Small Angle X-Ray Scattering

Small Angle Scattering of X-Rays

Small-angle scattering (SAS) of x-rays and neutrons is a fundamental tool in the study of biological macromolecules. The major advantage of the method lies in its ability to provide structural information about partially or completely disordered systems. SAS allows one to study the structure of native particles in near physiological environments and to analyse structural changes in response to variations in external conditions. In this review we concentrate on SAS studies of isotropic systems, in particular, solutions of biological macromolecules, an area where major progress has been achieved during the last decade. Solution scattering studies are especially important, given the challenge of the ‘post-genomic’ era with vast numbers of protein sequences becoming available. Numerous structural initiatives aim at large-scale expression and purification of proteins for subsequent structure determination using x-ray crystallography and NMR spectroscopy. Because of the requirement of good crystals for crystallography and the low molecular mass requirement of NMR, a significant fraction of proteins cannot be analysed using these two high-resolution methods. Progress in SAS instrumentation and novel analysis methods, which substantially improve the resolution and reliability of the structural models, makes the method an important complementary tool for these initiatives. The review covers the basics of x-ray and neutron SAS, instrumentation, mathematical methods used in data analysis and major modelling techniques. Examples of applications of SAS to different types of biomolecules (proteins, nucleic acids, macromolecular complexes, polyelectrolytes) are presented. A brief account of the new opportunities offered by third and fourth generation synchrotron radiation sources (time-resolved studies, coherent scattering and single molecule scattering) is also given.

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Small-angle scattering studies of biological macromolecules in solution

Publisher Summary Hydration can be considered a process of adding water incrementally to dry protein, until a level of hydration is reached beyond which further addition of water produces no change and only dilutes the protein. The hydration process has several stages and an end point, reflected similarly in different types of measurements. Time-average measurements appear to have a common pattern and most closely fit a single picture of the process. Dynamic measurements sometimes show a dependence on hydration level that lies outside the common pattern of the time-average results. The chapter summarizes the literature that bears on the protein hydration process and the hydration shell, categorized by type of measurement, and provides picture of the hydration process and the hydration shell and an assessment of the ways in which the hydration shell may modulate enzyme and other protein functions. The percolation model is discussed that focuses on the long-range connectivity established at a threshold coverage of a surface or volume with conducting or otherwise functional elements.

Protein hydration and function.

Analytical ultracentrifugation (AU) is reemerging as a versatile tool for the study of proteins. Monitoring the sedimentation of macromolecules in the centrifugal field allows their hydrodynamic and thermodynamic characterization in solution, without interaction with any matrix or surface. The combination of new instrumentation and powerful computational software for data analysis has led to major advances in the characterization of proteins and protein complexes. The pace of new advancements makes it difficult for protein scientists to gain sufficient expertise to apply modern AU to their research problems. To address this problem, this review builds from the basic concepts to advanced approaches for the characterization of protein systems, and key computational and internet resources are provided. We will first explore the characterization of proteins by sedimentation velocity (SV). Determination of sedimentation coefficients allows for the modeling of the hydrodynamic shape of proteins and protein complexes. The computational treatment of SV data to resolve sedimenting components has been achieved. Hence, SV can be very useful in the identification of the oligomeric state and the stoichiometry of heterogeneous interactions. The second major part of the review covers sedimentation equilibrium (SE) of proteins, including membrane proteins and glycoproteins. This is the method of choice for molar mass determinations and the study of selfassociation and heterogeneous interactions, such as protein–protein, protein–nucleic acid, and protein–small molecule binding.

/pdf/modern-analytical-ultracentrifugation-in-protein-science-a-svev0tssfn.pdf

Modern analytical ultracentrifugation in protein science: A tutorial review

Publisher Summary The partial specific volume of a solute is a characteristic parameter that can be used in investigations of protein associations and changes in conformation, as well as in studies on protein solvent interactions and various other intermolecular interactions. It provides information needed for the determination of particle mass by means of ultracentrifugation and small-angle X-ray scattering. The precision density measurement in the apparatus described in the chapter is based on the determination of the natural frequency of an electronically excited, mechanical oscillator, its effective mass being composed of its own unknown mass and the well-defined, but also unknown, volume of the sample under investigation. To assure that this volume be well defined, the oscillator is made of a hollow, U-shaped glass tube that can be filled with the liquid sample. The mode of vibration is that of a bending-type oscillator. The positions of its vibrating nodes, which in fact determine the limits of the volume of sample taking part in the motion, is kept stable by the abrupt change in the cross-section of the glass tubes.

The determination of the partial specific volume of proteins by the mechanical oscillator technique.

