International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. C. ch. 2.6, p. 111

Section 2.6.2.7.5. Model fitting

R. Mayb

2.6.2.7.5. Model fitting

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As in small-angle X-ray scattering, the scattering curves can be compared with those of simple or more elaborate models. This is rather straightforward in the case of highly symmetric particles like icosahedral viruses that can be regarded as spherical at low resolution. The scattering curves of such viruses are easily adapted by spherical-shell models assigning different scattering-length densities to the different shells (e.g. Cusack, 1984[link]). Neutron contrast variation helps decisively to distinguish between the shells.

Fitting complicated models to the scattering curves is more critical because of the averaging effect of small-angle scattering. While it is correct and easy to show that the scattering curve produced by a model body coincides with the measured curve, in general a unique model cannot be deduced from the scattering curve alone. Stuhrmann (1970a[link],b[link],c[link]) has presented a procedure using Lagrange polynomials to calculate low-resolution real-space models directly from the scattering information. It has been applied successfully to the scattering curves from ribosomes (Stuhrmann et al., 1976[link]).

References

First citation Cusack, S. (1984). Neutron scattering studies of virus structure. Neutrons in biology; basic life sciences, Vol. 27, edited by B. P. Schoenborn, pp. 173–188. New York: Plenum.Google Scholar
 First citation Stuhrmann, H. B. (1970a). Interpretation of small-angle scattering functions of dilute solutions and gases. A representation of the structures related to a one-particle-scattering function. Acta Cryst. A26, 297–306.Google Scholar
 First citation Stuhrmann, H. B. (1970b). Ein neues Verfahren zur Bestimmung der Oberflächenform und der inneren Struktur von gelösten globulären Proteinen aus Röntgenkleinwinkelmessungen. Z. Phys. Chem. 72, 177–184.Google Scholar
 First citation Stuhrmann, H. B. (1970c). Die Bestimmung der Oberflächenform von gelöstem Myoglobin aus Röntgenkleinwinkelmessungen. Z. Phys. Chem. 72, 185–198.Google Scholar
 First citation Stuhrmann, H. B., Haas, J., Ibel, K., de Wolf, B., Koch, M. H. J., Parfait, R. & Crichton, R. R. (1976). New low resolution model for 50S subunit of Escherichia coli ribosomes. Proc. Natl Acad. Sci. USA, 73, 2379–2383.Google Scholar








































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