Molecular shapes from small-angle X-ray scattering: extension of the theory to higher scattering angles

Journal Article · Thu Feb 05 04:00:00 EST 2009 · Acta Crystallographica. Section A, Foundations of Crystallography

DOI:https://doi.org/10.1107/s0108767309003237· OSTI ID:1060425

Shneerson, V. L. ^[1]; Saldin, D. K.

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1. University of Wisconsin-Milwaukee

A low-resolution shape of a molecule in solution may be deduced from measured small-angle X-ray scattering I(q) data by exploiting a Hankel transform relation between the coefficients of a multipole expansion of the scattered amplitude and corresponding coefficients of the electron density. In the past, the radial part of the Hankel transform has been evaluated with the aid of a truncated series expansion of a spherical Bessel function. It is shown that series truncation may be avoided by analytically performing the radial integral over an entire Bessel function. The angular part of the integral involving a spherical harmonic kernel is performed by quadrature. Such a calculation also allows a convenient incorporation of a molecular hydration shell of constant density intermediate between that of the protein and the solvent. Within this framework, we determine the multipole coefficients of the shape function by optimization of the agreement with experimental data by simulated annealing.

• Research Organization: Univ. of Wisconsin, Milwaukee, WI (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• DOE Contract Number: FG02-84ER45076
• OSTI ID: 1060425
• Report Number(s): DOE/FG02/84ER45076; MIL100474
• Journal Information: Acta Crystallographica. Section A, Foundations of Crystallography, Journal Name: Acta Crystallographica. Section A, Foundations of Crystallography Journal Issue: 2 Vol. 65; ISSN 0108-7673
• Publisher: International Union of Crystallography
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
Molecular shapes Small-angle x-ray scattering