Effects of inert volume-excluding macromolecules on protein fiber formation. II. Kinetic models for nucleated fiber growth.

A sequential model for nucleated protein fiber formation is proposed that is similar in broad outline to models proposed previously (Thermodynamics of the Polymerization of Protein, Academic Press, New York, (1975); Biophys. J. 50 (1986) 583) but generalized to allow for thermodynamic nonideality resulting from a high degree of volume occupancy by inert macromolecular cosolutes (macromolecular crowding). The effect of volume occupancy on the rate of fiber formation is studied in the transition-state rate-limited regime through systematic variation of rate-limiting step (prenuclear oligomer formation, nucleus formation or fiber growth), shape of prenuclear oligomer, size of nucleus, extent of reversibility, nature of inert cosolute (hard globular particle or random coil polymer) and size of inert cosolute relative to that of fiber-forming protein. It is found that crowding can accelerate the rate of fiber formation by as much as several orders of magnitude. The extent of acceleration for a given degree of volume occupancy depends upon several factors, the most conspicuous of which is the stoichiometry of the nucleus. In contrast, the rate of redistribution of fiber length, which occurs on a much slower time scale than polymer formation, is found to be insensitive to the extent of crowding.