Section 15.1.2.1.1. Introduction

Biological molecules are typically irregular in shape, often taking roughly globular forms. When they are packed regularly to form a crystal lattice, there are gaps left between them, and these spaces are filled with the solvent in which the crystallization was performed. This solvent is a disordered liquid, and thus the arrangement of atoms in the solvent regions varies between unit cells, except in those small regions near the surface of the protein. The X-ray image forms an average of electron density over many cells, so the electron density over much of the solvent region appears to be constant to a good approximation.

The existence of a flat solvent region in a crystal places strong constraints on the structure-factor phases. The constraint of solvent flatness is implemented by identifying the molecular boundaries and replacing the densities in the solvent region by their mean density value.

When solving a structure, the contents of the unit cell are usually known, and so an estimate can be formed of how much of the cell volume is taken up by solvent (Matthews, 1968). If the solvent region can be located in the cell, then we can improve an electron-density map by setting the electron density in this region to the expected constant solvent density. Once the resulting modified phases are combined with the experimental data, an improvement can often be seen in the protein regions of the map (Bricogne, 1974).

The solvent region of a unit cell may usually be determined even from a poor MIR map using the following features:

A good method for locating the solvent region therefore takes into account information from both low- and high-resolution structure factors. Many methods have been proposed to locate the protein–solvent boundary. The first of these were the visual identification methods. The boundary was identified by digitizing a mini-map with the aid of a graphic tablet (Hendrickson et al., 1975; Schevitz et al., 1981). The hand-digitizing procedure was very time-consuming and prone to subjective judgmental errors. Nevertheless, these methods demonstrated the potential of solvent flattening and stimulated further improvement on boundary-identification methods. An automated method using a linked, high-density approach was first proposed by Bhat & Blow (1982). Based on the fact that the densities are generally higher in the protein region than in the solvent region, they defined the molecular boundary by locating the protein as a region of linked, high-density points.

Convolution techniques were subsequently adopted as an efficient method of molecular-boundary identification. Reynolds et al. (1985) proposed a high mean absolute density value approach. The electron density within the protein region was expected to have greater excursions from the mean density value than the solvent region, which is relatively featureless. The molecular boundary was located based on the value of a smoothed `modulus' electron density, which is the sum of the absolute values of all density points within a small box.