Rationalization of membrane protein crystallization with polyethylene glycol using a simple depletion model

Based on the importance of crystallizing membrane proteins in a rational way, cytochrome bc(1) complex (BC1) was crystallized using polyethylene glycol (PEG) as a sole crystallization agent. Interaction between protein-detergent complexes of BC1 was estimated by dynamic light scattering, and was compared with the numerical calculation using the Derjaguin-Landau-Verwey-Overbeek potential plus a depletion potential, without considering specific surface properties of the protein-detergent complexes. The experiments and calculation were found to be consistent and we obtained a relation between PEG molecular weight M and the range of depletion zone delta as delta approximately M(0.48+/-0.02). The stability of liquid phase of BC1 solutions was controlled by a ratio of (the range of depletion zone)/(the radius of a BC1 particle), which was consistent with recent theoretical predictions. The crystallization was most successful under a condition where the stability of the liquid phase changed from stable to unstable. The PEG molecular weight that fulfilled this condition coincided with the one used empirically to crystallize BC1 in the past by a number of groups. These results are compared to the fact that membrane proteins were often successfully crystallized close to the detergent cloud point.