the present system can be described by assuming soft interaction which is modeled by a square-step potential. Received: 12 May 1997 Accepted: 9 July 1997     

Counting ions around DNA with anomalous small-angle X-ray scattering

The majority of charge-compensating ions around nucleic acids form a diffuse counterion "cloud" that is not amenable to investigation by traditional methods that rely on rigid structural interactions. Although various techniques have been employed to characterize the ion atmosphere around nucleic acids, only anomalous small-angle X-ray scattering (ASAXS) provides information about the spatial distribution of ions. Here we present an experimentally straightforward extension of ASAXS that can be used to count the number of ions around nucleic acids.     

Polysiloxane network formation observed by time-resolved small-angle X-ray scattering

Time-resolved small-angle X-ray scattering was observed on systems undergoing gelation. A polysiloxane network was used as a model system, where the polysiloxane network was formed by hydrosylation of VT-M with F4-C. The Flory-Stockmayer model for gelation was found to be satisfactory to describe the polysiloxane network formation. No inhomogeneous distribution of densely crosslinked region exists, and in this respect the gel formed by the polysiloxane network is homogeneous. The invariance of the correlation length ξ evaluated from the Lorenzian term suggests that the local network architecture would not change by gelation.     

High brilliance small-angle X-ray scattering applied to soft matter

This article reviews some recent applications of high brilliance small-angle X-ray scattering (SAXS) to soft matter and closely related systems in biology. Owing to the burgeoning literature in this field, examples presented are restricted to those exploiting the high brightness of the synchrotron source. Three types of experiments are discussed; (1) dynamic processes in systems driven out of equilibrium, (2) transient processes in extremely dilute systems, and (3) microbeam technique probing the local nanostructure of hierarchically organized specimens. In addition, recent advances in sample environments specifically adapted to microbeam applications are described. Present limitations and suggestions for future developments are discussed.     

Applications of small-angle X-ray scattering/small-angle neutron scattering and cryogenic transmission electron microscopy to understand self-assembly of surfactants

The self-assembling structures and dynamics of surfactants determine most of their macroscopic physicochemical properties and performances. Herein, we review recent work on the self-assembly of surfactants by small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS) in conjunction with cryogenic transmission electron microscopy (Cryo-TEM) from the perspective of researchers having only limited theoretical knowledge of these techniques but expert in surfactants. Emphasis is placed on the structural analysis of typical surfactant aggregates over a wide range of size scales from nanometers up to microns, including spherical and rod-like micelles, wormlike micelles, vesicles, liquid crystals and coacervates, by combining different numerical approaches to the treatment of small-angle scattering data with the direct Cryo-TEM imaging method. Furthermore, the complementarity between SAXS and SANS, and between the scattering techniques and Cryo-TEM, that is, specific contributions of these techniques, is also covered.