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.     

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.     

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.

---

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.

---

---

With 6 figures in 7 details and 2 tables     

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.

---

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.

---

---

With 6 figures in 7 details     

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.     

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.     

Calculation of small-angle neutron scattering by macromolecules in the semicrystalline state

Summary The conformation of macromolecules in the semicrystalline state has been studied by various authors with respect to the validity of the adjacent re-entry — or switchboard model by application of small-angle neutron scattering. Analytical as well as Monte-Carlo calculations show that the experimental results for melt crystallized polyethylene and isotactic polypropylene can be interpreted on the basis of the solidification model. In this model it is assumed that crystallization occurs by straightening of coil sequences without a long range diffusion process.

---

Zusammenfassung Die Konformation von Makromolekülen im teilkristallinen Zustand wurde von verschiedenen Autoren im Hinblick auf die Gültigkeit des adjacent re-entry- oder switchboard-Modells mit Hilfe der Neutronenkleinwinkelstreuung untersucht. Sowohl analytische Rechnungen als auch Monte-Carlo Rechnungen zeigen, dag die an schmelzkristallisiertem Polyäthylen und isotaktischem Polypropylen gefundenen experimentellen Ergebnisse auf der Basis des Erstarrungsmodells interpretiert werden können. In diesem Modell wird angenommen, daß sich Knäuelsequenzen wahrend der Kristallisation ausrichten, ohne dag weitreichende Diffusionsprozesse erfolgen.

---

---

With 8 figures and 3 tables     

Polymer characterization by size-exclusion chromatography with multiple detection.

Size-exclusion chromatography with coupled multiangle light scattering and differential refractometry detectors has been used to obtain molecular mass and radius of gyration distributions of polydisperse polymer samples. From these data the scaling law between dimensions and the absolute molecular mass is obtained with just one sample of each polymer. Three different kinds of polymers are presented: polystyrene which serves as reference polymer, polyphosphazenes which behave abnormally in solution and poly(ethylene oxide) which is soluble in water. Since the relationship between dimensions and molecular mass depends on the extent of interactions between chain segments and solvent molecules, the scaling law provides information about the solution properties of the polymer.     

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.     

Effect of draining of macromolecules on the results of size-exclusion chromatography measurements

Summary Using chromatographic analysis and viscometric investigations of polyamic acids, it has been shown that the linear relationship of the logarithm of intrinsic viscosity and the logarithm of molecular weight of flexible-chain macromolecules exhibits a break on passing from the oligomeric to the polymeric range. Simultaneously, the Huggins constant also changes. These changes result from a decrease in the draining of macromolecules with increasing number of statistical segments. In particular, draining affects the hydrodynamic dimensions determining the SEC-behavior of macromolecules. Semi-empirical expressions have been obtained for the Flory constant Φ and the constants in the Mark-Kuhn-Houwink equation as functions of the draining of macromolecules, the number of their statistical segments and the parameter of volume interaction characterizing the thermodynamic strength of solvent. For this purpose the solution of an integral equation for eigen-functions in the Zimm theory found by Tschoegl was applied.     

The combined use of size-exclusion and reversed-phase high-performance liquid chromatography for characterization of beta-endorphin processing pathways

A method is described for the separation and analysis of multiple molecular forms of immunoreactive beta-endorphin and its alpha-N-acetylated congeners by a combination of reversed-phase and size-exclusion high-performance liquid chromatography coupled with two specific radioimmunoassays. Both chromatographic procedures are fast (less than 50 min per analysis) providing good resolution and high recovery (greater than 90%). The solvents used in both systems are ultraviolet transparent (less than 214 nm), non-corrosive, low salt (less than 0.05 M) and after evaporation fully compatible with subsequent radioimmunoassay. We have evaluated these techniques using both synthetic and purified peptide standards and have applied these procedures to characterize immunoreactive beta-endorphin and alpha-N-acetylendorphin in rat and sheep pituitary extracts, and the low levels found in sheep hypothalamus and rat ovary. These chromatographic procedures are not only applicable to the study of pro-opiomelanocortin-derived peptides, but also could be employed to examine the processing pathways of other biologically active polypeptides, in both central and peripheral tissue extracts.     

X-ray microfocussing combined with microfluidics for on-chip X-ray scattering measurements

This work describes the fabrication of thin microfluidic devices in Kapton (polyimide). These chips are well-suited to perform X-ray scattering experiments using intense microfocussed beams, as Kapton is both relatively resistant to the high intensities generated by a synchrotron, and almost transparent to X-rays. We show networks of microchannels obtained using laser ablation of Kapton films, and we also present a simple way to perform fusion bonding between two Kapton films. The possibilities offered using such devices are illustrated with X-ray scattering experiments. These experiments demonstrate that structural measurements in the 1 A-20 nm range can be obtained with spatial resolutions of a few microns in a microchannel.     

