Protein crystallization using incomplete factorial experiments.

Abstract

We have studied the crystallization of Bacillus ste- arothermophilus tryptophan tRNA synthetase. Exper- imental conditions used in 35 different crystallization trials were chosen by systematic assignment of varia- bles in accordance with the two principles of randomi- zation and balance, which are characteristic of incom- plete factorial experiments. Polymorphism in the re- sulting precipitated, microcrystalline, or crystalline protein samples was identified and rated numerically on a rough but quantitative scale. Correlations between these estimates of crystal quality and all experimental variables were identified by stepwise multiple regres- sion analysis. Several variables proved to be signifi- cantly correlated with crystal quality. Having established a favorable precipitation proce- dure and ionic composition within broad limits, we next carried out a complete factorial experiment with four factors using two pH values and two temperatures in the presence or absence of two low molecular weight substrates, tryptophan and ATP. These experiments clearly established a favorable pH and produced large (0.5 mm) single crystals with each of the four possible substrate permutations. At least one crystal form, en- zyme plus tryptophan, is suitable for structural studies by x-ray diffraction. The factorial approach appears to be an advantageous alternative to classical controlled single factor and full factorial designs for establishing cause and effect relationships in protein crystallization. Rational exploration of cause and effect relationships gov- erning the crystallization of proteins has traditionally been eschewed, owing to the potentially very large number of controlled experiments required for a systematic study. The essential difficulty is that a number of different experimental conditions, pH, temperature, various mono- and divalent ions, and different organic solutes, may interact in apparently ca- pricious ways to provide a favorable environment in which crystals will eventually grow (an excellent review is Mc- Pherson, 1976a). Despite this seemingly overwhelming difficulty, small quan- tities of protein can be used quite efficiently by using the factorial approach to experimental design (Fisher, 1942). This approach is counter-intuitive: no attempt is made to identify the effects of varying individual factors by controlled experi- ments in which other factors remain constant. Rather, effi- ciency in a factorial experiment arises from two rather differ- * This work was supported by Research Grant GM21991 from the National Institutes of Health and by a fellowship in academic medi- cine from the Jefferson Pilot Corporation (C!. W. C. Jr.). The costs of publication of this article were defrayed in part by the payment of