KINETIC EFFECTS IN PROTEIN CRYSTALS .2. GEOMETRY AND MISALIGNMENT TOLERANCE WITH EXPERIMENTAL RESULTS

A geometric model for protein crystallization and attachment kinetics is considered. The tolerance for misalignment is found for random vers us preferred orientation. The protein growth unit can either be modell ed as a sphere or as a rough and stringy fractal. It is found that the larger surface area available for a fractal makes its attachment orie ntation more critical than for a solidly modelled protein. The magnitu de of such tolerance increases threefold compared with a simple sphere . The probability of successful (aligned) binding varies as the expone ntial of the number of attachment sites, so larger protein building bl ocks place a premium on correct orientation. Larger proteins (more res idues) or oligomeric growth units are thus predicted to show marked se nsitivity to solution conditions that favour or disfavour preferred or ientation. For an octameric (N = 8) fractal aggregate, these tolerance s reach a 1000-fold narrowing compared with single molecular spheres. Very weak electric fields (V) as low as 50D(2), where D is the surface diffusion coefficient, are found to be of the same order of magnitude as the randomizing surface diffusion and thus offer one experimentall y realizable condition for setting a particular molecular alignment. I n conclusion, protein geometry is found to be a significant factor in determining crystallization and attachment kinetics in solution-sensit ive growth.