1997
DOI: 10.1107/s0021889897001714
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Shape Determination from Solution Scattering of Biopolymers

Abstract: Practical aspects of low‐resolution shape determination in small‐angle scattering studies of biological macromolecules in solution are considered. The shape restoration method using spherical harmonics [Svergun, Volkov, Kozin & Stuhrmann (1996). Acta Cryst. A52, 419–426] is extended to account for deviations from the idealized model and to work directly on raw experimental data sets. An algorithm to restore the structure of homodimeric particles in terms of the shape of the monomer and the separation between t… Show more

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Cited by 65 publications
(69 citation statements)
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“…SAXS hRXR␣⌬AB tetramer models obtained by two independent ab initio approaches. a, upper row shows a superposition of the envelop model obtained by SASHA (34) to the average of ten DAM calculated by DAMMIN (31), and the lower row represents the superposition of the same ten DAM to the x-ray structure of the hRXR␣⌬ LBD tetramer (21) and four hRXR␣ DBDs (23). Grid space is 2 nm.…”
Section: Discussionmentioning
confidence: 99%
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“…SAXS hRXR␣⌬AB tetramer models obtained by two independent ab initio approaches. a, upper row shows a superposition of the envelop model obtained by SASHA (34) to the average of ten DAM calculated by DAMMIN (31), and the lower row represents the superposition of the same ten DAM to the x-ray structure of the hRXR␣⌬ LBD tetramer (21) and four hRXR␣ DBDs (23). Grid space is 2 nm.…”
Section: Discussionmentioning
confidence: 99%
“…In the first procedure (33,34), the shape is represented by an angular envelope function, parameterized in terms of spherical harmonics using multipole expansion methods (35). The maximum number of the spherical harmonics L is selected to keep the number of free parameters M ϭ (L ϩ 1) Ϫ 6 close to the number of Shannon channels N s ϭ D max q max / in the experimental data (36).…”
Section: Small-angle X-ray Scattering Measurements and Data Analysis-mentioning
confidence: 99%
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“…The multipole expansion method proposed by Stuhrmann (28) and developed by Svergun et al (29) was used to obtain the molecular shape of human ETF. The smoothed scattering profile of reduced human ETF was fitted ab initio by the scattering from an envelope function starting from an ellipsoidal initial approximation (consistent with the experimental R g and D max values).…”
Section: Methodsmentioning
confidence: 99%
“…Rotation of the monomer by the Euler angles ␣, ␤, and ␥, followed by its displacement by the vector r ϭ (r,,) and generation of all symmetry mates, permits one to construct a symmetric oligomer. The partial scattering amplitudes of the rotated and shifted monomer (B lm (s) ϭ B lm (s,␣,␤,␥,r)) can be analytically expressed via the amplitudes (A lm (s)) and the elements of the finite rotation matrix (25) as described (26). Assuming without loss of generality that the n-fold axis coincides with the z axis and that the 2-fold axis in the case of Pn2 symmetry coincides with the y axis, symmetry mate generation leads to selection rules for the spherical harmonics so that the scattering from the entire oligomer is as in Equation 4,…”
Section: Methodsmentioning
confidence: 99%