Publisher Summary This chapter discusses small-angle scattering experiments with particles in solution—i.e., the particles are nonoriented. A large number of particles contribute to the scattering and the resulting spatial average leads to a loss in information. The information contained in the three-dimensional electron density distribution is thereby reduced to the one-dimensional distance distribution function. This function is proportional to the number of lines with length, which connect any volume element i with any volume element k of the same particle. The spatial orientation of these connection lines is of no account to the function. The connection lines are weighted by the product of the number of electrons situated in the volume elements i and k , respectively. The correlation between the function and the structure of the particle is also discussed in the chapter. The connection between the distance distribution function and the measured experimental scattering curve is also shown. It is observed that the each distance between two electrons of the particle, which is part of the function, leads to an angular-dependent scattering intensity. This physical process of scattering can be mathematically expressed by a Fourier transformation, which defines the way in which the information in “real space” (distance distribution function) is transformed into “reciprocal space” (scattering function). The chapter also discusses monochromatization and the camera type developed in Graz.

[11] Small-angle x-ray scattering

Eine neue Methode zur Präzisionsmessung der Dichte von Flüssigkeiten

X-ray small angle scattering was performed on solutions of the bacteriophages fr and R17. The scattering curves of the phages are nearly identical. The radius of gyration was found to be 105.2 A, the molecular weight as obtained from a high precision measurement is 3.62 × 106. The radial excess electron density distribution, derived from measurements in 0.02 M Tris-Cl buffer pH 7.2 containing 0.15 M NaCl and 1 mM EDTA, indicates that the phages have a mean outer radius of 131.7 A and consist of a shell and a less dense core. The core consists of RNA as is shown by measurements in sucrose solutions. It contains only about 80% of the RNA, the remaining 20% are considered to penetrate into the shell. Models calculated assuming the mean outer radius of the RNA to be 107.8 A yield a mean inner radius of the protein shell of 104.9 A. The amount of water associated with the phages is found to be about 0.9 g/g.

https://febs.onlinelibrary.wiley.com/doi/pdf/10.1111/j.1432-1033.1971.tb01206.x

An X‐Ray Small Angle Study of the Bacteriophages fr and R17

Structural changes of yeast glyceraldehyde-3-phosphate dehydrogenase as a function of saturation with NAD have been measured with the X-ray small-angle scattering technique. Samples of yeast glyceraldehyde-3-phosphate dehydrogenase were investigated at pH 8.5 and 40° and five different degrees of saturation with the coenzyme NAD (degree of saturation Y = 0, 0.23, 0.46, 0.72, 0.99). Because of the temperature-sensitivity of the sample, the use of a special flow device became necessary to keep the time of exposure of the samples to 40° and to X-ray irradiation below 1 h.



Apo-enzyme revealed a contraction in volume depending upon the degree of saturation. Fully saturated the contraction amounts to 7%. As the observed degree of contraction is not linearly proportional to the degree of saturation, the simple sequential mechanism cannot explain the observations. To the extent that they coincide with the quantitative predictions of the allosteric model for this particular enzyme, based on calculations involving the equilibrium constants obtained from chemical relaxation experiments under identical conditions, they strongly support the latter mechanism.



Comparison of the experimental scattering curves with theoretical scattering curves of compact full cylinders did not bring about satisfactory agreement in the range of the first submaximum. Hollow circular cylinders with h:2r1= 0.6:1 (apo-enzyme) or h:2r1= 0.58:1 (holo-enzyme) may be regarded as sufficiently equivalent in scattering as far as the form of the main maximum is concerned as well as the position and relative intensity of the submaximum. Even if the molecule consists of four subunits they consequently must be arranged in such a way that the entire particle is very similar to a hollow cylinder.



The experimental determination of the radius of gyration (R= 32.1 A in the case of the apo-enzyme, or 31.7 A in the case of the holo-enzyme) leads to the calculation of the absolute particle dimensions: Apo-enzyme: h= 48.5 A, r1= 40.4 A, r2= 6.1 A, Holo-enzyme: h= 46.4 A, r1= 40.2 A, r2= 6.0 A.



The nature of the structural changes occuring in the allosteric transition can now be described in terms of an increase of the inherent anistropy and of a considerable decrease in the solvent included in the tetrameric assembly.



Exposure of the enzyme to 40° over a longer period of time leads to significant alterations in the scattering curves. These can be interpreted on the basis of growing aggregates in polydisperse solutions. This process is accompanied by a considerable decrease of enzyme activity.

https://febs.onlinelibrary.wiley.com/doi/pdf/10.1111/j.1432-1033.1971.tb01282.x

O. Kratky

Papers

The determination of the partial specific volume of proteins by the mechanical oscillator technique.

[11] Small-angle x-ray scattering

Eine neue Methode zur Präzisionsmessung der Dichte von Flüssigkeiten

An X‐Ray Small Angle Study of the Bacteriophages fr and R17

X-ray small-angle scattering of yeast glyceraldehyde-3-phosphate dehydrogenase as a function of saturation with nicotinamide-adenine-dinucleotide.