Theoretical description of the spatial dependence of sickle hemoglobin polymerization

We have generalized the double nucleation mechanism of Ferrone et al. (Ferrone, F. A., J. Hofrichter, H. Sunshine, and W. A. Eaton. 1980. Biophys. J. 32:361-377; Ferrone, F. A., J. Hofrichter, and W. A. Eaton. 1985. J. Mol. Biol. 183:611-631) to describe the spatial dependence of the radial growth of polymer domains of sickle hemoglobin. Although this extended model requires the consideration of effects such as monomer diffusion, which are irrelevant to a spatially uniform description, no new adjustable parameters are required because diffusion constants are known independently. We find that monomer diffusion into the growing domain can keep the net unpolymerized monomer concentration approximately constant, and in that limit we present an analytic solution of the model. The model shows the features reported by Basak, S., F. A. Ferrone, and J. T. Wang (1988. Biophys J. 54:829-843) and provides a new means of determining the rate of polymer growth. When spatially integrated, the model exhibits the exponential growth seen in previous studies, although molecular parameters derived from analysis of the kinetics assuming uniformity must be modified in some cases to account for the spatially nonuniform growth. The model developed here can be easily adapted to any spatially dependent polymerization process.