International
Tables for
Crystallography
Volume F
Crystallography of biological macromolecules
Edited by E. Arnold, D. M. Himmel and M. G. Rossmann

International Tables for Crystallography (2012). Vol. F, ch. 10.1, p. 243   | 1 | 2 |

Section 10.1.2.3. Effect on resolution

H. Hopea* and S. Parkinb

aDepartment of Chemistry, University of California, Davis, One Shields Ave, Davis, CA 95616–5295, USA, and bDepartment of Chemistry, University of Kentucky, Lexington, Kentucky, USA
Correspondence e-mail:  hhope@ucdavis.edu

10.1.2.3. Effect on resolution

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The effects on radiation damage and mechanical stability are clear-cut, and provide the main reasons for using cryotechniques. Resolution can also be affected, but the connection between temperature and resolution is neither simple nor obvious.

In any crystal, the Boltzmann distribution law is an important factor in determining the accuracy of the replication of structure from one unit cell to another. For many small-molecule crystals, just one arrangement corresponds to a distinct energy minimum. The result is a well ordered structure. With macromolecules, the typical situation is one where a number of arrangements correspond to similar energies. Accordingly, a number of atomic arrangements will be expressed in the crystal. Although the relative values of local minima depend on the temperature, one cannot count on a significant change in ordering by cooling the crystal. Instead, some distribution will be frozen in.

If poor resolution is the result of rapid radiation damage, data collection at cryotemperature can lead to much improved resolution. However, if poor resolution is caused mainly by inexact replication from one unit cell to another, lowering the temperature may have little effect on resolution. If the mosaic spread in the crystal increases upon cooling, resolution may even deteriorate.

In a model proposed by Hope (1988[link]), a relationship between resolution r and temperature T is given by [r_{2} = r_{1}[(B_{0} + bT_{2})/(B_{0} + bT_{1})]^{1/2}.]Here [r_{1}] is the resolution at [T_{1}], [r_{2}] is the resolution at [T_{2}], [B_{0}] is the value of B at [T = 0] and b is a proportionality constant. There are two underlying assumptions: (1) the overall atomic distribution does not change significantly with temperature and (2) for any given T, the temperature factor [i.e. [\exp(-B\sin^{2}\theta/\lambda^{2})]] at the resolution limit has the same value; thus the effects of scattering factors and Lorentz–polarization factors are ignored. We see that if [B_{0}] is the predominant term, lowering T will not have much effect, whereas for small [B_{0}] (a relatively well ordered structure) the effect of T on r can be large. For example, if the room-temperature resolution is 1.5 Å, the resolution at 100 K can be around 1 Å, but if the room-temperature resolution is around 3 or 4 Å, little change can be expected. A qualitative assessment of these effects was clearly stated by Petsko (1975)[link].

References

Hope, H. (1988). Cryocrystallography of biological macromolecules: a generally applicable method. Acta Cryst. B44, 22–26.
Petsko, G. A. (1975). Protein crystallography at sub-zero temperatures: cryoprotective mother liquors for protein crystals. J. Mol. Biol. 96, 381–392.








































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