# A direct approach to estimate the anisotropy of protein structures from small-angle X-ray scattering

## Abstract

In the field of small-angle X-ray scattering (SAXS), the task of estimating the size of particles in solution is usually synonymous with the Guinier plot. The approximation behind this plot, developed by Guinier in 1939, provides a simple yet accurate characterization of the scattering behavior of particles at low scattering angle or momentum transferq, together with a computationally efficient way of inferring their radii of gyrationR _{G}. Moreover, this approximation is valid beyond spherical scatterers, making its use ubiquitous in the SAXS world. However, when it is important to estimate further particle characteristics, such as the anisotropy of the scatterer's shape, no similar or extended approximations are available. Existing tools to characterize the shape of scatterers rely either on prior knowledge of the scatterers' geometry or on iterative procedures to infer the particle shapeab initio. In this work, a low-angle approximation of the scattering intensityI(q) for ellipsoids of revolution is developed and it is shown how the size and anisotropy information can be extracted from the parameters of that approximation. The goal of the approximation is not to estimate a particle's full structure in detail, and thus this approach will be less accurate than well known iterative andab initioreconstruction toolsmore »

- Authors:

- Publication Date:

- Research Org.:
- Energy Frontier Research Centers (EFRC) (United States). Center for Direct Catalytic Conversion of Biomass to Biofuels (C3Bio); Purdue Univ., West Lafayette, IN (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1566704

- DOE Contract Number:
- SC0000997

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Applied Crystallography (Online)

- Additional Journal Information:
- Journal Volume: 52; Journal Issue: 2; Journal ID: ISSN 1600-5767

- Publisher:
- International Union of Crystallography

- Country of Publication:
- United States

- Language:
- English

- Subject:
- catalysis (homogeneous), catalysis (heterogeneous), biofuels (including algae and biomass), bio-inspired, materials and chemistry by design, synthesis (self-assembly), synthesis (scalable processing)

### Citation Formats

```
Roig-Solvas, Biel, Brooks, Dana, and Makowski, Lee.
```*A direct approach to estimate the anisotropy of protein structures from small-angle X-ray scattering*. United States: N. p., 2019.
Web. doi:10.1107/s1600576719000918.

```
Roig-Solvas, Biel, Brooks, Dana, & Makowski, Lee.
```*A direct approach to estimate the anisotropy of protein structures from small-angle X-ray scattering*. United States. doi:10.1107/s1600576719000918.

```
Roig-Solvas, Biel, Brooks, Dana, and Makowski, Lee. Tue .
"A direct approach to estimate the anisotropy of protein structures from small-angle X-ray scattering". United States. doi:10.1107/s1600576719000918.
```

```
@article{osti_1566704,
```

title = {A direct approach to estimate the anisotropy of protein structures from small-angle X-ray scattering},

author = {Roig-Solvas, Biel and Brooks, Dana and Makowski, Lee},

abstractNote = {In the field of small-angle X-ray scattering (SAXS), the task of estimating the size of particles in solution is usually synonymous with the Guinier plot. The approximation behind this plot, developed by Guinier in 1939, provides a simple yet accurate characterization of the scattering behavior of particles at low scattering angle or momentum transferq, together with a computationally efficient way of inferring their radii of gyrationRG. Moreover, this approximation is valid beyond spherical scatterers, making its use ubiquitous in the SAXS world. However, when it is important to estimate further particle characteristics, such as the anisotropy of the scatterer's shape, no similar or extended approximations are available. Existing tools to characterize the shape of scatterers rely either on prior knowledge of the scatterers' geometry or on iterative procedures to infer the particle shapeab initio. In this work, a low-angle approximation of the scattering intensityI(q) for ellipsoids of revolution is developed and it is shown how the size and anisotropy information can be extracted from the parameters of that approximation. The goal of the approximation is not to estimate a particle's full structure in detail, and thus this approach will be less accurate than well known iterative andab initioreconstruction tools available in the literature. However, it can be considered as an extension of the Guinier approximation and used to generate initial estimates for the aforementioned iterative techniques, which usually rely onRGandDmaxfor initialization. This formulation also demonstrates that nonlinearity in the Guinier plot can arise from anisotropy in the scattering particles. Beyond ideal ellipsoids of revolution, it is shown that this approximation can be used to estimate the size and shape of molecules in solution, in both computational and experimental scenarios. The limits of the approach are discussed and the impact of a particle's anisotropy in the Guinier estimate ofRGis assessed.},

doi = {10.1107/s1600576719000918},

journal = {Journal of Applied Crystallography (Online)},

issn = {1600-5767},

number = 2,

volume = 52,

place = {United States},

year = {2019},

month = {2}

}

Works referenced in this record:

##
*DAMMIF*, a program for rapid *ab-initio* shape determination in small-angle scattering

journal, January 2009

- Franke, Daniel; Svergun, Dmitri I.
- Journal of Applied Crystallography, Vol. 42, Issue 2, p. 342-346

##
*PRIMUS*: a Windows PC-based system for small-angle scattering data analysis

journal, September 2003

- Konarev, Petr V.; Volkov, Vladimir V.; Sokolova, Anna V.
- Journal of Applied Crystallography, Vol. 36, Issue 5, p. 1277-1282

##
Determination of the regularization parameter in indirect-transform methods using perceptual criteria

journal, August 1992

- Svergun, D. I.
- Journal of Applied Crystallography, Vol. 25, Issue 4, p. 495-503