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.
Highlights
The aggregation of amyloid fibrils in biological processes is associated with neurodegenerative diseases such as Alzheimer’s, Parkinson’s and Huntington’s or prion diseases [1,2,3]
We develop the kinetic formulas to study the nucleation processes of amyloid fibrils
A microscopic model with three states including coil, helix and sheet is constructed to explore the mechanism of amyloid formation
Summary
The aggregation of amyloid fibrils in biological processes is associated with neurodegenerative diseases such as Alzheimer’s, Parkinson’s and Huntington’s or prion diseases [1,2,3]. Some computational techniques could be used to predict the assembly of amyloid in solution and their secondary structure changes [10,11]. These computational simulations are only feasible for millisecond time scale. The random-coil like proteins exist in an unfolded state and the helix is very similar to folded state These simple models have been used to explore the nucleation processes of amyloid fibrils. A microscopic model of the assembly process is developed to explore the mechanism of amyloid fibrils and explain the transitions between the various assembly pathways as well as how side chain interactions determine the sheet structure in the aggregate phase. The theoretical predictions are in agreement with the experimental results
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