A lattice-gas model for amyloid fibril aggregation

A simple lattice-gas model, with two fundamental energy terms —elongation and nucleation effects, is proposed for understanding the mechanisms of amyloid fibril formation. Based on the analytical solution and Monte Carlo simulation of 1D system, we have thoroughly explored the dependence of mass concentration, number concentration of amyloid filaments and the lag-time on the initial protein concentration, the critical nucleus size, the strengths of nucleation and elongation effects, respectively. We also found that thickening process (self-association of filaments into multi-strand fibrils) is not essential for the modeling of amyloid filaments through simulations on 2D lattice. Compared with the kinetic model recently proposed by Knowles et al., highly quantitative consistency of two models in the calculation of mass fraction of filaments is found. Moreover our model can generate a better prediction on the number fraction, which is closer to experimental values when the elongation strength gets stronger.