QUANTITATIVE-ANALYSIS IN THE CHARACTERIZATION AND OPTIMIZATION OF PROTEIN CRYSTAL-GROWTH

Protein crystal growth often depends on the combination of many differ ent factors. Some affect protein solubility directly; others may act i ndirectly by causing conformational changes. Systematic characterizati on of these factors can be important for generating good crystals. It can also provide useful insight into the biochemical behavior of the p rotein being crystallized. Here we focus on statistical methods to ach ieve these two objectives. (1) Characterization of a protein system by analyzing patterns of crystal polymorphism under different levels of biochemical parameters, such as ligands and pH. Tests of the reproduci bility of crystal growth experiments indicate that quantitative scales of crystal quality can be statistically significant. Analysis of vari ance for a replicated, full-factorial design in which four factors wer e tested at two levels has been used to demonstrate highly significant , biochemically relevant, two-factor interactions strongly implicating pH and ligand-dependent conformational changes. (2) Optimization of c rystal growth via response-surface methods. 'Minimum predicted varianc e' designs provide for efficient response-surface experiments aimed at constructing quadratic models in several dimensions. We have used suc h models to improve crystal size and quality significantly for three f orms of Bacillus stearothermophilus tryptophanyl-tRNA synthetase. In o ne case we can now avoid having to increase the size by repeated seedi ng, a difficult procedure that also produces unwanted growth of satell ite crystals. Graphs of two-dimensional level surfaces reveal a number of ridges, where the same result is obtained for many combinations of the factors usually varied when trying to improve crystals. An import ant inference is that it may be better to sample simultaneously for th e effects of protein concentration and supersaturation. For a system i nvolving only one crystallizing agent, supersaturation can be approxim ated as the product of protein and precipitant concentrations. Use of this search direction significantly improves the performance of respon se-surface experiments. Advantages of growing crystals at stationary p oints of their response surfaces include better crystals and higher re producibility, since crystal growth at stationary points is insulated from the deleterious effects of experimental fluctuations. This arises because the derivatives of the response are by definition zero with r espect to the experimental variables. Quantitative analysis of appropr iately designed crystal growth experiments can thus be a powerful way to characterize complex and interacting biochemical dependencies in ma cromolecular systems and optimize parameters important to the crystall ography.