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.     

The effect of crystallite shape on small-angle X-ray scattering

Summary Diffraction by a linear crystallite system was calculated to explain different shapes of small-angle reflections. The calculations show that various SAXS patterns observed can be obtained theoretically if the shape of certain crystallites are accounted for. Various reflection shapes can be explained chiefly by the changes in the crystallite shape and size. Dash, four-point and two-point reflections are associated with rectangular and oblique crystallite of small lateral dimensions. In the case of radial reflections the crystallite represents a plate and the fibril — a stack of plates. Structural changes in oriented samples with planar crystallite texture caused by shrinkage were studied. The principal process of shrinkage consists in the growth of lateral (with respect to the texture axis) crystallite dimensions and in their transformation into plates. Simultaneously the rotation of the macromolecule axis takes place. At the second stage of the shrinkage the layers twist around an axis perpendicular to the film plane. Then isotropic structure is formed. Transition between the two kinds of reflections are typical of various processes taking place in the course of polymer deformation and shrinkage.

---

Zusammenfassung Die Röntgen-Beugung eines Systems aus linearen Kristalliten wurde berechnet, um verschiedene Formen von Kleinwinkelreflexionen zu erklären. Die Berechnungen zeigen, daß die beobachteten verschiedenen SAX-Beugungsbilder theoretisch erhalten werden können, wenn die Form der verschiedenen Kristallite in geeigneter Weise gewählt wird. Verschiedene Beugung kann im wesentlichen mit Änderungen von Kristallitgestalt und -große gedeutet werden. Strich-, 2-Punkt- und 4-Punkt-Beugung sind mit rechteckigen und plättchenförmigen Kristalliten von kleinen lateralen Dimensionen verknüpft. Im Fall von radialen Reflektionen ist der einzelne Kristallit ein Plättchen, und eine Fibrille ist ein Stapel von Plättchen. Strukturänderungen in orientierten Proben mit planarer Kristallittextur, erzeugt durch Schrumpfung, wurden studiert. Der Hauptvorgang bei Schrumpfung besteht im Wachsen der lateralen (mit Hinblick auf die Texturachse) Kristallit-dimensionen und in ihrer Überführung in Plättchen. Gleichzeitig findet eine Drehung der Achsen der Makromoleküle statt. Im 2. Stadium der Schrumpfung schrauben sich die Schichten um eine Achse senkrecht zur Filmebene. Dann bildet sich die isotrope Struktur. Der Übergang zwischen den beiden Arten von Beugungen ist für die verschiedenen Prozesse typisch, die im Laufe einer Deformation und einer Schrumpfung von Polymeren stattfinden.

---

---

Dedicated to Prof.R. Hosemann on the occasion of his 60th birthday     

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.     

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     

Complexation of DNA with cationic surfactants as studied by small-angle X-ray scattering

The phase behaviors of the complex formed by didodecyldimethylammonium bromide(DDAB)and cetyltrimethylammonium bromide(CTAB)interacting with three different types of DNAs,salmon testes DNA(~2000 bp),21-bp double-stranded oligonucleotides(oligo-ds DNA),and 21-nt single-stranded oligonucleotides(oligo-ss DNA)were studied by synchrotron small-angle X-ray scattering.It was found that the DNA length and flexibility,together with the positive/negative charge ratio,determined the final structure.At higher charge ratios,the DNA length exhibited negligible effect.Both oligo-ds DNA and salmon DNA formed inverted hexagonal packing of cylinders with CTAB,as well as bilayered lamella with DDAB.However,at lower charge ratios,oligo-ds DNA formed a distorted hexagonal phase with CTAB and a new structure with DDAB,which was different from the behaviors of salmon DNA.The flexible oligo-ss DNA formed rich structures that were subject to environmental disturbance.Kinetic study also indicated that the structures of the complex formed by oligo-ss DNA took much longer to mature than the structures formed by oligo-ds DNA.We attributed this result to the conformational adjustment of oligo-ss DNA in the complex.     

Electron microscopy of oriented high-density polyethylene: Comparison with small-angle X-ray scattering

The morphology of cold-drawn, rolled and annealed high-density polyethylene was investigated by transmission electron microscopy of stained sections. From the electron micrographs, a model of the structure was developed and the scattering pattern calculated. This was then compared with the corresponding small-angle X-ray scattering (SAXS) pattern, in order both to aid in the interpretation of SAXS patterns of oriented polymers, and to assess the effects of staining with chlorosulphonic acid on the morphology.