Figure 2.

The central composite experimental design (Box & Hunter, 1957 ▶) shown in three dimensions. This is one of several well known multivariate designs that are recommended for optimizing processes that have several important experimental parameters. For example, protein concentration, temperature, pH, precipitant concentration, additive concentration etc. need to be optimized in protein crystallization experiments. Ideally, all of these parameters should be varied in each experimental run, and the central composite efficiently achieves this goal. This can find the best direction to move in, since several parameters may need to be adjusted simultaneously. The design comprises one or more centre points (red), which are the crystallizer’s ‘best guess’ for the best crystallization conditions (for example, a hit from a screening experiment). These points are surrounded by a set of ‘factorial’ points (green) and ‘axial’ points (blue). The details of the experiment are not important: the important principle is that the points surround the central point reasonably evenly in the multidimensional space. A three-dimensional version is shown in Fig. 2 ▶, but higher numbers of dimensions can be used. For example, six-dimensional central composites have been used in crystallization (Shaw Stewart & Baldock, 1999 ▶). Less formal designs that occupy several dimensions in the crystallization hyperspace can achieve similar results (see text for examples), although they may be more wasteful of time and materials.