Abstract
The assembly mechanism for aggregation of amyloid fibril is important and fundamental for any quantitative and physical descriptions because it needs to have a deep understanding of both molecular and statistical physics. A theoretical model with three states including coil, helix and sheet is presented to describe the amyloid formation. The corresponding general mathematical expression of N molecule systems are derived, including the partition function and thermodynamic quantities. We study the equilibrium properties of the system in the solution and find that three molecules have the extreme value of free energy. The denaturant effect on molecular assemble is also discussed. Furthermore, we apply the kinetic theories to take account of the nucleation and growth of the amyloid in the solution. It has been shown that our theoretical results can be compared with experimental results.