Simulations of polymer crystallization and amyloid fibrillization
This dissertation describes computer simulations and theoretical analyses of polymer crystallization and amyloid fibrillization. Langevin Dynamics simulations of polymer chains in dilute solutions suggest that chains are prefolded before crystallization, in contradiction with the traditional view that chain folding occurs only on the growth front. The prefolded chain reveals a thickness plateau in low-temperature region (solving the puzzle of "δL catastrophe"), suggesting that lamellar thickness might be a predetermined equilibrium result. Based on the above prefolding and predetermined thickness concepts, the prefolded chains are then taken as the smallest dynamic units in Monte Carlo simulations, where an anisotropic aggregation model is proposed to study single crystals, shish-kebab crystals, and crystal melting. This model is further extended to amyloid fibrillization.
The single crystal study shows a rough-flat-rough habit transition, solving a long-standing puzzle for the existing theories. The lamellar growth rate is confirmed to vary exponentially with temperature and concentration. The shish-kebab study confirms that the distribution of kebab spacings is lognormal. In contrast to Pennings' and Hill's models, a new model is proposed to describe the relation between the spacing and temperature: the logarithm of the spacing growth rate is proportional to the inverse of temperature. The spacing is also found to be proportional to the inverse of polymer concentration. A broad melting transition for shish-kebab crystals is observed in simulations. The melting point is confirmed to be proportional to the square root of heating rate, increase exponentially with crystallization temperature, and increase with the logarithm of crystallization time in sigmoidal fashion. It is proposed that the melting point is related to the lamellar diameter, rather than the lamellar thickness in the traditional view. The seeding phenomenon for amyloid fibrils is reproduced in simulations. It is proposed that nucleation of the amyloid fibril is due to its semi-two-dimensional nature, because a pure one-dimensional growth does not require nucleation and does not exhibit sigmoidal curves. The importance of the second layer of β-sheet is stressed. It is proposed that Ostwald ripening (bigger fibrils grow at the expense of smaller ones) is the dominating mechanism for amyloid fibril growth.