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. 153   | 1 | 2 |

Section 5.2.5. Experimental estimation of hydration

E. M. Westbrooka*

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

5.2.5. Experimental estimation of hydration

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During refinement of crystal structures, crystallographers must decide how many solvent molecules are actually bound to the macromolecule and for which refined coordinates are meaningful. The weight fraction of bound solvent to macromolecule in the crystal, w, is estimated for most protein crystals to be about 0.25 (Matthews, 1974[link], 1985[link]). However, its true value can be derived experimentally in the following manner. Since all relevant studies identify the bound solvent as water, it is reasonable to set the density of bound solvent as [\rho_{bs} = 1.0 \ \hbox{g ml}^{-1}]. Therefore, w can be expressed algebraically as [w = {m_{bs} \over m_{m}} = {\varphi_{bs} \rho_{bs} \overline{\upsilon}_{m} \over \varphi_{m}} = {\varphi_{bs} \overline{\upsilon}_{m} \over \varphi_{m}}. \eqno(]For crystals in which the rules-of-thumb [w = 0.25] and [\overline{\upsilon}_{m} = 0.74 \ \hbox{cm}^{3} \hbox{ g}^{-1}] are valid, ([link]) implies that bound solvent occupies about one-third of the volume occupied by protein.

The crystal density, [\rho_{c}], changes linearly with the density of free solvent surrounding the crystal. Let [\rho_{o}] be defined as the density the crystal would have if all its solvent were pure water [(\rho_{s} = 1.0\hbox{ g ml}^{-1})]: [\rho_{o} = 1 + \varphi_{m} (1/\overline{\upsilon}_{m} - 1). \eqno(]A plot of crystal density against density of the supernatant (free solvent) solution should be a straight line with an intercept (at [\rho_{fs} = 1.0\hbox{ g ml}^{-1}]) of [\rho_{o}] and a slope of [\varphi_{fs}]. Therefore, by making a few crystal-density measurements, each with the crystal first equilibrated in solutions of varying densities, experimental values for [\rho_{o}] and [\varphi_{fs}] can be derived. If the partial specific volume is known for this molecule, [\varphi_{m}], [\varphi_{bs}] and w can be derived from the expressions above. This approach was used by Coleman & Matthews (1971[link]) and Matthews (1974[link]) to measure molecular weights of six crystalline proteins, assuming [w = 0.25], but their measurements could alternatively have assigned more accurate values to w, had the molecular weights been previously known. Scanlon & Eisenberg (1975[link]) measured w for four protein crystals by this method (values betwen 0.13 and 0.27 were observed) and also confirmed that bound solvent exhibited a density of [1.0 \hbox{ g ml}^{-1}].


Coleman, P. M. & Matthews, B. W. (1971). Symmetry, molecular weight, and crystallographic data for sweet potato β-amylase. J. Mol. Biol. 60, 163–168.
Matthews, B. W. (1974). Determination of molecular weight from protein crystals. J. Mol. Biol. 82, 513–526.
Matthews, B. W. (1985). Determination of protein molecular weight, hydration, and packing from crystal density. Methods Enzymol. 114, 176–187.
Scanlon, W. J. & Eisenberg, D. (1975). Solvation of crystalline proteins: theory and its application to available data. J. Mol. Biol. 98, 485–502.

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