Tables for
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. 5.2, p. 156   | 1 | 2 |

Section 5.2.7. How to handle the solvent density

E. M. Westbrooka*

aMolecular Biology Consortium, Argonne, Illinois 60439, USA
Correspondence e-mail:

5.2.7. How to handle the solvent density

| top | pdf |

It is necessary to have an accurate estimate of the mean solvent density, [\rho_{s}], in ([link]). The Ficoll gradient-tube method is particularly convenient for this reason: the gradient can be made without any significant solute other than Ficoll. Since the free-solvent compartment of the crystal is entirely water, [\rho_{s} = \rho_{bs} = \rho_{fs} = 1.0 \hbox{ g ml}^{-1}]. Therefore, in Ficoll density gradients, the crystal density becomes [\rho_{o}], as defined in ([link]), and the packing number n can be calculated from [n = {VN_{o} \over M} {(\rho_{c} - 1) \over (1 - \overline{\upsilon}_{m})}. \eqno(]

Another way to set [\rho_{s} = 1.0 \hbox{ g ml}^{-1}] is to cross-link the crystals with glutaraldehyde (Quiocho & Richards, 1964[link]; Cornick et al., 1973[link]; Matthews, 1985[link]), making the crystals insoluble even in the absence of stabilizing solutes. Once cross-linked, crystals can be transferred to a water solution prior to the density measurement, thereby substituting water for its free solvent. Care must be taken with cross-linking, however. Overnight soaking in 2% glutaraldehyde solutions can substantially increase the crystal density, while destroying its crystalline order (Matthews, 1985[link]). Even 0.5% glutaraldehyde concentrations may change the observed density of some crystals if the exposure is for many hours – which may be necessary to render the crystal completely insoluble. Therefore, the densities observed from cross-linked crystals should be regarded with caution.

If it is necessary to carry out density measurements in an organic solvent gradient, then it is necessary in general to measure the crystal density at more than one free solvent density, since the relative volume fractions of the crystal's components are not known a priori. However, if this is a well behaved protein crystal, by setting [\overline{\upsilon}_{m} = 0.74 \hbox{ ml g}^{-1}], [V_{M} = 2.4\ \hbox{\AA}^{3} \hbox{ Da}^{-1}] and [w = 0.25] g bound water per g protein, one can guess the crystal's volume compartments to be: [\varphi_{m} = 0.51, \qquad \varphi_{fs} = 0.32, \qquad \varphi_{bs} = 0.17,]and the mean solvent density to use in ([link] would be [\rho_{s} \simeq 0.35 + 0.65 \rho_{fs}. \eqno( ]This may give reasonably reliable derivations for n in ([link]), with just one crystal-density measurement. Over-reliance on parameter estimates, however, can lead to bogus results, and ([link]) should be used with caution.


Cornick, G., Sigler, P. B. & Ginsberg, H. S. (1973). Characterization of crystals of type 5 adenovirus hexon. J. Mol. Biol. 73, 533–538.
Matthews, B. W. (1985). Determination of protein molecular weight, hydration, and packing from crystal density. Methods Enzymol. 114, 176–187.
Quiocho, F. A. & Richards, F. M. (1964). Intermolecular cross linking of a protein in the crystalline state: carboxypeptidase-A. Proc. Natl Acad. Sci. USA, 52, 833–839.

to end of page
to top of page